[{"key": "0", "content": "The school has four interest classes: dance, singing, Go, and painting. Xiaoyu, Xiaoming, and Xiaoli, three children, plan to enroll, each can only enroll in one class and each in a different one, there are a total different ways to enroll."}, {"key": "1", "content": "There are $$2$$ different English books, $$4$$ different Chinese books, and $$3$$ different math books on the bookshelf. Now, if we want to take out $$2$$ books, and they cannot be from the same subject, there are a total of different ways to do this."}, {"key": "2", "content": "Use $$5$$ different colors to color the figure below, requiring that adjacent areas (two areas with a common edge are considered adjacent) be colored in different colors. If colors can be reused, there are a total of different coloring methods. \n question_2-image_0"}, {"key": "3", "content": "Use four colors to color the three areas shown in the diagram, requiring adjacent areas to be colored differently, then there are a total of different coloring methods.\n question_3-image_0"}, {"key": "4", "content": "Make sentences with the words given in the table below, each sentence must include a person, a means of transportation, and a destination. How many different sentences can be made? Dad takes a plane to Beijing Mom takes a train to Lhasa I take a car to Taipei"}, {"key": "5", "content": "The following image is a deformed mushroom, divided into six regions. Now it needs to be colored with four different colors, with the requirement that two adjacent regions (two regions sharing a common edge are considered adjacent) must be colored differently. If colors can be reused, then there are a total of different coloring methods. question_5-image_0"}, {"key": "6", "content": "Xiaomei bought two pieces of clothes and two skirts at the supermarket. Please help Xiaomei to organize them, there are some different ways to wear them.\n question_6-image_0"}, {"key": "7", "content": "The postal worker has $$5$$ routes from village $$A$$ to village $$B$$, and $$6$$ routes from village $$B$$ to village $$C$$. There are, in total, different ways for the postal worker to go from village $$A$$ through village $$B$$ to village $$C$$."}, {"key": "8", "content": "The picture below is a side view of a toy staircase, with each step being $$10$$ cm wide and $$8$$ cm high. The perimeter of this staircase's side view is centimeters.\n question_8-image_0"}, {"key": "9", "content": "As shown in the figure below, a large rectangle is divided into four smaller rectangles, two of which have perimeters of $$20$$ and $$24$$ centimeters, respectively, and these values are marked inside them in the figure. What is the perimeter of the large rectangle in centimeters?\n question_9-image_0"}, {"key": "10", "content": "As shown in the diagram, the line segment $$a=12$$ cm, $$b=9$$ cm, $$c=4$$ cm, $$d=6$$ cm, the perimeter of the figure is in centimeters.\n question_10-image_0"}, {"key": "11", "content": "A piece of vegetable land, as shown in the diagram, is known that $$a=b=30$$ meters, $$c=3$$ meters, $$d=9$$ meters, what is the perimeter of this land in meters? question_11-image_0"}, {"key": "12", "content": "(1) Use a 40cm long rope to form a square, the side length of this square = cm;\n(2) There is a rectangular stone slab with a perimeter of 20 decimeters, length is 8 decimeters, the width of this stone slab = decimeters."}, {"key": "13", "content": "A large rectangle is divided into $$9$$ smaller rectangles, with the perimeter of $$4$$ pieces already marked. Therefore, the perimeter of the large rectangle is centimeters.\n question_13-image_0"}, {"key": "14", "content": "In the figure below, adjacent edges are perpendicular to each other, thus the perimeter of this shape is.\n question_14-image_0"}, {"key": "15", "content": "As shown in the diagram, a large rectangle is divided into $$9$$ smaller rectangles, among which the perimeters of $$5$$ smaller rectangles are marked on the diagram. Then, the perimeter of the large rectangle is.\n question_15-image_0"}, {"key": "16", "content": "The length of a rectangle is $$18$$ cm, and the width is $$12$$ cm, the perimeter of the rectangle is centimeters."}, {"key": "17", "content": "In the diagram below, adjacent sides are perpendicular to each other, so the perimeter of this shape is\uff0e question_17-image_0"}, {"key": "18", "content": "The right diagram is made up of $$3$$ identical small rectangles. Given that the width of the small rectangle is $$5$$ cm, the perimeter of the resulting large rectangle is cm. question_18-image_0"}, {"key": "19", "content": "Join two identical rectangles to form a square, and the perimeter decreases by $$20$$ centimeters. The perimeter of this square is centimeters. question_19-image_0"}, {"key": "20", "content": "There is a square flowerbed with a side length of $$5$$ meters, with a $$1$$ meter wide path laid around the perimeter. The area of the path is ( ) square meters.\n question_20-image_0"}, {"key": "21", "content": "As shown in the right diagram, a large rectangle is made up of $$5$$ identical small rectangles. If the perimeter of a small rectangle is $$40$$ cm, then the perimeter of the large rectangle is cm.\n question_21-image_0"}, {"key": "22", "content": "A rectangle and a square partially overlap. The non-overlapping shaded areas differ in area.\n question_22-image_0"}, {"key": "23", "content": "As shown in the figure, the length and width of a rectangle are respectively $$7$$ cm and $$5$$ cm. Making $$2$$ cuts parallel to the length and width, you get several rectangles. The total perimeter is in centimeters. question_23-image_0"}, {"key": "24", "content": "Using two small rectangles, each measuring $$5$$ cm in length and $$2$$ cm in width, to form a larger rectangle (as shown in the image), the perimeters of the formed large rectangle are cm and cm. question_24-image_0"}, {"key": "25", "content": "As shown in the figure below, $$5$$ small rectangles of the same size are combined to form a large rectangle. It is known that the length of the small rectangle is $$12$$ cm, then the perimeter of the large rectangle is cm.\n question_25-image_0"}, {"key": "26", "content": "There is a square flower bed in the park (the shaded part in the figure), and a path with a width of $$2$$ meters is built around its perimeter. The area of the path is $$48$$ square meters. The area of the flower bed in the middle is square meters. question_26-image_0"}, {"key": "27", "content": "Two squares of the same size are combined into a rectangle, and the perimeter of the rectangle is $$14$$ cm less than the total perimeter of the original two squares. The perimeter of one of the original squares is in centimeters.\n question_27-image_0"}, {"key": "28", "content": "Calculate the perimeter and area of the shapes shown in the diagram. question_28-image_0 Figure$$1$$\uff1aPerimeter: centimeters, Area: square centimeters. Figure$$2$$\uff1aPerimeter: centimeters, Area: square centimeters."}, {"key": "29", "content": "Zhang, Wang, and Li are workers at Factory A, Factory B, and Factory C, respectively working as a machinist, a fitter, and an electrician.\u2460Zhang is not in Factory A; \u2461Wang is not in Factory B; \u2462The one in Factory A is not a fitter; \u2463The one in Factory B is a machinist; \u2464Wang is not an electrician. Thus, Zhang works in Factory , Wang works in Factory , Li works in Factory ."}, {"key": "30", "content": "The rabbit's carrot was lost, so it went to report the case to the Black Cat Sheriff. The Black Cat Sheriff eventually narrowed down the suspects to four animals: the fox, the tiger, the lion, and the wolf. The criminal is among them.\nThe fox said: I did not steal the carrot;\nThe tiger said: The wolf stole the carrot;\nThe lion said: The tiger stole the carrot;\nThe wolf said: I have never stolen a carrot.\nAfter investigation, it was found that only one of the four animals was telling the truth. Who stole the carrot? ( )"}, {"key": "31", "content": "Xiao Ming, Xiao Qiang, and Xiao Hua participated in the Hua Cup competition. They are contestants from Luohu District, Futian District, and Nanshan District, respectively, and they won the first, second, and third prizes respectively. Now we know: (1) Xiao Ming is not from Luohu District; (2) Xiao Qiang is not from Futian District; (3) The contestant from Luohu District did not win the first prize; (4) The contestant from Futian District won the second prize; (5) Xiao Qiang is not the third prize winner. Based on the above situation, Xiao Hua is a contestant from ______ District, and he won the ______ prize (fill in the blanks with Chinese characters for first, second, or third)."}, {"key": "32", "content": "Before the horse race, five spectators made predictions about the rankings of the five horses $$ABCDE$$. A said: \"$$B$$ third, $$C$$ fifth.\" B said: \"$$E$$ fourth, $$D$$ fifth.\" C said: \"$$A$$ first, $$E$$ fourth.\" D said: \"$$C$$ first, $$B$$ second.\" E said: \"$$A$$ third, $$D$$ fourth.\" If each spectator guessed only half right, then horse $$C$$ ranked ( )."}, {"key": "33", "content": "The little white rabbit, little black rabbit, little flower rabbit, and little gray rabbit had a race. After the race, the little white rabbit, little black rabbit, and little flower rabbit spoke the following sentences, while the little gray rabbit did not speak. Little white rabbit: \"The little flower rabbit came first, I came third;\" little black rabbit: \"I came first, the little gray rabbit came fourth;\" little flower rabbit: \"The little gray rabbit came second, I came third.\" After the race results were announced, it was found that they all spoke only half-truths, and the little flower rabbit came in ___ place."}, {"key": "34", "content": "In a certain math competition, among three people A, B, and C, only one person won a prize. A said: 'I won the prize.' B said: 'I did not win the prize.' C said: 'A did not win the prize.' Only one of their statements is true, so the winner is ( )."}, {"key": "35", "content": "Calculate: $$178\\times 15+15\\times 22=$$\uff0e"}, {"key": "36", "content": "Calculate: $$31\\times 28+31\\times 85-31\\times 13=$$\uff0e"}, {"key": "37", "content": "Calculate the following expressions: (1) $$36\\times 19+64\\times 19=$$\uff0e\u3000\u3000\u3000\u3000(2) $$268\\times 75-68\\times 75=$$\uff0e"}, {"key": "38", "content": "Calculate using a simplified method: (1) \\((40+8) \times 25=\\). (2) \\(15 \times (40-8)=\\)."}, {"key": "39", "content": "Calculate: $$26\\times 464+52\\times 518+24\\times 520=$$\uff0e"}, {"key": "40", "content": "Calculate: $$12\\times 38+24\\times 23+48\\times 29=$$\uff0e"}, {"key": "41", "content": "Calculate: $39\\times 56-39\\times 2+39\\times 46$=."}, {"key": "42", "content": "Calculate: (1) $$32\\times 37+64+61\\times 32=$$\uff0e(2) $$33\\times 77-99+33\\times 26=$$\uff0e"}, {"key": "43", "content": "Calculate:\n$$171+171\\times 173+171\\times 26=$$\uff0e"}, {"key": "44", "content": "There is a square pool, with a pathway 2 meters wide around its perimeter. The area of the pathway is 64 square meters. Find the area of the middle pool (blank part) in square meters. question_44-image_0"}, {"key": "45", "content": "Compute: $$65\\times 34+65\\times 45+79\\times 35=$$\uff0e"}, {"key": "46", "content": "Xiaoqiang, Xiaoming, and Xiaoyong each participated in a math competition. They come from three different schools, A, B, and C, and won first, second, and third prize respectively. It is known that:\n(1) Xiaoqiang is not from School A;\n(2) Xiaoming is not from School B;\n(3) The contestant from School A did not win the first prize;\n(4) The contestant from School B won the second prize;\n(5) Xiaoming did not win the third prize.\nBased on the information above, it can be concluded that Xiaoyong is from School __, and he won the __ prize."}, {"key": "47", "content": "As shown in the figure, there is a rectangular piece of paper, the length is $$8$$ centimeters, and the width is $$5$$ centimeters, cut with scissors $$3$$ times, the sum of the perimeters of these $$6$$ small rectangles is centimeters.\n question_47-image_0"}, {"key": "48", "content": "As shown in the figure, the diagram is composed of $$9$$ identical rectangular pieces of paper. The dimensions of the shaded rectangle are $$11$$ cm in length and $$8$$ cm in width. What are the dimensions of the rectangular paper pieces in cm? question_48-image_0"}, {"key": "49", "content": "Three people, Jia, Yi, and Bing, participate in a running race. Three people, A, B, and C, make predictions about the race results. A says,'Jia will definitely be first.' B says, 'Jia is not the last.' C says, 'Jia will definitely not be first.' Only one of them makes a correct prediction about the race result. The one who predicts correctly is ( )."}, {"key": "50", "content": "Damao, Ermao, and Sanmao are good friends. Among them, one is a teacher, one is a doctor, and one is a driver. Now we only know that Sanmao is older than the driver, Damao and the doctor are not of the same age, and the doctor is younger than Ermao. The question is: who is the teacher, who is the doctor, and who is the driver?"}, {"key": "51", "content": "$$85\\times 25+85\\times 33+85\\times 42=$$."}, {"key": "52", "content": "After a math competition, A, B, and C guess their rankings. A says: I am 1st, B is 2nd; B says: I am 1st, C is 2nd; C says: I am 2nd, A is 3rd. It is known that each of them got exactly half right, then A ranks the ___."}, {"key": "53", "content": "One rectangle overlaps partially with another rectangle. The lengths and widths of both rectangles are marked on the drawing. The area of the non-overlapping shaded part differs. question_53-image_0"}, {"key": "54", "content": "Set up vertical calculations: ($$1$$) $$78\\div 6=$$ ($$2$$) $$676\\div 13=$$ ($$3$$) $$225\\div 15=$$ ($$4$$) $$4738\\div 46=$$"}, {"key": "55", "content": "Set up in columns for calculation\uff1a\uff08$$1$$\uff09$687\\div3=$\uff0e\uff08$$2$$\uff09$2562\\div7=$\uff0e"}, {"key": "56", "content": "The sequence $$3$$, $$9$$, $$15$$, $$21$$, $$\\dots$$ The $$33rd$$ term is."}, {"key": "57", "content": "Compute: $$12+15+18+21+24+27+30=$$\uff0e"}, {"key": "58", "content": "Calculate:$$41000\\div 25=$$$$48900\\div 25\\div 4$$$$6300\\div \\left( 3\\times 25 \\right)$$="}, {"key": "59", "content": "$$(2005+2006+2007+2008+2009+2010+2011)\\div 2008$$\uff1d."}, {"key": "60", "content": "Sum: $$1 + 3 + 5 +\\cdots + 61 + 63 + 65=$$\uff0e"}, {"key": "61", "content": "Calculate the following problems: (1) $$390\\times 8\\div 39$$= (2) $$125\\div 25\\times 8\\div 4$$="}, {"key": "62", "content": "Given that the first term of an arithmetic sequence is $$4$$, and the $$8^{th}$$ term is $$284$$, then, the common difference of this sequence is\uff0e"}, {"key": "63", "content": "Calculate: $$114\\div 8+126\\div 8$$.  ( )"}, {"key": "64", "content": "Arithmetic sequence calculation: $$2+5+8+\\cdots+59=$$."}, {"key": "65", "content": "As shown in the diagram: the numbers on the left side of each row and the top of each column represent the number of consecutive black blocks in that row or column. Which cell in the following diagram should be colored black? (Counting spaces from left to right)\n question_65-image_0"}, {"key": "66", "content": "There is a rectangle (including square) in the picture.\n question_66-image_0"}, {"key": "67", "content": "There are a total of squares in the image.\n question_67-image_0"}, {"key": "68", "content": "Every $$20$$ meters around a $$400$$ meters circular track, a colored flag is placed, a total of ( ) colored flags can be placed."}, {"key": "69", "content": "There are a total of line segments in the diagram.\n question_69-image_0"}, {"key": "70", "content": "The figure below contains several line segments. question_70-image_0"}, {"key": "71", "content": "A train has a total length of $$220$$ meters, where the length of the locomotive is $$20$$ meters, and each of the other carriages has a length of $$24$$ meters. It is also known that the distance between every two carriages is $$1$$ meter. This train has a total number of carriages (including the locomotive)."}, {"key": "72", "content": "A snail walks at a constant speed, taking 110 minutes to go from the front door of its house to the 11th tree. How many trees would the snail pass if it walked for 240 minutes? (There are no trees at the front door)"}, {"key": "73", "content": "There is a wall clock that strikes once every hour, striking as many times as the hour, at 6 o\u2019clock, it takes $$5$$ seconds to strike completely, then how many seconds will it take to strike completely at $$12$$ o\u2019clock."}, {"key": "74", "content": "A train consists of $$13$$ carriages (including the locomotive as one carriage), the locomotive is $$10$$ meters long, each of the other carriages is $$12$$ meters long, and the gap between the carriages is $$1$$ meter long, the total length of the train is meters."}, {"key": "75", "content": "On a greenbelt in the middle of the highway, workers plant a pine tree every $$3$$ meters, a total of $$50$$ pine trees were planted. They plan to plant a willow tree every $$1$$ meter between two adjacent pine trees, then the required number of willow trees is ."}, {"key": "76", "content": "1) The distance between two buildings is $$40$$ meters. If a cedar is planted every $$4$$ meters, how many cedars can be planted in total? (The width of the trees is negligible) 2) There is a $$60$$ meters long pathway in the school, and the plan is to plant trees on both sides of the pathway. If a tree is planted every $$10$$ meters, and trees are planted at both ends, how many trees are needed in total? (The width of the trees is negligible)"}, {"key": "77", "content": "1) During the Children's Day gala held by the school, there were balloons hanging on a string from one end to another, totaling $$12$$ balloons. The distance between every two adjacent balloons was $$5$$ meters. Therefore, the length of this string is in meters. (The width of the balloons is negligible) 2) In front of the \"Youth and Children's Activity Center,\" there's a straight road with trees planted on one side of it (not planting at the end closest to the door), totaling $$30$$ trees, each spaced $$5$$ meters apart. Thus, the length of this road is in meters. (The width of the trees is negligible)"}, {"key": "78", "content": "Xiaofei wants to reach the 8th floor of a building, it took him 60 seconds to go from the 1st floor to the 4th floor. If he continues at the same speed, how many more seconds will it take to reach the 8th floor."}, {"key": "79", "content": "Eddie wrote characters following the pattern \"spring, summer, autumn, winter, spring, summer, autumn, winter$$\\cdots\\cdots$$\", totalling $$23$$ characters. How many \"spring\" characters did he write in total?"}, {"key": "80", "content": "Eddie had some glass marbles, after he gave $$5$$ to Vi, he then went to the store and bought another $$10$$, now he has a total of $$30$$ marbles. Please ask how many glass marbles Eddie originally had."}, {"key": "81", "content": "October 1, 2016, was a Saturday, and 20 days later is a week ( )."}, {"key": "82", "content": "A primary school playground is decked with colorful flags arranged in the order shown in the following picture, totaling $$42$$ flags. Among these $$42$$ flags, there are red flags and yellow flags.\n question_82-image_0"}, {"key": "83", "content": "Multiply a number by $$7$$, add $$5$$, the result is $$54$$. The number is."}, {"key": "84", "content": "A number, divided by $$4$$, then add $$4$$, multiply by $$4$$, and finally subtract $$4$$, the result is $$16$$. So, this number is ( )."}, {"key": "85", "content": "A barrel of oil, the first time half of it was used, and the second time another half of the remaining oil was used, leaving $$12$$ kilograms. The original weight of the barrel of oil was kilograms."}, {"key": "86", "content": "The yard originally had a certain number of tons of coal$$.$$ The first time, half of the original coal was shipped out, the second time $$150$$ tons were shipped in, the third time $$50$$ tons were shipped out, resulting in $$300$$ tons remaining, how many tons of coal were there originally in the yard."}, {"key": "87", "content": "A number is first increased by $$3$$, then multiplied by $$3$$, then divided by $$2$$, and finally decreased by $$2$$. The result is $$10$$. Question: What is the original number?"}, {"key": "88", "content": "A construction team needs to repair a path. On the first day, they repaired more than half of the entire length plus $$6$$ meters, and on the second day, they repaired less than half of the remaining part by $$2$$ meters. At this point, there were still $$6$$ meters left unrepaired. Then, the length of this path in meters is."}, {"key": "89", "content": "There are a total of $$27$$ birds on three trees, with $$2$$ birds flying from the first to the second tree, $$3$$ birds flying from the second to the third tree, and $$4$$ birds flying from the third back to the first tree. At this point, each of the three trees has the same number of birds. Originally, there were birds on the first tree, birds on the second tree, and birds on the third tree."}, {"key": "90", "content": "Li Bai took a jug to buy wine. At each store he doubled the amount of wine he had, and for every flower he saw, he drank eight taels. After encountering stores and flowers three times each, he drank all the wine in the jug. The jug initially contained two taels of wine. (Encounters with stores and flowers alternated, starting with a store)"}, {"key": "91", "content": "There are three piles of apples, labeled A, B, and C, totaling $$96$$ apples. The first action involves taking the same number of apples from pile A as there are in pile B and placing them into pile B. The second action involves taking from pile B the same number of apples as there are in pile C and placing them into pile C. The third action involves taking from pile C the same number of apples as the remaining in pile A and placing them into pile A, at which point the number of apples in all three piles is equal. Originally, pile A had __ apples, pile B had __ apples, and pile C had __ apples."}, {"key": "92", "content": "Person A and Person B each have some glass balls. If Person A gives the same number of glass balls to Person B, and then Person B also gives the same number of glass balls from their current ones to Person A, at this point both persons exactly have $$20$$ glass balls. How many glass balls did Person A originally have?"}, {"key": "93", "content": "Xiao Ming paid $$1$$ yuan to enter the first shop, and then spent half of the remaining money inside. When he left the shop, he paid another $$1$$ yuan. After that, he paid another $$1$$ yuan to enter the second shop, where he spent half of the remaining money, and paid another $$1$$ yuan when leaving the shop. Then, he followed the same pattern for the third shop. After leaving the third shop, he only had $$1$$ yuan left. How much money did he have before entering the first shop?"}, {"key": "94", "content": "Wei Er makes 200 flowers in 10 minutes, she makes flowers per minute."}, {"key": "95", "content": "Jiajia found many Russian nesting dolls, and gave half of them to Wei'er, and then half of the remaining to Aidi, leaving Jiajia with $$4$$ dolls. Please calculate how many Russian nesting dolls Jiajia originally found."}, {"key": "96", "content": "After the math test scores were released, Iron Mom asked Little Iron what his score was. Little Iron said, my score minus $$20$$, then multiplied by $$2$$, then divided by $$3$$, and then if you add $$54$$ to it, it becomes $$100$$ points. So, what was Little Iron's actual score?"}, {"key": "97", "content": "There is a peach tree in the orchard. One day, two little monkeys came to pick peaches. The first monkey ate 1 peach and picked half of the remaining peaches. Then the second monkey ate 2 peaches and picked half of the remaining peaches. At this time, there were exactly 14 peaches left on the tree. Originally, there were a total of peaches on the tree."}, {"key": "98", "content": "Xiao Ming walked $$180$$ meters in $$3$$ minutes, at this speed, he needs $$15$$ minutes from home to school. The distance from Xiao Ming's home to school is meters."}, {"key": "99", "content": "3 vehicles transport coal at the same time, in 4 days they transported 480 tons, averaging tons per vehicle per day."}, {"key": "100", "content": "5 persons repair 700 meters of road in 10 days, according to this calculation, 10 persons repair meters in 3 days."}, {"key": "101", "content": "4 people repair 400 meters of road in 10 days, according to this calculation, 10 people repair meters in 3 days."}, {"key": "102", "content": "Aunt Wang has $$5$$ different styles of tops, $$7$$ different pairs of pants, and $$6$$ different pairs of leather shoes. She picks one of each to wear every time she goes out. There are a total of different combinations that can be formed."}, {"key": "103", "content": "There are a total of $$22$$ candies. Chenchen quickly took some, leaving Yuanyuan to take the rest. Seeing that Chenchen took too many, Yuanyuan snatched $$4$$ candies from Chenchen; Yuanyuan was unhappy, so Chenchen had to give Yuanyuan $$2$$ more candies. At this point, Yuanyuan and Chenchen had the same number of candies. Please ask how many candies Chenchen originally took."}, {"key": "104", "content": "As shown in the figure below, a large rectangle is divided into four sections: $$A$$, $$B$$, $$C$$, and $$D$$. It is known that the perimeter of section $$A$$ is $$5$$ cm, and the perimeter of section $$D$$ is $$15$$ cm. The perimeter of the large rectangle is centimeters.\n question_104-image_0"}, {"key": "105", "content": "The perimeter of a rectangle is $$38$$ meters, with the length being $$10$$ meters, its width is meters, and the area is square meters."}, {"key": "106", "content": "Count, how many triangles are there in the following picture.\n question_106-image_0"}, {"key": "107", "content": "As shown in the diagram: the numbers on the left side of each row and the top of each column represent the count of consecutive black squares in that row or column. Kids, in this $$5\\times5$$ grid, is the square in the third row and fifth column a black square?\n question_107-image_0"}, {"key": "108", "content": "Arithmetic sequence calculation: $$4+8+12+\\cdot \\cdot \\cdot +28+32+36=$$."}, {"key": "109", "content": "Given the sequence $$4$$, $$10$$, $$16$$, $$22\\cdots$$, what is the $$61st$$ number in this sequence? ( )\uff0e"}, {"key": "110", "content": "$$40\\div 12+9\\div 12+11\\div 12=$$"}, {"key": "111", "content": "If there are $$2016$$ students lined up in a row, counting in the order of $$1$$, $$2$$, $$3$$, $$4$$, $$3$$, $$2$$, $$1$$, $$2$$, $$3$$, $$4$$, $$3$$, $$2$$, $$1$$......, then the number called by the $$2016th$$ student is."}, {"key": "112", "content": "As shown in the figure, a rectangle is divided into four rectangles of unequal sizes by two line segments, among which the areas of three rectangles are $$20$$ square meters, $$30$$ square meters, and $$36$$ square meters respectively. The area of the other rectangle is square meters.\n question_112-image_0"}, {"key": "113", "content": "Tang Tang took $$8$$ minutes to walk from the first tree to the ninth tree, assuming the distance between each adjacent tree is the same, at this pace, after another $$15$$ minutes, Tang Tang should reach the tree number."}, {"key": "114", "content": "Among the classmates Xiao Hua, Xiao Li, and Xiao Lv, one person helped the sick Xiao Hong complete her notes. When Xiao Hong asked who did the good deed, Xiao Hua said, \u201cXiao Li did it.\u201d Xiao Li said, \u201cIt wasn't me.\u201d Xiao Lv said, \u201cIt wasn't me either.\u201d In fact, two people were lying, and only one was telling the truth. So, it was ( ) who helped Xiao Hong complete her notes."}, {"key": "115", "content": "Little Red Riding Hood's mother rode her bike to the market to do some shopping. The distance from home to the market is $$600$$ meters, and it took Little Red Riding Hood's mother a total of $$3$$ minutes. Hence, the speed of Little Red Riding Hood's mother was ( ) meters/minute."}, {"key": "116", "content": "To fill a reservoir with water, it can hold a total of $$144$$ liters. It takes $$18$$ hours to fill it using $$8$$ hoses. Following this rate, if now $$12$$ hoses are used to fill the water, it requires hours to fill the reservoir."}, {"key": "117", "content": "The future supermarket is promoting a carton of milk for $$72$$ yuan, with each carton containing $$24$$ boxes, and each box of milk costs yuan."}, {"key": "118", "content": "4 students clean 24 pieces of glass in 3 hours, at this rate, 5 students can clean pieces of glass in 4 hours."}, {"key": "119", "content": "$$5$$ people need $$3$$ hours to dig a trench $$3$$ meters long, according to this speed, then $$50$$ hours are needed for $$5$$ workers to dig a trench $$50$$ meters long."}, {"key": "120", "content": "Pipi climbs from the $$6$$th floor to the $$8$$th floor in $$4$$ minutes. Using the same speed, how long does it take her to climb from the $$1$$st floor to the $$6$$th floor?"}, {"key": "121", "content": "In the diagram below, the class with the largest number of students is ( ) class.\n question_121-image_0"}, {"key": "122", "content": "$$3$$ mice eat $$30$$ ears of corn in $$5$$ days, according to this rate, $$10$$ mice need to eat $$80$$ ears of corn in $$X$$ days."}, {"key": "123", "content": "Master Wang processed $$60$$ parts in $$2$$ hours; based on this calculation, he can process parts for $$8$$ hours a day."}, {"key": "124", "content": "During the Spring Festival, Xue Xue and his parents went back to their hometown to visit his grandparents, taking a long-distance bus for $$2$$ hours. The speed of the long-distance bus is $$85$$ kilometers per hour. Therefore, the total distance Xue Xue travels from home to his grandparents' home is kilometers."}, {"key": "125", "content": "1 chicken has a head, legs. 1 rabbit has a head, legs. Now, a crazy farmer locked up $$2$$ chickens and $$5$$ rabbits in a cage, in total there are heads, legs."}, {"key": "126", "content": "The school conducted a satisfaction survey on school cultural and sports activities, dividing satisfaction into five levels from $$1-5$$. Among the $$200$$ returned surveys, the data is shown in Figure $$8-15$$. Therefore, the highest level of satisfaction is.\n question_126-image_0"}, {"key": "127", "content": "The figure below is a bar chart survey of 'My Favorite Fruit' conducted among kindergarten students. According to the chart, a total of $$24$$ students like oranges, and a total of $$27$$ students like watermelon.\n question_127-image_0"}, {"key": "128", "content": "The chart below is a bar graph of the number of students in each class of the third grade at a certain school. Based on the statistics, the following statement that is incorrect is ( ).\n question_128-image_0"}, {"key": "129", "content": "Statistics table on donations to drought regions from two primary schools (each with $$5$$ grades):\n question_129-image_0 \n\uff081\uff09The fifth grades from both schools together donated yuan;\n\uff082\uff09The first grade from School 1 donated the most;\n\uff083\uff09The grade from School 2 donated the least;\n\uff084\uff09In total, School 1 donated yuan."}, {"key": "130", "content": "Class 6(1) organized a cultural activity, with 9 people performing song and dance programs, 12 performing sketch programs, and 5 participating in both types of programs. In total, there were people participating in these two types of programs."}, {"key": "131", "content": "Chickens and rabbits in the same cage, with a total of $$30$$ chickens and rabbits, and the number of chicken legs equals the number of rabbit legs. Thus, there are chickens and rabbits."}, {"key": "132", "content": "Chickens and rabbits in a cage, together making up $$60$$ feet, it is known that the number of chickens and rabbits is the same, then there are chickens and rabbits each\uff0e"}, {"key": "133", "content": "During a trip to the forest park, Xiao Hei saw a total of $$100$$ lions and ostriches and counted a total of $$202$$ feet. So, how many lions and ostriches did Xiao Hei see?"}, {"key": "134", "content": "There are chickens and rabbits in a cage, it is known that the number of chickens is $$2$$ times the number of rabbits. Counting the legs, there are a total of $$120$$ legs. How many rabbits and how many chickens? "}, {"key": "135", "content": "In the zoo, ostriches and zebras live on the same grassland. There are a total of $$55$$ animals. The number of legs of ostriches is $$2$$ times that of the zebras. Then, there are ____ zebras."}, {"key": "136", "content": "A cricket has $$6$$ legs, a spider has $$8$$ legs. There are crickets and spiders totaling $$9$$, with $$60$$ legs altogether. Crickets have ____, spiders have ___."}, {"key": "137", "content": "A forest park raised some chickens and rabbits. It is known that the number of rabbits is equal to the number of chickens, and together they have $$102$$ legs. Therefore, there are chickens, and there are rabbits."}, {"key": "138", "content": "There are $$15$$ chickens and rabbits in total, locked in the same cage, with a total of $$34$$ legs in the cage. Try to calculate, the number of chickens and rabbits in the cage."}, {"key": "139", "content": "In an office, there are $$7$$ people who love to drink tea, $$10$$ people who love to drink coffee, and $$3$$ people who love both tea and coffee. If everyone loves to drink at least one of tea or coffee, then there are a total of people in this office."}, {"key": "140", "content": "There are $$30$$ soldiers in the navy SEALs, each of whom is skilled in either shooting or hand-to-hand combat, or both. If there are $$12$$ soldiers skilled in shooting and $$23$$ soldiers skilled in hand-to-hand combat, then, the number of soldiers skilled in both is ."}, {"key": "141", "content": "Recently, a survey was conducted at a busy airport to understand where people usually love to go for tourism. In the past year, 20 people visited Spain, 15 people visited France, 10 people visited Germany. 5 people visited both Spain and France, 3 people visited both Spain and Germany, 2 people visited both France and Germany. There was 1 person who visited all three places. Therefore, the total number of surveyed people is ."}, {"key": "142", "content": "Xiao Wang reads a storybook of $$200$$ pages, he reads $$30$$ pages every day, he should start from page on the $$5$$th day."}, {"key": "143", "content": "The Youth Palace winter vacation enrollment. The calligraphy class enrolled $$29$$ students, the fine arts class enrolled $$28$$ students, and the instrumental music class enrolled $$27$$ students. Among these students, $$13$$ enrolled both in calligraphy and fine arts, $$12$$ enrolled both in calligraphy and instrumental music, $$11$$ enrolled both in fine arts and instrumental music, and $$5$$ enrolled in all three subjects. The Youth Palace enrolled a total of $$100$$ students for the winter vacation, including those who enrolled in classes other than calligraphy, fine arts, and instrumental music."}, {"key": "144", "content": "Class 3(1) has $$30$$ students. Among them, $$15$$ have watched the animated movie \"Lotus Lantern\", $$12$$ have watched \"Journey to the West\", and $$6$$ have watched both of these animated movies. Therefore, the number of students who have watched only one of these two animated movies is ____. The number of students who have not watched either of these two animated movies is ____. "}, {"key": "145", "content": "To enrich their knowledge, the lobster and the crab went to the library to read books. After one month, the lobster read a total of $$48$$ books, and the crab read a total of $$32$$ books. They both read $$12$$ books in common, so the actual total number of books they read together is books."}, {"key": "146", "content": "The Super Special Forces team has $$25$$ members, each of whom knows at least one skill: invisibility or shape-shifting. There are $$14$$ members who know how to become invisible, and $$18$$ members who know how to shape-shift. Therefore, there are people who know both skills."}, {"key": "147", "content": "On a hot summer day, several children went to a cold drink shop, with each one ordering at least one type of cold drink. Among them, $$6$$ kids ordered popsicles, $$6$$ ordered soda, $$4$$ ordered Sprite. There were $$3$$ kids who ordered both popsicles and soda, $$1$$ kid who ordered both popsicles and Sprite, and $$1$$ kid who ordered both soda and Sprite; $$1$$ kid ordered all three types. Then, the total number of children who went to the cold drink shop was."}, {"key": "148", "content": "There is a dictionary that only has $$100$$ pages, please ask how many digits are used in total when printing the page numbers."}, {"key": "149", "content": "A certain novel used $$255$$ digits in total for page numbering, this collection of poems has a total of pages."}, {"key": "150", "content": "A book has a total of $$500$$ pages, how many times does the number $$2$$ appear?"}, {"key": "151", "content": "Conan has an old book with $$182$$ pages in the main text. Due to its age, pages $$16$$ to $$27$$ and pages $$62$$ to $$83$$ have been damaged by insects.\nThe number of pages in the main text of the book that have not been damaged by insects is pages."}, {"key": "152", "content": "The figure below contains a parallelogram.\n question_152-image_0"}, {"key": "153", "content": "A book has $$35$$ pages, the total number of digits used in page numbers from 1~35 is."}, {"key": "154", "content": "The page numbers of a novel used $$210$$ digits in printing, this novel has a total of pages."}, {"key": "155", "content": "Journey to the West is one of the Four Great Classical Novels of China, narrating the story of Sun Wukong, Zhu Bajie, and Sha Wujing who protect Tang Sanzang on his journey to the West to obtain sacred texts, overcoming ninety-nine and eighty-one difficulties, conquering demons along the way, and finally acquiring the true scriptures. The children's version of \"Journey to the West\" has $$202$$ pages. How many pages are there from page $$32$$ to page $$187$$?"}, {"key": "156", "content": "The diagram below shows a parallelogram. Given that the area of the parallelogram is $$70$$ square centimeters, the length of $$AE$$ is $$5$$ centimeters, and the length of $$AF$$ is $$7$$ centimeters, then the perimeter of this parallelogram is centimeters.\n question_156-image_0"}, {"key": "157", "content": "The sum of the top and bottom bases of the trapezoid in the right figure is centimeters, and the height is centimeters.\n question_157-image_0"}, {"key": "158", "content": "In parallelogram $$ABCD$$, if $$CD=10$$ cm and $$AE=3$$ cm, then the area of parallelogram $$ABCD$$ equals square centimeters.\n question_158-image_0"}, {"key": "159", "content": "As shown in the figure, quadrilateral $$ABCD$$ is a rhombus (the two diagonals of the rhombus are perpendicular to each other), it is known that $$AC=14$$, $$BD=8$$, calculate the area of the rhombus ().\n question_159-image_0"}, {"key": "160", "content": "Using fences to enclose a trapezoidal chicken coop (as shown in the diagram below), where one side utilizes the house wall, it is known that the length of the fence is $$80$$ meters, then the area of the chicken coop is square meters. question_160-image_0"}, {"key": "161", "content": "As shown in the diagram, two identical parallelograms are placed horizontally and vertically, overlapping each other. It is known that the overlapping part is exactly a square with a side length of $$8$$ cm, and the length of $$AH$$ is $$3$$ cm. Then, the area covered by these two parallelograms is square centimeters.\n question_161-image_0"}, {"key": "162", "content": "The top base of a trapezoid is $$4$$ cm, the bottom base is $$7$$ cm, and the height is $$6$$ cm. The area of this trapezoid is square centimeters."}, {"key": "163", "content": "Dad drove to the neighboring city, spending $$3$$ hours, covering a total of $$240$$ kilometers, dad's average speed per hour in kilometers."}, {"key": "164", "content": "In parallelogram $$ABCD$$, the length of $$CD$$ is $$8$$ cm, then the length of $$AB$$ is cm.\n question_164-image_0"}, {"key": "165", "content": "The upper base of a trapezoid is $$5$$ meters, the lower base is $$8$$ meters, and the height is $$4$$ meters, its area is in square meters."}, {"key": "166", "content": "The figure below is a parallelogram, and its area is $$\\text{c}\\text{m}^{2}$$.\n question_166-image_0"}, {"key": "167", "content": "Xiao Wei and Xiao Shi race in a running competition. Xiao Wei runs $$160$$ meters per minute, while Xiao Shi runs $$140$$ meters per minute. Both start from the starting line at the same time, and after $$5$$ minutes, Xiao Wei runs more meters than Xiao Shi."}, {"key": "168", "content": "8 minutes later, a movie theater 1200 meters away from Weiwei's home will start showing a movie. If Weiwei leaves home and wants to arrive on time, she needs to walk at least ____ meters per minute."}, {"key": "169", "content": "Person A and Person B are in a 100-meter race. Person A runs 10 meters per minute, and Person B runs 8 meters per minute. When Person A reaches the finish line, Person B is still meters away from the finish line."}, {"key": "170", "content": "Person A and B walk from two places that are $$80$$ meters apart towards each other at the same time. If person A walks at $$15$$ meters per minute, and person B walks at $$5$$ meters per minute, then after how many minutes will the two meet for the first time at a distance of $$20$$ meters."}, {"key": "171", "content": "Places A and B are $$298$$ kilometers apart, Wei'er departs from place A to B, $$1$$ hour later, Eddie departs from place B to A. It is known that Eddie travels at $$52$$ kilometers per hour, and Wei'er travels at $$18$$ kilometers per hour. When the two meet, Eddie has traveled kilometers."}, {"key": "172", "content": "As shown, the school and home are $$1500$$ meters apart. Wei'er starts from the school heading to the stationery store. The doctor starts from home heading to the factory. Both start at the same time. Wei'er's speed is $$32$$ meters/min, and the doctor's speed is $$88$$ meters/min. After $$12$$ minutes, both arrive at their destinations at the exact same time. Therefore, the distance between the stationery store and the factory is meters. question_172-image_0"}, {"key": "173", "content": "After school one day, Han Leilei and Li Mei set off at the same time, walking in opposite directions. $$20$$ minutes later, they were $$3580$$ meters apart. The speed of Han Leilei is $$80$$ meters/min, and the speed of Li Mei is meters/min."}, {"key": "174", "content": "Da Bai and Xiao Ming set off from two places 1000 meters apart at the same time, heading towards each other. Da Bai walks 47 meters per minute, and Xiao Ming walks 53 meters per minute. The distance between them is 100 meters for the second time after they started."}, {"key": "175", "content": "Xiao Bai and Xiao Hua live 100 meters apart. Xiao Bai walks at a speed of 4 meters per minute, and Xiao Hua walks at a speed of 6 meters per minute. Both of them leave their homes at the same time and walk in opposite directions on the same road. After 5 minutes, the distance between the two is meters."}, {"key": "176", "content": "A and B are $$140$$ kilometers apart, Eddie drove a car from A to B in $$5$$ hours. At this speed, he drove from B to C for $$6$$ hours. The distance between B and C is kilometers."}, {"key": "177", "content": "An odd number plus an odd number results in ( )."}, {"key": "178", "content": "Chengcheng and Chuchu live 1000 meters apart. Chengcheng walks at 25 meters per minute and Chuchu walks at 45 meters per minute. Both start from their homes at the same time, walking towards each other on the same road. After 4 minutes, the distance between them is meters."}, {"key": "179", "content": "Eddie and Vi started from two places $$1650$$ meters apart at the same time, moving in the same direction, with Eddie behind and Vi in front. Eddie walks $$60$$ meters per minute, while Vi walks $$50$$ meters per minute. After how many minutes did Eddie catch up with Vi?"}, {"key": "180", "content": "The elder brother and the younger brother study at the same school. The elder brother walks at a speed of 60 meters per minute, while the younger brother walks at a speed of 40 meters per minute. One day, the younger brother left 5 minutes earlier than the elder brother, who then left the house. Minutes later, the elder brother caught up with the younger brother."}, {"key": "181", "content": "There is a lit lamp in the room. If Xiao Ming presses the switch $$1999$$ times in a row (the switch turns on with one press and off with the next), the lamp will be ( )."}, {"key": "182", "content": "Determine whether the result of the following arithmetic operations is odd or even. \uff08 \uff09\n\uff08$$1$$\uff09$$12+133-5+672-34+561$$\n\uff08$$2$$\uff09$$22\\times 31\\times 57\\times 111\\times 3539$$"}, {"key": "183", "content": "Calculate $$7485+343\\times 141-17\\times 232-119\\times 120+2014$$, Eddie got the result $$39639$$, please determine whether his calculation result is correct.\uff08\uff09"}, {"key": "184", "content": "Find two integers such that their sum is $$264$$ and their difference is $$57$$. Do such numbers exist? If yes, please write down these two numbers; if no, please explain why."}, {"key": "185", "content": "The sum of two natural numbers is $$698$$, and their difference is $$355$$. Can you find such two numbers? If so, please write them down; if not, please explain why."}, {"key": "186", "content": "The result of $31\\times 23+15\\times 66+11\\times 17$ is."}, {"key": "187", "content": "Is it possible to choose $$5$$ numbers from five $$7$$s, four $$5$$s, and three $$3$$s so that the sum of these $$5$$ numbers equals $$30$$? ( )"}, {"key": "188", "content": "As shown in the figure, fill in the blanks with appropriate numbers to make the multiplication equation valid. The product of this equation is.\n question_188-image_0"}, {"key": "189", "content": "Among the following $$5$$ natural numbers: $$152$$, $$430$$, $$375$$, $$504$$, $$2125$$, the number that can be divided by $$2$$ is ( )\uff0e"}, {"key": "190", "content": "Can the six-digit number $$123456$$ be divided by $$3$$? ( ) Can it be divided by $$9$$? ( )"}, {"key": "191", "content": "Among the following $$5$$ natural numbers: $$152$$, $$430$$, $$375$$, $$504$$, $$2125$$, the number of them that can be divided by $$5$$ is ( )."}, {"key": "192", "content": "Fill in a digit in $$\\square $$ so that the number is divisible by $$3$$. How many options are there? $$\\overline{475\\square} $$"}, {"key": "193", "content": "$$\\overline{183\\square }$$ is divisible by $$4$$, thus $$\\square $$ can be filled with, . (Fill in from smallest to largest)"}, {"key": "194", "content": "Jiajia and Jianjian got milk from a draw, each milk barrel has a number, milk barrels with odd numbers are adjacent to odd numbers, and even numbers are adjacent to even numbers.\n question_194-image_0 \nJiajia drew three numbers that are placed together, the sum of these three numbers equals $$9$$, and the three numbers are,, in ascending order."}, {"key": "195", "content": "The following $$5$$ natural numbers: $$152$$, $$430$$, $$375$$, $$504$$, $$2125$$, the number that can be divided by $$25$$ is (  )\uff0e"}, {"key": "196", "content": "In the equation below, the number represented by $$B$$ is.\n question_196-image_0"}, {"key": "197", "content": "The sum of $$101+103+105+107+109+1011+1013+1015+1017$$ is ( )."}, {"key": "198", "content": "Among the numbers $$1234$$, $$227$$, $$1358$$, $$669$$, there are odd numbers and even numbers."}, {"key": "199", "content": "Among the three-digit numbers written with $$0$$, $$7$$, $$5$$ without repeating digits, which ones can be divided by $$5$$? ( )"}, {"key": "200", "content": "Is there two integers such that their sum is $$89$$ and their difference is 22?"}, {"key": "201", "content": "In the following mathematical equation, the same letters represent the same digits, and different letters represent different digits. Then, the two-digit number represented by $$\\overline{AB}$$ is.\n question_201-image_0"}, {"key": "202", "content": "$$6741$$ $$5232$$ $$5868$$ $$585$$ $$7579$$ $$2992$$ $$2009$$ can be divided by $$8$$, there are () of them."}, {"key": "203", "content": "The image shows an incomplete division long-division problem. The dividend in this long-division problem is ( ) .\n question_203-image_0"}, {"key": "204", "content": "The same Chinese characters represent the same digits, and different Chinese characters represent different digits. Please fill in the appropriate digits to make the multiplication vertical method work, the three-digit number \"$$\\overline{study and think}$$\" equals.\n\n\n\n\nstudy\nand\nthink\n\n\nX\n\n\n9\n\n\n1\n3\n2\n3"}, {"key": "205", "content": "The five-digit number $$\\overline{3A21A}$$ is divisible by both $$3$$ and $$5$$, then this five-digit number is."}, {"key": "206", "content": "Fill in the appropriate number in the $$\\square$$ below to make the equation valid. The result of this equation is.\n question_206-image_0"}, {"key": "207", "content": "Fill in the appropriate number in the square of the division below so that the division is valid, where the dividend is.\n question_207-image_0"}, {"key": "208", "content": "As shown in the figure, fill in the blanks with suitable numbers to make the multiplication vertical format correct, so the product $$=$$ .\n\n\n\n\n\u25a1\n4\n\u25a1\n8\n\u25a1\n7\n\n\nX\n\n\n\n\n\n\u25a1\n\n\n\n4\n\u25a1\n8\n\u25a1\n7\n1"}, {"key": "209", "content": "$7\\times9999=$"}, {"key": "210", "content": "As shown in the diagram, please fill in the appropriate numbers in the blanks in the diagram so that the multiplication vertical method is correct, the product $$=$$.\n\n\n\n\n5\n\u25a1\n7\n\n\nX\n\n\n\u25a1\n\n\n\u25a1\n\u25a1\n4\n1"}, {"key": "211", "content": "Fill in the appropriate number in the \"$$\\square$$\" below to make the vertical operation correct, where the dividend is.\n question_211-image_0"}, {"key": "212", "content": "Please fill in the correct numbers in the box below to make the vertical operation valid. The product of this operation is .\n 1 7 \u00d7 2  3  3 4 3 3"}, {"key": "213", "content": "$1235+2351+3512+5123=$"}, {"key": "214", "content": "$$123123123=123\\times $$\uff0e"}, {"key": "215", "content": "Calculate the following problem\n$$235+523+352=$$."}, {"key": "216", "content": "Starting from $$1$$, fill in the table below according to a certain rule, then the numbers in the first column form an arithmetic sequence with a common difference.\n question_216-image_0"}, {"key": "217", "content": "$344+443+434=$"}, {"key": "218", "content": "$$135135135=135\\times $$\uff1b$$12341234=$$$$\\times 10001$$ ."}, {"key": "219", "content": "As shown in the figure, consecutive natural numbers starting from $$1$$ are arranged according to the pattern shown below. Then, the number in the $$3$$rd row and $$7$$th column is.\n question_219-image_0"}, {"key": "220", "content": "Fill in the following table with natural numbers starting from $$1$$ according to a pattern. Then, the number $$2019$$ is in the row and column of the table. \n question_220-image_0"}, {"key": "221", "content": "Please circle three adjacent numbers in a row on the table, so that the sum of these three numbers is $$60$$. $$1$$$$2$$$$3$$$$4$$$$5$$$$6$$$$7$$$$8$$$$9$$$$10$$$$11$$$$12$$$$\\cdots $$$$\\cdots $$$$\\cdots $$$$\\cdots $$"}, {"key": "222", "content": "Starting from $$1$$, the consecutive natural numbers are arranged according to the rules shown in the diagram, and five numbers are framed with a cross. Is it possible to make the sum of these five numbers equal to $240$? question_222-image_0"}, {"key": "223", "content": "Thirty-six pots, divided into nine boats for transportation. Only odd numbers are allowed, even numbers are not. Is it possible to transport these pots? ( )"}, {"key": "224", "content": "Find two integers such that their sum is $$45$$ and their difference is $$12$$. Do such numbers exist? If yes, please write out these two numbers, if not, please explain the reason."}, {"key": "225", "content": "There is a book of $$500$$ pages, randomly tear off $$20$$ sheets of paper, can the sum of all the page numbers on these $$20$$ sheets be $$1999$$?"}, {"key": "226", "content": "A snack shop needs to make $$3$$ pancakes, and each pancake must be fried on both sides for $$1$$ minute each. Now there are $$2$$ stoves, and each stove can only fry one side of a pancake at a time. To properly fry all the pancakes, the minimum number of minutes required is ."}, {"key": "227", "content": "As shown in the diagram, starting from $$1$$, continuous natural numbers are filled into a table according to a rule. The number in the $$4th$$ row and the $$48th$$ column is\uff0e question_227-image_0"}, {"key": "228", "content": "$23456+34562+45623+56234+62345=$"}, {"key": "229", "content": "As shown in the figure below, when positive integers are arranged according to a certain pattern, the number in the $$10$$th row and $$3$$rd column is.\n question_229-image_0"}, {"key": "230", "content": "Xiao Huang ran $$180$$ meters in $$30$$ seconds, so Xiao Huang's speed is meters/second."}, {"key": "231", "content": "There are three cars needing to refuel at the neighborhood gas station, and the time they take to refuel are $$5$$, $$2$$, and $$3$$ minutes respectively. Currently, the gas station has only one fuel pump. In order to minimize the total refueling and waiting time for these three cars, the shortest time is minutes."}, {"key": "232", "content": "Beijing and Shanghai made the same model of lathes, 10 and 6 units respectively. These lathes are ready to be distributed to Shenzhen (12 units) and Guangzhou (4 units). The freight cost for each lathe is shown in the table, in yuan. What is the minimum total freight cost?\n\n\n\n\nDestination\nOrigin\n\nShenzhen\n\nGuangzhou\n\n\n\nBeijing\n\n$$800$$\n\n$$500$$\n\n\n\nShanghai\n\n$$700$$\n\n$$1000$$"}, {"key": "233", "content": "Eddie and Will are $$630$$ kilometers apart. They start traveling towards each other at the same time and meet after $$9$$ hours. The sum of their speeds is kilometers per hour. If Eddie travels at $$34$$ kilometers per hour, then Will travels at kilometers per hour."}, {"key": "234", "content": "Eddie and Viola set off for the library from school at the same time. $$10$$ minutes later, Eddie just arrived, while Viola was still $$100$$ meters away. If Viola walks $$60$$ meters per minute, do you know how many meters per minute Eddie walks?"}, {"key": "235", "content": "Places A and B are $$350$$ kilometers apart. A car departs from place A at $$8$$ AM, traveling towards place B at a speed of $$40$$ kilometers per hour. $$2$$ hours later, another car starts from place B towards A at a speed of $$50$$ kilometers per hour. The question is: at what time do the two cars meet on the road? ( )"}, {"key": "236", "content": "Teacher Xiao Hong and Xiao Ming set off from places $$A$$ and $$B$$ at the same time, heading towards each other. Teacher Xiao Hong travels at $$15$$ kilometers per hour, while Xiao Ming travels at $$10$$ kilometers per hour. They meet after $$10$$ hours, and the distance between places $$A$$ and $$B$$ is in kilometers.\n question_236-image_0"}, {"key": "237", "content": "It is known that a cat walks $$70$$ meters per minute, and a mouse walks $$60$$ meters per minute, they start at the same time from places $$A$$ and $$B$$, respectively. If they head towards each other, they meet after $$5$$ minutes; if they head in the same direction, then the minutes the cat needs to catch up to the mouse are _____."}, {"key": "238", "content": "Xiaomi and Xiao Hua are running in the same direction on the playground, with Xiao Hua in front. Initially, there is a distance of $$100$$ meters between them. Xiaomi\u2019s speed is $$3$$ meters/second, and Xiao Hua\u2019s speed is $$1$$ meter/second. Thus, after how many seconds will Xiaomi catch up with Xiao Hua for the first time."}, {"key": "239", "content": "Find the value represented by the symbol below.$$9\\times \\blacksquare =16 +5\\times \\blacksquare$$, then$$ \\blacksquare=$$"}, {"key": "240", "content": "Find the value represented by the symbol. $$6\\times( \\blacksquare+1) =26 -4\\times \\blacksquare$$ , then $$ \\blacksquare=$$"}, {"key": "241", "content": "Find the value represented by the symbol below.$$4\\times \\blacksquare +6\\times \\blacksquare =70$$, then $$\\blacksquare=$$"}, {"key": "242", "content": "Find the value represented by the following symbol.$$7x =24 +3x$$, then $$x=$$"}, {"key": "243", "content": "Find the value represented by the symbol below.$$2\\times \\blacksquare +3\\times \\blacksquare =100$$, then$$ \\blacksquare=$$"}, {"key": "244", "content": "Find the value represented by the following symbol. $$5(a+1)=29-a$$, then $$a=$$"}, {"key": "245", "content": "The age difference between the father and son is $$24$$ years, the age of the father is $$5$$ times that of the son, the son is years old."}, {"key": "246", "content": "Write the abbreviated form of the following expression (same letters should be combined): $$a\\times 4+3\\times a+2$$\uff0e"}, {"key": "247", "content": "Subtract twice a certain number from $$37$$, the difference is $$19$$, find this number."}, {"key": "248", "content": "Given $$47-3\u25b3=11$$, then $$\u25b3=$$\uff0e"}, {"key": "249", "content": "Person A and Person B set off from places $$A$$ and $$B$$ respectively at the same time, heading towards each other. Person A travels at $$12$$ kilometers per hour, and Person B travels at $$11$$ kilometers per hour. They meet after $$10$$ hours. The distance between places $$A$$ and $$B$$ in kilometers is."}, {"key": "250", "content": "Find the value represented by the following symbol.$$2\\times \\blacksquare +3\\times \\blacksquare =10$$  , then $\\blacksquare=$"}, {"key": "251", "content": "Egg Brother bought $$28$$ eggs. The number of eggs he bought is $$2$$ times more than Egg Sister plus $$4$$ eggs. Egg Sister bought eggs."}, {"key": "252", "content": "$$a\\times b+c=$$ ()\uff0e"}, {"key": "253", "content": "Vehicles A and B set off from places $$A$$ and $$B$$ respectively, heading towards each other. Vehicle A travels at $$48$$ kilometers per hour, and Vehicle B travels at $$50$$ kilometers per hour. If Vehicle A departs 1 hour earlier and meets Vehicle B after 5 more hours, then the distance between places $$A$$ and $$B$$ is kilometers."}, {"key": "254", "content": "Train A and B depart from two places that are $$770$$ kilometers apart, heading towards each other. Train A travels at $$45$$ kilometers per hour, and Train B at $$41$$ kilometers per hour. Train B departs $$2$$ hours before Train A. After a certain number of hours, Train A meets Train B."}, {"key": "255", "content": "Find the value represented by the symbol.$$4\\times( \\blacksquare-2) =22 +3\\times \\blacksquare$$, then $$ \\blacksquare=$$"}, {"key": "256", "content": "The students went to the orchard to pick fruit, and picked a total of $$26$$ pounds of oranges, which is $$3$$ times more than the bananas plus two pounds. The students picked pounds of bananas."}, {"key": "257", "content": "Locations A and B are 240 kilometers apart. Car A departs from location A at a speed of 60 kilometers per hour. At the same time, Car B departs from location B at a speed of 90 kilometers per hour. The two cars travel in the same direction, with Car B behind Car A. After a certain number of hours, Car B can catch up to Car A."}, {"key": "258", "content": "Find the value represented by the following symbol.$$7\\times \\blacksquare =12 +4\\times \\blacksquare$$, then$$ \\blacksquare=$$"}, {"key": "259", "content": "A class has $$25$$ boys, and the number of boys is $$3$$ more than $$2$$ times the number of girls. The class has girls."}, {"key": "260", "content": "An ant is at point $$A$$ on a rectangular grid paper and wants to go to point $$B$$ for fun. Can you find the shortest path for it.\n question_260-image_0"}, {"key": "261", "content": "The shortest route for Yaya to get home from school has several.\n question_261-image_0"}, {"key": "262", "content": "Pudding and Jelly go to the Youth Palace to participate in the $$2010$$ Shanghai World Expo volunteer training, the map between the Youth Palace and the school is as follows\nIf they set off from the school, there are a total of different shortest routes.\n question_262-image_0"}, {"key": "263", "content": "The perimeter of a square is $$12$$ meters, and the side length is ( ) meters."}, {"key": "264", "content": "A rectangle has a perimeter of $$20$$ meters, and its length is $$7$$ meters, then its width is ( ) meters."}, {"key": "265", "content": "The perimeter of this figure is centimeters. (Unit: cm) question_265-image_0"}, {"key": "266", "content": "Given a rectangular piece of paper is $$17$$ cm long and $$13$$ cm wide, then the perimeter of the rectangle is cm. question_266-image_0"}, {"key": "267", "content": "Find the perimeter of the figure below: ( )\uff0e\n question_267-image_0"}, {"key": "268", "content": "Given that the perimeter of a square is $$64$$ meters, the length of one of its sides is meters."}, {"key": "269", "content": "Using the numbers $$1$$, $$3$$, $$5$$, how many different two-digit numbers can be formed?"}, {"key": "270", "content": "Choose two numbers from the three numbers $$5$$, $$6$$, $$7$$, the largest two-digit number formed is ( )."}, {"key": "271", "content": "Using three digit cards $$0$$, $$1$$, $$9$$, how many different three-digit numbers can be formed."}, {"key": "272", "content": "In the following arithmetic expression, the same symbol represents the same digit, and different symbols represent different digits. Based on this equation, it can be inferred that: $$\\square +\\bigcirc +\\triangle +$$\u2606$$=$$\uff0e\n question_272-image_0"}, {"key": "273", "content": "Calculate using long multiplication: $$17\\times 209$$=\uff0e"}, {"key": "274", "content": "Perform vertical multiplication: $$36\\times14=$$."}, {"key": "275", "content": "Perform vertical calculation: $$276\\div 12$$=."}, {"key": "276", "content": "In a cattle farm, $$3$$ cows can consume $$24$$ bales of hay in $$2$$ days. Now, $$5$$ cows can consume $$100$$ bales of hay per day."}, {"key": "277", "content": "The greening team plants $99$ trees in $3$ days, and they still need to plant $66$ trees. According to this work efficiency, the total days required to complete the task are."}, {"key": "278", "content": "3 workers process 90 parts in 5 hours, at this rate, 10 workers process parts in 10 hours."}, {"key": "279", "content": "Wei's average score for the first four assignments is $$90$$ points, the total score for Wei's first four assignments is ( )."}, {"key": "280", "content": "There are $$8$$ boxes of apples, each box has $$40$$ apples, if they are evenly distributed among $$4$$ classes, each class will get ( ) apples."}, {"key": "281", "content": "At the sports meeting, class 1 of grade 3 had $$10$$ boys and $$8$$ girls participating, knowing the average score of boys is $$14$$ points, the average score of all participating students in class 1 is $$10$$ points, the average score of girls is points."}, {"key": "282", "content": "The number of people in class A and class B are $$40$$ and $$30$$, respectively. Knowing that the average score of class A is $$93$$ points, and the overall average score of both classes is $$90$$ points, find the average score of class B. "}, {"key": "283", "content": "The study group received $32$ red flowers for the first class, $32$ red flowers for the second class, and $26$ red flowers for the third class. Therefore, the study group received an average number of flowers per class."}, {"key": "284", "content": "Add another number to this group of numbers: $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, $$10$$. Now, the average of all the numbers is $$7$$. Find the added number."}, {"key": "285", "content": "Calculate: $$\\frac {3}{17}-\\frac {16}{27}-\\frac {3}{17}+\\frac {17}{27}=$$\uff0e"}, {"key": "286", "content": "$$\\frac{5}{9}=\\frac{45}{(\\ \\ \\ \\ )}=\\frac{(\\ \\ \\ \\ )}{99}$$\uff0cthe numbers that should be filled in the brackets in sequence are."}, {"key": "287", "content": "A fraction has a denominator of $$6$$ and a numerator of $$5$$, this fraction is\uff0e"}, {"key": "288", "content": "Max\u2019s Magic School Grand Parade, a total of $$31$$ floats participated in the inspection, the first float is $$6$$ meters long, each of the remaining floats is $$4$$ meters long, and the space between each float is $$5$$ meters. The total length of the parade is meters."}, {"key": "289", "content": "Trees are to be planted alongside a $$24$$ meter long road at every $$4$$ meters, not planting at both ends. The total number of trees that can be planted on this road is."}, {"key": "290", "content": "Eddie goes from the $$1^{st}$$ floor to the $$5^{th}$$ floor and it takes $$4$$ minutes. Therefore, using the same speed, how long will it take for him to go from the $$1^{st}$$ floor to the $$10^{th}$$ floor in minutes?"}, {"key": "291", "content": "For Children's Day, the teacher decorates the classroom with colored light bulbs, connecting them in the pattern of \"two red, one yellow, one green\", then the 37th light bulb is ( ) color."}, {"key": "292", "content": "$$A$$, $$B$$, and $$C$$ are three kids passing a ball to each other, starting with $$A$$ as the first to pass the ball. After $$2$$ passes, there are a total of different ways to pass the ball."}, {"key": "293", "content": "A, B, and C pass the ball to each other, each time it must be passed on. Starting with B passing it out counts as the first pass. How many ways are there for the ball to be passed to B for the 3rd time?"}, {"key": "294", "content": "A series of figures are arranged according to the following pattern: \u2606\u2606$$\\bigcirc \\bigcirc $$\u2606$$\\triangle \\triangle \\bigcirc \\bigcirc $$\u2606$$\\triangle \\triangle \\bigcirc \\bigcirc $$\u2606$$\\triangle \\triangle \\cdots \\cdots $$The correct statement about what the $$100$$th figure in this series is ( )\uff0e"}, {"key": "295", "content": "Observe the pattern change of black and white triangles in the diagram. So, in the first $$200$$ diagrams, there are white triangles.\n question_295-image_0"}, {"key": "296", "content": "$$8$$ members form a circle playing a passing game, starting from member no. \u2460, passing the ball in a clockwise direction to the next person. After passing the ball $$72$$ times, the ball is in the hands of member no. .\n question_296-image_0"}, {"key": "297", "content": "Vi and Eddy are playing a game, where they arrange black and white balls in a sequence following a certain pattern. Do you know what the 100th ball is? How many black balls are there among the first 100 balls?"}, {"key": "298", "content": "There are a total of $$2014$$ black and white chess pieces, arranged from left to right in a row according to the pattern shown in the picture, where the number of black chess pieces is\uff0equestion_298-image_0"}, {"key": "299", "content": "An electronic flea can jump from one circle to the adjacent circle in each move. Now, a red flea starts from the circle labeled with the number \"$$0$$\" and jumps $$71$$ steps clockwise, landing in a circle. A black flea also starts from the circle labeled with the number \"$$0$$\" but it jumps $$41$$ steps counter-clockwise, landing in another circle. The product of the numbers in these two circles is. question_299-image_0"}, {"key": "300", "content": "The order of painting the small wooden balls on the assembly line is: first $$5$$ red, $$4$$ yellow, $$3$$ green, $$2$$ black, $$1$$ white, and then it repeats $$5$$ red, $$4$$ yellow, $$3$$ green, $$2$$ black, $$1$$ white$$\\ldots \\ldots$$ continuing in this manner, up to the $$154$$th ball to be painted."}, {"key": "301", "content": "There are $$249$$ flowers, arranged in the sequence of $$5$$ red flowers, $$9$$ yellow flowers, $$13$$ green flowers in turns, what color is the last flower? Among these $$249$$ flowers, which color has the most and which has the least? How many fewer is the least compared to the most?"}, {"key": "302", "content": "As shown in the figure, there are $$16$$ chairs arranged in a circle, sequentially numbered from $$1$$ to $$16$$. Now a person moves clockwise from chair number $$1$$ for $$328$$ steps, then moves counterclockwise for $$485$$ steps, again moves clockwise for $$485$$ steps, then moves counterclockwise for $$328$$ steps, and finally moves clockwise for $$136$$ steps, at this point he arrives at chair number . question_302-image_0"}, {"key": "303", "content": "As shown in the figure, the text in each row of the table is cyclically repeated: the first row continuously repeats the four Chinese characters for \"Riemann Hypothesis\", the second row repeats the five Chinese characters for \"Poincar\u00e9 Conjecture\", and the third row repeats the six Chinese characters for \"Goldbach's Conjecture.\" What are the three Chinese characters from top to bottom in the $$200$$th column? question_303-image_0"}, {"key": "304", "content": "Xiao Ming counts numbers in the order of $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$\\cdots \\cdots$$ cyclically. When he has counted 600 numbers, the sum of the numbers Xiao Ming has counted is."}, {"key": "305", "content": "There are $$2018$$ natural numbers arranged in a row, where the sum of any four adjacent numbers equals $$30$$. The first number is $$3$$, the second number is $$7$$, the third number is $$13$$. Then, the last number is."}, {"key": "306", "content": "An even number plus an even number results in ( )."}, {"key": "307", "content": "A string of beads arranged in the order of $$3$$ black beads, $$2$$ white beads, $$3$$ black beads, $$2$$ white beads... Hence, the color of the $$38$$th bead is."}, {"key": "308", "content": "Determine the parity of each of the following expressions.\n\u2460$$1\\times 2\\times 3\\times \\cdots \\times 98\\times 99\\times 100$$ ( )\uff0e\n\u2461$$1\\times 3\\times 5\\times \\cdots \\times 95\\times 97\\times 99$$ ( )\uff0e"}, {"key": "309", "content": "The result of the calculation $$2017\\times 37+37+1995-31\\times 111$$ is ( )."}, {"key": "310", "content": "Find two integers such that their sum is $$264$$ and their difference is $$57$$. Do such numbers exist? ( )"}, {"key": "311", "content": "Calculate\n$$4\\times 9\\times 25=$$"}, {"key": "312", "content": "Calculate: (1)$$23\\times 4\\times 25=$$(2)$$125\\times 13\\times 8=$$"}, {"key": "313", "content": "$$1\\times 2\\times 3\\times 4\\times 5+6+7+8+9$$ is the result odd or even?"}, {"key": "314", "content": "The simplified calculation of $25\\times52$ is ( )."}, {"key": "315", "content": "The simplified operation for $17\\times99$ is ( )."}, {"key": "316", "content": "$5\\times21+5\\times79$ simplified operation is ( )."}, {"key": "317", "content": "Calculate: $$(350-49)\\div 7=$$\uff0e"}, {"key": "318", "content": "Calculate: $3700\\div74=$."}, {"key": "319", "content": "Calculate: $$(560+88)\\div 8=$$\uff0e"}, {"key": "320", "content": "Compute: $$23\\times 70\\times 22\\div 11\\div 7=$$\uff0e"}, {"key": "321", "content": "Calculate:\n($$1$$) $$4900\\div 4\\div 25=$$.\n($$2$$) $$7000\\div 2\\div 125\\div 4=$$."}, {"key": "322", "content": "$136\\div5+364\\div5$ the simplified calculation is ()."}, {"key": "323", "content": "$72\\div\\left( 6\\times5\\right)\\times5$ The simplified operation is ( )."}, {"key": "324", "content": "The simplified operation of $700\\div4\\div25$ is ( )."}, {"key": "325", "content": "The side length of the square is $$3$$ cm, the area of the square is square cm; the length of the rectangle is $$6$$ cm, its width is $$4$$ cm, the area of the rectangle is square cm."}, {"key": "326", "content": "The area of a square is $$36$$ square centimeters, so its side length is cm, and its perimeter is cm."}, {"key": "327", "content": "Everyone arrived at the Deer Park again. Eddie counted and found that there were a total of $$24$$ sika deer and giraffes, and the number of sika deer was $$4$$ less than $$3$$ times the number of giraffes. How many sika deer and giraffes did Eddie see?"}, {"key": "328", "content": "The Xiao Lin family raised $$30$$ rabbits, among which the number of big rabbits is $$2$$ times the number of small rabbits. Then, the number of big rabbits and small rabbits in the Xiao Lin family are."}, {"key": "329", "content": "Little monkeys Duo Duo and Dian Dian together have $$34$$ peaches, Duo Duo has $$3$$ times more peaches than Dian Dian plus $$2$$ more peaches. Duo Duo has peaches, Dian Dian has peaches."}, {"key": "330", "content": "In the diagram below, the area of the square is square centimeters. question_330-image_0"}, {"key": "331", "content": "In the figure below, the area of the rectangle is square centimeters. question_331-image_0"}, {"key": "332", "content": "The library has a total of $$360$$ books, including math books, science and technology books, and comic books. The number of math books is twice that of comic books, and the number of science and technology books is three times that of comic books. Therefore, there are math books, science and technology books, and comic books."}, {"key": "333", "content": "In this year\u2019s sales contest, Team A\u2019s sales were $$2$$ times plus $$15$$ million yuan more than Team B\u2019s sales, the total sales of the company were $$75$$ million yuan this year, so Team A sold million yuan, and Team B sold million yuan."}, {"key": "334", "content": "Xiao Zhang and Xiao Li have a total of $$60$$ yuan, among which Xiao Zhang has $$5$$ times the money Xiao Li has. Therefore, Xiao Zhang has yuan, and Xiao Li has yuan."}, {"key": "335", "content": "There are poplar trees, willow trees, and pine trees in the park. The number of willow trees is twice that of pine trees, and the number of poplar trees is three times that of willow trees. Then, the number of poplar trees is how many times that of pine trees."}, {"key": "336", "content": "Xiao Ai has $$20$$ rabbits at home. The number of baby rabbits is $$4$$ times the number of adult rabbits. There are adult rabbits and baby rabbits."}, {"key": "337", "content": "Xiaoming bounces the ball $$78$$ times, Xiaohua's number of bounces is more than twice Xiaoming's but less than three times. Xiaohua possibly bounced the ball ( ) times."}, {"key": "338", "content": "Farm A harvested 80 million tons more sorghum than Farm B, and the sorghum harvest of Farm A is 5 times that of Farm B. Thus, Farm A harvested million tons of sorghum, and Farm B harvested million tons of sorghum. question_338-image_0"}, {"key": "339", "content": "Farm A harvested 50 million tons more corn than Farm B, and the corn harvested by Farm A was 3 times more and 20 million tons more than that of Farm B, then Farm A harvested million tons of corn, and Farm B harvested million tons of corn. question_339-image_0"}, {"key": "340", "content": "Farm A harvested 50 million tons more wheat than Farm B, and the harvest of Farm A is 10 million tons less than 4 times that of Farm B. Therefore, Farm A harvested million tons of wheat, and Farm B harvested million tons of wheat. question_340-image_0"}, {"key": "341", "content": "Eddie, Vi, and Superman Jr. have some energy spheres. The number of Eddie's energy spheres is 5 times that of Superman Jr.'s, and the number of Vi's energy spheres is 2 times that of Superman Jr.'s. The difference between the number of Eddie's and Vi's energy spheres is 60. Calculate the number of energy spheres Eddie has."}, {"key": "342", "content": "Among three people, A, B, and C, A is 12 years older than B, C is 15 years older than A, and C's age is 4 times that of B. A's age is ____ years, B's age is ____ years, C's age is ____ years."}, {"key": "343", "content": "Originally, there were $$20$$ more bags of rice than flour in the grain store. After selling $$30$$ bags of rice and $$16$$ bags of flour, which is more now, rice or flour? And by how many bags? ( )"}, {"key": "344", "content": "Eddie and Vi went to the orchard to pick apples together. Eddie picked 3 times as many apples as Vi did. Moreover, Eddie picked 100 more apples than Vi. How many apples did Eddie pick, and how many did Vi pick?"}, {"key": "345", "content": "Qiangqiang has $$24$$ more storybooks than Mingming, and if each of them buys $$3$$ more books, then Qiangqiang still has more books than Mingming by ___."}, {"key": "346", "content": "If today is Saturday, counting from today, the $$60$$th day falls on a ."}, {"key": "347", "content": "On July 20th, mom started her vacation and went back to work on September 1st. She took a total of vacation days."}, {"key": "348", "content": "August 1, 2019, was a Thursday, so the August 31 was ( )."}, {"key": "349", "content": "International Children's Day in $$2013$$ was on Saturday, and International Children's Day in $$2014$$ was on Sunday ( )."}, {"key": "350", "content": "Given that the magic sum of a 3x3 magic square is $$60$$, then the center number of this 3x3 magic square is."}, {"key": "351", "content": "In a certain year, April 7th is a Wednesday. Calculate what day of the week April 12th falls on in the same year ( )."}, {"key": "352", "content": "Create a 3x3 magic square using $$11$$, $$13$$, $$15$$, $$17$$, $$19$$, $$21$$, $$23$$, $$25$$, $$27$$."}, {"key": "353", "content": "The deposit of A is $$4$$ times that of B, A deposits $$60$$ more than B, A has a deposit of yuan, B has a deposit of yuan."}, {"key": "354", "content": "The figure below is a part of a 3x3 magic square, $$X=$$\uff0e question_354-image_0"}, {"key": "355", "content": "Ancient China\u2019s \"River Map\" consists of a $$3\\times 3$$ grid, with each cell containing a different number of dots. The sum of the dots in every row, every column, and each diagonal is equal. The provided diagram shows a part of the \"River Map.\" Please calculate the dot diagram that corresponds to the position $$P$$. The correct answer is ( ) .\n question_355-image_0"}, {"key": "356", "content": "The picture has nine squares, requiring a different number to be filled in each square, so that the sum of the three numbers in each row, each column, and each diagonal is equal. Question: What is the number in the top-left corner of the picture?\n question_356-image_0"}, {"key": "357", "content": "Regarding the following four Olympic Games, the incorrect statement among the following is ( ). question_357-image_0"}, {"key": "358", "content": "The chart below is a statistical graph of the favorite ball sports among third and fourth graders at a certain school. Based on the information in the graph, the correct conclusion is ( ).\n question_358-image_0"}, {"key": "359", "content": "As shown in the figure, the incorrect statement among the following is ( ).\n question_359-image_0"}, {"key": "360", "content": "The diagram shows the heights of four classmates. There are no names on the chart, but it is known that Xiao Gang is the tallest, Xiao Li is the shortest, and Xiao Ming is taller than Xiao Hong. What is Xiao Hong's height ( )?\n question_360-image_0"}, {"key": "361", "content": "The figure below shows the apple sales situation of supermarkets A and B from January to March. In March, supermarket A sold ( ) boxes more than supermarket B.\n question_361-image_0"}, {"key": "362", "content": "In a bar chart, a 2 cm long bar represents 10 kg, a ( ) cm long bar represents 30 kg."}, {"key": "363", "content": "There are four seasons in a year, the following four images respectively represent spring, summer, autumn, and winter. Kids, please observe which one of the images can be drawn in one stroke. (No need to draw the frame around it)\n question_363-image_0"}, {"key": "364", "content": "The diagram below is a plan view of a park's pathways, to allow visitors to walk all paths without repetition, where should the entrance and exit be located respectively? ( )\uff0e\n question_364-image_0"}, {"key": "365", "content": "Chickens and rabbits in the same cage, a total of $$3$$ animals, $$10$$ legs, so there are chickens."}, {"key": "366", "content": "There are a total of $$25$$ chickens and rabbits together in a cage, and there are a total of $$80$$ legs in the cage, then there are $$15$$ rabbits."}, {"key": "367", "content": "Xiaolin has red and black signature pens, Xiaojue has black and blue signature pens, the two of them together have a total of different colors of signature pens."}, {"key": "368", "content": "A survey of the whole class found that there are $$20$$ people who can swim, $$25$$ people who can play basketball. There are $$10$$ people who can do both, and $$9$$ people who can do neither. The total number of people in this class is."}, {"key": "369", "content": "A certain number plus $$5$$, then multiplied by $$10$$, subtracted by $$5$$, and then divided by $$5$$, the final result is $$15$$. The number is."}, {"key": "370", "content": "A class has a total of $$42$$ students, $$21$$ students participated in the school-organized music activity, $$16$$ students participated in the sports activity, and $$6$$ students didn't participate in either activity, then the number of students who participated in both activities is."}, {"key": "371", "content": "Among all natural numbers from $$1\\sim 100$$, there are numbers that are multiples of $$2$$ or multiples of $$5$$."}, {"key": "372", "content": "Every student in class 1 of the fourth grade bought at least one book, 30 people bought storybooks, 12 people bought comic books, and 6 people bought both. How many people are in the class?"}, {"key": "373", "content": "Xue Xue did a problem like this: A number, added by $$3$$, subtracted by $$5$$, multiplied by $$4$$, and divided by $$6$$ equals $$16$$. This number is."}, {"key": "374", "content": "A toy store replenishes 20 toys every time half of the toys are sold. After selling half for the 2nd time, there are exactly 20 toys left. Therefore, the original number of toys in the toy store was ."}, {"key": "375", "content": "Bald Qiang took apples from the basket, the first time he took half of the total, the second time he took half of the remaining. After that, there were $$2$$ left in the basket. So, there were initially $$8$$ apples in the basket."}, {"key": "376", "content": "Class A and Class B each want to plant a certain number of trees. If Class A gives the same number of trees to Class B, and then Class B also takes the same number of trees from their existing ones to give to Class A, both classes end up with exactly $$28$$ trees each. How many trees did Class A and Class B originally have?"}, {"key": "377", "content": "A bundle of wire, the first use took half of its total length, the second use took half of the remaining length, and finally $$3$$ meters were left. The original length of this bundle of wire was in meters."}, {"key": "378", "content": "A number plus $$5$$, times $$5$$, subtract $$5$$, then divided by $$5$$, results in $$5$$, this number is."}, {"key": "379", "content": "Xiaoming wrote a number on the blackboard, and Xiaohong multiplied this number by $$2$$ then added $$4$$ to it, resulting in $$8$$. So, the number Xiaoming wrote on the blackboard is."}, {"key": "380", "content": "Fill in the blanks with numbers $$1\\sim 6$$, so that each row, each column, and each bold-lined palace contain unique numbers. Every shape in the Sudoku represents a number, and the same shape represents the same number, while different shapes represent different numbers (there are a total of $$6$$ shapes in the figure). Therefore, $$\\bigcirc\\times\\square=$$\uff0e question_380-image_0"}, {"key": "381", "content": "A corner has ( ) sides."}, {"key": "382", "content": "A number composed of $$8$$ ones, $$9$$ tenths, and $$4$$ thousandths is ( )."}, {"key": "383", "content": "The right picture shows the 100m dash results table for the first group, among them the fastest is (  ).\n\n\n\n\nName\n\nWang Ming\n\nLi Hua\n\nFang Qiang\n\nChen Li\n\n\n\nResult\n\n$$16.7$$ seconds\n\n$$17.5$$ seconds\n\n$$16.58$$ seconds\n\n$$16.08$$ seconds"}, {"key": "384", "content": "Use column addition to calculate $$0.35+0.46=$$ ( )."}, {"key": "385", "content": "Compare the magnitude of the following decimals:\n\n\n\n$$1.6$$$$2.4$$\n$$2.3$$$$20.3$$\n\n\n$$44.44$$$$4.444$$\n$$2.132$$$$2.13$$\n\n\n$$21.30$$$$21.3$$\n$$86.4$$$$68.4$$"}, {"key": "386", "content": "In the decimal $$4.67$$, the \u201c$$6$$\u201d represents having $$6$$ of them. Shrinking $$12$$ to its $$0.12$$."}, {"key": "387", "content": "In the figure below, it is known that $$\\angle 1=\\angle 2$$, then the degree of $$\\angle 1$$ is degrees. question_387-image_0"}, {"key": "388", "content": "As shown in the figure, it is known that $$\\angle 1=72{}^\\circ $$, find the degree of $$\\angle 2$$\uff0e question_388-image_0"}, {"key": "389", "content": "As shown in the figure, it is known that $$\\angle 1=30{}^\\circ $$, then $$\\angle 2=$$$${}^\\circ $$, $$\\angle 3=$$$${}^\\circ $$\uff0e question_389-image_0"}, {"key": "390", "content": "Divide a right angle into two angles, where one angle is an acute angle, the other angle must be ( )."}, {"key": "391", "content": "As shown in the figure, $$\\angle 1=50{}^\\circ $$, $$\\angle 2=$$ ( ).\n question_391-image_0"}, {"key": "392", "content": "Count the number of lines in the figure below.\n question_392-image_0"}, {"key": "393", "content": "As shown in the figure, composed of several small squares of the same side length, then, the total number of squares in this figure is.\n question_393-image_0"}, {"key": "394", "content": "Count the total number of squares in the image below.\n question_394-image_0"}, {"key": "395", "content": "There are a total of squares in the picture.\n question_395-image_0"}, {"key": "396", "content": "There are a total of several line segments in the figure.\n question_396-image_0"}, {"key": "397", "content": "This year, Xiao Qiang and Da Qiang have a total age of $$30$$ years, Da Qiang is $$6$$ years older than Xiao Qiang, so Da Qiang's age this year is ."}, {"key": "398", "content": "There are a total of squares in the following figure. question_398-image_0"}, {"key": "399", "content": "Count the number of triangles in the image below. question_399-image_0"}, {"key": "400", "content": "The picture in total has several line segments\uff0e question_400-image_0"}, {"key": "401", "content": "Li Ming is $$9$$ years old this year, the sum of his parents' ages is $$81$$ years, so the sum of their ages a year later will be $$120$$ years."}, {"key": "402", "content": "This year, the father's age is $$5$$ times that of his son. Three years from now, the combined age of the father and son will be $$54$$ years. So, the father's age this year is ____ years old.\n question_402-image_0"}, {"key": "403", "content": "$$12\\times 3+3\\times 15=$$( )\uff0e"}, {"key": "404", "content": "To prioritize calculating $$3\\times 2$$, it is necessary to add parentheses to the equation ( )."}, {"key": "405", "content": "$$62-(46-6)=$$ ( )\uff0e"}, {"key": "406", "content": "As shown in the figure, all the small segments in the picture are of the same length, and there are $$3$$ shortest paths from point $$A$$ to point $$B$$.\n question_406-image_0"}, {"key": "407", "content": "Place the appropriate operators and parentheses on the left side of the equation below, the option that makes the equation valid is ( ).\n$$8\\;\\;\\;\\;\\;\\;\\;\\;1\\;\\;\\;\\;\\;\\;\\;\\;5=35$$"}, {"key": "408", "content": "Using the four numbers $$2$$, $$3$$, $$3$$, $$7$$, fill in between them with $$+$$, $$-$$, $$\\times$$, $$\\div$$ and ( ), so that the result equals $$24$$. The correct option is ( )."}, {"key": "409", "content": "Choose the appropriate \"$$+$$, $$-$$, $$\\times$$, $$\\div$$\" to fill between each pair of numbers to make the following equation valid. The correct way to fill in is ( ).\n$$3$$$$3$$$$3$$$$3=2$$"}, {"key": "410", "content": "Fill in the blanks with \u201c$$+$$, $$-$$, $$\\times$$, $$\\div$$\u201d to make the following equation correct. The correct way to fill in is ( ).\n$$1$$$$2$$$$7$$\uff1d$$9$$"}, {"key": "411", "content": "In the street schematic below, passage is not possible at $$C$$ due to construction. How many shortest routes are there from $$A$$ to $$B$$? ( )\n question_411-image_0"}, {"key": "412", "content": "It started to rain, and the little ant needs to quickly return from point $$B$$ to its home at point $$C$$. If it can only walk along the gridlines, there are different shortest routes to choose from.\n question_412-image_0"}, {"key": "413", "content": "An ant is at point $$A$$ on a square grid paper, it wants to follow the grid lines to point $$B$$ for fun, but it doesn\u2019t know which path is the shortest. Kids, can you find it a different shortest path.\n question_413-image_0"}, {"key": "414", "content": "A plate of kiwifruit, to be shared among some children. If each child gets 3, there are 5 left over; if each child gets 4, they are exactly all distributed. How many children are there?"}, {"key": "415", "content": "As shown in the diagram, starting from point $$A$$ to point $$B$$, taking the shortest route, but must pass through $$C$$, how many different ways are there?\n question_415-image_0"}, {"key": "416", "content": "As shown in the rectangle $$ABCD$$, the total number of different methods to travel the shortest path from $$A$$ to $$C$$ along the lines in the diagram is. question_416-image_0"}, {"key": "417", "content": "The Monkey King distributed peaches to the little monkeys. If he gives each little monkey $$14$$ peaches, he would have $$10$$ peaches left over; if he gives each little monkey $$16$$ peaches, he would only have $$2$$ peaches left over. Therefore, there are a total of little monkeys."}, {"key": "418", "content": "On Children's Day, the school distributes balloons to each class for classroom decoration. If each class gets 20 balloons, there will be 130 balloons left; if each class gets 25 balloons, they will be exactly enough. There are a total of classes."}, {"key": "419", "content": "Eddie puts some small balls into boxes. If each box contains $$15$$ small balls, there are $$10$$ small balls missing in the end; if each box contains $$12$$ small balls, there are $$5$$ small balls extra in the end. There are a total of boxes."}, {"key": "420", "content": "The kindergarten gives candy to the award-winning children. If each child is given $$6$$ pieces, there will be $$12$$ pieces short. If each child is given $$9$$ pieces, there will be $$24$$ pieces short. How many children are there in total who won the award."}, {"key": "421", "content": "A teacher distributes candies to students. If each student gets $$4$$ candies, there are $$19$$ candies left. If each student gets $$5$$ candies, there is $$1$$ candy left. How many students are there in total?"}, {"key": "422", "content": "The teacher distributes $9$ candies between Dumb and Dumber, so that each of them has some candies.$$There are different ways of distribution."}, {"key": "423", "content": "Grandma Zhang went to the supermarket and bought $$12$$ boxes of milk, and she found that these boxes of milk needed to be packed into $$2$$ identical bags, with each bag able to hold a maximum of $$10$$ boxes. There are in total different methods for Grandma Zhang to pack the milk."}, {"key": "424", "content": "Dividing $$13$$ identical marbles into $$3$$ different piles, there are a total of different ways."}, {"key": "425", "content": "Break $$13$$ into the sum of three different nonzero natural numbers, but the three natural numbers can only be chosen from $$1\\sim 8$$, there are a total of different ways to break it up."}, {"key": "426", "content": "$$12$$ pieces of chocolate are distributed among three kids $$A$$, $$B$$, and $$C$$, with each getting at least $$3$$ pieces and at most $$6$$ pieces. There are different ways of distributing them."}, {"key": "427", "content": "Divide $$14$$ into the sum of three different non-zero natural numbers, there are a total of different ways to do this division."}, {"key": "428", "content": "Distribute $$8$$ tanks to three kids: Xiaoxiao, Zhongzhong, and Dada, each getting at least one tank. There is a method."}, {"key": "429", "content": "Split $$8$$ into the sum of $$3$$ natural numbers, there are a total of different methods."}, {"key": "430", "content": "Xiao Bai wants to put $$18$$ identical car models onto a $$3$$-tier shelf, with at least $$5$$ on each tier, there are different ways to do this."}, {"key": "431", "content": "Dividing $$12$$ identical balls into three piles, with each pile having at least two, there are types of divisions."}, {"key": "432", "content": "Distribute $$15$$ identical balls into three piles, with each pile having at least $$3$$, there are ways of distribution."}, {"key": "433", "content": "There are several different ways to divide $$7$$ identical apples into two piles."}, {"key": "434", "content": "Three pirates are sharing $$20$$ gold coins. If each pirate gets at least $$5$$ coins, there are a total of different methods to divide them."}, {"key": "435", "content": "How many different ways can you divide $$9$$ identical marbles into $$3$$ piles?"}, {"key": "436", "content": "Divide $$10$$ apples into $$3$$ piles of different quantities, there are a total of different methods."}, {"key": "437", "content": "The teacher bought $$7$$ balloons and distributed them among Xiaoyunyun, Xiaojuanjian, and Xiaoxiaoxiao, three people (each person gets at least one, otherwise, they will cry!), how many ways are there to divide?"}, {"key": "438", "content": "$$13\\times 5+7\\times 5=$$."}, {"key": "439", "content": "Calculate: (1) $$57\\times 99+57=$$\uff0e(2) $$67\\times 47+52\\times 67+67=$$\uff0e"}, {"key": "440", "content": "Calculate: (1) $$234-38-62=$$\uff0e(2) $$128-(28+71)=$$\uff0e"}, {"key": "441", "content": "There are apricot trees and cypress trees in the park, totaling $$50$$ trees. The number of apricot trees is $$10$$ more than that of cypress trees. So, how many apricot trees are there?"}, {"key": "442", "content": "If a rectangle is cut horizontally and vertically, what is the total perimeter of the $$4$$ rectangles after cutting? ( ) question_442-image_0"}, {"key": "443", "content": "Xiao Qi, Xiao Ling, Xiao Jun, Xiao Li$$4$$ students stand in a row for a photo. There are ( ) different arrangements."}, {"key": "444", "content": "With the following outfits, how many different ways can they be paired? ( )\n question_444-image_0"}, {"key": "445", "content": "There are $$5$$ different types of toys and $$7$$ different types of comic books in the store. You want to pick a birthday gift for a good friend from them, there are ( ) choices."}, {"key": "446", "content": "As shown in the diagram, a large rectangle is divided into four smaller rectangles, with the area sizes as indicated in the diagram (unit: square meters). The area of the rectangle at the \"?\" position is square meters. question_446-image_0"}, {"key": "447", "content": "As shown in the diagram, a large rectangle is divided into $$3$$ small rectangles and one small square, wherein the area of the small square is $$16$$ square centimeters, and the areas of the two rectangles are respectively $$20$$ and $$36$$ square centimeters. The area represented by rectangle $$A$$ is square centimeters.\n question_447-image_0"}, {"key": "448", "content": "As shown in the figure, it is known that the area of the parallelogram is $$36$$ square centimeters, $$CD=9$$ centimeters, $$BC=6$$ centimeters, the length of $$AE$$ is ( ) centimeters. question_448-image_0"}, {"key": "449", "content": "Which of the following parallelograms has the correct height above its base? ( )"}, {"key": "450", "content": "The figure below is a parallelogram, with an area of ( ) square centimeters. question_450-image_0"}, {"key": "451", "content": "There are two small islands in the middle of a river, with six bridges connecting the islands to both banks. Please find a route that starts from one bank, crosses all the bridges without repeating any, and then reaches the opposite bank. question_451-image_0"}, {"key": "452", "content": "The following figure is the floor plan of a museum. The museum has $$6$$ exhibition halls, with doors connecting every two halls. Little horse wants to start from a certain room, pass through all the doors without repeating, and reach room $$F$$. Therefore, the room he starts from is room . question_452-image_0"}, {"key": "453", "content": "Natural numbers $$12$$, $$135$$, $$1349$$ share a common characteristic, which is that they have at least two digits, and for any two adjacent digits, the digit on the left is less than the digit on the right. We call these 'ascending numbers'. Using the digits $$5$$, $$6$$, $$7$$, $$8$$, we can form several two-digit 'ascending numbers'."}, {"key": "454", "content": "The natural numbers $$12$$, $$135$$, $$1349$$ share a common characteristic, having at least two digits, and for any two adjacent digits, the left digit is less than the right digit; we name these as \"ascending numbers.\" Using the four digits $$5$$, $$6$$, $$7$$, $$8$$, the number of \"ascending numbers\" that can be formed is"}, {"key": "455", "content": "Eddie is tidying up his desk, dividing $$9$$ identical pencils into $$3$$ piles, there are in total different ways to do so."}, {"key": "456", "content": "To divide $$10$$ identical ballpoint pens into $$3$$ piles, there are totally different methods."}, {"key": "457", "content": "There are $$14$$ identical exercise books divided into $$3$$ piles of different quantities, with a total of different methods of division."}, {"key": "458", "content": "Break down $$18$$ into the sum of three different non-zero natural numbers, but the three natural numbers can only be chosen from $$1\\sim 9$$. How many different breakdown methods are there? Please list them all."}, {"key": "459", "content": "The little rabbit's family planted three kinds of vegetables: carrots, cabbage, and spinach. Each day, they only eat one kind of vegetable, and they do not eat the same vegetable on two consecutive days. If they eat carrots on both the 1st and the 6th day, then there are several different arrangements for the continuous 6 days' menu."}, {"key": "460", "content": "As the figure shows, a frog jumps among five lotus leaves, moving from one to another adjacent leaf each time. If the frog starts on the lotus leaf $$A$$, and then jumps continuously $$4$$ times, there are a total of different ways to jump."}, {"key": "461", "content": "We can use matchsticks to form the numbers $$0\\sim 9$$. If given $$19$$ matchsticks (all to be used), the maximum number that can be formed is, and the minimum number that can be formed is. question_461-image_0"}, {"key": "462", "content": "With $$15$$ matchsticks, place a number in each rectangle such that the three numbers formed have all different digits, the largest possible sum of the created addition equation is, the smallest is. question_462-image_0"}, {"key": "463", "content": "Fill in the appropriate number in the blank to make the vertical subtraction equation in the figure correct, then the result of the subtraction is\uff0e question_463-image_0"}, {"key": "464", "content": "Answer the following question: Fill in the blanks with the appropriate numbers to make the vertical addition in the figure correct. What is the result of the addition? question_464-image_0"}, {"key": "465", "content": "Answer the following question: In the subtraction equation below, each shape represents a number, with different shapes representing different numbers. Then, \u25b3 = . question_465-image_0"}, {"key": "466", "content": "As shown in the figure, the numbers in the blanks are digits from $$3$$ to $$8$$ (which can be reused). What is the sum of the digits in these $$6$$ blanks? question_466-image_0"}, {"key": "467", "content": "Calculate $$237\\times 2\\times 5 $$="}, {"key": "468", "content": "Calculate $$4\\times 139\\times 25$$="}, {"key": "469", "content": "Calculate $$125\\times (8\\times 23)$$="}, {"key": "470", "content": "Calculate: $$25\\times 24$$="}, {"key": "471", "content": "Calculate: $$84\\times 25$$="}, {"key": "472", "content": "Calculate: $$125\\times 72$$="}, {"key": "473", "content": "Calculate: $$125\\times (30+8)$$=\uff0e"}, {"key": "474", "content": "Calculate: $$36\\times (200-1)$$=\uff0e"}, {"key": "475", "content": "Calculate: $$(300+2)\\times 23$$=\uff0e"}, {"key": "476", "content": "Calculate: $$(400-3)\\times 25$$=\uff0e"}, {"key": "477", "content": "Calculate: $$23\\times 99 =$$\uff0e"}, {"key": "478", "content": "Calculate: $$37\\times 101=$$\uff0e"}, {"key": "479", "content": "Calculate: $$52\\times 101$$=."}, {"key": "480", "content": "Calculate: $$53\\times 24+53\\times 75+53$$=."}, {"key": "481", "content": "Please answer the following question: Class A and Class B have a total of $$105$$ books. The number of books in Class A is $$3$$ times the number of books in Class B plus $$5$$ books. How many books does Class B have, and how many books does Class A have?"}, {"key": "482", "content": "Class A has $$130$$ books, and Class B has $$30$$ books. How many books does Class A need to give to Class B so that the number of books in Class A is $$2$$ times plus $$10$$ books more than the number of books in Class B?"}, {"key": "483", "content": "The flower shop has chrysanthemums, roses, and tulips totaling $$86$$ stems, among which chrysanthemums are twice the amount of roses, and tulips are $$3$$ times the amount of roses minus $$4$$ stems. Question: How many stems of roses are there, how many stems of chrysanthemums are there, and how many stems of tulips are there?"}, {"key": "484", "content": "Calculate the following problem where a monkey and a rooster share milk candies. The amount of milk candies shared by the rooster is 3 times more than that of the monkey, plus 3 more candies, and the rooster has 27 more candies than the monkey. How many candies did the monkey and the rooster each get?"}, {"key": "485", "content": "The combined age of dad and mom is now $$72$$ years; five years later, dad will be $$6$$ years older than mom. This year dad is $$ years old."}, {"key": "486", "content": "The sister is $$13$$ years old this year, and the brother is $$9$$ years old this year. When their combined age is $$40$$ years, the sister is $$ years old."}, {"key": "487", "content": "7 years ago, the mother's age was 7 times that of her daughter; 7 years later, the combined age of the mother and daughter is 76 years. Question: How old is the mother this year."}, {"key": "488", "content": "A said to B: \"When I was your current age, you were only $$5$$ years old.\" B said to A: \"When I am your current age, you will be $$50$$ years old.\" Therefore, A is currently years old, B is currently years old."}, {"key": "489", "content": "The whale baby said: \"Mom, when I grow up to be as big as you are now, you will be $$31$$ years old!\" The whale mother said: \"When I was your size, you were only $$1$$ years old.\" How old is the whale baby now, and how old is the mother now."}, {"key": "490", "content": "The combined age of the two brothers this year is $$30$$ years old. When the older brother was the current age of the younger brother, the younger brother's age was exactly half of the older brother's age at that time. The older brother's age this year is."}, {"key": "491", "content": "The picture contains a line segment. question_491-image_0"}, {"key": "492", "content": "There is a rectangle (including a square) in the picture. question_492-image_0"}, {"key": "493", "content": "The picture contains a total of rectangles (including squares). question_493-image_0"}, {"key": "494", "content": "The picture contains a square. question_494-image_0"}, {"key": "495", "content": "The picture contains a square. question_495-image_0"}, {"key": "496", "content": "Image ($$1$$) has a square, Image ($$2$$) has a square. question_496-image_0"}, {"key": "497", "content": "The teacher distributes candies to the students. If each person gets $$4$$ candies, there are $$17$$ left over; if each person gets $$7$$ candies, there are $$10$$ short. So, there are in total students, and the teacher prepared candies."}, {"key": "498", "content": "The school allocates dormitories for new students. If each room accommodates 3 people, there are 23 people too many; if each room accommodates 5 people, 3 rooms are left empty. How many dormitories are there, and how many new students are there?"}, {"key": "499", "content": "A class of students went boating. After calculating, if each boat holds $$4$$ people, one more boat is needed; if each boat holds $$5$$ people, one less boat is needed. Question: How many students are there in this class altogether. question_499-image_0"}, {"key": "500", "content": "Students from the experimental elementary school take a bus for their spring outing. If each bus seats $$60$$ people, then $$15$$ people will not be able to get on the bus; if each bus can take an additional $$5$$ people, exactly one more bus is needed. Hence, there are a total of students, and a total of buses."}, {"key": "501", "content": "Vera has $$7$$ different tops, $$5$$ different pairs of pants, and $$2$$ different pairs of shoes in her wardrobe to choose from before going to a party. \uff081\uff09She needs to select suitable outfits from these tops, pants, and shoes, so she has a total of different ways to match them."}, {"key": "502", "content": "Vi has $$7$$ different tops, $$5$$ different pants, and $$2$$ different pairs of shoes in her wardrobe, before going to the dance party. (2) If she also has $$3$$ hats, to pick suitable outfits from these hats, tops, pants, and shoes, then she has a total of different combinations to attend the dance party."}, {"key": "503", "content": "Wei has $$7$$ different tops, $$5$$ different pairs of pants, and $$2$$ different pairs of shoes in her wardrobe for going to a dance party. (3) If she also has $$3$$ hats, which can be chosen or not, then there are a total of different combinations for her to attend the dance party."}, {"key": "504", "content": "There are four running events in the sports meeting, which are $$50$$ meters, $$100$$ meters, $$200$$ meters, and $$400$$ meters, respectively. It is stipulated that each participant can only participate in one of them. Students A, B, C, and D registered for these four events. Question: (1) If each student can freely register for these four events, there are a total of how many registration methods."}, {"key": "505", "content": "Now we need to color the front and back sides of a Y-shaped toy, as shown below. Each region is colored with one of four colors: red, yellow, blue, green. The color of each part is the same on both sides, and two parts that share a common edge cannot be the same color. Given that the toy can be flipped, there are different methods of coloring. question_505-image_0"}, {"key": "506", "content": "There are $$2$$ different English books, $$4$$ different Chinese books, and $$3$$ different math books on the bookshelf. Now, if you want to take out $$2$$ books, and they cannot be from the same subject, there are a total of different ways to do so."}, {"key": "507", "content": "A signaler has one flag each of the colors red, yellow, blue, and green. When he hangs the signal flags on the flagpole, he can hang one, two, or three flags at a time (he cannot leave the flagpole empty), with different colors and different orders representing different signals. Therefore, this signaler can represent a total of different signals."}, {"key": "508", "content": "Using the numbers $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, how many unique five-digit numbers can be formed? Among them, there are several odd numbers."}, {"key": "509", "content": "The perimeter of the figure below is in centimeters. question_509-image_0"}, {"key": "510", "content": "The perimeter of the figure below is in centimeters. question_510-image_0"}, {"key": "511", "content": "A rectangle with a length of $$12$$ cm and a width of $$10$$ cm has a square with a side length of $$4$$ cm removed and attached to another side (as shown in the diagram). The perimeter of the resulting figure is in centimeters.\n question_511-image_0"}, {"key": "512", "content": "As shown in the figure, to calculate the perimeter of the shape, it is necessary to know the length of at least one side.\n question_512-image_0"}, {"key": "513", "content": "Fold a square with a side length of $$4$$ cm in half, then cut along the fold line to get two rectangles. How many centimeters is the total perimeter of these two rectangles greater than the perimeter of the original square?\n question_513-image_0"}, {"key": "514", "content": "As shown in the diagram, a square piece of paper with a side length of 10 cm is cut horizontally twice and vertically once, dividing it into 6 small rectangular pieces. The total perimeter of these 6 small rectangles is equal to cm. question_514-image_0"}, {"key": "515", "content": "There is a rectangular piece of paper, the length is $$10$$ cm, and the width is $$8$$ cm, cut once horizontally and once vertically with scissors (as shown in the figure below), the sum of the perimeters of these $$4$$ rectangles is cm."}, {"key": "516", "content": "As shown in the figure, a large rectangle is made up of $$5$$ identical small rectangles. If the perimeter of a small rectangle is $$40$$ centimeters, then the perimeter of the large rectangle is ______ centimeters.\n question_516-image_0"}, {"key": "517", "content": "Using four identical rectangles and one small square to form a larger square with a side length of $$25$$ cm, the perimeter of each rectangle is cm. question_517-image_0"}, {"key": "518", "content": "As shown in the figure, the length and width of a rectangle are $$7$$ cm and $$5$$ cm, respectively, cut $$2$$ times parallel to the length and width, respectively, to get rectangles, the total perimeter is cm. question_518-image_0"}, {"key": "519", "content": "As shown in the figure: (2) Figure \u2461 is a rectangle with an area of $$112\\text{cm}^{2}$$, and it is known that its width is $$8\\text{cm}$$, its length is in centimeters. question_519-image_0"}, {"key": "520", "content": "As shown in the figure: (3) Figure \u2462 is a rectangle with an area of $$72\\text{d}{{\\text{m}}^{2}}$$ and it is known that its width is $$4\\text{dm}$$, and its length is dm. question_520-image_0"}, {"key": "521", "content": "As shown in the diagram, a large rectangle is divided into four smaller rectangles, of which three have areas of $$24$$ square centimeters, $$18$$ square centimeters, and $$16$$ square centimeters respectively. The area of the rectangle represented by $$A$$ is square centimeters. question_521-image_0"}, {"key": "522", "content": "The area of the given figure $$1$$ is square centimeters. question_522-image_0 question_522-image_1"}, {"key": "523", "content": "In the park, there is a square flowerbed (the shaded part in the drawing) surrounded by a path 1 meter wide, the path has an area of 12 square meters, then the area of the flowerbed in the middle is square meters. question_523-image_0"}, {"key": "524", "content": "There is a square pool, with a path 1 meter wide laid around the perimeter. The area of the path is 24 square meters. Calculate the area of the central pool (blank part) in square meters.\n question_524-image_0"}, {"key": "525", "content": "As shown in the diagram, in a square garden with a side length of $$8$$ meters, there are $$2$$ paths with a width of $$1$$ meter each (the shaded areas in the diagram), and the area of the garden (blank areas) is in square meters $$.$$\uff0e question_525-image_0"}, {"key": "526", "content": "Calculate: (1) $$12200\\div 25=$$."}, {"key": "527", "content": "Calculate: (2) $$27000\\div 4\\div 25=$$\uff0e"}, {"key": "528", "content": "Calculate: (2) $$3500\\div 25\\div 4=$$\uff0e"}, {"key": "529", "content": "Calculate: (3) $$4200\\div (25\\times 7)=$$\uff0e"}, {"key": "530", "content": "Calculate: (3) $$6300\\div \\left( 25\\times 9 \\right)=$$\uff0e"}, {"key": "531", "content": "Compute: (4) $$(54\\times 24)\\div (9\\times 4)=$$."}, {"key": "532", "content": "Calculate: (4) $$\\left( 72\\times 45 \\right)\\div \\left( 5\\times 8 \\right)=$$."}, {"key": "533", "content": "First observe, then calculate: $$3\\times 5\\times 7\\times 11\\times 13\\times 17\\div \\left( 51\\times 65\\times 77 \\right)=$$."}, {"key": "534", "content": "First observe, then calculate the following expression: (2) $$\\left( 18000-720 \\right)\\div 9=$$\uff0e"}, {"key": "535", "content": "First observe, then compute the following expressions: (1) $$294\\div 7+56\\div 7=$$\uff0e"}, {"key": "536", "content": "First observe, then calculate the following expressions: (2) $$625\\div 5-125\\div 5=$$."}, {"key": "537", "content": "Calculate: (1)$$91\\div 9+89\\div 9=$$."}, {"key": "538", "content": "Calculate: (2)$$73\\div 5+127\\div 5=$$\uff0e"}, {"key": "539", "content": "The rule $$a$$\u203b$$b$$ represents $$3$$ times $$a$$ minus $$2$$ times $$b$$, that is $$a$$\u203b$$b=3a-2b$$. For example: $$4$$\u203b$$4=3\\times 4-2\\times 4=4$$; at the same time, $$a\\triangle b$$ represents $$3$$ times $$a$$ plus $$2$$ times $$b$$, that is $$a\\triangle b=3a+2b$$. For example $$1\\triangle 4=3\\times 1+2\\times 4=11$$. (2) Calculate: $$4\\triangle(3\\triangle5)=$$"}, {"key": "540", "content": "The rule $$a$$\u203b$$b$$ represents $$3$$ times $$a$$ minus $$2$$ times $$b$$, that is $$a$$\u203b$$b=3a-2b$$, for example: $$4$$\u203b$$4=3\\times 4-2\\times 4=4$$; simultaneously, $$a\\triangle b$$ represents $$3$$ times $$a$$ plus $$2$$ times $$b$$, that is $$a\\triangle b=3a+2b$$, for example $$1\\triangle 4=3\\times 1+2\\times 4=11$$. (3) Calculate: $$(8$$\u203b$$7)\\triangle9=$$."}, {"key": "541", "content": "\"$$*$$\" represents a new operator. For example: $$1*1=1$$, $$1*2=3$$, $$1*3=6$$, $$1*4=10$$, $$1*100=5050$$, $$100*2=201$$, $$\\cdots\\cdots$$ Based on the information above, infer: (1) $$3*4=$$."}, {"key": "542", "content": "Calculate: $$\\left( 26\\div 25 \\right)\\times \\left( 27\\div 17 \\right)\\times \\left( 25\\div 9 \\right)\\times \\left( 17\\div 39 \\right)=$$"}, {"key": "543", "content": "There is an operator $$\\Delta$$ that makes the following equations hold:\n$$4\\Delta 2=6$$, $$6\\Delta 4=10$$, $$10\\Delta 8=18$$, calculate the value of $$25\\Delta 48$$ according to this pattern."}, {"key": "544", "content": "Define the symbol \"$$\\Phi $$\" to represent a new operation, such as: $$1\\Phi 99=99$$, $$99\\Phi 1=99$$, $$5\\Phi 9=9$$, $$9\\Phi 5=9$$, $$7\\Phi 8=8$$, $$7\\Phi 9=9$$; define the symbol \"$$\\Delta $$\" to represent another new operation, such as: $$1\\Delta 99=1$$, $$99\\Delta 1=1$$, $$5\\Delta 9=5$$, $$9\\Delta 5=5$$, $$7\\Delta 8=7$$, $$7\\Delta 9=7$$. \nBased on the above information, please calculate: $$\\left( 3\\Delta 4 \\right)\\times \\left( 5\\Phi 6 \\right)+\\left( 7\\Phi 8 \\right)\\times \\left( 9\\Delta 10 \\right)=$$."}, {"key": "545", "content": "Calculate: (1) $$13\\div 10+117\\div 10= $$. (2) $$981\\div 50+19\\div 50=$$."}, {"key": "546", "content": "Calculate: $$1+2+3+4+\\cdots +19+20=$$."}, {"key": "547", "content": "Calculate: $$3+5+7+9+11+13+15+17=$$."}, {"key": "548", "content": "Fill in the blank as required. (3) $$6+10+14+18+22+26+30=$$."}, {"key": "549", "content": "The consecutive odd numbers starting from $$1$$, $$1$$, $$3$$, $$5$$, $$7$$, $$\u2026\u2026$$, $$21$$ is the nth number in this sequence."}, {"key": "550", "content": "Odd numbers starting from $$1$$: $$1$$, $$3$$, $$5$$, $$7$$, $$\\cdots $$, where the $$100$$th odd number is."}, {"key": "551", "content": "In each small square of a board divided into $$16$$ small squares, put in some stones. If the first small square has $$2$$ stones, the second small square has $$4$$ stones, the third small square has $$6$$ stones, and the fourth small square has $$8$$ stones, and so on, until the $$16$$ small squares are filled, how many stones are there in total."}, {"key": "552", "content": "A certain theater has $$20$$ rows of seats, with each successive row having $$2$$ more seats than the row before it; the first row has $$32$$ seats, and in total, the theater has __ seats."}, {"key": "553", "content": "Given a sequence, starting from the second number, each number is 3 greater than the previous one, the 17th item is 49, the first item of the sequence is."}, {"key": "554", "content": "In an arithmetic sequence, the difference between two adjacent numbers is $$8$$, if the $$12$$th term is $$108$$, then the $$7$$th term is."}, {"key": "555", "content": "Eddy was reading a storybook, starting from the second day, the number of pages he read each day was $$4$$ pages more than the day before. On the $$28th$$ day, he read $$110$$ pages, so on the $$8th$$ day, he read pages."}, {"key": "556", "content": "In an arithmetic sequence, the first term is $$11$$, the eleventh term is $$51$$, the difference between adjacent terms is."}, {"key": "557", "content": "Given the 6th and the 10th numbers in an arithmetic sequence are respectively $$38$$ and $$62$$, the difference between two adjacent numbers is."}, {"key": "558", "content": "To celebrate the festival, the park set up many rows of flowers, with the number of flowers in each row forming an arithmetic sequence. The 10th row has 62 pots of flowers. The 25th row has 152 pots of flowers. What is the difference in the number of pots of flowers between adjacent rows?"}, {"key": "559", "content": "There are 9 boxes numbered from 1 to 9, containing a total of 351 candies. It is known that each box has the same number of candies more than the previous box. If box number 1 contains 11 candies, how many more candies does each subsequent box have compared to the one before it."}, {"key": "560", "content": "In the audience seats of the World Cup, a certain area\u2019s seats are arranged in a trapezoidal shape. Starting from the $$2$$nd row, each row has a consistent number of seats more than the previous row. It is known that the $$5$$th row has $$22$$ seats, and the $$8$$th row has $$31$$ seats$.$ Find: (2) If this area has a total of $$11$$ rows of seats, how many spectators can it accommodate in total."}, {"key": "561", "content": "1) There is an arithmetic sequence, the first number is $$100$$, the second number is $$120$$, the common difference is. 2) There is an arithmetic sequence, the first number is $$100$$, the third number is $$120$$, the common difference is."}, {"key": "562", "content": "Teacher Li develops candy every day. Starting from the $$2$$nd day, he makes $$7$$ more candies each day than the previous day. On the $$11$$th day, he made $$72$$ candies. Then, on the $$6$$th day, he made candies."}, {"key": "563", "content": "In a sequence of numbers, starting from the $$2$$nd number, each number is $$4$$ more than the previous one. The $$26$$th number is $$103$$. The $$1$$st number is."}, {"key": "564", "content": "In an arithmetic sequence, the first number is $$15$$, and the seventh number is $$57$$. Find the difference between two adjacent numbers."}, {"key": "565", "content": "1) A five-layer bookshelf holds a total of $$450$$ books. For any two adjacent layers, the upper layer has $$10$$ fewer books than the lower layer. Therefore, the top layer holds books. 2) To celebrate a festival, a park arranged flowers in $$7$$ rows, totaling $$420$$ pots. The number of flowers increases in each row from front to back, forming an arithmetic sequence. The $$7th$$ row from the front has $$90$$ pots of flowers. Hence, the difference in the number of pots of flowers between two adjacent rows."}, {"key": "566", "content": "There is a pile of logs of uniform thickness, stacked in a trapezoidal shape. From top to bottom, the same number of logs is added with each layer down. In total, there are $$8$$ layers. The $$4$$th layer has $$21$$ logs, and the $$6$$th layer has $$33$$ logs. Therefore, this pile of logs has a total of logs."}, {"key": "567", "content": "The image shows characters formed with chess pieces to make the Chinese character '\u5de8'. Following the same pattern, continue to arrange until a total of $$16$$ '\u5de8' characters have been formed. Then the total number of chess pieces needed is\uff0e question_567-image_0 question_567-image_1"}, {"key": "568", "content": "Please insert $$3$$ numbers between $$12$$ and $$24$$ such that these $$5$$ numbers form an arithmetic sequence. The inserted $$3$$ numbers in ascending order are , , ."}, {"key": "569", "content": "As shown in the figure: The numbers marked on the left of each row and the top of each column represent the number of consecutive black squares in that row or column. Children, can you mark all the black squares based on these numbers? question_569-image_0"}, {"key": "570", "content": "As shown: The numbers marked on the left of each row and the top of each column represent the quantity of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_570-image_0"}, {"key": "571", "content": "As shown in the diagram: The numbers on the left of each row and the top of each column represent the number of consecutive black squares in that row or column. Children, can you mark all the black squares based on these numbers? question_571-image_0"}, {"key": "572", "content": "As shown in the figure: The numbers marked on the left side of each row and the top side of each column represent the count of consecutive black blocks in that row or column. Kids, based on these numbers, can you mark all the black blocks? The circled number \"$$1$$\" represents the black block in the $$2$$nd row, in the cell (from left to right).\n question_572-image_0"}, {"key": "573", "content": "As shown: The numbers labeled on the left of each row and on the top of each column represent the quantity of consecutive black blocks in that row or column. Children, can you mark all the black blocks based on these numbers? question_573-image_0"}, {"key": "574", "content": "As shown in the picture: The numbers marked on the left side of each row and the top side of each column represent the number of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_574-image_0"}, {"key": "575", "content": "Max Elementary School held its 20th Art Festival. During the opening ceremony, the representative teams of each grade entered the field in succession for their performances. The first-grade students formed a total of three solid square formations for their performance. (1) The students from class 1 of the first grade performed gymnastics, with the formation requirement being: 5 people per row, a total of 5 rows, and people from class 1 participated."}, {"key": "576", "content": "Mars Elementary School organized its 20th Art Festival. At the opening ceremony, representative teams from each grade entered the stadium for their performances one after the other. The first-grade students formed three solid squares for their performance. (2) Class 2 of the first grade performed martial arts, with the formation requiring 12 people per row, totaling 12 rows, Class 2 had people participating."}, {"key": "577", "content": "Max Elementary School held its 20th Art Festival. During the opening ceremony, teams from each grade entered one after another to perform. The first graders formed three solid squares for their performance. (3) The students from 1st Grade Class 3 performed a march, with a total of 121 participants, who arranged themselves into a square formation by rows and columns."}, {"key": "578", "content": "A solid square formation with a total of $$81$$ people, adding one more row and one column requires an increase of people."}, {"key": "579", "content": "Second-grade students are preparing for a chorus. All the boys in second grade class $$1$$ who participated in the chorus just managed to form a solid square. Then, $$17$$ girls joined, and one more row and one more column were added to the square, turning it into a slightly larger solid square. In total, there were boys from the second grade class $$1$$ participating in the chorus."}, {"key": "580", "content": "The fourth grade forms two solid square formations for a dance performance. (1) In the formation of class 1 of the fourth grade, there are 5 people on each side of the outermost layer, totaling people in the outermost layer."}, {"key": "581", "content": "The solid square formation of class $$1$$ of the fifth grade, the outermost layer has a total of $$36$$ people. (2) This square formation has a total of people."}, {"key": "582", "content": "Students in grade six are arranged in a solid square formation, with $$5$$ people left over. If one row is added to each side, forming a slightly larger solid square, then there are $$26$$ people short. (2) If $$26$$ people are added, the total number of people on the outermost layer is."}, {"key": "583", "content": "A certain school's third grade students form a solid square formation, with each side of the outer layer having $$10$$ people. How many people are there in the entire square?"}, {"key": "584", "content": "Students perform a formation drill, forming a square. If one row and one column are removed, 11 people need to be removed in total. The original square formation had people in it."}, {"key": "585", "content": "A group of classmates stand in a $$10\\times 10$$ square formation, please settle: How many people are there on each side of the outermost layer."}, {"key": "586", "content": "All third-grade students are to form a solid square formation. If arranged according to the original plan, there would be $$9$$ people surplus. If one row and one column are added to the square, then there would be $$16$$ people short. The total number of third-grade students is ."}, {"key": "587", "content": "A grade four class at a certain school formed a square matrix, with the number of people in the outermost layer being $$40$$ people. How many people are there on each side of the outermost layer of the matrix? How many people are there in this square matrix in total?"}, {"key": "588", "content": "The students in class 1, grade 4 participated in a broadcast gymnastics competition, forming a solid square formation with each row containing $$8$$ people and each column containing $$8$$ people. How many students are there in the square formation?"}, {"key": "589", "content": "During the Max Primary School Arts Festival, the third graders formed a solid square formation to perform magic, with the outermost layer having $$18$$ people on each side. ($$1$$) Therefore, the total number of people in the entire square formation is."}, {"key": "590", "content": "At the Max Primary School Art Festival, the third-grade students formed a solid square array for a magic show, with $$18$$ people on each side of the outermost layer, ($$2$$) The outermost layer has people."}, {"key": "591", "content": "Max Elementary School Art Festival, the third-grade students formed a solid square to perform magic, with $$18$$ people on each side of the outermost layer. (3) The second layer has a total of people."}, {"key": "592", "content": "At Max Primary School Art Festival, the third-grade students formed a solid square formation to perform magic, with each side of the outermost layer having $$18$$ people. (4) The total number of people in the outermost three layers is."}, {"key": "593", "content": "With $$64$$ pots of flowers, a two-layer hollow square can be formed. If one more layer is to be added on the outside, the number of pots of flowers needed to be increased."}, {"key": "594", "content": "Using $$72$$ pieces to form a two-layer hollow square matrix, if you want to add another layer inside, how many more pieces are needed?"}, {"key": "595", "content": "There are $$120$$ students in the third grade of elementary school. They are arranged into a three-layer hollow square formation. Question: (2) How many people are there on each side of the outermost layer."}, {"key": "596", "content": "There are $$120$$ students in the third grade of elementary school. They are arranged into a three-layer hollow square formation. The question is: (4) Based on (3), if another layer is added inside to turn it into a five-layer hollow square formation, how many more people are needed."}, {"key": "597", "content": "There is a group of students arranged in a three-layer hollow square formation, with 9 more people. If the hollow part is increased by two layers, there are 15 fewer people. How many students are there?"}, {"key": "598", "content": "(1) The school organizes $$16$$ people to participate in the badminton competition. They are paired in twos for elimination matches. To decide the champion, a total of matches need to be held."}, {"key": "599", "content": "(2) A city hosted a tennis tournament, with 32 people participating. They were paired up for knockout matches to determine the top three. How many matches need to be played in total?"}, {"key": "600", "content": "(1) Teams $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ participate in a round-robin tournament, meaning each pair of teams plays a match against each other. Thus, each of these $$5$$ teams needs to play matches, totaling matches to be played."}, {"key": "601", "content": "(2) If there are $$8$$ teams participating in a round-robin tournament, where each team has to play a match against every other team, then each of these $$5$$ teams would need to play matches, and a total of matches need to be played."}, {"key": "602", "content": "$$A$$, $$B$$, $$C$$, $$D$$, $$E$$, and Eddie six people are in a round-robin tournament, part of the matches have been played already. It is known that $$A$$ has played $$5$$ matches, $$B$$ has played $$4$$ matches, $$C$$ has played $$3$$ matches, $$D$$ has played $$2$$ matches, $$E$$ has played $$1$$ match, then Eddie has played matches."}, {"key": "603", "content": "Teams $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ are playing in a round-robin tournament (i.e., each pair of teams plays $$1$$ match). After some time has passed, team $$A$$ has played $$4$$ matches, team $$B$$ has played $$2$$ matches, team $$C$$ has played $$2$$ matches, and team $$E$$ has played $$1$$ match. At this point, team $$D$$ has played at most, and at least, how many matches."}, {"key": "604", "content": "In a class, four students participate in a checkers competition, where every two students have a match. The winner of each match gets $$2$$ points, if it's a draw each gets $$1$$ points, and the loser gets $$0$$ points. (1) The total score of the four students is points."}, {"key": "605", "content": "In Chinese chess competitions, there are three possible outcomes: win, draw, and lose. A win earns $$2$$ points, a draw earns $$1$$ point, and a loss earns $$0$$ points. Now, six people compete in a round-robin tournament. It is known that five of them have scores of $$7$$, $$6$$, $$5$$, $$4$$, and $$3$$ respectively. So, the score of the last person is ."}, {"key": "606", "content": "Four soccer teams play in a round-robin tournament, with each pair of teams playing one game against each other. If a game is drawn, each team receives $$1$$ point, otherwise, the winning team receives $$3$$ points and the losing team receives $$0$$ points. (1) The minimum total points the four teams could score is points, and the maximum is points."}, {"key": "607", "content": "Jack, Jimmy, Tom, and Sanji were dividing gold coins in front of the pirate ship, sharing $$560$$ gold coins among the four of them. Jack said: \"I got $$22$$ fewer gold coins than Jimmy, $$30$$ more than Tom, and $$40$$ fewer than Sanji.\" So, Sanji got gold coins\uff0e"}, {"key": "608", "content": "Eddy and Viola arrived at the tourist rest area, where they found: there are $$300$$ trees in total, including poplar trees, willow trees, and locust trees. Moreover, the number of poplar trees is $$3$$ times that of willow trees, and the number of locust trees is $$2$$ times that of poplar trees. Therefore, the total number of trees to be planted is willow trees, poplar trees, locust trees."}, {"key": "609", "content": "Among three people, A, B, and C, the age of A is twice the age of B minus 3 years, the age of B is twice the age of C, and the sum of their ages is 102 years. The age of A is years."}, {"key": "610", "content": "When two positive integers are divided, the quotient is $$6$$, and the remainder is $$5$$. The sum of the dividend, divisor, quotient, and remainder is $$233$$. The dividend is, and the divisor is."}, {"key": "611", "content": "There are $$129$$ pieces of clothing in the Weier clothing store, men's clothing is twice the amount of children's clothing, and women's clothing is twice the number of men's clothing plus $$3$$ pieces. The number of pieces of women's clothing is ."}, {"key": "612", "content": "The number of books in version $$A$$ of Xueersi School is $$50$$ more than that in version $$B$$, and the number of books in version $$A$$ is $$3$$ times that in version $$B$$. How many books are there in version $$A$$ and version $$B$$ respectively?"}, {"key": "613", "content": "A strongman can carry $$20$$ books with one hand, while Xiaobai can only carry $$10$$ books with both hands combined. The two collaborate to move $$450$$ books from place A to place B. It is known that the number of times the strongman carries books is twice that of Xiaobai. Therefore, the strongman carried a total of books, and Xiaobai carried a total of books. (Both the strongman and Xiaobai use both hands to carry books)"}, {"key": "614", "content": "Xiao Ming, Xiao Liang, and Xiao Gang, three kids, went fishing. Counting the number of fish they caught, it was found that: the fish Xiao Ming caught were 4 times the number Xiao Liang caught, Xiao Liang caught 5 fewer fish than Xiao Gang, and Xiao Gang caught 7 fewer fish than Xiao Ming. Xiao Ming caught fish."}, {"key": "615", "content": "One day, Master Li produced a batch of parts and divided them into two piles, A and B. If he takes $$15$$ pieces from pile A to pile B, then the number of parts in the two piles becomes equal; if he takes $$15$$ pieces from pile B to pile A, then the number of parts in pile A is $$3$$ times that of pile B. The original number of parts in pile A and the total number of parts produced by Master Li that day are."}, {"key": "616", "content": "The number of green butterflies is $$5$$ times that of yellow butterflies, the number of red butterflies is $$2$$ times that of yellow butterflies, and there are $$36$$ more green butterflies than red butterflies. The number of green butterflies is ."}, {"key": "617", "content": "Dividing two numbers, the quotient is $$4$$, and the sum of the dividend, divisor, and quotient is $$124$$. The dividend is."}, {"key": "618", "content": "The number of monkeys in the park is $$10$$ more than the gorillas, and the number of monkeys is $$2$$ times the number of gorillas. How many monkeys are there?"}, {"key": "619", "content": "Teacher Niu took $$37$$ students for a spring outing in the wild. During the rest, Eddie asked: 'How old are you this year, Teacher Niu?' Teacher Niu interestingly replied: 'My age multiplied by $$2$$, then subtract $$16$$, divided by $$2$$, and add $$8$$, the result is exactly the total number of people participating in today's activity.' Kids, do you know how old Teacher Niu is this year."}, {"key": "620", "content": "A little bird pecks at the rice. The first time, it ate more than half the amount of rice by $$10$$ grains. The second time, it ate $$12$$ grains less than half of the remaining rice. The third time, it ate $$14$$ grains. Finally, there were $$15$$ grains of rice left.$$.$$ How many grains of rice were there originally?"}, {"key": "621", "content": "A bundle of wires, the first time half of the total length was used, the second time another half of the remaining length was used, the third time $$15$$ meters were used, and finally, $$7$$ meters were left. The original length of this bundle of wire was meters."}, {"key": "622", "content": "There is a peach tree at the top of the mountain, a monkey stole more than half of the total number by 2 peaches. At this time, there are 6 peaches left, originally there were how many peaches on the tree."}, {"key": "623", "content": "$$A$$, $$B$$, $$C$$ each had a different number of bricks. $$A$$ handed out a portion of their bricks to $$B$$ and $$C$$, making these two people's bricks each increase by a double; then $$B$$ also handed out a portion of their bricks to $$A$$ and $$C$$, making these two people's bricks each increase by a double; next, $$C$$ also handed out a portion of their bricks to $$A$$ and $$B$$, making these two people's bricks each increase by a double. At this time, the number of bricks each of the three people had was $$48$$. The original number of bricks $$A$$ had, the original number of bricks $$B$$ had, the original number of bricks $$C$$ had."}, {"key": "624", "content": "Eddie, when doing the multiplication of a three-digit number by a one-digit number, accidentally copied the three-digit number $$789$$ as $$786$$, resulting in a result that is $$18$$ less than the correct answer. The one-digit number is."}, {"key": "625", "content": "Three brothers divided $$24$$ oranges among themselves, with each person getting a number of oranges equal to their age three years ago. If the youngest first shares half of his oranges equally with the eldest and the middle brother, then the middle brother shares half of his current oranges equally with the youngest and the eldest, and finally, the eldest shares half of his current oranges equally with the middle brother and the youngest, each person ends up with the same number of oranges. Thus, the current ages of the eldest, middle, and youngest brothers are ____ years old, ____ years old, and ____ years old, respectively."}, {"key": "626", "content": "There is a sequence of numbers arranged in the order $$11428571142857114\\ldots \\ldots$$, totaling $$100$$ numbers. How many $$8$$s are there?"}, {"key": "627", "content": "There is a sequence of numbers arranged in the order of $$11428571142857114\\ldots \\ldots$$, totaling $$100$$ numbers. Number $$1$$ appears times."}, {"key": "628", "content": "There is a series of numbers arranged in the order of $$11428571142857114\\ldots \\ldots$$, totaling $$100$$ numbers. The sum of these numbers is."}, {"key": "629", "content": "$$12$$ people in black clothes form a circle to play a game of passing a box, as shown in the diagram. Starting from the person in black clothes number $$1$$, the box is passed clockwise $$100$$ times, the box should end up in the hands of the person with number . question_629-image_0 \u200b"}, {"key": "630", "content": "$$12$$ people in black clothes form a circle to play a game of passing the box, as shown in the picture. question_630-image_0 Starting from the person in black clothes numbered $$1$$, the box is passed counter-clockwise $$100$$ times, and the box should end up in the hands of the person numbered ____.\u200b"}, {"key": "631", "content": "$$12$$ people in black clothes form a circle to play a game of passing a box, as shown in the figure. Starting with the person in black clothes number $$1$$, they first pass it clockwise $$160$$ times, then anticlockwise $$80$$ times, the box should be in the hands of the person in black clothes number. question_631-image_0"}, {"key": "632", "content": "As shown, stretch out your left hand, and then start counting from your thumb. question_632-image_0 When you count to $$200$$, you will exactly count to"}, {"key": "633", "content": "As shown in the figure, extend your left hand, and then start counting from the thumb. question_633-image_0 When you count to $$400$$, you will exactly count to"}, {"key": "634", "content": "As shown, extend your left hand, and then start counting from the thumb. question_634-image_0 When counting to $$1007$$, the count precisely ends on"}, {"key": "635", "content": "$$2018$$ year $$10$$ month $$1$$ day is Monday. Starting from this day, the $$25$$th day is on a"}, {"key": "636", "content": "$$2018$$ year $$10$$ month $$1$$ day is Monday. 2018 year $$12$$ month $$1$$ day is a week"}, {"key": "637", "content": "$$2018$$ year $$10$$ month $$1$$ day is Monday. 2019 year $$10$$ month $$1$$ day is a week"}, {"key": "638", "content": "$$2017$$ year $$4$$ month $$12$$ day is Wednesday, 2018 year $$10$$ month $$1$$ day is Monday"}, {"key": "639", "content": "The year $$2016$$ has $$52$$ Thursdays, $$53$$ Fridays, August $$1$$, $$2017$$ falls on a"}, {"key": "640", "content": "Mace Elementary School's upper-grade students arrived at the expansion base, and the doctor was ready to distribute mineral water to the third-grade class 1. If each group is given $$2$$ boxes, there will be $$20$$ boxes left over; if each group is given $$5$$ boxes, there will be $$2$$ boxes left over. The third-grade class 1 has groups, and the doctor prepared boxes. question_640-image_0"}, {"key": "641", "content": "Eddy is responsible for distributing mineral water to Class Three Grade Three. He has prepared less mineral water. If he distributes $$4$$ boxes to each group, he will be short of $$2$$ boxes; if he distributes $$6$$ boxes to each group, he will be short of $$14$$ boxes. Then, Class Three Grade Three has in total groups, and Eddy has prepared boxes of mineral water. question_641-image_0"}, {"key": "642", "content": "The second class of the fourth grade distributed mosquito repellent patches. If each person is given 4 patches, then there are 28 patches left over; if 4 people each get 6 patches, 6 people each get 4 patches, and the rest each get 5 patches, then the patches are distributed exactly. The second class of the fourth grade has people, a total of mosquito repellent patches."}, {"key": "643", "content": "The expansion coach distributed some badminton shuttlecocks to the students. Each person receives $$5$$ shuttlecocks, with $$10$$ left over; if the number of people triples, and if each person were to receive $$2$$ shuttlecocks, then there would be $$8$$ short. Therefore, the coach prepared a total of shuttlecocks."}, {"key": "644", "content": "In a box, there are several red and white balls. If each time one red ball and one white ball are taken out until no red balls are left, there will be 50 white balls remaining; if each time one red ball and three white balls are taken out, then when there are no white balls left, there will be 50 red balls remaining. So, the total number of red balls in the box is."}, {"key": "645", "content": "In the future canteen, a batch of kiwifruits and Hami melons are used to make a fruit platter. If each platter contains $$5$$ kiwifruits and $$3$$ Hami melons, there are $$4$$ kiwifruits left over in the end, while the Hami melons are exactly used up; if each platter contains $$7$$ kiwifruits and $$3$$ Hami melons, there are $$12$$ Hami melons left over in the end, while the kiwifruits are exactly used up. Thus, there are kiwifruits and Hami melons."}, {"key": "646", "content": "Answer the following question: The distance between places $$A$$ and $$B$$ is $$4800$$ meters. If a person walks $$60$$ meters per minute, how many minutes does it take for the person to walk from $$A$$ to $$B$$?"}, {"key": "647", "content": "Answer the following question: Cities $$A$$ and $$B$$ are $$300$$ kilometers apart. If a car originally planned to travel from city $$A$$ to city $$B$$ in $$6$$ hours, then the average speed the car should travel per hour is kilometers."}, {"key": "648", "content": "Answer the following question: A car travels $$150$$ kilometers in $$3$$ hours, based on this speed, how many kilometers will it travel in $$10$$ hours."}, {"key": "649", "content": "Eddie and Viola set off from the base to go to Mason Forest Park for fun. When they went there, the speed of the car was $$80$$ kilometers per hour, and it took $$3$$ hours to reach the destination. If the speed of the car increases by $$40$$ kilometers per hour on the way back, then they could return to the base after hours from departing the forest park."}, {"key": "650", "content": "Eddie and Vera set off from the base to visit Mason Forest Park together. The speed of the car was $$80$$ kilometers per hour, and it took $$3$$ hours to reach the destination. It actually started to rain lightly on the way back, and it took $$3$$ hours longer for the car to return to the base. During the return trip, the speed of the car was kilometers per hour."}, {"key": "651", "content": "Daming and Xiaobai live in the same building. They climb the stairs at the same speed and spend the same amount of time for each floor. It takes $$180$$ seconds to reach the $$6$$th floor. If they keep the same pace, Xiaobai lives on the $$10$$th floor, it requires seconds for him to get home from the $$1$$st floor."}, {"key": "652", "content": "$$5$$ workers take $$2$$ hours to make $$80$$ parts. At that rate, how many parts can $$15$$ workers make in $$6$$ hours."}, {"key": "653", "content": "Grandma Wang has $$5$$ milk cows, producing $$630$$ kilograms of milk in $$7$$ days. Based on this calculation, $$8$$ milk cows can produce kilograms of milk in $$15$$ days."}, {"key": "654", "content": "Little monkeys in the Huaguo Mountain eating peaches, if $$6$$ little monkeys eat $$180$$ peaches in $$3$$ days, according to this calculation, one little monkey can eat $$400$$ peaches in $$5$$ days."}, {"key": "655", "content": "In Huaguoshan, a little monkey is eating peaches. If $$6$$ little monkeys eat $$180$$ peaches in $$3$$ days, according to this calculation, it would take $$10$$ monkeys $$2$$ days to eat $$200$$ peaches."}, {"key": "656", "content": "$$9$$ individuals can complete $$12$$ pieces of work in $$6$$ days, at this pace, $$3$$ individuals can complete work in $$3$$ days. $$21$$ individuals can complete work in $$12$$ days."}, {"key": "657", "content": "The aquarium prepared $$230$$ kilograms of fish for the $$8$$ walruses in the museum, and in the first two days, these $$8$$ walruses ate a total of $$80$$ kilograms of fish. Two days later, $$2$$ of the walruses were transported away. Assuming each walrus eats the same amount of fish every day, the remaining fish can last for how many more days for the walruses left."}, {"key": "658", "content": "Eddie completed $$27$$ problems in $$3$$ hours. At this rate, he can complete problems in $$8$$ hours, and if completing $$108$$ problems requires hours."}, {"key": "659", "content": "Xiaoming reads an extracurricular book, reading $$6$$ pages every day, and finishes half of the book in $$8$$ days. Afterwards, he reads $$2$$ more pages each day, so to finish the book, in total he needs $$14$$ days."}, {"key": "660", "content": "$$2$$ machines produce paper $$20$$ minutes for $$80$$ tons, according to this calculation, $$1$$ machine produces paper tons in $$1$$ hour."}, {"key": "661", "content": "Chickens and rabbits are kept in the same cage, with a total of $$27$$ animals. It is known that both types of animals have the same number of legs. Therefore, there are chickens and rabbits."}, {"key": "662", "content": "Chickens and rabbits are in the same cage, totaling $$40$$ animals. It is known that the number of chicken legs is $$2$$ times the number of rabbit legs. Therefore, there are chickens and rabbits respectively."}, {"key": "663", "content": "Chickens and rabbits in the same cage, there are $$45$$ chickens and rabbits in total, the number of legs of the rabbits is $$60$$ more than the number of legs of the chickens, there are chickens, and rabbits."}, {"key": "664", "content": "A school spring outing used a total of $$16$$ buses (all fully seated), with each large bus seating $$60$$ people, and each small bus seating $$20$$ people. The large buses have $$560$$ more seats in total than the small buses. There are buses for the smaller ones."}, {"key": "665", "content": "There are a total of $$57$$ ostriches and zebras in the zoo, living on the same grassland. The number of legs of ostriches is the same as that of zebras, there are zebras, there are ostriches."}, {"key": "666", "content": "Lele Department Store commissioned the transportation station to deliver $$100$$ vases. The two parties agreed on a shipping fee of $$1$$ yuan per vase, but if any were damaged, not only would the shipping fee not be given, but also a compensation of $$1$$ yuan would be required for each broken vase. As a result, the transportation station received a total of $$92$$ yuan in shipping fees. A total of vases were broken during the transportation process."}, {"key": "667", "content": "1) NiuNiu counts the number of chickens and rabbits in the cage, there are $$90$$ heads in total, and the number of chicken legs is the same as the number of rabbit legs. There are $$60$$ chickens. 2) In the zoo, $$55$$ ostriches and zebras live on the same grassland, and the number of legs of ostriches is $$2$$ times that of zebras, so there are $$11$$ zebras."}, {"key": "668", "content": "1) Chickens and rabbits are in the same cage, and there are equal numbers of chickens and rabbits, totaling $$48$$ legs. Then, there are chickens.2) Chickens and rabbits are in the same cage, and the number of rabbits is $$3$$ times the number of chickens, totaling $$140$$ legs. Then, there are chickens, and there are rabbits."}, {"key": "669", "content": "1) Chickens and rabbits are in the same cage, with chickens outnumbering rabbits by 26, and a total of 274 legs. Then, the number of chickens and the number of rabbits are respectively. 2) There are a total of 50 oil bottles, big and small combined. Each big bottle can hold 4 kilograms of oil, and each small bottle can hold 2 kilograms. The big bottles can hold 20 kilograms more oil in total than the small bottles (each oil bottle is filled). Then, the number of big bottles and small bottles are respectively."}, {"key": "670", "content": "Among the natural numbers from $$1-60$$, there are several numbers that can be divided by $$2$$ or $$3$$."}, {"key": "671", "content": "A class has a total of $$46$$ people, $$12$$ of them are in the art group, $$23$$ of them are in the music group, and $$5$$ people are in both groups. The number of people in the class who are in neither the art group nor the music group is."}, {"key": "672", "content": "Three fund managers invested in a number of stocks. Manager Zhang bought 66 of them, Manager Wang bought 40 of them, and Manager Li bought 23 of them. Both Manager Zhang and Manager Wang bought 17 of the same stocks, both Manager Wang and Manager Li bought 13 of the same stocks, both Manager Li and Manager Zhang bought 9 of the same stocks, and all three managers bought 6 of the same stocks. Question: How many different stocks have these three managers collectively bought?"}, {"key": "673", "content": "The experimental elementary school features calligraphy and mathematical thinking training. There are a total of $$245$$ students in the fifth grade of the school, among which, the number of students participating in calligraphy training exceeds those in mathematical thinking training by $$82$$ people. There are $$44$$ students participating in both calligraphy and mathematical thinking training, and $$63$$ students do not participate in either training. Thus, the number of fifth-grade students in the experimental elementary school participating in mathematical thinking training is ."}, {"key": "674", "content": "In the evening, the rabbits hold a dance party, with $$2000$$ lights on, each controlled by a pull cord switch, now numbered in sequence as $$1$$, $$2$$, $$3$$, $$\\cdots$$, $$2000$$. Then, they pull the cord of lights numbered with multiples of $$2$$, followed by pulling the cord of lights numbered with multiples of $$3$$, and finally pulling the cord of lights numbered with multiples of $$5$$. After three pulls, the number of lights that remain on is."}, {"key": "675", "content": "Every student in a certain class signed up for the cup competitions. Among them, 12 people signed up for the Hercules Cup, 15 people signed up for the Calabash Cup, and 21 people signed up for the Xueersi Cup. 5 people signed up only for both the Hercules Cup and the Calabash Cup, 4 people signed up only for both the Hercules Cup and the Xueersi Cup, 7 people signed up only for both the Xueersi Cup and the Calabash Cup, and 2 people signed up for all three cups. Therefore, this class has a total of people."}, {"key": "676", "content": "At the New Year's party, a total of $$90$$ people participated in performances of three activities: dancing, singing, and playing instruments. If the number of people who only participated in dancing was three times the number of those who only participated in singing; the number of people who only participated in playing instruments was $$4$$ more than those who participated in both playing instruments and dancing but did not participate in singing; $$50$$ people did not participate in singing; $$10$$ people participated in both dancing and singing but did not participate in playing instruments; $$40$$ people participated in playing instruments; then, the number of people who participated in both playing instruments and dancing but did not participate in singing was ____."}, {"key": "677", "content": "Eddie and Viola start towards each other from two places that are $$42$$ kilometers apart at the same time, with Eddie traveling at a speed of $$8$$ kilometers per hour and Viola at $$6$$ kilometers per hour, they meet after hours."}, {"key": "678", "content": "On a straight road, Dr. and Da Kuan start simultaneously from locations $$100$$ meters apart, heading towards each other. Da Kuan runs at $$6$$ meters per second, and the doctor runs at $$4$$ meters per second. They meet after a certain number of seconds."}, {"key": "679", "content": "Eddie and Vi drive towards each other from two cities that are $$480$$ kilometers apart. After $$4$$ hours, they meet. Eddie's car travels at $$50$$ kilometers per hour. Vi's speed is kilometers per hour."}, {"key": "680", "content": "A doctoral student and Da Kuan agree to leave their homes at the same time, walking towards each other. It is known that the distance between their homes is 2000 meters and they meet after 10 minutes. The doctoral student walks at a speed of 90 meters per minute, while Da Kuan walks at a speed of meters per minute."}, {"key": "681", "content": "$$A$$ and $$B$$ are $$780$$ kilometers apart, a truck travels at $$56$$ kilometers per hour, and a passenger car travels at $$74$$ kilometers per hour. The truck and passenger car start simultaneously from both places and head towards each other. It asks: (1) How many hours after they start do the two vehicles first become $$130$$ kilometers apart."}, {"key": "682", "content": "Locations $$A$$ and $$B$$ are $$780$$ kilometers apart, a freight truck travels at $$56$$ kilometers per hour, and a passenger bus travels at $$74$$ kilometers per hour. The freight truck and passenger bus start from the two locations at the same time, heading towards each other. Calculate: (2) The number of hours between the first and second times they are $$130$$ kilometers apart."}, {"key": "683", "content": "Vehicle A and vehicle B set off simultaneously from locations A and B, respectively, which are $$280$$ kilometers apart, heading towards each other. After $$8$$ hours, they meet. After the meeting, both vehicles continue on their way, and after another $$6$$ hours, vehicle A reaches location B. At this point, vehicle B is still kilometers away from location A."}, {"key": "684", "content": "Cars A and B are traveling towards each other from two places $$942$$ kilometers apart. Car A travels at $$45$$ kilometers per hour, and Car B travels at $$41$$ kilometers per hour. Car B starts $$2$$ hours before Car A. After Car A has been traveling for several hours, it meets Car B."}, {"key": "685", "content": "Locations A and B are 480 kilometers apart. A car departs from location A at 8 am, traveling towards location B at a speed of 40 kilometers per hour. 3 hours later, another car starts from location B towards location A at a speed of 50 kilometers per hour. The question is: At what time do the two cars meet on the road? (24-hour clock)"}, {"key": "686", "content": "Locations A and B are $$200$$ kilometers apart. Wei Er\u2019s speed going there is $$10$$ kilometers/hour, and her speed coming back is $$40$$ kilometers/hour. The average speed of Wei Er\u2019s round trip is kilometers/hour."}, {"key": "687", "content": "From $$A$$ to $$B$$ is a downhill road of $$12$$ kilometers, from $$B$$ to $$C$$ is a flat road of $$8$$ kilometers, and from $$C$$ to $$D$$ is an uphill road of $$4$$ kilometers. Xiao Zhang walks, with a downhill speed of $$6$$ kilometers/hour, a flat road speed of $$4$$ kilometers/hour, and an uphill speed of $$2$$ kilometers/hour. Then, the average speed of Xiao Zhang from $$A$$ to $$D$$ is kilometers per hour."}, {"key": "688", "content": "Wei'er and Eddie live $$1170$$ meters apart. They leave their homes at the same time and walk towards each other on the same road. Wei'er walks at a speed of $$60$$ meters per minute, and Eddie walks at a speed of $$70$$ meters per minute. The two meet after minutes."}, {"key": "689", "content": "Places A and B are $$300$$ meters apart, Jiajia's speed going there is $$10$$ meters per minute, and the speed coming back is $$15$$ meters per minute, Jiajia's average speed for the round trip is meters per minute."}, {"key": "690", "content": "Eddie and Vi start driving towards each other from cities $$A$$ and $$B$$ respectively at the same time. Eddie's car travels at $$56$$ kilometers per hour, and Vi's car travels at $$43$$ kilometers per hour. They meet after $$5$$ hours. The distance between the two cities in kilometers is."}, {"key": "691", "content": "For a journey of $$600$$ kilometers, Xiaomei walks the first half at a speed of $$10$$ kilometers/hour and progresses the second half at a speed of $$15$$ kilometers/hour. The average speed of Xiaomei throughout the entire process is ( ) kilometers/hour."}, {"key": "692", "content": "Locations $$A$$ and $$B$$ are $$780$$ kilometers apart. A truck travels at $$56$$ kilometers per hour, while a bus travels at $$74$$ kilometers per hour. Both vehicles depart from location $$A$$ towards location $$B$$ at the same time, and immediately return after reaching location $$B$$. After how many hours will the two vehicles meet for the first time, and how many kilometers from location $$B$$ will they meet?"}, {"key": "693", "content": "Vehicles A and B start from two places $$901$$ km apart towards each other, with vehicle A traveling at $$45$$ km per hour and vehicle B traveling at $$41$$ km per hour. Vehicle B departs $$1$$ hour before vehicle A. After how many hours will vehicle A meet vehicle B?"}, {"key": "694", "content": "Professor Su Buqing is a famous mathematician in our country. Once, he encountered a renowned German mathematician on the tram, who gave him an interesting problem to solve. The problem was: \"Two places are $$50$$ kilometers apart, and two people, A and B, start walking towards each other from these places at the same time. A walks at $$3$$ kilometers per hour, B at $$2$$ kilometers per hour. A has a dog that walks at $$5$$ kilometers per hour. The dog starts walking with A, turns around when it meets B, heads back towards A upon meeting him, and keeps going back and forth until the two people meet. How many kilometers did the dog walk in total?\" After briefly thinking, Professor Su Buqing gave the correct answer to the German mathematician before even getting off the tram. Students, you try as well. How many kilometers did the dog walk in total?"}, {"key": "695", "content": "There is a bridge, to cross the bridge one must first go uphill, then walk a flat distance, and finally go downhill. The total distance is $$18$$ kilometers, and the distance of the uphill, flat road, and downhill are equal. When a person walks across the bridge, the speeds of going uphill, walking on flat ground, and going downhill are $$2$$ kilometers/hour, $$3$$ kilometers/hour, and $$6$$ kilometers/hour, respectively. His average speed across the bridge is kilometers/hour."}, {"key": "696", "content": "As shown in the figure, the side length of parallelogram $$ABCD$$ is $$DC=15$$ cm, and the height $$AE=6$$ cm on this side, a segment $$AF$$ divides this parallelogram into two parts, and their areas differ by $$18$$ square centimeters. Question: What is the area of trapezoid $$ABCF$$ in square centimeters. question_696-image_0"}, {"key": "697", "content": "As shown in the figure, it is known that the area of trapezoid $$ABCD$$ is $$50$$ square centimeters, the height $$AE$$ is $$5$$ centimeters long, and segment $$CD$$ is $$4$$ centimeters longer than $$AB$$. Then, the lengths of $$AB$$ and $$CD$$ are respectively in centimeters and centimeters. question_697-image_0"}, {"key": "698", "content": "The area of the diamond in the figure below is square centimeters. (Unit: cm) question_698-image_0"}, {"key": "699", "content": "Eddie and Vel raced, it is known that Eddie runs $$150$$ meters per minute, and Vel runs $$120$$ meters per minute. (2) They start at the same time, moving in the same direction, with Vel in front and Eddie behind. After $$10$$ minutes, Eddie caught up with Vel. The question is, how far apart were they originally."}, {"key": "700", "content": "Plane A and plane B take off at the same time from two airports that are $$160$$ kilometers apart, with plane B leading and plane A following, both flying in the same direction. Plane B flies at a speed of $$340$$ kilometers per hour, while plane A flies at a speed of $$420$$ kilometers per hour. Plane A can catch up to plane B in one hour."}, {"key": "701", "content": "Trucks and passenger cars set off from places A and B, which are $$360$$ kilometers apart, at the same time, in the same direction, with the truck in front and the passenger car behind. The truck travels at $$50$$ kilometers per hour and is overtaken by the passenger car after $$9$$ hours. The speed of the passenger car is kilometers$$/$$hour."}, {"key": "702", "content": "A slow vehicle departs from Point A to Point B, traveling at $$40$$ kilometers per hour. After departing for $$5$$ hours, a fast vehicle also departs from Point A to Point B at a speed of $$90$$ kilometers per hour. The fast vehicle catches up with the slow vehicle at the midpoint between Point A and Point B. The distance between Points A and B is in kilometers."}, {"key": "703", "content": "Third-grade students start from school for a spring outing, walking at $$72$$ meters per minute. After $$15$$ minutes, there is an urgent matter in the school requiring informing the students, so Teacher Li is sent on a bicycle from the school at a speed of $$132$$ meters per minute to catch up with the students. How long does Teacher Li need to catch up, and if Teacher Li wants to catch up in $$9$$ minutes, how many meters per minute does he need to travel."}, {"key": "704", "content": "Locations A and B are $$240$$ kilometers apart. A slow train departs from location A, traveling $$60$$ kilometers per hour. At the same time, a fast train departs from location B, traveling $$90$$ kilometers per hour. Both trains are moving in the same direction, with the fast train behind the slow train. After how many hours can the fast train catch up with the slow train?"}, {"key": "705", "content": "Xiao Bai and Xiao Xin raced, Xiao Xin is ahead of Xiao Bai by $$1200$$ meters, they started at the same time and run in the same direction, knowing that Xiao Xin runs $$150$$ meters per minute, $$10$$ minutes later, Xiao Bai caught up with Xiao Xin, then Xiao Bai runs meters per minute."}, {"key": "706", "content": "Locations A and B are $$220$$ kilometers apart. Xiao Ming and Xiao Li start driving from locations A and B at the same time, heading in the same direction, with Xiao Ming in front and Xiao Li behind. It is known that Xiao Ming drives at $$50$$ kilometers per hour, and Xiao Li drives at $$60$$ kilometers per hour. It takes Xiao Li ( ) hours to catch up with Xiao Ming."}, {"key": "707", "content": "Person A and Person B set off simultaneously from two places heading towards each other. Person A travels at $$5$$ kilometers per hour, while Person B travels at $$4$$ kilometers per hour. They meet when they are $$3$$ kilometers away from the midpoint. The distance between the two places in kilometers."}, {"key": "708", "content": "Person A and person B ride bicycles from location $$A$$ to location $$B$$ at the same time. Person A travels at $$150$$ meters per minute, and person B travels at $$120$$ meters per minute. After reaching location $$B$$, person A immediately returns and meets person B at location $$C$$. If location $$C$$ is $$300$$ meters away from location $$B$$, find the distance between location $$A$$ and location $$B$$ in meters."}, {"key": "709", "content": "Eddie and Vi start from two places $$1500$$ meters apart at the same time. If they walk towards each other, they meet in $$10$$ minutes; if they walk in the same direction, it takes Eddie $$75$$ minutes to catch up with Vi. Then, the speeds of Eddie and Vi are meters/min and meters/min, respectively"}, {"key": "710", "content": "The distance between two places is $$900$$ kilometers. It takes person A $$15$$ days and person B $$12$$ days to travel. Now if person A departs $$2$$ days earlier than person B, how many kilometers does person B have to travel to catch up with person A?"}, {"key": "711", "content": "The tortoise and the hare have a $$1000$$ meters race. The speed of the hare is $$5$$ times the speed of the tortoise. When they start at the same time from the starting point, the tortoise keeps running, while the hare runs to a certain point and starts to sleep. When the hare awakens, the tortoise has already taken the lead. The hare dashes to catch up, but when the tortoise reaches the finish line, the hare is still $$10$$ meters behind. Calculate how many meters the tortoise ran while the hare was sleeping."}, {"key": "712", "content": "After the results of an exam were released, the doctoral student held a paper with $$98$$ points in one hand and a paper with $$89$$ points in the other hand and said: \"Multiplying the number in my left hand by $$5$$, and the number in my right hand by $$4$$, then adding these two products together, this sum is an odd number.\" Therefore, the paper in the doctoral student\u2019s left hand has a score of _____."}, {"key": "713", "content": "Write the three integers $$2$$, $$3$$, and $$5$$ on the blackboard, and then erase one and replace it with the sum of the other two. Continue this operation. Is it possible to end up with $$100$$, $$144$$, $$244$$? Please explain your reasoning."}, {"key": "714", "content": "There are $$7$$ cups placed in the cabinet, all facing up. Flip one of them the first time, two the second time, three the third time, four the fourth time, $$\\cdots\\cdots$$ seven the seventh time. Is it possible to find a way to flip the cups so that after flipping them $$7$$ times, all the cups are facing down? If yes, please describe the method; if no, please explain why."}, {"key": "715", "content": "There is a magical machine on Max's planet, inserting one gold coin will produce 99 silver coins, and inserting one silver coin will produce 99 gold coins. Now, Eddie brought a gold coin over and hopes to have an equal number of gold and silver coins after several operations. Question: Is it possible for Eddie to achieve this? If yes, please describe the method of operation; if not, please explain why."}, {"key": "716", "content": "After the New Year, school started again, and some students needed to buy new school uniforms. Wei Er collected the school uniform fees from $$9$$ students (each person paid the same amount) and gave it to the teacher. The teacher gave Wei Er a note, which read \"Paid school uniform fee of $$\\overline{2\\square 38}$$ yuan\", but a drop of ink had smudged the number in the square making it unclear. Eddie looked at it and quickly calculated the number in the square. Smart kids, this number is."}, {"key": "717", "content": "There are the following $$9$$ three-digit numbers: $$452$$, $$387$$, $$228$$, $$975$$, $$525$$, $$882$$, $$715$$, $$775$$, $$837$$. Among these numbers, the number of those divisible by $$3$$ is ; the number divisible by $$9$$ is ."}, {"key": "718", "content": "Among the following numbers, there are those that can be divided by $$2$$; divided by $$4$$; divided by $$8$$.\n$$23487$$, $$3568$$, $$8875$$, $$6765$$, $$5880$$, $$7538$$, $$198954$$, $$6512$$, $$93625$$, $$864$$, $$407$$."}, {"key": "719", "content": "As shown in the figure, fill in the blank space with the appropriate number to make the division vertical calculation valid. Then, the dividend in the equation is. question_719-image_0"}, {"key": "720", "content": "As shown in the diagram, fill in the blank spaces with appropriate numbers to make the multiplication vertical expression valid. Therefore, the product is.\n question_720-image_0"}, {"key": "721", "content": "The units digit of the calculation result of the formula $$3+33+333+\\cdots +\\underbrace{33\\cdot \\cdot \\cdot 3}_{9 threes}$$ is."}, {"key": "722", "content": "The calculation result of the formula $$3+33+333+\\cdots +\\underbrace{33\\cdots 3}_{50 \\text{ threes }}$$, the last three digits are."}, {"key": "723", "content": "Calculate the following: $$19+199+1999+19999+199999+1999999=$$\uff0e"}, {"key": "724", "content": "Calculate the following: $$1234+2341+3412+4123=$$."}, {"key": "725", "content": "Calculate the following problems: $$23456+34562+45623+56234+62345=$$\uff0e"}, {"key": "726", "content": "Calculate the following equation. $$(2345+3452+4523+5234)\\div 7=$$\uff0e"}, {"key": "727", "content": "Calculate: $$(34567+45673+56734+67345+73456)\\div 5=$$."}, {"key": "728", "content": "Calculate the following questions. $$(123+234+345+456+567+671+712)\\div 7=$$\uff0e"}, {"key": "729", "content": "Compute: $$222222\\times 999999=$$"}, {"key": "730", "content": "Calculate the following: $$999999\\times 123=$$."}, {"key": "731", "content": "Calculate the following: $$18\\times 20202020-2020\\times 180018=$$."}, {"key": "732", "content": "Calculate: $$9999\\times 5555=$$."}, {"key": "733", "content": "Calculate: $$79+799+7999+79999+799999+7999999+79999999=$$."}, {"key": "734", "content": "Starting from $$1$$, consecutive natural numbers are arranged according to the rules shown in the diagram, and five numbers are framed with a cross. The sum of these five numbers cannot be: ( ).\n question_734-image_0"}, {"key": "735", "content": "Starting from $$1$$, consecutive natural numbers are arranged according to the rule shown in the figure. By framing six numbers with a $$3\\times 2$$ rectangle, is it possible to make the sum of these six numbers equal to $$357$$? The smallest number in the frame is. question_735-image_0"}, {"key": "736", "content": "As shown in the figure, consecutive natural numbers starting from $$1$$ are to be filled into the table following a certain rule. Please answer: (1) In which row and column should $$126$$ be placed.$$1$$$$2$$$$3$$$$4$$$$5$$$$6$$$$7$$$$8$$$$9$$$$10$$$$11$$$$12$$$$13$$$$14$$$$15$$$$16$$$$17$$$$18$$$$19$$$$20$$$$21$$\u2026\u2026"}, {"key": "737", "content": "As shown in the figure, starting from $$1$$, sequential natural numbers are filled into the table according to a rule. Please answer: (2) What is the number in the $$30$$th row and the $$3$$rd column? $$1$$$$2$$$$3$$$$4$$$$5$$$$6$$$$7$$$$8$$$$9$$$$10$$$$11$$$$12$$$$13$$$$14$$$$15$$$$16$$$$17$$$$18$$$$19$$$$20$$$$21$$\u2026\u2026"}, {"key": "738", "content": "As shown in the figure, starting from $$1$$, consecutive natural numbers are filled into a table according to a pattern. Please answer: (1) In which row and column should $$400$$ be placed? question_738-image_0"}, {"key": "739", "content": "As shown in the figure, starting from $$1$$, consecutive natural numbers are filled into the table according to a rule. Question: (2) What is the number in the $$4th$$ row and $$48th$$ column? question_739-image_0"}, {"key": "740", "content": "As shown in the figure, starting with $$5$$, consecutive natural numbers are filled into the table according to a pattern. Please answer: (1) In which row and column should $$100$$ be placed? question_740-image_0"}, {"key": "741", "content": "As shown in the figure, consecutive natural numbers starting from $$5$$ are filled into a table according to a pattern. The question is: (2) What is the number in the $$15$$th row and $$4$$th column? question_741-image_0"}, {"key": "742", "content": "As shown in the figure, consecutive natural numbers starting from $$5$$ are filled into a table according to a pattern. Please answer: (1) What is the number in the $$3rd$$ row and $$100th$$ column. question_742-image_0"}, {"key": "743", "content": "As shown in the figure, consecutive natural numbers starting from $$5$$ are filled into the table according to a pattern. The question is:  (2) In which column should $$213$$ be placed? question_743-image_0"}, {"key": "744", "content": "Fill in the appropriate number in the \"$$\\square$$\" in the division vertical format below to make the vertical format valid, the dividend is.\n 7 3  2   9 0"}, {"key": "745", "content": "There are 7 cups placed upside-down on the table. Is it possible to flip 3 cups at a time to make all 7 cups face up? question_745-image_0"}, {"key": "746", "content": "There is a book with $$216$$ pages, and if you randomly tear off $$15$$ pages, can the sum of all the page numbers on these $$15$$ pages be $$102$$ ( )."}, {"key": "747", "content": "Fill in the appropriate number in the blank space in the figure, so that the division operation is correct, the dividend of this division operation is.\n question_747-image_0"}, {"key": "748", "content": "Find two integers whose sum is $$263$$ and difference is $$57$$. Do such numbers exist? ( )"}, {"key": "749", "content": "Fill in the blanks with appropriate numbers in the diagram so that the multiplication operation is correct.\n\n\n\n\n9\n\n2\n\n\nX\n\n\n\n\n\n6\n\n5\n4"}, {"key": "750", "content": "The sum of the formula $$201+203+205+207+209+2011+2013+2015+2017$$ is ( )\uff0e"}, {"key": "751", "content": "5 people each take a bucket and wait in front of the tap to draw water. The time they need to fill up their buckets is 1 minute, 2 minutes, 3 minutes, 4 minutes, and 5 minutes respectively. If there is only one tap, then the minimum total time for them to queue up and draw water is minutes."}, {"key": "752", "content": "As shown in the figure, there is one worker each at $$A$$, $$B$$, $$C$$, and $$D$$ along the workflow line. It is now required to place a toolbox on the workflow line so that the total distance from the 4 people to the toolbox is shortest. The position of the toolbox should be placed at ( ).\n question_752-image_0"}, {"key": "753", "content": "It is known that Eddie walks $$90$$ meters per minute, and Vi walks $$60$$ meters per minute. They start from locations $$A$$ and $$B$$ simultaneously. If they walk towards each other, they meet after $$10$$ minutes; if they walk in the same direction, then the time it takes for Eddie to catch up with Vi is minutes."}, {"key": "754", "content": "The small animals in the forest go out for a picnic, forming a line that is $$40$$ meters long, moving forward at a speed of $$3$$ meters per second. The little rabbit needs to rush from the end of the line to the front and immediately return to the end. The speed of the rabbit is $$5$$ meters per second. Therefore, the total seconds it takes for the rabbit to return to the end are."}, {"key": "755", "content": "A column of troops is $$600$$ meters long and advances at a speed of $$2$$ meters per second. A soldier needs to rush from the end of the column to the front and immediately return to the end. If he walks at $$3$$ meters per second, then the total distance for the round trip is meters."}, {"key": "756", "content": "Eddy and Vi stood at both ends A and B of a straight road 200 meters in length, facing each other. Before Eddy set out, a dog ran uniformly at a speed of 8 meters per second from location A towards Vi. After the dog had been running for 5 seconds, Eddy and Vi both started running to chase the dog (all of their movements were in a straight line). It is known that both Vi and Eddy\u2019s speeds were 12 meters per second. The question is: who meets the dog first?"}, {"key": "757", "content": "Cars A and B set off from places $$A$$ and $$B$$ towards each other at the same time and meet after $$4$$ hours. Car A continues for another $$3$$ hours to reach place $$B$$. Car A travels $$20$$ kilometers per hour faster than Car B. The distance between places $$A$$ and $$B$$ in kilometers."}, {"key": "758", "content": "The Big Fat Sheep School organizes the little lambs to line up and walk for a field trip, with the queue being a total length of $$630$$ meters and the walking speed being $$60$$ meters per minute. The sheep at the end of the line, Boiling Sheep, catches up to the front of the line at a speed of $$150$$ meters per minute, then immediately returns to the end of the line, using a total of minutes."}, {"key": "759", "content": "A fast train leaves Station A for Station B, traveling at $$65$$ kilometers per hour, while a slow train leaves Station B for Station A at the same time, traveling at $$60$$ kilometers per hour. When they meet, the fast train has traveled $$10$$ kilometers more than the slow train. The distance between Station A and Station B is kilometers."}, {"key": "760", "content": "Find the value represented by the following symbol. $$$$\u2606$$\\times10-6\\times$$\u2606$$-2\\times$$\u2606$$ =15-1$$, $$$$\u2606$$=$$."}, {"key": "761", "content": "Find the value represented by the following symbols. $$5x +3x-6x=17+3$$\uff0e$$x =$$."}, {"key": "762", "content": "Find the value represented by the symbol below. $$4\\times \\triangle +3=3\\times \\triangle +8$$, $$\\triangle =$$\uff0e"}, {"key": "763", "content": "Find the value represented by the symbol below $$10\\times \\triangle -3\\times \\triangle-16$$=$$6\\times \\triangle+11$$\uff0e$$ \\triangle $$=."}, {"key": "764", "content": "Find the value represented by the symbol below. $$70-(2\\times \u25a0+5)=\u25a0\\times 3$$\uff0e$$\u25a0=$$."}, {"key": "765", "content": "Find the value represented by the symbol below. $$10\\times {\\blacksquare }+3\\times (6-{\\blacksquare })=15\\times {\\blacksquare }-14$$\uff0c$${\\blacksquare }=$$."}, {"key": "766", "content": "Find the value represented by the following symbol. $$12x -2\\times (5+x )=4x+14$$, $$x=$$."}, {"key": "767", "content": "First find the equal relationship, then answer the following question: (1\uff09 The sum of $78$ and $$x$$ is $$155$$, $$x$$ is."}, {"key": "768", "content": "First, find the equation, and then answer the following question: (2) Bigmouth Monster ate some hamburgers, and Hugemouth Monster ate $$10$$ more than it did. Hugemouth Monster ate $$88$$ hamburgers, Bigmouth Monster ate ___."}, {"key": "769", "content": "The students went picking and picked $$27$$ baskets of tomatoes, which is $$3$$ times the amount of cucumbers, and the students picked baskets of cucumbers."}, {"key": "770", "content": "There are $$31$$ boys in a class, and the number of boys is $$5$$ less than $$2$$ times the number of girls, there are girls."}, {"key": "771", "content": "Set up equations to solve application problems: NiuNiu has $$100$$ more points cards than DingDing. It is known that the number of points cards NiuNiu has is $$8$$ less than 3 times the number DingDing has. How many points cards does DingDing have?"}, {"key": "772", "content": "The age difference between father and son is $$30$$ years, and the father is $$6$$ times older than his son, the father is years old."}, {"key": "773", "content": "Three years ago, the father's age was exactly $$6$$ times the age of his son, Xiaogang. This year, the sum of the father and son's ages is $$55$$ years. Xiaogang is years old this year."}, {"key": "774", "content": "Look at the diagram, set up an equation and solve it. $$x=$$. question_774-image_0"}, {"key": "775", "content": "The teacher distributes strawberries to the children in the class. If each child gets $$5$$ strawberries, there is 1 missing; if each child gets $$6$$ strawberries, there are $$4$$ missing. There is a child."}, {"key": "776", "content": "The figure below shows a $$5\\times 5$$ area with $$5$$ trees planted. Now, tents need to be set up on the empty ground where there are no trees, and the tents must be placed next to a tree. Any two tents cannot share a common point, and the number of tents in each row is shown on the extreme right, and the number of tents in each column is shown at the bottom. Then, the tent in the $$1$$st row is in which column. question_776-image_0"}, {"key": "777", "content": "The figure below shows a $$5\\times 5$$ area with $$7$$ trees planted. It is now required to set up tents on the vacant ground where no trees are planted, and the tents must be set up next to a tree. No two tents can share a common edge, and the number of tents in each row is shown on the far left, with the number of tents in each column shown at the top. Then, the tent in the $$2$$nd row is in which column. question_777-image_0"}, {"key": "778", "content": "The picture below is an $$8\\times 8$$ area with $$12$$ trees planted. Now, it is required to set up tents on the open ground where no trees are planted, and the tents must be set up beside a tree. Any two tents do not share a common point, and the number of tents in each row is as shown on the far right, and the number of tents in each column is as shown at the bottom. Then, the tent in the $$2$$nd column is in the row. question_778-image_0"}, {"key": "779", "content": "Xiaojun's home to school route is shown in the diagram. There are different ways to get from Xiaojun's home to school. (You can only walk towards the right or downwards as shown in the diagram) question_779-image_0"}, {"key": "780", "content": "Eddie and Viola are preparing to visit Grandma Li at the nursing home, as shown in the following picture: How many shortest routes are there from the school through the city center to the nursing home? question_780-image_0"}, {"key": "781", "content": "Aidy and Ver are planning to visit Grandma Li at the nursing home, as shown in the following diagram: If they don't want to pass through the city center, how many shortest routes are there to the nursing home? question_781-image_0"}, {"key": "782", "content": "Eddie and Viola prepare to visit Grandma Li at the nursing home, as shown in the following picture: In the evening, a heavy rain fell near the city center, and the nearby roads were impassable. How many shortest routes are there from the school to the nursing home at this time? question_782-image_0"}, {"key": "783", "content": "As shown in the figure, the English name of the scientist \"Einstein\" is spelled as \"$$Einstein$$\". Following the direction indicated by the arrows in the figure, there is a certain number of different methods to spell out the English word \"$$Einstein$$\". \n question_783-image_0"}, {"key": "784", "content": "As shown in the table, please read out the phrase \"We learn fun math\" consisting of $$9$$ characters, requiring that the $$9$$ characters you choose are consecutive (i.e., neighboring characters in the table are also adjacent left-to-right or top-to-bottom). How many complete ways are there to read \"We learn fun math\"? question_784-image_0"}, {"key": "785", "content": "The picture shows $$10$$ numbered rooms. You can move from a room with a smaller number to an adjacent room with a larger number, but cannot move from a room with a larger number to a room with a smaller number. How many different ways are there to walk from room $$1$$ to room $$10$$? question_785-image_0"}, {"key": "786", "content": "Wei needs to choose one top and one pair of pants from $$2$$ tops and $$2$$ pairs of pants for an outfit to go out, then she has several ways to wear."}, {"key": "787", "content": "In the shaded areas of the figure, mark squares that are mines with \"$$X$$\" and safe areas with \"$$O$$\". How many mines are there in each of the following three questions? question_787-image_0"}, {"key": "788", "content": "$$\\frac{5}{6}$$ represents the meaning of dividing the unit \"$$1$$\" evenly into parts, taking of those parts, and its fractional unit is."}, {"key": "789", "content": "The figure below shows a $$5\\times 5$$ area with $$5$$ trees planted. Now, it is required to set up tents on the empty land without trees, and the tents must be set up beside the trees. No two tents occupy squares with common points, and the number of tents in each row is shown on the far left, and the number of tents in each column is shown at the top. Is there a tent at the \u201c?\u201d location? ( )\n question_789-image_0"}, {"key": "790", "content": "The school plans to plant trees along one side of a $$60m$$ long path, planting a tree every $$5m$$ (including both ends), a total of trees are to be planted."}, {"key": "791", "content": "Eddie plans to tour the cities A, B, and C. To visit all three cities, he has a total of different orders in which he can visit. (Each city is visited only once)"}, {"key": "792", "content": "As shown in the figure, a frog jumps among points $$A$$, $$B$$, and $$C$$. If the frog starts jumping from point $$A$$, there are a total of different ways it can jump $$3$$ times.\n question_792-image_0"}, {"key": "793", "content": "Xiao Tie, Xiao Ye, and Xiao Zin passed the ball to each other, starting with Xiao Tie. After $$3$$ passes, the ball coincidentally returned to Xiao Tie's hands. Therefore, there are a total of different ways to pass the ball."}, {"key": "794", "content": "As shown in the figure, an ant starts from the vertex $$A$$ of a regular tetrahedron, traveling along the edges of the tetrahedron to visit each of the $$4$$ vertices and then returns to vertex $$A$$. The question is: how many different ways can this little ant take to complete its journey.\n question_794-image_0"}, {"key": "795", "content": "As shown in the figure, a frog jumps among five lotus leaves, moving from one to another adjacent leaf each time. If the frog starts on lotus leaf $$D$$, and then jumps consecutively $$3$$ times, there are a total of different ways it can jump.\n question_795-image_0"}, {"key": "796", "content": "Eddie practices running, for the first $$10$$ days he runs an average of $$400$$ meters per day, for the next $$5$$ days he averages $$700$$ meters per day, over these $$15$$ days he averages meters per day."}, {"key": "797", "content": "Xiao Ming, Xiao Jun, Xiao Ding, and Xiao Zhen have heights of $$107$$ cm, $$109$$ cm, $$108$$ cm, and $$116$$ cm respectively. The average height of the four people is cm."}, {"key": "798", "content": "The average of four numbers is $$98$$, after removing one number, the average of the remaining three numbers becomes $$89$$, the number removed is."}, {"key": "799", "content": "There is a string of beads in two colors, black and white, arranged according to the following pattern: the $$45$$th bead in this string is ( ) color."}, {"key": "800", "content": "In the table shown in the figure, form a word pair with the two characters in each column, one above the other. For example, the first word pair is (Spring\u6295), and the second word pair is (Wind\u6211). What is the 48th word pair? SpringWindFlowersGrassFragranceSpringWindFlowersGrassFragranceSpringWindFlowersGrassFragrance$$...$$PeachMeWithPeachesInReturnForPlumsPeachMeWithPeachesInReturnForPlums$$...$$"}, {"key": "801", "content": "The distance between two buildings is $$64$$ meters, and a poplar tree is planted every $$4$$ meters, for a total of poplar trees. (The width of the trees is negligible)"}, {"key": "802", "content": "As shown in the figure, a frog jumps between four lotus leaves $$A$$, $$B$$, $$C$$, and $$D$$, each time jumping from one lotus leaf to another adjacent one. If the frog starts on $$B$$ and then jumps continuously for $$3$$ times, there are a total of different methods of jumping. question_802-image_0"}, {"key": "803", "content": "Eddie and others were planting trees in the garden, in the order of $$1$$ poplar tree, $$2$$ coconut trees, and $$2$$ pine trees, for a total of $$48$$ trees. How many coconut trees were planted?"}, {"key": "804", "content": "As shown in the table, each column pairs the top and bottom characters together, for example, the first pair is (\u5c0f, \u53cc), the second pair is (\u670b, \u624b) $$\\cdots\\cdots$$ then the $$55$$th pair is ().\n question_804-image_0"}, {"key": "805", "content": "A square picture frame with a side length of $$5$$ decimeters, its perimeter is decimeters."}, {"key": "806", "content": "Find the perimeter of the shape in the right image.\nAnswer: $$\\text{cm}$$.\n question_806-image_0"}, {"key": "807", "content": "The perimeters of the two shapes in the right image are the same.\n question_807-image_0 question_807-image_1"}, {"key": "808", "content": "Using the numbers $$7,8,9$$, you can form different two-digit numbers. (Numbers can be reused)"}, {"key": "809", "content": "Using the three cards $$3$$, $$4$$, $$6$$, you can form (  ) three-digit numbers (cards can be rotated)."}, {"key": "810", "content": "Using three digit cards question_810-image_0, question_810-image_1, question_810-image_2, you can arrange different three-digit numbers."}, {"key": "811", "content": "Set up the division: $$3212\\div 4=$$"}, {"key": "812", "content": "Perform vertical division calculation: $$7200\\div 60=$$"}, {"key": "813", "content": "Among the following numbers, there are some odd numbers and some even numbers.\n$$42$$, $31$, $2017$, $0$, $32154$, $321$"}, {"key": "814", "content": "The result of $$215+23$$ is"}, {"key": "815", "content": "In integers, numbers that can be divided by $$2$$ are called even numbers, and those that cannot be divided by $$2$$ are called odd numbers. Can you quickly determine which of the following numbers are odd and which are even? There are several odd numbers and several even numbers. $$8$$, $$5$$, $$17$$, $$54$$, $$894$$, $$271$$, $$9865$$, $$9752$$, $$15782$$, $$94113$$, $$18929$$"}, {"key": "816", "content": "The equation that results in an odd number is ( )."}, {"key": "817", "content": "Is the result of the expression $$123+325-462\\times 101+233\\times 722$$ odd or even ( )\uff0e"}, {"key": "818", "content": "$$957\\times 317\\times 415\\times 813$$ Is the result odd or even? ( )."}, {"key": "819", "content": "Xiaomei has a box of black and white beads, which she arranges as follows: ($$1$$) The $$18$$th bead should be this color; ($$2$$) There are this many white beads among the first $$20$$ beads. question_819-image_0"}, {"key": "820", "content": "Using cards $$3$$ and $$4$$, you can form different two-digit numbers."}, {"key": "821", "content": "With the numbers $$1$$, $$2$$, it is possible to form different two-digit numbers (numbers can be repeated)."}, {"key": "822", "content": "Using the three numbers $$1$$, $$2$$, $$3$$, how many three-digit numbers can be formed without repeating any digits."}, {"key": "823", "content": "Using $$2$$, $$4$$, $$7$$, $$1$$ to form two-digit numbers with no repeated digits, you can form ( ) numbers."}, {"key": "824", "content": "Using the three digits $$0$$, $$4$$, $$7$$, how many distinct three-digit numbers can be formed?"}, {"key": "825", "content": "Among the two-digit numbers formed using the digits $$3$$, $$5$$, $$0$$, $$8$$ from these $$4$$ digital cards, what is the smallest odd number? ( )"}, {"key": "826", "content": "Planting $45$ trees in $5$ hours, on average, $1$ hour per tree."}, {"key": "827", "content": "$$6$$ kids eating, each with one rice bowl, every two kids share one dish bowl, every $$3$$ kids share one soup bowl, calculate in total how many bowls were used."}, {"key": "828", "content": "A pile of cabbages weighs $$300$$ pounds, Xiaoqiang can eat $$10$$ pounds per hour, so Xiaoqiang needs ( ) hours to finish this pile of cabbages."}, {"key": "829", "content": "The teacher wants to distribute $$54$$ apples among students in two classes, so how many apples are distributed to each class on average?"}, {"key": "830", "content": "Student Xiao Yang's final exam scores in three subjects were: $$88$$, $$93$$, $$89$$, the average score of these three subjects is\uff0e"}, {"key": "831", "content": "Master Wang said, \"I make 6 chairs a day,\" Master Li said, \"I make 20 chairs in 4 days.\" Who works faster? ( )"}, {"key": "832", "content": "Divide the unit '$$1$$' into $$10$$ equal parts and take $$7$$ of those parts, which is expressed as a fraction ( )."}, {"key": "833", "content": "The following ( ) indicates the number of colored triangles is $$\\frac{2}{3}$$ of the total number of triangles."}, {"key": "834", "content": "Represent the shaded part in the diagram with (\u3000\u3000).\n question_834-image_0"}, {"key": "835", "content": "On one side of a small road at the entrance of the library, a willow tree is planted every $$9$$ meters. If the total length of the road is $$180$$ meters, then the number of willow trees that can be planted is."}, {"key": "836", "content": "On one side of a certain road, there are some utility poles, with a billboard between every two poles. It is known that there are $$25$$ billboards, so there are utility poles."}, {"key": "837", "content": "Planting trees along a $$240$$ meter long water channel, planting $$1$$ tree every $$3$$ meters. Planting at both ends, a total of trees planted."}, {"key": "838", "content": "There is a circular pond in the park near Eddie's house with a circumference of $$1500$$ meters. A tree is planted every $$3$$ meters, resulting in the total need for seedlings to be trees."}, {"key": "839", "content": "A lumberjack saws wood in the forest, it takes him $$20$$ minutes to saw a log into $$5$$ segments, then to saw the log into $$10$$ segments takes minutes."}, {"key": "840", "content": "At the entrance of the community, there is a $$100$$ meter long road. Now, it is planned to plant trees on one side of this road, with one tree every $$10$$ meters, and trees should be planted at both ends of the road. A total number of trees needed to be planted is."}, {"key": "841", "content": "Eddie lives on the first floor, and Vier lives on the tenth floor. Eddie wants to visit Vier's home. How many flights of stairs must he climb from the first floor to the tenth floor?"}, {"key": "842", "content": "There is a circular flowerbed in the center of the park with a circumference of $$90$$ meters. It is planned to place chairs around the flowerbed for visitors to rest. If a chair is placed every $$6$$ meters, then the total number of chairs needed is. (The length of the chairs is negligible)"}, {"key": "843", "content": "Using the numbers $$1$$, $$2$$, $$7$$, different three-digit numbers can be formed."}, {"key": "844", "content": "Using three cards $$2$$, $$4$$, and $$5$$, how many different three-digit numbers can be formed? (Each card is used only once)"}, {"key": "845", "content": "Using the digits $$1$$, $$3$$, and $$9$$, you can form different natural numbers with no repeated digits."}, {"key": "846", "content": "With four different coins, each of $$1$$ piece as shown in the figure, a total of different amounts of money can be formed. question_846-image_0"}, {"key": "847", "content": "Using the digits $$0$$, $$2$$, and $$3$$, how many different natural numbers without repeated digits can be formed?"}, {"key": "848", "content": "In the following equation, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers. Find the numbers that the Chinese characters represent to satisfy the equation, and calculate: \u201c$$\\overline{I love math}$$\u201d=$$\uff0e question_848-image_0"}, {"key": "849", "content": "In the following shape, $$\\square$$, $$\\bigcirc$$, and $$\\triangle$$ represent different numbers, then $$\\square=$$, $$\\triangle=$$, $$\\bigcirc=$$.\n question_849-image_0"}, {"key": "850", "content": "Fill in the appropriate number in the blank space to make the addition vertical method in the diagram valid. Then, the sum in the vertical method is.\n question_850-image_0"}, {"key": "851", "content": "Among the calculations below, four small pieces of paper each cover a number. What is the total sum of the four numbers covered?\n question_851-image_0"}, {"key": "852", "content": "If the following column operation holds true, the final result of the column operation is .\n question_852-image_0"}, {"key": "853", "content": "A small snail crawls $$6$$ minutes for $$12$$ decimeters, at this speed, how many decimeters it crawls in $$30$$ minutes."}, {"key": "854", "content": "$$3$$ people plant $$15$$ trees in $$5$$ hours. If each person plants the same number of trees per hour, how many trees do $$6$$ people plant in $$7$$ hours?"}, {"key": "855", "content": "$$5$$ monkeys ate $$80$$ peaches in $$4$$ days, at this rate, $$280$$ peaches will be enough for $$7$$ monkeys for $$10$$ days."}, {"key": "856", "content": "$$8$$ workers can make $$72$$ machine parts in $$3$$ hours, if the number of workers is halved and the time is increased by $$5$$ hours, they can make ( ) parts."}, {"key": "857", "content": "In the zoo, $$3$$ monkeys can eat $$60$$ peaches in $$7$$ days. According to this speed, $$9$$ monkeys can eat peaches in $$14$$ days."}, {"key": "858", "content": "Xiaotie writes 60 characters in 6 minutes. At this rate, how many minutes are needed to write 80 characters?"}, {"key": "859", "content": "4 bottles of lemon juice, $$3$$ bottles of grape juice, $$3$$ bottles of orange juice, mixed into one beverage. Given that each bottle of lemon juice costs $$5$$ yuan, each bottle of grape juice costs $$6$$ yuan, and each bottle of orange juice costs $$4$$ yuan. Then, the average cost per bottle of the mixed beverage is yuan."}, {"key": "860", "content": "Xiao Fei's final exam scores in Chinese, Mathematics, and Science had an average score of $$93$$ points. After including the English score, the average score increased by $$1$$ point. Therefore, Xiao Fei's English score is."}, {"key": "861", "content": "Fill $$5$$ identical cups with water, the water levels are respectively $$16$$ cm, $$27$$ cm, $$18$$ cm, $$19$$ cm, $$20$$ cm, the average height of the water levels in these $$5$$ cups is centimeters."}, {"key": "862", "content": "There are coins of four different denominations, each having $$1$$ piece as shown in the figure. In total, there can be different amounts of money formed.\n question_862-image_0"}, {"key": "863", "content": "With the numbers $$0$$, $$2$$, $$3$$, you can form different natural numbers without repeating digits."}, {"key": "864", "content": "If the following vertical subtraction is valid, the minuend is; the subtrahend is; the difference is.\n question_864-image_0"}, {"key": "865", "content": "With the numbers $$1$$, $$2$$, and $$3$$, you can form natural numbers with no repeated digits."}, {"key": "866", "content": "$$1470\\div 70 $$="}, {"key": "867", "content": "With question_867-image_0, three cards can form different three-digit numbers. (Cards can be rotated)"}, {"key": "868", "content": "The same letter represents the same number, and different letters represent different numbers. In the calculation below, $$A=$$; $$B=$$.\n question_868-image_0"}, {"key": "869", "content": "$$256\\div 8$$="}, {"key": "870", "content": "Please calculate the perimeter of the following shapes. The perimeter of the rectangle is in centimeters, and the perimeter of the square is in decimeters.\n question_870-image_0"}, {"key": "871", "content": "As shown in the diagram is the floor plan of a school, it is known that the line segment $$a=120$$ meters, $$b=70$$ meters. Teacher Yang jogs around the school $$3$$ times every morning. How many meters does he run each day?\n question_871-image_0"}, {"key": "872", "content": "In the equation below, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers, making the equation valid. Then, the four-digit number \"$$\\overline{{\u7f8e\u597d\u672a\u6765}}$$\" is.\n$$\\begin{matrix}&& &&Lai \\\\& &&Wei & Lai \\\\&& Hao&Wei&Lai\\\\+&Mei&Hao&Wei&Lai\\\\\\hline &8&1&0&2\\end{matrix}$$"}, {"key": "873", "content": "The green team plants $$21$$ trees in $$3$$ hours, and still needs to plant $$77$$ more trees. Given this work efficiency, the total hours needed to complete the task are\uff0e"}, {"key": "874", "content": "There are five numbers in a row, and their average is $$11$$. It is also known that the average of the first three numbers is $$9$$, and the average of the last three numbers is $$13$$. Then, the third number is."}, {"key": "875", "content": "Third-grade students made some handmade flowers, producing a total of $$76$$ flowers in the first $$3$$ days and then an average of $$30$$ flowers per day in the next $$4$$ days. The average number of flowers made per day by the third-grade students over these $$7$$ days is ."}, {"key": "876", "content": "Calculate $$\\frac{7}{23}-\\frac{4}{19}+\\frac{16}{23}-\\frac{5}{19}=$$."}, {"key": "877", "content": "Compare the size of the following fractions.\n$$\\frac{2}{7}$$ $$\\frac{3}{7}$$, $$\\frac{1}{11}$$ $$\\frac{1}{12}$$."}, {"key": "878", "content": "In the figure below, adjacent sides are perpendicular to each other, so the perimeter of this figure is.\n question_878-image_0"}, {"key": "879", "content": "Please simplify the following problems: (1) $16\\times72+16\\times28=$. (2) $4\\times8+4\\times17=$. (3) $46\\times102-46\\times2=$."}, {"key": "880", "content": "Calculate: $$78\\times (100+2)=$$."}, {"key": "881", "content": "Calculate: (1) $$33\\times 99=$$. (2) $$25\\times 11=$$."}, {"key": "882", "content": "Calculate: ($$1$$) $$16\\times 25\\times 25=$$\uff0e\n($$2$$) $$125\\times 32=$$\uff0e"}, {"key": "883", "content": "Calculate the following problems using simple methods. \uff081\uff09$78\\times 101=$\uff082\uff09$61\\times 99=$"}, {"key": "884", "content": "Da Mao, Er Mao, and San Mao, the three brothers, are passing the ball to each other, starting with Da Mao for the first pass. They want the ball to return to Da Mao's hands on the 4th pass. In total, there are different methods of passing."}, {"key": "885", "content": "The result of $$789\\times 790\\times 791\\times 1111$$ is odd or even? ( )"}, {"key": "886", "content": "Xiao Ming wrote a series of numbers on the ground: $$7$$, $$0$$, $$2$$, $$5$$, $$3$$, $$7$$, $$0$$, $$2$$, $$5$$, $$3$$, $$7$$, $$0$$, $$2$$, $$5$$, $$3\\cdots \\cdots $$ What is the $$81$$st number he wrote?"}, {"key": "887", "content": "$$48\\times9\\div8=$$"}, {"key": "888", "content": "$$50\\div5\\div2=$$"}, {"key": "889", "content": "$$6\\div5\\div(2\\div5)=$$"}, {"key": "890", "content": "As shown in the diagram, what is the 30th figure? $$\\bigcirc \\square \\triangle \\bigcirc \\square \\triangle \\bigcirc \\square \\triangle \\cdots \\cdots $$"}, {"key": "891", "content": "Calculate: $$25\\times 13\\times 4=$$."}, {"key": "892", "content": "Is the sum of the series $$1+3+5+7+9+\\dots+19$$ odd or even? ( )."}, {"key": "893", "content": "Columnar calculation: (1) $$140\\times18\\div14=$$ (2) $$3900\\times15\\div13=$$"}, {"key": "894", "content": "Cascade calculation: (1) $$(144\\div 36)\\times (36\\div 9)\\times (9\\div 3)=$$ (2) $$2 \\div \\left( {5 \\div 7} \\right) \\div \\left( {7 \\div 11} \\right) \\div \\left( {11 \\div 16} \\right) \\div \\left( {16 \\div 35} \\right) =$$"}, {"key": "895", "content": "Perform column subtraction calculations for the following expressions: (1) $$(140+77)\\div 7=$$ (2) $$(2400-666)\\div 6=$$"}, {"key": "896", "content": "Column subtraction calculation: (1) $$91\\div 5+9\\div 5=$$\uff0e(2) $$294\\div 7+56\\div 7=$$\uff0e(3) $$24\\div 3+24\\div 2+24\\div 1=$$\uff0e"}, {"key": "897", "content": "Column subtraction calculation: (1) $$999\\div 27=$$\uff0e(2) $$3300\\div 55=$$\uff0e"}, {"key": "898", "content": "Columnar subtraction calculation: $$20\\div 3+40\\div 9+80\\div 9=$$"}, {"key": "899", "content": "$$170\\times23\\div17=$$"}, {"key": "900", "content": "$$45\\div4+33\\div4+22\\div4=$$"}, {"key": "901", "content": "$$689000\\div25\\div4=$$"}, {"key": "902", "content": "If the divisor is multiplied by $$8$$, in order to keep the quotient the same, the dividend should. If the divisor is divided by $$100$$, in order to keep the quotient the same, the dividend should."}, {"key": "903", "content": "Which slice of bread has a larger area? \uff08 \uff09"}, {"key": "904", "content": "In the picture (unit: cm), the perimeter of the square is cm, and the perimeter of the rectangle is cm.\n question_904-image_0"}, {"key": "905", "content": "Fill in the blanks. (1) The perimeter of a square is $$36$$ meters, the side length of this square is meters, and the area of this square is square meters; (2) The perimeter of a rectangle is $$40$$ meters, the length is $$12$$ meters, the area of this rectangle is square meters."}, {"key": "906", "content": "Fill in the blanks. (1) The area of a square is $$49$$ square meters, the side length of this square is meters, and the perimeter of this square is meters; (2) The area of a rectangle is $$4000$$ square decimeters, the length is $$8$$ meters, the width is meters, and the perimeter of this rectangle is meters."}, {"key": "907", "content": "Unit conversion: (1) $$5{{\\text{m}}^{2}}=$$$$\\text{d}{{\\text{m}}^{2}}$$; $$3\\text{d}{{\\text{m}}^{2}}=$$$$\\text{c}{{\\text{m}}^{2}}$$. (2) $$1200$$$$\\text{c}{{\\text{m}}^{2}}$$=$$\\text{d}{{\\text{m}}^{2}}$$; $$3800$$$$\\text{d}{{\\text{m}}^{2}}$$=$${{\\text{m}}^{2}}$$."}, {"key": "908", "content": "$$25\\times32\\times25=$$"}, {"key": "909", "content": "$$7000\\div125\\div8=$$"}, {"key": "910", "content": "Determine the parity of the result for the following expression: $$127\\times 238-18\\times 71+339\\times 165-23\\times 114$$."}, {"key": "911", "content": "(1) The area of a rectangle is $$42$$ square meters, the length is $$7$$ meters, and the width is meters; \n(2) The area of a square is $$64$$ square meters, and the side length is meters."}, {"key": "912", "content": "The perimeter of a rectangle and a square are the same, if the length of the rectangle is $$10$$ and its width is $$8$$, then the area of the square is."}, {"key": "913", "content": "Unit conversion: $$5{{\\text{m}}^{2}}=$$$$\\text{d}{{\\text{m}}^{2}}$$; $$3\\text{d}{{\\text{m}}^{2}}=$$$$\\text{c}{{\\text{m}}^{2}}$$."}, {"key": "914", "content": "The figure below shows a square and a rectangle with known side lengths. The area of the square is $$\\text{c}{{\\text{m}}^{2}}$$, and the area of the rectangle is $$\\text{c}{{\\text{m}}^{2}}$$.\n question_914-image_0 question_914-image_1"}, {"key": "915", "content": "Eddy and Vi have a total of $$90$$ pictures. Eddy's pictures are twice as many as Vi's, Vi originally had number of pictures."}, {"key": "916", "content": "Li Ming and Zhao Fang participated in the pumpkin picking activity at the farm. The pumpkins picked by Li Ming were 3 times the amount picked by Zhao Fang. Together, they picked 56 kilograms of pumpkins. Li Ming picked ____ kilograms of pumpkins. Zhao Fang picked ____ kilograms of pumpkins."}, {"key": "917", "content": "In the figure below, the area of the rectangle in square centimeters. question_917-image_0"}, {"key": "918", "content": "In the following figure, the area of the square is square centimeters. question_918-image_0"}, {"key": "919", "content": "Simplified calculation: $$99\\times17+17=$$"}, {"key": "920", "content": "$$4000\\div (125\\times 4)=$$."}, {"key": "921", "content": "The weekend arrived, and the doctor took Eddie and Vill to the zoo. They first came to the pandas, where Uncle Liu, the keeper, introduced: 'There are $$36$$ pandas in total, including panda babies and their mothers, and the number of panda babies is $$3$$ times that of the panda mothers.' There are panda babies and panda mothers."}, {"key": "922", "content": "Everyone arrived at Deer Park again. Eddie counted a total of $$24$$ deer, including sika deer and giraffes, and found that the number of sika deer was $$4$$ less than three times the number of giraffes. So, how many sika deer and how many giraffes did Eddie see?"}, {"key": "923", "content": "There are three types of monkeys on Monkey Mountain, namely the golden monkey, the macaque, and the black leaf monkey. There are a total of $$56$$ monkeys, and the number of golden monkeys is $$2$$ times that of macaques, the number of black leaf monkeys is $$4$$ times that of macaques. So, how many macaques, golden monkeys, and black leaf monkeys are there respectively?"}, {"key": "924", "content": "The sum of the father and son's age is $$40$$ years, the father's age is $$4$$ times the son's age, then the son's age is\uff0e"}, {"key": "925", "content": "Mom bought some lychees and grapes, spending a total of $$58$$ yuan. It is known that the amount spent on lychees is $$5$$ times more plus $$4$$ yuan than that on grapes, so how much was spent on lychees in yuan."}, {"key": "926", "content": "The orchard has peach trees, pear trees, and apple trees totaling $$392$$ trees. The peach trees are $$12$$ more than twice the number of pear trees, and there are $$20$$ fewer apple trees than pear trees, then there are peach trees, pear trees, and apple trees respectively."}, {"key": "927", "content": "There are $$47$$ novels on the bookshelf, they are either fairy tales or science fiction novels. It is known that the number of fairy tale novels is $$3$$ less than $$4$$ times the number of science fiction novels. Then there are $$10$$ science fiction novels."}, {"key": "928", "content": "The school purchased a total of $$49$$ basketballs, soccer balls, and volleyballs. The number of basketballs is $$3$$ times the number of soccer balls. The school bought more volleyballs than soccer balls by $$4$$. The number of basketballs, soccer balls, and volleyballs the school purchased were."}, {"key": "929", "content": "Eddy bought $$5$$ comic books, Vi bought $$20$$ comic books, the number of comic books Vi bought is times the number Eddy bought, Vi bought more comic books than Eddy by ."}, {"key": "930", "content": "Vi has $$10$$ yuan more pocket money than Edi. It is known that Vi's pocket money is twice that of Edi's, then Edi has yuan of pocket money."}, {"key": "931", "content": "The professor gave Eddie $$5$$ large buns and gave Vi $$15$$ large buns. The number of buns Vi has is multiple times of Eddie\u2019s, and Vi has more buns than Eddie by multiple times."}, {"key": "932", "content": "Farm A harvested 80 million tons more sorghum than Farm B, and the sorghum harvested by Farm A is 5 times that of Farm B. Therefore, Farm A harvested million tons of sorghum, and Farm B harvested million tons of sorghum question_932-image_0"}, {"key": "933", "content": "Farm A harvested 50 million tons more corn than Farm B, and the corn harvested by Farm A was 20 million tons more than 3 times that of Farm B. How much corn did Farm A and Farm B each harvest? question_933-image_0"}, {"key": "934", "content": "The number of boys and girls in the competitive arena was the same, later the total number of girls decreased by $$10$$, while the total number of boys increased by $$30$$. At this time, the number of boys was exactly $$3$$ times the number of girls. How many boys and girls were there originally?"}, {"key": "935", "content": "Eddy and Oleg $$PK$$, Oleg's energy value is $$62$$, Eddy's energy value is $$38$$. After the first round, both consumed the same amount of energy, and Oleg's remaining energy is 3 times that of Eddy's. So, what is Eddy's and Oleg's remaining energy value now? question_935-image_0"}, {"key": "936", "content": "The area of a square is $$100$$ square meters, the side length of this square is meters, the perimeter of this square is meters."}, {"key": "937", "content": "Compute: $$1\\div (4\\div 7)\\div (7\\div 13)\\div (13\\div 16)=$$."}, {"key": "938", "content": "In the orchard, there are $$24$$ more pear trees than apple trees, and the number of pear trees is exactly $$3$$ times the number of apple trees. Now there are apple trees and pear trees."}, {"key": "939", "content": "The elder brother and the younger brother went to plant trees. It is known that the elder brother planted 37 more trees than the younger brother. The number of trees planted by the elder brother is 19 less than 5 times the number planted by the younger brother. So, how many trees did the elder brother plant?"}, {"key": "940", "content": "In the orchard, there are $$50$$ more pear trees than apple trees, and the number of pear trees is exactly $$6$$ times the number of apple trees. There are now apple trees, pear trees in the orchard."}, {"key": "941", "content": "Big Fatty ate 45 more chicken legs than Little Fatty, and the number of chicken legs Big Fatty ate was 4 times more than Little Fatty's, plus 3 more. So, how many chicken legs did Little Fatty eat?"}, {"key": "942", "content": "The large barrel contains $$35$$ kilograms of oil, and the small barrel contains $$25$$ kilograms. After selling the same amount of oil from both barrels, the oil left in the large barrel is twice as much as that in the small barrel. At this point, the large barrel still has kilograms left, and the small barrel still has kilograms left."}, {"key": "943", "content": "There are $$80$$ fewer red balloons than yellow balloons in the square, and the yellow balloons are $$20$$ more than twice the number of red balloons. So, there are  red balloons and  yellow balloons."}, {"key": "944", "content": "$$2011$$ on September $$28$$th is Wednesday, then October $$1$$st, $$2011$$ is Saturday ( )."}, {"key": "945", "content": "$$5$$, $$6$$, $$7\\cdots \\cdots \\cdots 50$$ has a total count of numbers."}, {"key": "946", "content": "Complete the following questions: (1) Today is Thursday. Starting from this day, what day of the week is the $$25$$th day?"}, {"key": "947", "content": "Complete the following questions: (1) March 12 of every year is Arbor Day. It is known that Arbor Day of a certain year falls on a Monday. What day of the week is March 28 of that year? (Enter the number) (2) Children's Day on June 1 of a certain year is a Monday. What day of the week is August 5 of that year? (Enter the number)"}, {"key": "948", "content": "To beautify the environment, the school paved a lawn on the playground, and the area of this lawn is square meters. (Unit: meters)\n question_948-image_0"}, {"key": "949", "content": "Grandpa Li has 18 more ducks than geese, and the number of ducks is 3 times the number of geese. Do you know how many ducks Grandpa Li has?"}, {"key": "950", "content": "There are a total of $$72$$ monkeys on the Monkey Hill in the zoo. The number of big monkeys is $$8$$ less than $$3$$ times the number of small monkeys. There are small monkeys and big monkeys on Monkey Hill."}, {"key": "951", "content": "$$2016$$ year $$6$$ month $$1$$ day is Wednesday, calculate what day of the week is $$2016$$ year $$9$$ month $$1$$ day. (Fill in the number)"}, {"key": "952", "content": "Today is Wednesday, then starting from today (counting today as day $$1$$), the $$365$$th day falls on ( ) of the week."}, {"key": "953", "content": "January 4th, $$2017$$ was a Wednesday. What day of the week was March 4th of the same year? (Fill in the Arabic numerals)"}, {"key": "954", "content": "June 7, 2013 was a Friday, then what day of the week is July 6 of that year?"}, {"key": "955", "content": "In the nine squares in the picture, the sum of the three numbers in each row, each column, and each diagonal is equal, then $$A=$$\uff0e\n question_955-image_0"}, {"key": "956", "content": "As shown in the figure, fill in some numbers in a $$3\\times 3$$ grid so that the sum of the numbers in each row, each column, and each diagonal is the same. What number should be filled in the \"?\".\n question_956-image_0"}, {"key": "957", "content": "Place the numbers $$1\\sim 9$$ into each cell of a $$3\\times 3$$ grid below so that the sum of the numbers in each row, each column, and along both diagonals are the same. What is this sum?\n question_957-image_0"}, {"key": "958", "content": "Mom bought some lychees and grapes, spending a total of $$16$$ yuan. It is known that the amount spent on lychees is $$2$$ times that of grapes plus $$4$$ yuan. So, the money spent on lychees was yuan."}, {"key": "959", "content": "June 1, 2017, was Thursday, then what day of the week was October 11 of that year?"}, {"key": "960", "content": "Vi's lollipops are 80 more than Eddie's, Vi's lollipops are 3 times more than Eddie's plus 20, Vi has lollipops."}, {"key": "961", "content": "In a $$3\\times 3$$ grid array, the sum of each row, each column, and each diagonal is the same, find $$a=$$.\n question_961-image_0"}, {"key": "962", "content": "The following picture is a third-order magic square, \"?\"=.\n question_962-image_0"}, {"key": "963", "content": "The image below is an unfinished order-four magic square. Thus, in the blanks $$A=$$, $$B=$$.\n question_963-image_0"}, {"key": "964", "content": "As shown in the diagram, some cells in the third-order magic square have already been filled with numbers, then the value of $$X$$ is. question_964-image_0"}, {"key": "965", "content": "During the physical education class, the 1-minute jump rope scores of the nine students in the first group are as follows: $$95$$ $$97$$ $$91$$ $$91$$ $$95$$ $$91$$ $$93$$ $$93$$ $$91$$. Answer the following questions: question_965-image_0 (1) Based on the information above, complete the following statistics table: Statistics table of the first group's 1-minute jump rope scores Number of jumps/$$91$$ $$93$$ $$95$$ Number of students/$$1$$ (2) What is the average score of the first group's 1-minute jump rope? (3) What is the most common number of jumps? (4) If you arrange all students' number of jumps from highest to lowest, what is the number of jumps in the middle position?"}, {"key": "966", "content": "Hongxing Elementary School organized a tree planting event on Tree Planting Day, with 32 students from Class 1 participating, and on average, each person planted 3 trees; Class 2 had 35 participants, planting a total of 70 trees; Class 3 planted a total of 99 trees, with an average of 3 trees planted per person. (1) The number of participants in Class 3's tree planting activity. (2) The total number of trees planted in this event."}, {"key": "967", "content": "Below is the monthly average temperature change statistics chart for a certain place in $$2018$$. Please answer the following questions based on the statistical chart: question_967-image_0 (1) Which month had the highest average temperature? Which month had the lowest average temperature? (2) Between which months did the average temperature rise the fastest? Between which months did the average temperature drop the fastest? (3) Based on the information in the bar chart, what other questions can you come up with?"}, {"key": "968", "content": "January 4, 2016, is a Monday, so March 4, 2016, is a Friday ( )."}, {"key": "969", "content": "Grade 3 Class 1 has $$27$$ more students than Class 2, and the number of students in Class 1 is $$9$$ less than $$4$$ times that of Class 2. Therefore, Class 1 has $$39$$ students and Class 2 has $$12$$ students."}, {"key": "970", "content": "The nine squares in the picture below have been filled with three numbers, please fill in six more non-zero natural numbers so that the sum of the three numbers in any row or any column are equal, then $$A$$=.\n question_970-image_0"}, {"key": "971", "content": "Participants A and B took part in a speech competition, judged by a total of $$5$$ judges. The scores given were as follows: $$A$$ $$B$$ $$C$$ $$D$$ $$E$$ Participant A $$154$$ $$177$$ $$161$$ $$153$$ $$165$$ Participant B $$174$$ $$171$$ $$148$$ $$154$$ $$158$$ (1) Who had the higher average score between the two participants? (2) Generally, in competitions, when calculating the average score, the highest and the lowest scores are discarded before calculating the average score. So, who had the higher average score after applying this rule?"}, {"key": "972", "content": "In the grid of the right figure, fill in the numbers respectively, so that the sum of the three numbers in each row, each column, and each diagonal is equal, then $$x=$$\uff0e$$x$$$$2$$$$37$$$$16$$"}, {"key": "973", "content": "Can the figure below be drawn in one stroke? ( ). \n question_973-image_0"}, {"key": "974", "content": "There are four seasons in a year, the following four pictures respectively represent spring, summer, autumn, and winter. Children, please observe which one of the pictures is drawn in a single stroke.\n question_974-image_0 question_974-image_1 question_974-image_2 question_974-image_3"}, {"key": "975", "content": "Among the left and right images below, the one that can be drawn with one stroke is ( ).\n question_975-image_0"}, {"key": "976", "content": "The following image is the floor plan of Wei's new home. The new home has $$6$$ rooms, with doors connecting adjacent rooms. She wants to start from a certain room and pass through all the doors without repeating any, with one room being the starting point, and another the ending point. question_976-image_0"}, {"key": "977", "content": "On the right is a statistical chart of four students reading extracurricular books in May. The following statements are incorrect\uff08 \uff09.\n question_977-image_0"}, {"key": "978", "content": "There is a magic square as shown in the figure, then $$a=$$\uff0e\n question_978-image_0"}, {"key": "979", "content": "October 1, 2015 is Thursday, December 25, 2015 is on a week."}, {"key": "980", "content": "The figure below has a singular point.\n question_980-image_0"}, {"key": "981", "content": "The diagram below is a street map of a neighborhood in a city, where a postal worker needs to deliver letters. The numbers on the map represent the kilometers of each street segment. Starting from the post office, they need to cover all streets and eventually return to the post office. To pass through each street with the shortest possible distance, the total distance they need to walk in kilometers is.\n question_981-image_0"}, {"key": "982", "content": "The minimum number of strokes required to draw the following three figures are: Figure 1 strokes, Figure 2 strokes, Figure 3 strokes.\n question_982-image_0"}, {"key": "983", "content": "Among the figures below, there are several that can be drawn in one stroke without repeating.\n question_983-image_0 question_983-image_1 question_983-image_2 question_983-image_3 question_983-image_4"}, {"key": "984", "content": "The picture shows the floor plan of a supermarket, which has a total of six doors. Zhang Ming wants to walk through all the aisles without repeating any route. Can he do it? If yes, please design an entry and exit method for him. If no, please explain why. question_984-image_0"}, {"key": "985", "content": "The teacher asked all the students of the 4th grade, class 7, to gather on the playground, students who can draw to stand inside the big circle on the left, and students who can play the piano to stand inside the big circle on the right, so the students who can only draw should stand in the area (fill in a capital letter).\n question_985-image_0"}, {"key": "986", "content": "The teacher asked all the students of Grade 4 Class 7 to gather on the playground, students who can draw stand in the circle on the left, and students who can play the piano stand in the circle on the right, so the students who can both draw and play the piano should stand in the area (fill in the letter).\n question_986-image_0"}, {"key": "987", "content": "Xiaoming's family raised some chickens and rabbits, which were kept together in the same cage. Xiaoming counted them and found that they had a total of $$35$$ heads and $$110$$ feet. Therefore, the number of rabbits raised by Xiaoming's family is."}, {"key": "988", "content": "Ultraman loves to fight little monsters, each of which has $$2$$ legs, and each big monster has $$5$$ legs. Now there are $$10$$ monsters in total, big and small, with $$35$$ legs in total. So, there are how many little monsters."}, {"key": "989", "content": "Pengpeng played a game, for each question answered correctly a reward of $$2$$ gold coins was given, for each question answered incorrectly $$1$$ gold coin was deducted. Pengpeng answered a total of $$10$$ questions and won $$14$$ gold coins, Pengpeng answered the correct number of questions."}, {"key": "990", "content": "After adding $$6$$ to the number of Xiao Ai's reward points cards and then multiplying by $$10$$, it happens to be $$100$$ cards, please ask how many reward points cards Xiao Ai has."}, {"key": "991", "content": "Fill in the appropriate number to make the equation valid.\n$$\\times 8=72$$\n$$\\div 3=20$$"}, {"key": "992", "content": "There are $$24$$ birds on three trees, with $$3$$ birds flying from the first tree to the second tree, and $$5$$ birds flying from the second tree to the third tree. Eventually, each of the three trees had the same number of birds. How many birds were there originally on each tree? (Fill in from the most to the least)"}, {"key": "993", "content": "There are a total of $$96$$ apples in three piles labeled A, B, and C. First, the same number of apples as in pile B is taken from pile A and put into pile B; secondly, the same number of apples as in pile C is taken from pile B and put into pile C; thirdly, the same number of apples as the remaining in pile A is taken from pile C and put into pile A. At this point, the number of apples in the three piles is equal. Originally, pile A had $$ apples, pile B had $$ apples, and pile C had $$ apples."}, {"key": "994", "content": "The following image must be completed with at least pencils.\n question_994-image_0"}, {"key": "995", "content": "Chickens and rabbits are in the same cage, totaling $$20$$ animals. There are $$50$$ legs in the cage. How many chickens and rabbits are there?"}, {"key": "996", "content": "A certain restaurant's signature dish, Xiaoyue has tried $$13$$ of them, Dongdong has tried $$7$$ of them, and there are $$2$$ dishes that both have tried, also there are $$5$$ dishes that neither have tried. How many signature dishes are there in total?"}, {"key": "997", "content": "A bundle of wires, the first time half of the total length is used, the second time half of the remaining is used again, and the third time $$15$$ meters are used, leaving $$7$$ meters in the end. This bundle of wires originally had meters."}, {"key": "998", "content": "At the top of the mountain there is a peach tree, a monkey stole peaches from it. On the first day, it stole more than half of the total by $$2$$, and on the second day, it stole more than half of the remaining by $$2$$, leaving $$1$$ peach on the tree. Originally, there were how many peaches on the tree."}, {"key": "999", "content": "Second-grade students have $$56$$ participants in two extracurricular interest groups, dance and Go. Among them, $$24$$ students are in the dance group, $$10$$ students are in both groups, and there are people in the Go group."}, {"key": "1000", "content": "Yucai Primary School's fourth grade class 2 has a total of $$46$$ students, of which $$21$$ students participate in the Chinese interest group, $$18$$ students participate in the math interest group, and $$9$$ students participate in both. Therefore, there are students who have not participated in either interest group."}, {"key": "1001", "content": "There is a math test with a total of $$2$$ questions, $$25$$ people got the first question right, $$22$$ people got the second question right, $$9$$ people got both questions right, and $$5$$ people got both questions wrong. How many people participated in the test?"}, {"key": "1002", "content": "Among $$1$$~$$40$$, the number of multiples of either $$2$$ or $$3$$ is."}, {"key": "1003", "content": "The school held a badminton competition, and students in the school badminton team must participate in at least one type of competition. There were a total of $20$ people, among which $12$ people participated in singles matches, and $16$ people participated in doubles matches; therefore, there were people who participated in both singles and doubles matches."}, {"key": "1004", "content": "Among the following methods, the method to turn the diagram below into a single line drawing is ( )\n question_1004-image_0"}, {"key": "1005", "content": "Da Bai bought a total of $$12$$ apples and pears, spending $$29$$ yuan altogether. Knowing that apples cost $$3$$ yuan each and pears $$2$$ yuan each, then Da Bai bought apples and pears."}, {"key": "1006", "content": "Compare the sizes: $$10.1$$ ( ) $$1.01$$."}, {"key": "1007", "content": "Which of the following numbers is a decimal ( )."}, {"key": "1008", "content": "The decimal part of the decimal $$31.408$$ has digits."}, {"key": "1009", "content": "Which of the following calculations is correct ( )?"}, {"key": "1010", "content": "Which of the following numbers is closest to the number represented by the abacus? ( )\uff0e\n question_1010-image_0"}, {"key": "1011", "content": "In $$5246$$, the numbers represented by $$2$$ and $$4$$ differ by ( )."}, {"key": "1012", "content": "Observe the results of the following four students running 50 meters. question_1012-image_0 (1) The shorter (longer/shorter) the time, the faster the run. (2) The first place is, the second place is, the third place is, the fourth place is. (Fill in names)"}, {"key": "1013", "content": "Fill in the blank\n(1) Right angle =\u00b0\n(2) Straight angle =\u00b0"}, {"key": "1014", "content": "The figure below has ( ) line segments.\n question_1014-image_0"}, {"key": "1015", "content": "There are ( ) triangles in the figure below.\n question_1015-image_0"}, {"key": "1016", "content": "Count, in the diagram below there are a total of rectangles.\n question_1016-image_0"}, {"key": "1017", "content": "As shown in the figure, if $$\\angle 1=110{}^\\circ $$, then $$\\angle 2=$$$${}^\\circ $$.\n question_1017-image_0"}, {"key": "1018", "content": "The relationship between the size of an angle and the length of sides is ( )."}, {"key": "1019", "content": "Two acute angles combined form an angle, the resulting angle cannot be ( )."}, {"key": "1020", "content": "Among the following statements, the correct one is ( )."}, {"key": "1021", "content": "Given that $$\\angle AOC$$ and $$\\angle BOD$$ are both right angles, $$\\angle AOB=60{}^\\circ $$, $$\\angle COD=$$____${}^\\circ $$. question_1021-image_0"}, {"key": "1022", "content": "As shown, $$\\angle 1=40{}^\\circ $$, $$\\angle 2=90{}^\\circ $$, then $$\\angle 3=$$$${}^\\circ $$. question_1022-image_0"}, {"key": "1023", "content": "Using a magnifying glass with 10 times magnification to look at an angle of $$30{}^\\circ$$, the angle seen is ( )."}, {"key": "1024", "content": "Tiantian is $$4$$ years old this year, and her elder sister's age is twice that of Tiantian's this year. $$4$$ years later, the elder sister will be older than Tiantian by years."}, {"key": "1025", "content": "Keke is $$10$$ years old this year, Linlin is $$15$$ years old this year. How many years younger is Keke compared to Linlin? $$20$$ years later, how many years younger will Keke be compared to Linlin?"}, {"key": "1026", "content": "As shown in the figure: $$6$$ cabbages $$=$$ carrots.\n question_1026-image_0"}, {"key": "1027", "content": "The weight of $$2$$ rabbits equals the weight of $$6$$ chicks, the weight of $$3$$ kangaroos is equal to the weight of $$4$$ rabbits, then the weight of $$1$$ kangaroo is equal to the weight of how many chicks."}, {"key": "1028", "content": "(1) When $$a=3$$, $$4a+3=$$;\n(2) When $$m=2$$, $$6+6m=$$."}, {"key": "1029", "content": "The elder sister is $$4$$ years older than the younger sister, when the sum of their ages is $$50$$ years, how old is the younger sister?"}, {"key": "1030", "content": "This year, Dad's age is $$5$$ times that of Wei'er. $$1$$ year later, Dad and Wei'er have a total age of $$50$$ years. Dad's age this year is ."}, {"key": "1031", "content": "This year, Teacher Song's age is 6 times that of Li Lei. In 5 years, the sum of their ages will be 45 years. Li Lei's age this year is ____. "}, {"key": "1032", "content": "This year, the sister is $$13$$ years old, and the brother is $$10$$ years old. When the sum of their ages reaches $$101$$ years old, the sister will be, and the brother will be years old."}, {"key": "1033", "content": "The uncle is $$20$$ years older than Xiao Lin, next year uncle's age will be $$3$$ times that of Xiao Lin. Xiao Lin's age this year is ___."}, {"key": "1034", "content": "The sister is $$10$$ years old this year, and the brother is $$5$$ years old this year. When the sum of their ages is $$35$$ years, the sister is __ years old, and the brother is __ years old. ( )"}, {"key": "1035", "content": "Xiaofang is $$12$$ years younger than her elder sister. This year, the age of the elder sister is exactly $$3$$ times that of Xiaofang. The elder sister is ( ) years old this year."}, {"key": "1036", "content": "This year, mom is $$35$$ years old, son is $$9$$ years old, then $$3$$ years later, the difference in their ages is ( )."}, {"key": "1037", "content": "Which of the following equations is correct ( )."}, {"key": "1038", "content": "Among the following equations, the multiplication sign can be omitted in ( )."}, {"key": "1039", "content": "As shown in the figure, $$\\angle 1=30^\\circ $$, then $$\\angle 2=$$$$^\\circ $$.\n question_1039-image_0"}, {"key": "1040", "content": "Honghong has $$a$$ extracurricular books, Liangliang has $$5$$ fewer books than Honghong, Liangliang has books, together they have books."}, {"key": "1041", "content": "Li Ming has $$m$$ stamps, Wang Hua has $$30$$ less than $$4$$ times the number of stamps Li Ming has, Wang Hua has stamps, if Li Ming has $$100$$ stamps, then Wang Hua has stamps."}, {"key": "1042", "content": "The price of each table is $$m$$ yuan, and the price of each chair is $$n$$ yuan. The cost for buying $$50$$ sets of tables and chairs is ( ) yuan."}, {"key": "1043", "content": "The final result of simplifying the following expression is ( ).\n$$a\\times2+3\\times(a+b)=$$"}, {"key": "1044", "content": "Eddy has $$a$$ lollipops, Da Kuan has $$2$$ times more than Eddy plus $$3$$ more, Da Kuan has ( ) lollipops."}, {"key": "1045", "content": "Given an arithmetic sequence $$9$$, $$13$$, $$17$$, $$21$$, $$25$$, $$\\dots$$, $$93$$ is the nth term."}, {"key": "1046", "content": "$$3$$, $$6$$, $$9$$, $$12$$, \u2026 the 10th number in this sequence is."}, {"key": "1047", "content": "Calculate: $$105+107$$+$$\\cdots $$+$$115+117$$=\uff0e"}, {"key": "1048", "content": "Arithmetic sequence: $$2$$, $$8$$, $$14$$, $$20$$, $$\\cdots $$, $$80$$, this sequence has a total of numbers."}, {"key": "1049", "content": "Starting from $$1$$, adding up $$24$$ consecutive natural numbers: $$1+2+3+4+5+\\cdots +24=$$."}, {"key": "1050", "content": "$$6+10+14+\\cdots +50+54$$=\uff0e"}, {"key": "1051", "content": "Arithmetic sequence sum: $$12+16+20+24+28+32+36+40=$$."}, {"key": "1052", "content": "The 15th number in the arithmetic sequence $$3$$, $$13$$, $$23$$, $$33$$, $$\\cdots$$ is."}, {"key": "1053", "content": "Arithmetic sequence $$8$$, $$11$$, $$14$$, $$17$$, $$\\cdots$$, among which $$41$$ is the -th number of this sequence."}, {"key": "1054", "content": "The solid square formation of Class 3, Grade 3, has a total of $$56$$ people on the outermost layer. (1) People per side on the outermost layer; (2) The total number of people in this square formation."}, {"key": "1055", "content": "Wei Er wants to go from home to the dessert shop, there are a total of ( ) different shortest routes.\n question_1055-image_0"}, {"key": "1056", "content": "Eddie wants to go from place $$A$$ to place $$B$$ along a line segment, there are ( ) different shortest routes.\n question_1056-image_0"}, {"key": "1057", "content": "The phrase \u201c\u5b66\u800c\u601d\u201d in the figure below has different ways to go from \u201c\u5b66\u201d to \u201c\u601d\u201d. question_1057-image_0"}, {"key": "1058", "content": "Fill in the appropriate operator symbols and parentheses on the left side of the equation below, the option that makes the equation hold is ( ). $$8\\;\\;\\;\\;\\;\\;\\;\\;1\\;\\;\\;\\;\\;\\;\\;\\;5=35$$"}, {"key": "1059", "content": "Tian Tian goes from point $$A$$ at home to point $$B$$ at the school, but must pass through point $$C$$ at Niu Niu\u2019s house on the way, the different shortest routes in total are ___\uff0e question_1059-image_0"}, {"key": "1060", "content": "A basket of strawberries is shared among $$10$$ children. If each person gets $$2$$ strawberries, there are $$10$$ left over. How many strawberries are there in total?"}, {"key": "1061", "content": "Xiao Zhang went to buy pencils with $$48$$ yuan, each pencil costs $$5$$ yuan, Xiao Zhang can buy at most pencils, and still have yuan left."}, {"key": "1062", "content": "A kindergarten teacher distributed fruits to the children, if each child gets $$3$$ there remain $$10$$, if each gets $$5$$ there remain $$2$$. How many children are there?"}, {"key": "1063", "content": "The teacher of Class 2, Grade 3, distributes notebooks to the students. If each student is given $$2$$ notebooks, there are still $$10$$ notebooks short; if each student is given $$1$$ notebook, there are still $$2$$ notebooks short. There are a total of students, and a total of notebooks."}, {"key": "1064", "content": "Squirrel mom gives pine nuts to the little squirrels. Each little squirrel gets 4 plus an extra 6, but if each little squirrel gets 6, they would be short by 4. How many little squirrels are there, and how many pine nuts do they have?"}, {"key": "1065", "content": "The teacher distributes some pencils to the children. If each child gets 8 pencils, there are 23 pencils short; if each child gets 5 pencils, there are 5 pencils short. There are a total of pencils."}, {"key": "1066", "content": "Divide a plate of strawberries among the children. If each child gets $$2$$ then there are $$12$$ left; if each child gets $$5$$ then there are $$6$$ short. This plate of strawberries has $$.$$ pieces."}, {"key": "1067", "content": "The product of two natural numbers is $$25$$. There are a total of different situations. (The order of the two numbers is not considered)"}, {"key": "1068", "content": "There are $$2$$ natural numbers whose product is $$8$$. There are a total of different situations for these two numbers. (Without considering the order of the two numbers)"}, {"key": "1069", "content": "Dividing $$3$$ identical apples into two piles, there are different methods of division."}, {"key": "1070", "content": "There are $7$ identical cakes placed into $3$ identical plates, with at least one cake on each plate. There are a total of different methods to do this"}, {"key": "1071", "content": "Dividing a total of $$17$$ candies between Pingping and Longlong with each getting no more than $$10$$ candies, there are a total of different methods."}, {"key": "1072", "content": "Split $13$ into two different non-zero integers, there are several different ways."}, {"key": "1073", "content": "Dakuan, Eddie, and Vi collectively have $$5$$ extracurricular books, with each person having at least one book. There are a total of different situations."}, {"key": "1074", "content": "Place $$7$$ identical balls into $$3$$ different plates, with at least one ball in each plate, there are several ways to do this."}, {"key": "1075", "content": "$$22\\times 84+42\\times 156=$$"}, {"key": "1076", "content": "Calculate: $$97\\times 22+97\\times 78=$$."}, {"key": "1077", "content": "Calculate: $$117-81+83-19=$$\uff0e"}, {"key": "1078", "content": "Compute: $$6\\times 87+2\\times 39=$$."}, {"key": "1079", "content": "Calculate: $$35\\times 20+35\\times 82=$$\uff0e"}, {"key": "1080", "content": "Teacher Lele from $$A$$ to $$B$$, the total number of shortest routes is ( ).\n question_1080-image_0"}, {"key": "1081", "content": "Insert arithmetic operators or parentheses between the two adjacent numbers in the equation below, which of the following options makes the equation correct ( ).\n$$4$$ $$5$$ $$3$$$$=$$$$2$$ $$1$$"}, {"key": "1082", "content": "If each bench seats $$8$$ people, then there are $$50$$ people without seats; if each bench seats 12 people, then there are $$10$$ seats left empty. If each bench seats $$7$$ people, how many students are left without seats?"}, {"key": "1083", "content": "Divide $$6$$ identical glass balls into $$2$$ piles, there are a total of ( ) different ways."}, {"key": "1084", "content": "How many ways can $$9$$ balls be divided into three piles?"}, {"key": "1085", "content": "Calculate: $$33\\times 67+67\\times 76+67\\times 91$$\uff0e"}, {"key": "1086", "content": "Calculate: $$853-148-53-52$$"}, {"key": "1087", "content": "The doctor wants to go from home to the library to borrow books, there are a total of ( ) different shortest routes.\n question_1087-image_0"}, {"key": "1088", "content": "Monkeys participate in a banana eating contest. Initially, the zookeeper prepared some bananas. If each monkey is given $$5$$ bananas, there are $$20$$ bananas left. If each monkey is given $$4$$ more bananas, there would be a shortage of $$16$$ bananas. How many bananas did the zookeeper initially prepare?"}, {"key": "1089", "content": "The perimeter of the rectangle below is.\n question_1089-image_0"}, {"key": "1090", "content": "In the figure below, adjacent sides are perpendicular to each other, therefore the perimeter of this shape is.\n question_1090-image_0"}, {"key": "1091", "content": "The perimeter of a rectangle is $$20$$ cm, the possible length and width of this rectangle are ( )."}, {"key": "1092", "content": "The school bought a total of $$240$$ table tennis balls and badminton shuttlecocks, with the number of table tennis balls being $$3$$ times the number of shuttlecocks. How many table tennis balls and shuttlecocks were bought respectively? ( )"}, {"key": "1093", "content": "Car A and Car B originally had a total of 43 passengers. After reaching a certain location, 5 passengers got off Car A, and 2 passengers got on Car B. At this time, the number of passengers in Car A was exactly 3 times the number of passengers in Car B. The original number of passengers in Car B; the original number of passengers in Car A. question_1093-image_0"}, {"key": "1094", "content": "Xiao Ming and his dad both have some marbles. After Xiao Ming gives his dad $$4$$ marbles, Xiao Ming ends up having $$2$$ fewer marbles than his dad. How many more marbles did Xiao Ming originally have than his dad?"}, {"key": "1095", "content": "There are two shelves of books, totaling $$180$$ books. After removing $$30$$ books from the second shelf, the books on the second shelf are twice the number of the books on the first shelf. Thus, the first shelf has ( ) books."}, {"key": "1096", "content": "The number of people in Class B is exactly $$4$$ times that of Class A. If $$30$$ people were transferred from Class B to Class A, then the number of people in both Class A and Class B would be the same. The original number of people in Class B is ____ people."}, {"key": "1097", "content": "Eddie goes out to eat, choosing a set meal that includes one burger and one drink. Given that the fast food restaurant has $$2$$ types of burgers and $$3$$ types of drinks, Eddie has several choices."}, {"key": "1098", "content": "There are $$2$$ different kinds of fruit candies, $$3$$ different kinds of chocolate candies, $$4$$ different kinds of lollipops in the store. Xiao Ming wants to buy one type of candy for his friend, so he has different choices."}, {"key": "1099", "content": "Weiwei is going to the clothing store to buy clothes. It is known that one top and one pair of pants make a set. Weiwei has several different combinations.\n question_1099-image_0"}, {"key": "1100", "content": "The amount of apples in basket A is $$7$$ times the amount of apples in basket B. If $$24$$ apples are taken from basket A and put into basket B, then the two baskets will have the same amount of apples. How many apples were originally in basket B?"}, {"key": "1101", "content": "Xiaoqing and Dapeng originally had $$32$$ pieces of chocolate together. After Xiaoqing gave $$4$$ pieces to Dapeng, Dapeng's amount of chocolate was three times that of Xiaoqing's. Xiaoqing now has pieces of chocolate."}, {"key": "1102", "content": "Both sister and younger sister have some hairpins. After the elder sister gave the younger sister $$6$$ hairpins, she still had $$3$$ more than the younger sister. How many more hairpins did the elder sister originally have than the younger sister?"}, {"key": "1103", "content": "In the sports meeting, athletes A, B, C, and D $$4$$ form a team to participate in the relay race. (1) If A must run the first leg, how many different starting orders are there in total? (2) If A cannot run the first leg, how many different starting orders are there in total?"}, {"key": "1104", "content": "The school bought a total of $$520$$ ping-pong balls and badminton shuttlecocks. After taking away $$20$$ ping-pong balls, the number of ping-pong balls was $$4$$ times the number of badminton shuttlecocks. The number of ping-pong balls and badminton shuttlecocks bought were respectively."}, {"key": "1105", "content": "Xiao Hong and Xiao Lan have a total of $$80$$ stamps. If Xiao Hong adds another $$10$$ stamps and Xiao Lan uses $$6$$ stamps, then Xiao Hong's number of stamps will be three times as many as Xiao Lan's. Xiao Hong originally had $$ stamps."}, {"key": "1106", "content": "Niu Niu and Zhuang Zhuang each have some apples, and the total number of Niu Niu's apples is exactly three times that of Zhuang Zhuang's. If Niu Niu gives Zhuang Zhuang 20 apples, Niu Niu will only have 10 more apples than Zhuang Zhuang. So, how many apples did Niu Niu and Zhuang Zhuang originally have?"}, {"key": "1107", "content": "How many total paths can Wei choose from the library to the park? \nquestion_1107-image_0"}, {"key": "1108", "content": "At the sports meeting, four athletes, A, B, C, and D, form a team to participate in the relay race. How many different sequences can the 4 people appear in? ( )"}, {"key": "1109", "content": "There are $$2$$ kinds of chocolate candies in the store: milk flavor, hazelnut flavor; there are $$3$$ kinds of fruit candies: apple flavor, pear flavor, orange flavor. Xiao Ming wants to buy some candies for his little friends.\n($$1$$) If Xiao Ming only buys one kind of candy, how many choices does he have?\n($$2$$) If Xiao Ming wants to buy one kind of fruit candy and one kind of chocolate candy, how many choices does he have?"}, {"key": "1110", "content": "Jojo wants to leave home, first go to Meimei's house, and then go to school with Meimei. So, Jojo has a total of several different routes to choose from school.\n question_1110-image_0"}, {"key": "1111", "content": "\nMeal Requirements: Each set meal must include one meat dish and one vegetarian dish, plus a beverage.\nMeat dishes: Braised Belt Fish, Boiled Pork Slices\nVegetarian dishes: Braised Eggplant, Pine Nut Corn\nBeverages: Orange Juice, Cola\nThere are different methods of meal pairing."}, {"key": "1112", "content": "Chicks, ducklings, and puppies line up to take a photo, there are a total of different ways to stand.\n question_1112-image_0"}, {"key": "1113", "content": "As shown in the figure, the two diagonals of quadrilateral $$ABCD$$ are perpendicular to each other. It is known that: $$AC=6$$, $$BD=9$$. Therefore, the area of the quadrilateral $$ABCD$$ is. question_1113-image_0"}, {"key": "1114", "content": "As shown in the diagram, a rectangle is divided into four smaller rectangles by two lines, among which three have areas of $$5$$ square centimeters, $$9$$ square centimeters, and $$10$$ square centimeters, respectively. Then, the area of the shaded rectangle is square centimeters. question_1114-image_0"}, {"key": "1115", "content": "As shown in the square $$ABCD$$, the length of the diagonal is $$4$$ cm. Then, the area of the square is square centimeters. question_1115-image_0"}, {"key": "1116", "content": "As shown in the diagram, in the square $$ABCD$$, the length of diagonal $$AC$$ is $$20$$ cm. Then, the area of the square is square centimeters. question_1116-image_0"}, {"key": "1117", "content": "Complete the following fill-in-the-blank:\n$$21\\div 5=\\square \\cdots \\cdots \\square $$\nFill in the boxes in order,\uff0e"}, {"key": "1118", "content": "Let's calculate, in the equation below what the divisor should be.\n$$17\\div \\square=4\\cdots \\cdots 1$$"}, {"key": "1119", "content": "In a division equation, the quotient is $$6$$, the remainder is $$7$$, the minimum possible divisor is ( )."}, {"key": "1120", "content": "When two numbers are divided, the quotient is $$4$$ with a remainder of $$8$$. The sum of the dividend, divisor, quotient, and remainder equals $$415$$.\n\u2460The sum of the dividend and divisor is.\n\u2461The dividend is how many times the divisor plus.\n\u2462The dividend is."}, {"key": "1121", "content": "Dividing two numbers, the quotient is $$30$$, and the remainder is $$14$$. The smallest possible dividend is."}, {"key": "1122", "content": "If a number is divided by $$11$$ and the quotient is $$4$$ with a remainder of $$5$$, then this number is."}, {"key": "1123", "content": "$$95\\div$$$$=8\\cdots \\cdots 7$$"}, {"key": "1124", "content": "In a division equation, the remainder is $$8$$, and the quotient is $$4$$. The minimum dividend is."}, {"key": "1125", "content": "When dividing two numbers, the quotient is $$4$$ with a remainder of $$3$$. If both the dividend and the divisor are multiplied by $$10$$, the result would be ( )."}, {"key": "1126", "content": "The road ahead will soon pass through a tunnel, where speed will be measured over a distance, with a speed limit of $$60$$ kilometers per hour (equivalent to $$1000$$ meters per minute). The total distance for speed measurement is $$4500$$ meters, and it took the doctor $$5$$ minutes to drive through. Did the doctor's car exceed the speed limit? question_1126-image_0 question_1126-image_1"}, {"key": "1127", "content": "A and B are $$3000$$ meters apart, and the doctor plans to cycle from A to B in $$20$$ minutes. Just as he was about to leave, the bicycle broke down, delaying him by $$5$$ minutes. The doctor hopes to arrive at B at the originally planned time. (1) What is the doctor's cycling time in minutes? (2) How many meters should the doctor cycle per minute?"}, {"key": "1128", "content": "Locations A and B are $$240$$ kilometers apart, and a car originally planned to travel from A to B in $$6$$ hours. (1) It takes hours to travel half the distance. (2) In reality, the car broke down after traveling half the distance and was stalled for $$1$$ hour. To arrive at location B as originally planned, how many kilometers per hour must the car travel in the second half of the journey?"}, {"key": "1129", "content": "Mom adds a lace around the edge of a tablecloth, the length of this lace refers to the ( ) of this tablecloth."}, {"key": "1130", "content": "Shapes without a perimeter are ( )."}, {"key": "1131", "content": "The right figure is composed of squares with a side length of $$1$$ cm each, comparing the perimeter of figures A and B, the result is ( ) .\n question_1131-image_0"}, {"key": "1132", "content": "Using the numbers $$1$$, $$3$$, $$5$$, different natural numbers without repeating digits can be formed."}, {"key": "1133", "content": "Calculate: $$12\\div \\left( 3\\div 2 \\right)\\times \\left( 6\\div 7 \\right)\\div \\left( 8\\div 7\\div 5\\times 2 \\right)\\div \\left( 5-2 \\right)=$$."}, {"key": "1134", "content": "A string of colored lights is arranged in the following pattern: red, yellow, yellow, blue, blue, green, red, yellow, yellow, blue, blue, green, red, yellow, yellow, blue, blue, green... Among the statements about the color of the 65th light, the correct one is ()."}, {"key": "1135", "content": "$$6$$ students form a circle to play a game of passing a handkerchief. At the start, the handkerchief is with student number $$1$$, and after being passed clockwise $$62$$ times, the handkerchief is passed to the hands of student number. question_1135-image_0"}, {"key": "1136", "content": "To supplement nutrition for the children, the school has prepared three types of fruits: apples, grapes, and oranges. The principal plans to distribute one type of fruit each day, ensuring that the same type of fruit is not distributed on two consecutive days. If the plan is to distribute apples on both next Monday and Friday, then for these consecutive five days, the principal has a total number of different fruit distribution plans."}, {"key": "1137", "content": "Use the numbers $$1$$ to $$5$$ to form some six-digit numbers, where the difference between any two adjacent digits is $$1$$. The number of such six-digit numbers is . (Not every digit must appear)"}, {"key": "1138", "content": "As shown in the figure, walk from the starting point to the end point along the line, and it is required to collect the flags on each station, with each station being passed only once. There are several different ways to do this.\n question_1138-image_0"}, {"key": "1139", "content": "Write three integers on the blackboard, then erase one and replace it with the sum of the remaining two. Continue this operation until you get $$88$$, $$66$$, $$99$$. Can the original three integers be $$1$$, $$3$$, $$5$$?"}, {"key": "1140", "content": "Xiaoyong's family has $$24$$ more white rabbits than black rabbits. The quantity of white rabbits is $$4$$ times that of black rabbits. How many white rabbits does Xiaoyong's family have?"}, {"key": "1141", "content": "Eddie and Dodo were practicing running on the playground. After some time, Eddie ran $$80$$ meters more than 3 times the distance Dodo ran. If Dodo ran $$500$$ meters less than Eddie, how many meters did Dodo and Eddie run together?"}, {"key": "1142", "content": "There are two shelves, originally having the same number of books. Now, taking $$10$$ books from the upper shelf and $$30$$ books from the lower shelf, the number of books on the upper shelf is $$2$$ times the number of books on the lower shelf. How many books were there originally on the lower shelf?"}, {"key": "1143", "content": "The number of storybooks in the library is $$50$$ more than the comic books, and the total number of storybooks is $$3$$ times that of comic books. Then, there are ______ storybooks and ______ comic books."}, {"key": "1144", "content": "$$2016$$ year $$1$$ month $$1$$ day is Friday, $$2018$$ year $$1$$ month $$1$$ day is Monday."}, {"key": "1145", "content": "$$2017$$ year $$10$$ month $$1$$ day is Sunday, $$2017$$ year $$10$$ month $$30$$ day is the weekday ( )."}, {"key": "1146", "content": "November 11, 2016 is a Friday, then what day of the week is December 31 of the same year? ()"}, {"key": "1147", "content": "The doctor's birthday is on October 22nd. Knowing that September 1st, 2019 is a Sunday, what day of the week is the doctor's birthday in 2019? (Fill in the number)"}, {"key": "1148", "content": "In a certain year, February has $$5$$ Fridays, then January $$31$$ of that year is on a Thursday."}, {"key": "1149", "content": "May 29, 2015 was a Friday, 5 days later it will be Wednesday ( )."}, {"key": "1150", "content": "$$2018$$ year's $$1$$st of January is Monday, so what day of the week is $$2019$$ year's $$1$$st of January?\n question_1150-image_0"}, {"key": "1151", "content": "Adding together the weekdays of every day in February of a certain year, the sum is $$115$$. The February 1st of this year is a weekday."}, {"key": "1152", "content": "Eddie and Dengdeng were practicing running on the playground. After some time, Eddie ran a distance that was twice as much as Dengdeng's plus 10 meters. If Eddie ran 110 meters more than Dengdeng, Dengdeng ran meters, Eddie ran meters."}, {"key": "1153", "content": "In the library, there are $$150$$ more science and technology books than comic books, and the number of science and technology books is $$4$$ times the number of comic books minus $$30$$ books, with a number of books for science and technology books, and a number of books for comic books."}, {"key": "1154", "content": "In the Asian Cup final, the number of Chinese journalists was $$3$$ times the number of foreign journalists. After the match ended, $$180$$ Chinese journalists left the venue, and $$40$$ foreign journalists left the venue. The remaining number of Chinese and foreign journalists was equal. Originally, there were people among Chinese journalists, and people among foreign journalists."}, {"key": "1155", "content": "In the orchard, there are $$270$$ more pear trees than apple trees, and the number of pear trees is exactly $$6$$ times the number of apple trees. There are currently pear trees in the orchard."}, {"key": "1156", "content": "Eddy's pocket money is $$2$$ times that of Dakuang, and Vi's pocket money is $$5$$ times that of Dakuang, and Vi's pocket money is $$24$$ yuan more than Eddy's, then Eddy's pocket money is yuan, and Vi's pocket money is yuan."}, {"key": "1157", "content": "Two ropes of the same length, the first one is cut by $$31$$ meters, and the second one is cut by $$19$$ meters, the remaining length of the second rope is $$4$$ times that of the first one, the original length of both ropes in meters."}, {"key": "1158", "content": "There are two strips of paper, one is $$13$$ cm long and the other is $$5$$ cm long. After cutting the same segment from both strips, the remaining length of the longer strip is $$3$$ times the remaining length of the shorter strip. The length of the cut segment is in cm."}, {"key": "1159", "content": "The number of students in grade five of a certain school is 154 fewer than that in grade six. If 46 more students transfer to grade six, then the number of students in grade six will be 3 times that of grade five. Originally, there were people in grade five and people in grade six."}, {"key": "1160", "content": "There are a total of $$160$$ red and white balloons in the square. Eddie, who is very attentive, discovers that the number of red balloons is exactly $$3$$ times the number of white balloons. So, there are red balloons and white balloons."}, {"key": "1161", "content": "Xiao Hong and her sister have a total of $$22$$ years this year, and the sister is $$2$$ years younger than twice the age of Xiao Hong. So, the sister is $$14$$ years old this year, and Xiao Hong is $$8$$ years old."}, {"key": "1162", "content": "The little white rabbit and the little gray rabbit have a total of $$50$$ carrots, and the little gray rabbit has $$5$$ times more carrots than the little white rabbit plus $$2$$ more. The little white rabbit has carrots, and the little gray rabbit has carrots."}, {"key": "1163", "content": "In the unfinished magic square below, the magic sum is. question_1163-image_0"}, {"key": "1164", "content": "The figure below is part of a 3x3 order magic square, $$\\rm X=$$\uff0e question_1164-image_0"}, {"key": "1165", "content": "As shown in the diagram, each of the nine small squares contains a two-digit number, and the sum of the three integers in every row, every column, and the two diagonals are equal. Then the value of $$X$$ is.\n question_1165-image_0"}, {"key": "1166", "content": "In the third-order magic square below, two numbers $$97$$ and $$17$$ have already been filled in. Try to find the number represented by $$a$$.\n question_1166-image_0"}, {"key": "1167", "content": "Fill in the squares below with the appropriate numbers so that the sum of the three numbers in every horizontal row, vertical column, and diagonal line is equal. Then, the number filled in the shaded square in the diagram is.\n question_1167-image_0"}, {"key": "1168", "content": "Please complete the following magic square, the cell at the far right of the third row should be filled with .\n question_1168-image_0"}, {"key": "1169", "content": "In the following $$4\\times 4$$ magic square, fill in the missing numbers so that the sum of the four numbers in each row, each column, and each diagonal line is equal. The second in the first row is, the first in the second row is, the third in the second row is, the third in the third row is, the fourth in the third row is, the second in the fourth row is, the third in the fourth row is. question_1169-image_0"}, {"key": "1170", "content": "Fill in the appropriate numbers at $$A$$, $$B$$, $$C$$, $$D$$ in the diagram below to make it a third-order magic square. $$A=$$, $$B=$$, $$C=$$, $$D=$$. question_1170-image_0"}, {"key": "1171", "content": "$$2020$$ year $$1$$ month $$10$$ day is Friday, so $$1$$ month $$31$$ day is a week ( )."}, {"key": "1172", "content": "In Disneyland, Donald Duck and Mickey Mouse ran together, with Donald Duck running $$300$$ meters more than Mickey Mouse. The distance Donald Duck ran is $$5$$ times the distance that Mickey Mouse ran plus an extra $$20$$ meters. How far did Mickey Mouse run in meters?"}, {"key": "1173", "content": "The number of technology-related books in the library is $$240$$ books less than the number of literature books, the number of literature books is $$4$$ times the number of technology books, the number of technology books is\uff0e"}, {"key": "1174", "content": "$$2019$$ year $$3$$ month $$1$$ day is Friday, then the $$3$$ month $$30$$ day of that year is Saturday."}, {"key": "1175", "content": "The school plans to plant a total of $$300$$ trees, including poplars, willows, and locust trees. The number of poplar trees is $$3$$ times that of willow trees, and the number of locust trees is $$2$$ times that of willow trees. So, the total number of willow trees, poplar trees, and locust trees to be planted are, respectively,"}, {"key": "1176", "content": "Huaneng Cable Factory has a total of $$464$$ employees, among which the number of female employees is $$3$$ times the number of male employees. There are male employees and female employees."}, {"key": "1177", "content": "Eddie and Vi have some balloons. Eddie has $$60$$ more balloons than Vi, and the number of Eddie's balloons is $$4$$ times that of Vi's minus $$9$$. Calculate how many balloons Vi has; Eddie has."}, {"key": "1178", "content": "Xuexue and Sisi together have $$60$$ candies, Xuexue has $$3$$ times plus $$4$$ candies more than Sisi, how many candies does Sisi have."}, {"key": "1179", "content": "December 31, 2010, was a Friday, and December 31, 2011, was a Saturday ( )."}, {"key": "1180", "content": "$$2018$$ year $$4$$ month $$20$$ day is Friday, $$2018$$ year $$5$$ month $$19$$ day is a week."}, {"key": "1181", "content": "Below is the statistical table of call counts for the four branches and headquarters in each quarter of $$2015$$:\n\n\n\nFirst Quarter Call Count Statistics\n\n\nBranch\nTeaching\nFinance\nResearch and Development\nMarketing\n\n\nCount\n$45$\n$85$\n$70$\n$75$\n\n\n\n\n\n\n\n\n\n\n\n\nSecond Quarter Call Count Statistics\n\n\nBranch\nTeaching\nFinance\nResearch and Development\nMarketing\n\n\nCount\n$20$\n$35$\n$90$\n$80$\n\n\n\n\n\n\n\n\n\n\n\n\nThird Quarter Call Count Statistics\n\n\nBranch\nTeaching\nFinance\nResearch and Development\nMarketing\n\n\nCount\n$35$\n$45$\n$80$\n$75$\n\n\n\n\n\n\n\n\n\n\n\n\nFourth Quarter Call Count Statistics\n\n\nBranch\nTeaching\nFinance\nResearch and Development\nMarketing\n\n\nCount\n$65$\n$50$\n$75$\n$65$\n\n\n\nCan you organize them into a table.\n\n\n\nCall Count Summary for $$2015$$\n\n\nBranch\nTeaching\nFinance\nResearch and Development\nMarketing\nTotal\n\n\nFirst Quarter\n\n\n\n\n\n\n\n\nSecond Quarter\n\n\n\n\n\n\n\nThird Quarter\n\n\n\n\n\n\n\nFourth Quarter\n\n\n\n\n\n\n\nTotal"}, {"key": "1182", "content": "A field is $$10$$ meters long and $$5$$ meters wide. After expansion, its length increased by $$5$$ meters and its width by $$2$$ meters. Calculate the increase in the area of this field in square meters."}, {"key": "1183", "content": "The side length of the square is $$10$$ cm, the area of this square is square centimeters.\nThe length of the rectangle is $$10$$ cm, and the width is $$7$$ cm, the area of this rectangle is square centimeters."}, {"key": "1184", "content": "The perimeter of the rectangle is $$50$$ meters, and the length is $$20$$ meters, so the width of the rectangle is meters, and the area of the rectangle is square meters."}, {"key": "1185", "content": "Calculate: $$(96\\div 8)\\times (8\\div 4)\\times (4\\div 1)=$$."}, {"key": "1186", "content": "Calculate: $$6000\\div 2\\div 25\\div3 =$$"}, {"key": "1187", "content": "The area of a rectangle is $$132$$ square meters, and the width is $$6$$ meters, so the length is meters."}, {"key": "1188", "content": "Calculate: $$21\\times 32+21\\times 69-21=$$."}, {"key": "1189", "content": "Calculate: $$408\\times 25=$$"}, {"key": "1190", "content": "Calculate: $$\\left( 64+88+56 \\right)\\div 8$$=\uff0e"}, {"key": "1191", "content": "Calculate: $$31\\times 99=$$."}, {"key": "1192", "content": "Visitors are walking on the forest path as shown in the figure below. The numbers indicate the length of the path (unit: kilometers). Is it possible to walk all the paths without repeating and return to the starting point? If not, what kind of route should be chosen to make the entire journey the shortest? What is the shortest distance in kilometers? question_1192-image_0"}, {"key": "1193", "content": "A city's street map is made up of rectangles, as shown in the figure. A police officer must start from point $$A$$, patrol and pass each road section at least once before returning to point $$A$$. What is the minimum distance in meters he must walk. question_1193-image_0"}, {"key": "1194", "content": "As shown in the diagram, there are two islands at the confluence of two rivers, connected by seven bridges to each other and to the riverbanks. Question: Can a walker (can, cannot) walk all seven bridges once without repetition. question_1194-image_0 \u200b"}, {"key": "1195", "content": "Among the following figures, the one that cannot be drawn with a single line is ( )."}, {"key": "1196", "content": "In each of the figures below, what is the minimum number of strokes needed to draw it. question_1196-image_0 \u200b\uff081\uff09\uff082\uff09\uff083\uff09\uff084\uff09"}, {"key": "1197", "content": "The image is the floor plan of a greenhouse, consisting of $$6$$ exhibition rooms, each connected to the next by a door. We also need to add an exit (fill in the letter) so that Eddie can enter from entrance $$A$$, pass through all the doors once without repeating, and finally exit the greenhouse. \n question_1197-image_0"}, {"key": "1198", "content": "As shown in the figure, there are three small islands in the middle of a river, connected by $$5$$ bridges. Can a path be found that traverses all the bridges without repetition? question_1198-image_0"}, {"key": "1199", "content": "The following figure is a statistical graph of the number of tourists in a scenic area in $$2016$$. The incorrect information obtained from the graph is ( ).\n question_1199-image_0"}, {"key": "1200", "content": "The image below is a part of a third-order magic square, $$\\rm X=$$\uff0e question_1200-image_0"}, {"key": "1201", "content": "The image below is a part of a third-order magic square, $$A=$$.\n question_1201-image_0"}, {"key": "1202", "content": "The figure below has an odd number of points, so at least one line needs to be removed to make it drawable in one stroke. question_1202-image_0"}, {"key": "1203", "content": "Can the following figure be drawn in one stroke? Please select ( ).\n question_1203-image_0"}, {"key": "1204", "content": "Aunt Li accidentally dirtied the shopping receipt. Can you help her calculate the unit price of the volleyballs? Item Name Unit Price/Yuan Quantity/Units Total Price/Yuan Basketball $$57$$$$1$$$$145$$ Volleyball $$4$$"}, {"key": "1205", "content": "In the unfinished magic square below, the magic sum is.\n question_1205-image_0"}, {"key": "1206", "content": "Observe the figure below, the correct statements are ( ) sentences.\n\u2460 The vertical axis represents the average lifespan, the horizontal axis represents the animal species.\n\u2461 $$1$$ grid represents $$10$$ years.\n\u2462 The average lifespan of an elephant is $$70$$ years.\n\u2463 The average lifespan of a hippopotamus is $$4$$ times that of a dog.\n question_1206-image_0"}, {"key": "1207", "content": "Among the students in class 1 of grade 4, there are $$23$$ people who like to eat grapes, $$27$$ people who like to eat strawberries, $$19$$ people who like both, and $$6$$ people who don't like either. There are a total of people in class 1 of grade 4."}, {"key": "1208", "content": "A class consists of $$46$$ students, $$12$$ of whom are in the art group, and $$23$$ are in the music group. There are $$5$$ students who have joined both groups. There are students in the class who have not joined either the art group or the music group."}, {"key": "1209", "content": "There are $$35$$ students in Class 2 of Grade 6 at Guangming Primary School, among which $$20$$ students participated in the math activity group, $$11$$ students participated in both the writing group and the math activity group, $$10$$ students did not participate in any groups, some students participated in the writing group."}, {"key": "1210", "content": "Among all natural numbers from $$1\\sim 100$$, the number of numbers that are neither multiples of $$3$$ nor multiples of $$5$$ is."}, {"key": "1211", "content": "Among the students from four Grade 3 classes who registered for the sports meet, there are $$74$$ students not from Class 1, $$92$$ students not from Class 4, and a total of $$46$$ students from Class 2 and Class 3 registered. The total number of Grade 3 students participating in the competition is ."}, {"key": "1212", "content": "Among the natural numbers from $$1\\sim 90$$, there are some that are neither multiples of $$3$$ nor $$5$$."}, {"key": "1213", "content": "$$\\text{X}$$ Special Team has $$25$$ members, each person knows at least one of the skills: invisibility or shape-shifting, with $$14$$ people knowing how to become invisible, and $$18$$ people knowing how to shape-shift. There are people who know both skills."}, {"key": "1214", "content": "$$A$$, $$B$$, and $$C$$ each had a different number of bricks. $$A$$ gave away some of his bricks to $$B$$ and $$C$$, causing the number of bricks each of them had to double. Then, $$B$$ also gave away some of his bricks to $$A$$ and $$C$$, causing the number of bricks each of them had to double again. Next, $$C$$ also gave away some of his bricks to $$A$$ and $$B$$, causing the number of bricks each of them had to double once more. At this time, all three people had 48 bricks each. $$A$$, $$B$$, and $$C$$ originally had ____ bricks respectively."}, {"key": "1215", "content": "The doctor allocates his monthly salary in the following manner: half of the monthly salary is deposited in the bank, half of the remaining money minus $$300$$ is used to pay the mortgage, and half of the remaining money plus $$300$$ is used for meal expenses, leaving him with $$800$$. What is the doctor's monthly salary in yuan?"}, {"key": "1216", "content": "Xiao Ming paid $$1$$ yuan to enter the first store, and then spent half of the remaining money in the store. When he left the store, he paid another $$1$$ yuan. After that, he paid $$1$$ yuan to enter the second store, spent half of the remaining money in the store, and paid another $$1$$ yuan when leaving the store. Then, he entered the third store in the same way. After leaving the third store, he only had $$1$$ yuan left. He had yuan before entering the first store."}, {"key": "1217", "content": "The yard originally had a certain number of tons of coal. In the first shipment, half of the original coal was shipped out. In the second shipment, 150 tons were shipped in. In the third shipment, 50 tons were shipped out. As a result, there were still 300 tons left. How many tons of coal were there originally in the yard?"}, {"key": "1218", "content": "There is a pile of peaches, the first monkey took away half of them then put back $$1$$ peach; the second monkey took away half of the remaining ones then put back $$1$$ peach; the third monkey took away half of the remaining ones then put back $$1$$ peach$$\\cdots \\cdots $$continuing in this manner, the $$2018$$th monkey took away half of the remaining ones then put back one, leaving $$2$$ peaches. Calculate the original number of peaches."}, {"key": "1219", "content": "There are a total of $$27$$ birds on three trees. $$2$$ birds flew from the first tree to the second tree, $$3$$ birds flew from the second tree to the third tree, and $$4$$ birds flew from the third tree back to the first tree. At this time, the three trees each have the same number of birds. Originally, the first, second, and third trees had __, __, __ birds respectively."}, {"key": "1220", "content": "Xiao Bai and Xiao Hua saw a magical insect, which doubles in size every hour, and can grow to 20cm in 1 day. The time required for the insect to grow to 5cm is __ hours."}, {"key": "1221", "content": "Given $$\\angle 1=28\u00b0$$, then $$\\angle 2=$$\u00b0, $$\\angle 3=$$\u00b0, $$\\angle 4=$$\u00b0, $$\\angle 5=$$\u00b0.\n question_1221-image_0"}, {"key": "1222", "content": "As shown in the figure, $$\\angle AOD=\\angle BOD=\\angle COE=90{}^\\circ $$, $$\\angle 1=38{}^\\circ $$, $$\\angle AOC=$$$${}^\\circ $$.\n question_1222-image_0"}, {"key": "1223", "content": "As shown in the right diagram, the angle formed is ( ).\n question_1223-image_0"}, {"key": "1224", "content": "As shown in the figure, $$\\angle 1=$$, $$\\angle 2=$$.\n question_1224-image_0"}, {"key": "1225", "content": "As shown in the figure, $$\\angle BCE=25{}^\\circ$$, then, $$\\angle DCE$$ is degrees.\n question_1225-image_0"}, {"key": "1226", "content": "Among the four figures below, which one can use $$\\angle 1$$, $$\\angle AOB$$, and $$\\angle O$$ to represent the same angle ( )."}, {"key": "1227", "content": "As shown in the diagram, $$\\angle 2$$ is three times $$\\angle 1$$. Then, the degree of $$\\angle 1$$ is $${}^\\circ $$.\n question_1227-image_0"}, {"key": "1228", "content": "As shown in the figure, it is known that $$OE$$ and $$OF$$ are perpendicular, a straight line $$AB$$ passes through point $$O$$, if $$\\angle EOA=2\\angle AOF$$, then $$\\angle BOF=$$ degrees.\n question_1228-image_0"}, {"key": "1229", "content": "There is a triangle in the figure below. question_1229-image_0"}, {"key": "1230", "content": "Count the number of squares in the picture below.\n question_1230-image_0"}, {"key": "1231", "content": "Count, how many squares are there in the figure below in total.\n question_1231-image_0"}, {"key": "1232", "content": "Count the number of squares in the picture.\n question_1232-image_0"}, {"key": "1233", "content": "As shown in the figure, there are several line segments in total.\n question_1233-image_0"}, {"key": "1234", "content": "The picture contains a total number of squares. \n question_1234-image_0"}, {"key": "1235", "content": "How many squares are there in the picture below?\n question_1235-image_0"}, {"key": "1236", "content": "Count the number of triangles in the following image. question_1236-image_0"}, {"key": "1237", "content": "There is a triangle in the picture.\n question_1237-image_0"}, {"key": "1238", "content": "As shown, there is a rectangle.\n question_1238-image_0"}, {"key": "1239", "content": "The combined age of the siblings this year is $$25$$ years old, the brother is $$3$$ years older than the sister, the brother's age this year is , the sister's age this year is ."}, {"key": "1240", "content": "The sum of the father and son's ages is $$40$$ years. In $$5$$ years, the father's age will be exactly $$4$$ times the son's age. How old is the father this year?"}, {"key": "1241", "content": "In three years, the young elephant will be $$18$$ years old. The adult elephant said to the young elephant: \"When you are as old as I am, I will be $$61$$ years old.\" How old is the adult elephant this year."}, {"key": "1242", "content": "When the mother was as old as the daughter is now, the daughter was $$2$$ years old. When the daughter becomes as old as the mother is now, the mother will be $$59$$ years old. Now the mother's age is years, and the daughter's age is years."}, {"key": "1243", "content": "The total age of dad, mom, grandpa, and Qiangqiang this year is $$146$$ years, and after a year, their total age will be $$170$$ years."}, {"key": "1244", "content": "A family of three, last year the sum of their ages was $$69$$ years. This year, the mother's age is $$4$$ times that of the child, and the father is the same age as the mother. What is the child's age this year?"}, {"key": "1245", "content": "Xiaodi is $$8$$ years old this year, Xiaohua is $$10$$ years old this year. When their combined age is $$30$$ years old, Xiaodi will be $$14$$ years old, Xiaohua will be $$16$$ years old."}, {"key": "1246", "content": "The combined age of mom and dad is $$72$$ years old, and dad is $$6$$ years older than mom. This year mom is years old."}, {"key": "1247", "content": "Solve the equation: $$a+6=19$$, find $$a=$$."}, {"key": "1248", "content": "Find the pattern and fill in the numbers: $$1$$, $$3$$, $$5$$, $$7$$, , ."}, {"key": "1249", "content": "Looking at an acute angle through a magnifying glass, what is seen is ( )."}, {"key": "1250", "content": "Count, in the figure below, how many line segments are there in total.\n question_1250-image_0"}, {"key": "1251", "content": "The angle difference between an obtuse angle and an acute angle is ( )."}, {"key": "1252", "content": "As shown in the figure, it is known that \u22201 = 45\u00b0, find \u22202 = degrees, \u22203 = degrees, \u22204 = degrees.\n question_1252-image_0"}, {"key": "1253", "content": "There are some toys in the toy store, please arrange them in order from cheapest to most expensive, connecting them with a less than symbol. The correct answer is ( )\n question_1253-image_0"}, {"key": "1254", "content": "To enlarge $$29.3$$ by $$100$$ times, just move the decimal point  places. \uff08 \uff09"}, {"key": "1255", "content": "There are ( ) squares in the picture.\n question_1255-image_0"}, {"key": "1256", "content": "Count, how many triangles are there in total in the image below.\n question_1256-image_0"}, {"key": "1257", "content": "The price of a pencil case is 9 dollars and 5 dimes, represented as a decimal in dollars."}, {"key": "1258", "content": "Arithmetic sequence: $$5$$, $$9$$, $$13$$, $$17$$, $$\\cdots$$, the $$21st$$ term is."}, {"key": "1259", "content": "Calculate: $$3+6+9+12+15+18+21+24+27=$$."}, {"key": "1260", "content": "The 'pagoda' in the figure below is made up of equilateral triangles, with different numbers of layers. For example: the first layer has $$1$$ equilateral triangle, the second layer has $$3$$ equilateral triangles, observe carefully and fill in the blanks: (1) The bottom layer of the 'pagoda' with $$10$$ layers contains ____ small triangles. (2) The entire $$10$$-layer 'pagoda' contains a total of ____ small triangles. question_1260-image_0"}, {"key": "1261", "content": "A clock chimes $$1$$ time at $$1$$ o'clock, $$2$$ times at $$2$$ o'clock, $$3$$ times at $$3$$ o'clock, $$\\cdots\\cdots$$, continuing in this manner, from $$1$$ o'clock to $$12$$ o'clock, then starting again from $$1$$ time at $$13$$ o'clock, $$2$$ times at $$14$$ o'clock, $$\\cdots\\cdots$$, like this from $$1$$ o'clock to $$24$$ o'clock, the clock chimes a total of."}, {"key": "1262", "content": "Sum: $$6+14+22+30\\cdots +78+86+94$$=\uff0e"}, {"key": "1263", "content": "For the sequence $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$19$$...$$, the $$10$$th number is, $$49$$ is the $$nth$$ number of this sequence."}, {"key": "1264", "content": "Teacher Si Si gives students cards, on the first day each student gets $$2$$ cards, on the second day each student gets $$5$$ cards, and each day thereafter, each student gets $$3$$ more cards than the previous day. There is one day when Teacher Si Si gives each student $$83$$ cards, so this is the day count since Teacher Si Si started giving out cards."}, {"key": "1265", "content": "During the PE class, the teacher instructed everyone to line up. Eddie stood at the front of the line, and Vi stood at the end of the line. Counting from the front to the end in order, if a total of $$12$$ students counted, and Eddie counted $$3$$, each student counting a number that is $$2$$ more than the previous one, then Vi would count."}, {"key": "1266", "content": "The diagram below has a total of points.\n question_1266-image_0"}, {"key": "1267", "content": "The students arranged themselves into a three-layer hollow square formation, with each side of the outermost layer having $$16$$ people, so the outermost layer has a total of people"}, {"key": "1268", "content": "Third-grade students form a solid square formation for a gymnastics performance, with the number of people on the outermost layer being $$32$$, so each side of this outermost layer of the square has people, and this square formation consists of a total of third-grade students."}, {"key": "1269", "content": "Niu Niu arranged the chess pieces into a solid square matrix, using a total of $$64$$ pieces, with equal numbers of pieces on each side of the outer layer."}, {"key": "1270", "content": "At the sports meet, the teachers formed a solid square formation. It is known that there are $$116$$ people on the outermost layer of the square, with people on each side."}, {"key": "1271", "content": "The volunteers formed a hollow square formation for a group photo, with $$52$$ people on the outermost layer, a total of $$4$$ layers, summing up to a total number of volunteers."}, {"key": "1272", "content": "As the festival approaches, the students arranged a hollow flowerbed on the playground using potted plants, with the outermost layer of each side having $$15$$ pots, totaling $$3$$ layers, using a total of potted plants."}, {"key": "1273", "content": "Eddie is fond of Go, and he arranged the pieces on the Go board to form a two-layer hollow square array, with each side of the outer layer containing $$14$$ pieces, using a total of pieces.\n question_1273-image_0"}, {"key": "1274", "content": "If there are $$100$$ people standing in a solid square formation, then the outermost layer of this formation has a total of people."}, {"key": "1275", "content": "A certain school's fourth-grade students form a solid square formation, with the number of people on the outermost layer being $$40$$ people. There are people on each side of the square's outermost layer. This square formation has a total of people."}, {"key": "1276", "content": "If $$49$$ people stand in a solid square formation, then each side of the outer layer of this square has people."}, {"key": "1277", "content": "A solid square formation, with a total of $$36$$ people on the outermost layer. To add one row and one column to this square formation, additional people are needed."}, {"key": "1278", "content": "During military training, the students formed a three-layer hollow square formation, with $$60$$ people in the innermost layer. Then, how many people are there on each side of the outermost layer?"}, {"key": "1279", "content": "Students of Class 1, Grade 4 participated in a calisthenics competition, forming a solid square formation with $$14$$ students per row and $$14$$ students per column, with a total of students in the square."}, {"key": "1280", "content": "If a solid square formation is made with $$25$$ flower pots, then each side of the outer layer of the square formation has flower pots."}, {"key": "1281", "content": "The image below shows a partial street map of a city. Someone wants to go from street entrance $$A$$ to street entrance $$B$$. To make the journey the shortest, there are ( ) different ways to do so.\n question_1281-image_0"}, {"key": "1282", "content": "Xiao Ming wants to go to the park from home, but he doesn't know which way is the shortest. Observing the map below, there are a total of different shortest routes. question_1282-image_0"}, {"key": "1283", "content": "In the schematic diagram of the streets in the picture below, several blocks are flooded and impassable. How many shortest routes are there from $$A$$ to $$B$$?\n question_1283-image_0"}, {"key": "1284", "content": "In the figure below, there are routes from point $$A$$ to point $$B$$. question_1284-image_0"}, {"key": "1285", "content": "As shown in the figure, starting from point $$F$$ and following the segments in the figure to point $$G$$, there are several different ways to take the shortest path. \n question_1285-image_0"}, {"key": "1286", "content": "As shown in the diagram, walk in the order of 'good health' (it is required to walk only in horizontal or vertical directions), there are a total of different ways. question_1286-image_0"}, {"key": "1287", "content": "Max School purchased a batch of new books. If each class borrows 20 books, then they are exactly all borrowed; if each class borrows 24 books, then there are 72 books short. The total number of new books purchased by the school is. question_1287-image_0"}, {"key": "1288", "content": "The teacher wants to distribute some exercise books to the students. If each student gets $$5$$ books, there will be $$90$$ books left over; if each student gets $$7$$ books, then the distribution is just right. Thus, there are students in this class."}, {"key": "1289", "content": "Xiaojin needs to complete a certain number of math application problems within a specified number of days. If he does $$9$$ problems each day, then there will be $$5$$ problems left unfinished within the specified days; if he does $$12$$ problems per day for the first three days and $$7$$ problems per day for the remaining days, then he will just finish these problems within the specified days. So, Xiaojin needs to complete a certain number of math application problems within the specified days."}, {"key": "1290", "content": "Teacher Wang distributed bananas to the children. If each child gets $$3$$ bananas, there will be $$4$$ bananas left; if each child gets $$4$$ bananas, there would be $$3$$ bananas short. So, how many children are there and how many bananas did Teacher Wang bring?"}, {"key": "1291", "content": "The teacher distributes a bunch of apples among the children. If each child gets $$9$$ apples, then there are $$40$$ apples left; if each child gets $$12$$ apples, there are only $$10$$ apples left. Therefore, there are a total of children. This batch of apples totals ."}, {"key": "1292", "content": "There are some envelopes and letter paper on the desk. If each letter uses $$2$$ pieces of letter paper, after using all the envelopes, there are $$20$$ pieces of letter paper left; if each letter uses $$3$$ pieces of letter paper, after using all the letter paper, there are $$10$$ envelopes left. How many pieces of letter paper and how many envelopes are there on the desk?"}, {"key": "1293", "content": "The school bought a batch of small footballs to distribute to each class: if each class gets 4 footballs, there will be 66 footballs short; if each class gets 2 footballs, then it exactly uses them all, the school has a total of classes, and bought footballs."}, {"key": "1294", "content": "An elementary school organized a visit for the sixth-grade students. The original plan was to rent several 45-seat buses, but there were 15 students without seats; if the same number of 60-seat buses were rented, there would be one extra bus, and the rest of the buses would be filled exactly. The number of sixth-grade students is."}, {"key": "1295", "content": "Autumn has arrived, Little White Rabbit harvested a basket of carrots. Calculating the number of days it plans to eat, if it eats $$4$$ carrots per day, there will be $$48$$ carrots left over; if it eats $$6$$ per day, there will be $$8$$ carrots left over, Little White Rabbit harvested a total of carrots."}, {"key": "1296", "content": "Teacher Lele has a bucket of chocolates, to be shared among third-grade children. If each child gets 6 pieces, there will be 10 pieces short; if each one gets 8 pieces, there will be 24 pieces short. In total, Teacher Lele has pieces of chocolate."}, {"key": "1297", "content": "The kindergarten teacher distributes apples to the children, giving each child $$4$$ apples, resulting in $$12$$ extra apples; but if each child is given $$6$$ apples, there are $$12$$ apples short. How many apples are there in total?"}, {"key": "1298", "content": "Calculate: $$7\\times 23+7 \\times29+52 \\times60+52 \\times33=$$."}, {"key": "1299", "content": "Calculate: $$80\\times 75-150\\times3+75\\times 26=$$."}, {"key": "1300", "content": "Calculate: $$30\\times 19+3\\times 810=$$."}, {"key": "1301", "content": "Calculate: $$12\\times 38+12\\times 34+24\\times 14=$$."}, {"key": "1302", "content": "Calculate: (1) $$33\\times 66+33\\times 34=$$\uff0e(2) $$16\\times 43+16\\times 31+16\\times26=$$\uff0e"}, {"key": "1303", "content": "Calculate: $$78 \\times 12+78 \\times84+22 \\times96=$$."}, {"key": "1304", "content": "Calculate: (1) $$13\\times61+13 \\times42=$$. (2) $$48\\times72+48\\times27=$$."}, {"key": "1305", "content": "Calculate: (1) $$743-(343+52)=$$\uff0e(2) $$157+639-(57+239)=$$\uff0e"}, {"key": "1306", "content": "Calculate: $$201+196+203+199+202=$$."}, {"key": "1307", "content": "Calculate: $$96\\times 36+72\\times2=$$."}, {"key": "1308", "content": "Mother rabbit divides bok choy among the little rabbits. If each little rabbit gets 3 pieces, there will be 8 pieces left over. If each little rabbit gets 5 pieces, there will be 2 pieces left over. In total, there are little rabbits."}, {"key": "1309", "content": "Insert '$$+$$' or '$$-$$' between the numbers below so that the equation becomes true. '$$(Only insert $$+$$ or $$-$$$$)$$. $$1$$ $$3$$ $$4$$ $$5$$ $$6=1$$"}, {"key": "1310", "content": "At the sports meeting, the class monitor distributed mineral water to the competitors. If each competitor gets 4 bottles, it's exactly enough; if each one gets 5 bottles, they would be short by 10 bottles. So, how many competitors are there, and how many bottles of water are there?"}, {"key": "1311", "content": "Fill in $$+$$, $$-$$, $$\\times $$, $$\\div $$ between the numbers to make the equation valid. The correct way to fill it is ( ).\n$$12\\ \\ 4\\ \\ 4=10\\ \\ 3$$"}, {"key": "1312", "content": "From the four numbers and the symbols \"$$+$$\", \"$$-$$\", \"$$\\times $$\", \"$$\\div $$\", or parentheses, form an equation that equals $$24$$. It can be filled as $$(8$$$$2$$$$8)$$$$3=24$$."}, {"key": "1313", "content": "A batch of exercise books was distributed to students. If each student gets 5 books, there are 70 books left over. If each student gets 7 books, there are 10 books short. How many students and how many exercise books are there in this class?"}, {"key": "1314", "content": "The counselor needs to arrange rooms for students participating in the 'summer camp'. If each room accommodates $$3$$ people, there will be $$23$$ people left over; if each room accommodates $$5$$ people, there will be $$11$$ people short. There are people participating in the 'summer camp'."}, {"key": "1315", "content": "The equation that is equal to $$18\\times 30$$ is ( )."}, {"key": "1316", "content": "The simple calculation of $$643-318-82$$ is ( )."}, {"key": "1317", "content": "The expression equal to $$73\\times35+73\\times 65$$ is \uff08 \uff09."}, {"key": "1318", "content": "A rectangular flower bed is evenly divided into $$7$$ small squares, knowing that the perimeter of each small square is $$12$$ meters, the perimeter of the large rectangle is meters. question_1318-image_0 \u200b"}, {"key": "1319", "content": "In the figure below, the adjacent edges are perpendicular to each other, so the perimeter of this shape is. question_1319-image_0"}, {"key": "1320", "content": "The perimeter of the picture below is in centimeters.\n question_1320-image_0"}, {"key": "1321", "content": "In the diagram below, two adjacent sides are perpendicular to each other. The perimeter of this shape is in centimeters. (Unit: centimeters) question_1321-image_0"}, {"key": "1322", "content": "Besides passive defense measures, the doctor also developed a bionic robot\u2014Type $$A$$ Anteater. In one test, the Type $$A$$ Anteater moved up, down, left, right, and returned to the starting point after several movements, forming a mountain shape with a missing corner. It walked a total of meters.\n question_1322-image_0"}, {"key": "1323", "content": "There is a rectangular piece of paper, the length is $$10$$ cm, and the width is $$8$$ cm. If it is cut with scissors 3 times (as shown in the figure), then the sum of the perimeters of these 6 rectangles is cm.\n question_1323-image_0"}, {"key": "1324", "content": "All the small squares below have equal side lengths. Then, the perimeter of shape $$A$$ compared to the perimeter of shape $$B$$ is\uff0e\uff08Fill in \u201c>\u201d, \u201c<\u201d, or \u201c=\u201d\uff09 question_1324-image_0"}, {"key": "1325", "content": "One of the squares in the picture is divided into $$3$$ rectangles of the same size and shape, and the perimeter of each rectangle is $$8$$ meters, then the perimeter of the square is meters. question_1325-image_0"}, {"key": "1326", "content": "Using $$5$$ square pieces with a side length of $$1$$ cm to form a rectangle, the perimeter of this rectangle is in centimeters."}, {"key": "1327", "content": "As shown in the left picture, Xiaojia drew a figurine with a hat. As shown in the right picture, the hat is made of $$6$$ identical rectangles. If the length of these $$6$$ rectangles is $$6$$, then the perimeter of this hat shape is.\n question_1327-image_0"}, {"key": "1328", "content": "Cut a rectangular paper that is $$12$$ cm long and $$8$$ cm wide into $$4$$ identical small rectangles. Among the three cutting methods below, the perimeter of the small rectangle cut out in the figures is the shortest. question_1328-image_0 question_1328-image_1 question_1328-image_2 Figure \u2460 Figure \u2461 Figure \u2462"}, {"key": "1329", "content": "A rectangle with a length of $$20$$ cm and a width of $$15$$ cm, whether cut horizontally or vertically, after cutting $$3$$ times, the maximum total perimeter of the resulting figures is cm."}, {"key": "1330", "content": "Xiaohong's number of points cards is $$6$$ times that of Xiaolan's. If Xiaohong gives $$20$$ points cards to Xiaolan, she would still have $$5$$ more cards than Xiaolan. How many points cards did Xiaolan originally have?"}, {"key": "1331", "content": "Xiaomin has $$14$$ yuan, Xiaohua has $$10$$ yuan, Xiaohua gives Xiaomin yuan, so that Xiaomin's money is twice the amount of Xiaohua's $$2$$ times."}, {"key": "1332", "content": "Originally there were $$32$$ passengers on the bus, after a certain stop $$10$$ people got off the bus, and $$16$$ people got on the bus. At this time, there were passengers on the bus.\n question_1332-image_0"}, {"key": "1333", "content": "There are two baskets of apples, the apples in the first basket are $$4$$ times the apples in the second basket. If $$9$$ apples are taken from the first basket and put into the second basket, it is found that the apples in the first basket are actually $$6$$ less than those in the second basket. How many apples were originally in the first and second basket respectively."}, {"key": "1334", "content": "There are two sports teams, Team A and Team B, with an equal number of members. Due to training needs, $$10$$ people were transferred from Team A to Team B. At this point, the number of people in Team B is exactly $$3$$ times the number of people in Team A. The original number of people in Team A was."}, {"key": "1335", "content": "Huanhuan's number of cards is $$3$$ times that of Lele's. If Huanhuan gives Lele $$7$$ cards, they would have the same number of cards. How many cards did Huanhuan and Lele originally have?"}, {"key": "1336", "content": "Xiaoxin and Leilei collect stamps. Originally, Xiaoxin had 4 more stamps than Leilei. After Xiaoxin gave 8 stamps to Leilei, at this time, Leilei's number of stamps is twice that of Xiaoxin. How many stamps did Xiaoxin originally have?"}, {"key": "1337", "content": "Originally, there were a total of 561 spectators in sections A and B. Twenty minutes later, 40 people left section A and 10 people entered section B. At this point, the number of people in section A was exactly twice the number of people in section B. The current number of spectators in section A is."}, {"key": "1338", "content": "Xiaolin has $$30$$ pictures, and after giving $$5$$ pictures to Xiao Jun, both of them have the same number of pictures. Originally, Xiaolin had more pictures than Xiao Jun."}, {"key": "1339", "content": "Barrels A and B together contain $$160$$ kilograms of oil. If $$20$$ kilograms of oil are transferred from barrel B to barrel A, the amount of oil in barrel A becomes $$3$$ times the amount in barrel B. How many kilograms of oil were originally in barrel A and barrel B?"}, {"key": "1340", "content": "Sunflower Elementary School's third grade has $$3$$ classes, each with $$18$$ boys, $$20$$ boys, and $$16$$ boys respectively. There are several ways to choose one of them to be the flag raiser."}, {"key": "1341", "content": "Five people, A, B, C, D, and E, stand in a row, with A must stand in the very middle, and B must stand next to A, there is a method."}, {"key": "1342", "content": "Dad, mom, grandpa, and grandma are standing in a row to take a picture, grandpa can only stand at the furthest right position, they can take a total of different pictures."}, {"key": "1343", "content": "The class organized a picnic to the park, and Teacher Little Deer is trying to choose an outfit consisting of one item from each of the following: $$4$$ shirts, $$3$$ pairs of pants, $$3$$ pairs of shoes, and $$4$$ hats, with the hat being optional, leading to a total number of choices."}, {"key": "1344", "content": "Xiaoyuan is preparing to give Xiao Jie $$1$$ pencil and $$1$$ eraser. He has $$2$$ different pencils and $$3$$ different erasers (as shown below), so there are a total of different combinations.\n question_1344-image_0"}, {"key": "1345", "content": "Teacher Wang goes on a business trip from Chongqing to Nanjing, he can directly take a plane or a car to reach, or he can first go to Wuhan, then from Wuhan to Nanjing. From Chongqing to Wuhan, he can take a boat or a train; from Wuhan to Nanjing, he can take a boat, train, or plane, as shown in the diagram. Thus, there are different ways for Teacher Wang to travel from Chongqing to Nanjing.\n question_1345-image_0"}, {"key": "1346", "content": "$$6$$ people line up in a row, with A at the head of the line, and B not at the end of the line, resulting in a total of different arrangements."}, {"key": "1347", "content": "Four people, A, B, C, and D, line up in a row to take a photo. There are several ways to line up."}, {"key": "1348", "content": "Sisi and her family are going on a trip and can travel by train, by car, or by plane. After searching online, on the day of departure, there are $$5$$ trains, $$4$$ buses, and $$3$$ flights available. They have a total of different choices to take these modes of transportation."}, {"key": "1349", "content": "A chick, a duckling, and a puppy stand on three steps respectively, the chick cannot stand in the middle, and the duckling cannot stand on the right. There are a total of different ways to stand."}, {"key": "1350", "content": "As shown, quadrilateral $$ABCD$$ is a rhombus (the diagonals of a rhombus are perpendicular to each other), given $$AC=6$$, $$BD=3$$, find the area of the rhombus . question_1350-image_0"}, {"key": "1351", "content": "As shown in the figure, the quadrilateral $$ABCD$$ is a square, and it is known that the diagonal $$AC$$ is $$12$$ cm long. The area of the square $$ABCD$$ is square centimeters. question_1351-image_0"}, {"key": "1352", "content": "The two diagonals of quadrilateral $$ABCD$$ are perpendicular to each other. It is known that the area of quadrilateral $$ABCD$$ is $$35$$ and $$BD=5$$, $$AC=$$\uff0e question_1352-image_0"}, {"key": "1353", "content": "As shown in the diagram, rectangle $$ABCD$$ is divided into $$9$$ smaller rectangles. The area of $$5$$ of these smaller rectangles is shown in the diagram. The area of rectangle $$ABCD$$ is. question_1353-image_0"}, {"key": "1354", "content": "As shown in the figure, a rectangle is divided into $$6$$ small rectangles, and the area of the shaded part is. question_1354-image_0"}, {"key": "1355", "content": "As shown in the figure, in a quadrilateral, the diagonals are perpendicular to each other, $$AD=10$$, $$BC=5$$, the area of the quadrilateral is.\n question_1355-image_0"}, {"key": "1356", "content": "As shown in the figure, a large rectangle is divided into $$6$$ smaller rectangles, among which the area of $$4$$ small rectangles is shown in the figure (unit: square centimeters), then the area of the rectangle represented by $$B$$ is square centimeters. question_1356-image_0"}, {"key": "1357", "content": "As shown in the diagram, a large rectangle is divided into four smaller rectangles, where the areas of three of the rectangles are $$48$$, $$24$$, and $$30$$ square decimeters, respectively. The area of the shaded rectangle is in square decimeters question_1357-image_0"}, {"key": "1358", "content": "As shown in the figure, a rectangle is divided into four smaller rectangles by two lines. The areas of three of those rectangles are $$12$$ square centimeters, $$8$$ square centimeters, and $$20$$ square centimeters, respectively. Then, the area of the shaded rectangle is square centimeters. question_1358-image_0"}, {"key": "1359", "content": "As shown in the figure, quadrilateral $$ABCD$$ is a rhombus (a parallelogram with four equal sides). Given $$AC=18$$, $$BD=6$$, the area of the rhombus is. (The diagonals of a rhombus are perpendicular to each other and bisect each other)\n question_1359-image_0"}, {"key": "1360", "content": "As shown in the figure, a large rectangle is divided into four small rectangles, among which three small rectangles have areas of $$15$$, $$9$$, and $$18$$ square meters, respectively. What is the area of the shaded rectangle in square meters? question_1360-image_0"}, {"key": "1361", "content": "As shown in the figure, in a quadrilateral, the diagonals are perpendicular to each other. It is known that $$AC=10$$ cm, the area of quadrilateral $$ABCD$$ is $$25$$ square cm, $$BD=$$ ( ) cm. question_1361-image_0"}, {"key": "1362", "content": "Which of the following line segments is the height of parallelogram $$ABCD$$ on the side $$BC$$? question_1362-image_0"}, {"key": "1363", "content": "As shown in the figure, in the parallelogram, the height corresponding to the base of length $$9$$ is ( ). question_1363-image_0"}, {"key": "1364", "content": "Among the following groups, the set of four rods that cannot form a parallelogram is ( )."}, {"key": "1365", "content": "As shown in the diagram, this is a parallelogram vegetable plot, its area is square meters. question_1365-image_0"}, {"key": "1366", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, and $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$BC=12$$ cm, $$AE=6$$ cm, $$CD=9$$ cm. Then the length of line segment $$AF$$ is in cm. question_1366-image_0"}, {"key": "1367", "content": "Determine if the following figures can be drawn in one stroke\n question_1367-image_0"}, {"key": "1368", "content": "As shown in the diagram, there are three small islands in the middle of a river, interconnected by $$5$$ bridges. Please determine whether the following statement is correct: It is possible to find a route that crosses all the bridges once without repetition.\n question_1368-image_0"}, {"key": "1369", "content": "How many strokes are needed at least to draw the shapes below? ( )\n question_1369-image_0"}, {"key": "1370", "content": "Please fill in the following:\nFor figure ($$1$$) at least strokes;\nFor figure ($$2$$) at least strokes;\nFor figure ($$3$$) at least strokes;\nFor figure ($$4$$) at least strokes;\nFor figure ($$5$$) at least strokes;\nFor figure ($$6$$) at least strokes. (Fill in with Arabic numerals)\n question_1370-image_0 \n question_1370-image_1 question_1370-image_2 question_1370-image_3"}, {"key": "1371", "content": "Which line should be removed from the following figure to make it drawable in one stroke? ( )\n question_1371-image_0"}, {"key": "1372", "content": "The image is a floor plan of the greenhouse, consisting of $$6$$ exhibition rooms, with each adjacent two rooms interconnected by a door. We also need to add an exit (fill in the letter) to the room so that Eddie can enter through the entrance $$m$$, pass through all the doors without repeating, and finally exit the greenhouse through the exit. question_1372-image_0"}, {"key": "1373", "content": "As shown in the figure, the road in a certain residential area's garden consists of a rectangle that is 480 meters long and 200 meters wide; a diamond shaped area with a side length of 260 meters and two crisscrossing roads, one day, Mr. Wang entered the garden from point A, walked all the roads in the garden, and left from point A, then the minimum distance he needs to walk from entering to leaving the garden is __ meters.\n question_1373-image_0"}, {"key": "1374", "content": "Fill in the blank with appropriate numbers to make the vertical addition equation below valid, please write this equation:.\n question_1374-image_0"}, {"key": "1375", "content": "In the following graphic equation, each shape represents a number. Please calculate, $$\\square=$$; $$\\triangle= $$; $$\\bigcirc=$$.\n question_1375-image_0"}, {"key": "1376", "content": "Fill in the blanks with appropriate numbers in the diagram to make the vertical addition equation correct. The result of the equation is. question_1376-image_0"}, {"key": "1377", "content": "In the equations below, the same Chinese characters represent the same digits, and different Chinese characters represent different digits. Please find the sum of the digits represented by \u201c\u771f (true)\u201d, \u201c\u662f (is)\u201d, \u201c\u6709 (have)\u201d, and \u201c\u8da3 (interesting)\u201d respectively. question_1377-image_0"}, {"key": "1378", "content": "In the following equation, different Chinese characters represent different numbers, and the same Chinese characters represent the same number. If clever $$+$$ solution $$+$$ number $$+$$ digit $$+$$ puzzle $$= 30$$, then what is the five-digit number represented by \"$$\\overline{clever solution number digit puzzle}$$\"? question_1378-image_0"}, {"key": "1379", "content": "The vertical operation below contains exactly $$10$$ digits, which are from $$0$$ to $$9$$, one of each. The position of $$4$$ has been given. Please count: How many different vertical operations satisfying the requirements are there? question_1379-image_0"}, {"key": "1380", "content": "In the following equation, the same symbols represent the same digits, and different symbols represent different digits. Based on this equation, it can be deduced that: $$\\square +\\triangle +\\bigcirc =$$ question_1380-image_0"}, {"key": "1381", "content": "Fill in each blank of the figure with one of the numbers $$1$$, $$3$$, $$5$$, $$7$$, $$9$$ (reusable) to make it a correct addition sum. What is the sum of the numbers filled in? question_1381-image_0"}, {"key": "1382", "content": "As shown in the diagram, $$\\square $$, $$\\bigcirc $$ and $$\\triangle $$ each represent different numbers. Please identify what numbers they respectively represent. $$\\bigcirc =$$; $$\\square= $$; $$\\triangle =$$\uff0e question_1382-image_0"}, {"key": "1383", "content": "Insert the appropriate number inside the $$\\square$$ to make each vertical calculation correct. The result of the calculation is. question_1383-image_0"}, {"key": "1384", "content": "Fill in the blank with suitable numbers so that the addition vertical equation below is correct. The second addend is.\n question_1384-image_0"}, {"key": "1385", "content": "As shown in the figure below, fill in the appropriate numbers in the blank to make the column addition valid. The second addend is.\n question_1385-image_0"}, {"key": "1386", "content": "Fill in the appropriate numbers in the vertical operation to make it valid; therefore, the sum of the first vertical operation (which is also the minuend of the second vertical operation) is ( ).\n question_1386-image_0"}, {"key": "1387", "content": "Simplified calculation: (1) $55\\times65+45\\times65=$ (2) $97\\times99+97=$"}, {"key": "1388", "content": "Calculate: (1)$$25\\times \\left( 40+4 \\right)=$$; (2)$$\\left( 100-8 \\right)\\times 125=$$"}, {"key": "1389", "content": "$$23\\times 300$$="}, {"key": "1390", "content": "Calculate: $$9\\times 125-25\\times 29+75\\times 21+175\\times 3=$$."}, {"key": "1391", "content": "Calculate: (1) $$36\\times 19+64\\times 19=$$ (2) $$32\\times 25+68\\times 25=$$ (3) $$268\\times 75-68\\times 75=$$"}, {"key": "1392", "content": "Calculate: $$80\\times 75+22\\times 75-150=$$."}, {"key": "1393", "content": "Calculate: $$56\\times 14+56\\times 86=$$."}, {"key": "1394", "content": "$$24\\times \\left( 100+3 \\right)=$$"}, {"key": "1395", "content": "Calculate: \n(1)$$24\\times 5=$$\uff0e\n(2)$$32\\times 25=$$\uff0e\n(3)$$48\\times 125=$$\uff0e"}, {"key": "1396", "content": "Da Mao and Xiao Mao have a total of $$200$$ hair strands, Da Mao has $$40$$ more hair strands than Xiao Mao, so Da Mao has hair strands, and Xiao Mao has hair strands."}, {"key": "1397", "content": "The diagram below contains a line segment, a ray, and a straight line.\n question_1397-image_0"}, {"key": "1398", "content": "Fang Fang and Yuan Yuan have a total of $$70$$ books. If Fang Fang gives Yuan Yuan $$5$$ books, then Yuan Yuan will have $$4$$ more books than Fang Fang. The question is: how many books did Fang Fang and Yuan Yuan originally have each? \uff08 \uff09"}, {"key": "1399", "content": "The school bought $$15$$ more boxes of white chalk than colored chalk, and the number of boxes of white chalk is $$3$$ boxes less than $$4$$ times the number of boxes of colored chalk. How many boxes of white chalk did the school buy?"}, {"key": "1400", "content": "There are a total of $$260$$ peach trees and pear trees in the orchard, with the number of peach trees being $$20$$ more than that of pear trees. Thus, there are peach trees, pear trees."}, {"key": "1401", "content": "Two bookshelves, where the number of books stored in bookshelf A is equivalent to 5 times the number of books in bookshelf B plus 20 books. Bookshelf A has 140 books more than bookshelf B. Then, bookshelf A stores $$ books."}, {"key": "1402", "content": "Both person A and person B have some candies. If A gives B $$10$$ candies, then they will have the same number of candies; if both A and B eat $$8$$ candies, then the number of candies A has left is $$3$$ times the number that B has left. Together, they originally had a total of candies."}, {"key": "1403", "content": "Teachers Liu, Lian, and Yang together have $$1000$$ reward cards, among which Teacher Liu's reward cards are $$3$$ times of Teacher Yang's, and Teacher Lian's reward cards are $$6$$ times of Teacher Yang's. Therefore, Teacher Yang has reward cards, Teacher Liu has reward cards, and Teacher Lian has reward cards."}, {"key": "1404", "content": "The production of the new type of coating requires the mixing of Coating A and Coating B together. Currently, there are $$40$$ kilograms of Coating A and $$32$$ kilograms of Coating B. How many more kilograms of Coating B need to be added so that the weight of Coating B is $$3$$ times that of Coating A?"}, {"key": "1405", "content": "Warehouse A and B had a total of $$56$$ bags of rice. After transferring $$8$$ bags from Warehouse B to Warehouse A, both warehouses had the same number of rice bags. The original number of rice bags in Warehouse A and Warehouse B was."}, {"key": "1406", "content": "Grandma Wang has raised chickens, ducks, and geese, totaling $$250$$ animals. Among them, the number of ducks is $$10$$ less than $$2$$ times the number of geese, and the number of chickens is $$20$$ more than $$3$$ times the number of ducks. Grandma Wang has raised chickens, ducks, geese."}, {"key": "1407", "content": "Eddie and Will folded origami cranes together. Eddie folded $$90$$ more cranes than Will. The number of cranes Eddie folded is $$10$$ more than $$3$$ times the number Will folded. So, how many origami cranes did Eddie and Will fold respectively?"}, {"key": "1408", "content": "There are two bags of rice. Bag A has 18 kilograms less than Bag B. If another 6 kilograms are moved from Bag A to Bag B, at this point, the rice in Bag A is half that of Bag B. How much rice did each bag originally have? \uff08 \uff09"}, {"key": "1409", "content": "Dad is $$38$$ years old this year, Mingming is $$8$$ years old this year, Mingming is younger than his dad by years; when Mingming is $$10$$ years old, his dad will be years old."}, {"key": "1410", "content": "The older brother said to the younger brother: 'When I was as old as you are now, you were only $$2$$ years old.' The younger brother said to the older brother: 'When I am as old as you, you will already be $$17$$ years old.' So, the older brother is $$12$$ years old this year, and the younger brother is $$7$$ years old this year."}, {"key": "1411", "content": "Last year, the combined age of the mother and daughter was $$46$$ years. This year, the mother's age is $$3$$ times that of the daughter's age. So, this year the daughter is ____ years old."}, {"key": "1412", "content": "When the mother was as old as the daughter is now, the daughter was $$2$$ years old. When the daughter grows to be as old as the mother is now, the mother will be $$68$$ years old. Please ask what is the current age of the mother and the age of the daughter."}, {"key": "1413", "content": "Xiao Ming is $$8$$ years old this year, and his mother is $$44$$ years old. When was Xiao Ming's age exactly $$4$$ times less than his mother's age?"}, {"key": "1414", "content": "In a family, the current total age of all members is $$73$$ years. The family consists of a father, a mother, a daughter, and a son. The father is $$3$$ years older than the mother, and the daughter is $$2$$ years older than the son. Four years ago, the total age of everyone in the family was $$58$$ years. What is the age of each family member now? Answer: son $$3$$ years old, daughter $$5$$ years old, father $$34$$ years old, mother $$31$$ years old."}, {"key": "1415", "content": "Xiaoqiang's grandfather said: \"The number of days since my grandson was born is the same as the number of weeks since my son was born; the number of months since my grandson was born is the same as the number of years since I was born. The sum of ages of my grandson, my son, and myself is a hundred years.\" Please tell, this year, Xiaoqiang is years old, dad is years old, and grandfather is years old."}, {"key": "1416", "content": "Xiao Qing is $$3$$ years older than Xiao Yu. The sum of the ages of Xiao Qing $$3$$ years ago and Xiao Yu $$2$$ years later is $$20$$ years. Therefore, Xiao Yu is $$9$$ years old this year."}, {"key": "1417", "content": "The sum of the ages of the father and his two sons is 84 years old. In 12 years, the father's age will be exactly equal to the sum of the ages of the two sons. How old is the father now?"}, {"key": "1418", "content": "$$6$$ years ago, the sum of the ages of dad and Binbin was $$34$$ years old; $$3$$ years later, dad's age will be $$3$$ times that of Binbin's. Calculate Binbin's current age."}, {"key": "1419", "content": "The figure is composed of several small squares with the same side length. How many squares are there in total in this figure? question_1419-image_0"}, {"key": "1420", "content": "The picture below contains a total of triangles.\n question_1420-image_0"}, {"key": "1421", "content": "How many triangles are there in the picture? question_1421-image_0"}, {"key": "1422", "content": "After dividing each side of an equilateral triangle into four equal parts and then connecting the corresponding segments, the figure below is obtained. There are a total of triangles in the figure. question_1422-image_0"}, {"key": "1423", "content": "The total number of squares in the image below. question_1423-image_0"}, {"key": "1424", "content": "How many rectangles (including squares) are there in the image? question_1424-image_0"}, {"key": "1425", "content": "In the diagram below, there are a total of \uff08including squares\uff09 rectangles, both large and small. question_1425-image_0"}, {"key": "1426", "content": "Count the number: There are a total of squares in the picture.\n question_1426-image_0"}, {"key": "1427", "content": "How many rectangles are there below? question_1427-image_0"}, {"key": "1428", "content": "The picture contains a total of triangles.\n question_1428-image_0"}, {"key": "1429", "content": "Count the number of rectangles (including squares) in the image below. question_1429-image_0"}, {"key": "1430", "content": "The figure below has a total of line segments.\n question_1430-image_0"}, {"key": "1431", "content": "Count the number of triangles in the image below.\n question_1431-image_0"}, {"key": "1432", "content": "The picture contains a total of lines and intersection points.\n question_1432-image_0"}, {"key": "1433", "content": "As shown in the picture, a square paper with a side length of $$10$$ cm is vertically cut twice and horizontally cut once, dividing it into $$6$$ small rectangular pieces. The total perimeter of these $$6$$ small rectangular pieces equals centimeters.\n question_1433-image_0"}, {"key": "1434", "content": "The perimeter of the shape shown in the figure is.\n question_1434-image_0"}, {"key": "1435", "content": "A vegetable patch, shaped as shown in the figure, is known to have $$a=b=30$$ meters, $$c=3$$ meters, $$d=9$$ meters, the perimeter of this patch in meters is. question_1435-image_0"}, {"key": "1436", "content": "The length of the rectangle is $$6$$, and the width is $$5$$. The perimeter of this rectangle is, and the area is."}, {"key": "1437", "content": "For any two numbers $$a$$ and $$b$$, define $$a\\Theta b=3\\times a-b\\div 3$$, then $$8\\Theta 9=$$."}, {"key": "1438", "content": "Calculate: $$\\left( 4\\times 5\\times 7\\times 9\\times 11\\times 13 \\right)\\div \\left( 36\\times 77 \\right)$$=\uff0e"}, {"key": "1439", "content": "Calculate: (1) $$(1300+26)\\div 13=$$. (2) $$(1100-77-88)\\div 11=$$."}, {"key": "1440", "content": "$$1+2+3+4+5+\\cdots \\cdots +40=$$."}, {"key": "1441", "content": "Sum: $$1+5+9+\\cdots +41+45=$$."}, {"key": "1442", "content": "In the arithmetic sequence $$20$$, $$24$$, $$28$$, $$32$$, \u2026$$100$$, there are a total of terms."}, {"key": "1443", "content": "Calculate: $$1+5+9+13+17+21+25+29+33=$$."}, {"key": "1444", "content": "For the sequence $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$19$$ $$\\cdots$$, the $$10$$th number is $$31$$. $$49$$ is the nth number in this sequence."}, {"key": "1445", "content": "Using $$3$$ equal-length matchsticks to form an equilateral triangle, lay out a larger equilateral triangle with such triangles, as shown in the diagram. If the base of this larger equilateral triangle is made of $$10$$ matchsticks, then how many matchsticks are needed in total? question_1445-image_0"}, {"key": "1446", "content": "Calculate: $$3+8+13+18+23+28+33+38+43+48=$$."}, {"key": "1447", "content": "Arithmetic sequence: $$5$$, $$9$$, $$13$$, $$17$$, $$\\cdots$$, the $$21st$$ term is."}, {"key": "1448", "content": "The 10th term of an arithmetic sequence is 62, and the 25th term is 152, then the common difference of this arithmetic sequence is."}, {"key": "1449", "content": "Given a sequence of numbers, each number is $$2$$ greater than the previous one, the $$50$$th number is $$99$$, the $$18$$th number is."}, {"key": "1450", "content": "Every day, the little rabbit goes to the field to pull up radishes. On the first day, it pulled up $$7$$ radishes, and then every day it pulled up $$5$$ more radishes than the day before. How many radishes does the little rabbit need to pull up on the $$9$$th day?"}, {"key": "1451", "content": "A sequence of numbers consists of $$13$$ numbers, each of which is $$7$$ more than its previous one, and the $$13$$th number is $$125$$. Therefore, the $$1$$st number is."}, {"key": "1452", "content": "As shown in the figure: The numbers marked on the left side of each row and on the top side of each column represent the quantity of consecutive black squares in that row or column. Children, can you mark all the black squares based on these numbers? question_1452-image_0"}, {"key": "1453", "content": "All students in Grade 2 Class 2 who participated in the choir also formed a solid square formation. After $$13$$ people were transferred to the dance group, the outer row and column of the square were removed, forming a smaller solid square formation. Originally, there were people from Grade 2 Class 2 participating in the choir."}, {"key": "1454", "content": "To celebrate the \"May Day\" International Labour Day, the school arranged a square formation with flower pots on the small square. The outermost layer has $$100$$ pots of flowers. Thus, each side of the outer layer has pots of flowers."}, {"key": "1455", "content": "Third-grade students form a square matrix for a gymnastics performance, with $$32$$ people on the outermost layer. How many people are on each side of the outer layer of the matrix, and how many third-grade students are there in total in this square matrix?"}, {"key": "1456", "content": "If each side of the outermost layer of a solid square formation has $$16$$ chess pieces, then the total number of pieces in the outermost layer is ."}, {"key": "1457", "content": "If each side of the outermost layer of a solid square formation has $$16$$ pieces, then the total number in the outermost layer is pieces."}, {"key": "1458", "content": "At the opening ceremony of the school sports meet, the teachers formed a solid square formation, twisting their limbs in a regular pattern. It is known that the outermost layer of the square formation has $$116$$ people, then the third layer from the outside has people, and the total number of teachers who participated in the square formation is people"}, {"key": "1459", "content": "The students arranged 24 pots of flowers into a two-layer hollow square matrix. Later, they decided to add another layer outside to make it a three-layer square matrix, requiring more pots of flowers."}, {"key": "1460", "content": "A total of $$240$$ people form a $$5$$-layer hollow square formation. To add an internal layer and turn it into a $$6$$-layer hollow square formation, additional people are needed."}, {"key": "1461", "content": "A squad of soldiers forms a three-tiered hollow square formation with $$16$$ extra people. If one more tier is added to the hollow part, they are short by $$28$$ people. How many people are in this squad? If they form a solid square formation, how many people should there be on each side?"}, {"key": "1462", "content": "Eddie arranged some chess pieces into a two-layer hollow square. Later, he added $$28$$ chess pieces to make the pattern into a three-layer hollow square$.$$ Initially, the maximum number of chess pieces Eddie could have arranged is . The minimum number of chess pieces he could have arranged is ."}, {"key": "1463", "content": "Using $$84$$ chess pieces to form a three-layer hollow square matrix, how many pieces are on the outermost layer."}, {"key": "1464", "content": "Lingling watched a group gymnastics performance, where he saw a formation in the team change into a solid regular triangle array. He estimated the number of people in the team to be between $$30$$ and $$50$$, with someone in the team."}, {"key": "1465", "content": "Given that the number of people participating in a performance is $$360$$ people, and they want to form a hollow square formation with $$6$$ levels, ask how many people should be arranged on each side of the outermost layer."}, {"key": "1466", "content": "With $$152$$ chess pieces arranged into a two-layer hollow square array, if one wishes to add another layer on the outside, how many more chess pieces are needed?"}, {"key": "1467", "content": "As the festival approached, the students arranged a hollow flower bed on the playground using potted plants, with the outermost layer having $$15$$ pots of flowers on each side, totaling $$3$$ layers, and having used up a total number of pots of flowers."}, {"key": "1468", "content": "Ding Ding and Tian Tian have a total of $$58$$ books. Ding Ding has $$5$$ books less than Niu Niu, who has $$7$$ books less than Tian Tian. Ding Ding has books, and Tian Tian has books."}, {"key": "1469", "content": "Three little bears went to eat honey and together they ate $$23$$ kilograms. Bear A ate $$3$$ kilograms less than the total amount eaten by Bear B and Bear C together. Bear B ate $$1$$ kilogram more than Bear C. Calculate the amount eaten by Bear A, Bear B, and Bear C in kilograms."}, {"key": "1470", "content": "Three pieces of cloth have a total length of $$220$$ meters, the second piece is $$3$$ times the first piece, and the third piece is $$2$$ times the second piece. The first piece is meters, the second piece is meters, the third piece is meters."}, {"key": "1471", "content": "A construction team wants to repair a path. On the first day, they repaired more than half of the total length by $$6$$ meters, and on the second day, they repaired less than half of the remaining length by $$2$$ meters. At this point, there are $$6$$ meters left unrepaired. Thus, the length of this path is meters."}, {"key": "1472", "content": "Mengmeng's current age plus $$3$$, minus $$12$$, times $$3$$, divided by $$4$$, equals $$3$$. Mengmeng is currently $$ years old."}, {"key": "1473", "content": "Stretch out your left hand and count from your thumb as shown in the picture $$1$$, $$2$$, $$3$$, $$\\cdots$$; when you count to $$2012$$, you count on ( ).\n question_1473-image_0"}, {"key": "1474", "content": "Viola was born on September 29, 2012, which was a Saturday. What day of the week was her 7th birthday on?"}, {"key": "1475", "content": "$$2020$$ year $$4$$ month $$1$$ day is Wednesday, $$2019$$ year $$8$$ month $$20$$ day is a week."}, {"key": "1476", "content": "$$8$$ team members form a circle for a passing game, starting with member $$1$$, passing the ball in a clockwise direction to the next person. After passing it $$72$$ times, the ball is with member number. Passing the ball in an anti-clockwise direction to the next person $$30$$ times, the ball is with member number.\n question_1476-image_0"}, {"key": "1477", "content": "$$2018$$ year $$10$$ month $$10$$ day is Wednesday, $$2028$$ year $$10$$ month $$10$$ day is on a weekday."}, {"key": "1478", "content": "If a particular February has $$4$$ Mondays and $$5$$ Tuesdays, then February $$15$$th is a Tuesday ( )."}, {"key": "1479", "content": "The doctor asked Da Kuan to plant a row of trees on one side of the road. Initially, Da Kuan planted $$5$$ poplar trees in succession. Then, the doctor said: \"This is not the correct way to plant. You should follow the sequence of planting $$3$$ willow trees, $$1$$ pine tree, and then again $$3$$ willow trees, $$1$$ pine tree $$\\cdots \\cdots$$\" Following this, Da Kuan continued to plant according to this pattern. In total, Da Kuan planted $$187$$ trees. There are willow trees, pine trees. question_1479-image_0 \u200b\u200b"}, {"key": "1480", "content": "When students share apples, if each person gets $$3$$, then there are $$12$$ left over; if each person gets $$5$$, then there is a shortage of $$8$$. There are a total of apples."}, {"key": "1481", "content": "As shown in the picture, an electronic flea can jump from one circle to the adjacent circle with each jump. Now, a red flea starts from the circle marked with the number \"$$1$$\" and makes $$100$$ jumps in the clockwise direction, landing in a circle. The number in this circle is.\n question_1481-image_0"}, {"key": "1482", "content": "The teacher bought a basket of oranges to distribute among the children in the senior class. If three of them receive 6 each and the others 2 each, then there are 4 extra oranges. If one receives 6 and the others 4 each, then there are 16 oranges short. The teacher bought a total of oranges, and there are a total of children."}, {"key": "1483", "content": "The New Year is approaching, and both Beauty Sheep and Blister Sheep bought the same number of envelopes and the same number of New Year's cards. Beauty Sheep put $$1$$ New Year's card into each envelope, used up all the envelopes, and had $$50$$ New Year's cards left; Blister Sheep put $$3$$ New Year's cards into each envelope, used up all the New Year's cards, and had $$50$$ envelopes left. They bought several envelopes and New Year's cards."}, {"key": "1484", "content": "At the sports meeting, the class leader distributed mineral water to the contestants. If each contestant gets $$4$$ bottles, there would be $$5$$ bottles left; if each contestant gets $$5$$ bottles, there would be $$3$$ bottles short. Please answer: how many contestants, bottles of water."}, {"key": "1485", "content": "The Animal Kingdom distributed some bananas to the animals. If all were given to elephants, each elephant would get 4 bananas and there would be 7 bananas left; if all were given to monkeys, each monkey would get 7 bananas and there would be a shortage of 2 bananas. It is known that there are 3 more elephants than monkeys. Then the number of bananas is ( )."}, {"key": "1486", "content": "The teacher distributed bread to the students, with each bag containing $$10$$ slices. Initially, $$9$$ students arrived, and after distributing the same number of slices to each student, half a bag remained. Later, another $$5$$ students came, and the teacher found that two more bags of bread needed to be purchased to give the newly arrived students the same amount of slices. The teacher had prepared bags of bread initially."}, {"key": "1487", "content": "The teacher is preparing to distribute candies to the students. If each person gets 10 pieces, there will be 18 pieces left; if the number of students doubled, and each person gets 8 pieces, there will be a shortage of 6 pieces. How many candies does the teacher have in total."}, {"key": "1488", "content": "The school organizes students to go to farm stays. If each farm hosts 4 students, there would be 7 people without a place to stay; if each farm hosts 5 students, the last two farms would have no students staying in them. There are a total of people in this group of students."}, {"key": "1489", "content": "The zookeeper is preparing to distribute peaches to the monkeys in the zoo. If each monkey gets 6 peaches, there will be 5 peaches short. If the unique Monkey King gets 10 peaches and the rest each get 5, there will be 10 peaches surplus. So, there are a total of peaches."}, {"key": "1490", "content": "A porter transports $$1000$$ glass bottles, with a fee of $$0.3$$ yuan per bottle for transportation, but compensation of $$0.5$$ yuan for each broken bottle. After the transport, the porter earned a total of $$260$$ yuan in fees. How many bottles were accidentally broken during the transport?"}, {"key": "1491", "content": "In a cage with chickens and rabbits, the number of chickens is twice the number of rabbits, with a total of 104 legs. Then there are chickens, and there are rabbits."}, {"key": "1492", "content": "On a vacant lot, there are cars and tricycles totaling $$23$$ vehicles. The cars have $$4$$ wheels each, and the tricycles have $$3$$ wheels each. Altogether, these vehicles have $$75$$ wheels. How many tricycles are there?"}, {"key": "1493", "content": "A book of $$327$$ pages, its page numbers consist of digits."}, {"key": "1494", "content": "Count from $$1$$ to $$200$$, there is a digit \"3\"."}, {"key": "1495", "content": "In trapezoid $$ABCD$$, the length of the top base $$DC$$ is $$6$$ cm, the length of the bottom base $$AB$$ is $$9$$ cm, knowing that the area of the trapezoid is $$45$$ square centimeters, then the height $$DE$$ of the trapezoid is cm.\n question_1495-image_0"}, {"key": "1496", "content": "A big monkey picked a bunch of peaches and distributed them to a group of little monkeys to eat. If among them two little monkeys each received 4 peaches, and the rest each received 2 peaches, then 4 peaches remained in the end; if one of the little monkeys received 6 peaches, and the rest each received 4 peaches, then there were 12 peaches short. How many peaches did the big monkey pick in total, and how many little monkeys are there in total."}, {"key": "1497", "content": "The school cultural festival opens on September 20th and ends on the evening of November 1st. The festival is held for a total of days."}, {"key": "1498", "content": "Xiaohong has some chickens at home, there are $$13$$ more yellow chickens than black chickens, and $$18$$ less than white chickens. The number of white chickens is $$2$$ times that of yellow chickens, and the total number of white chickens, yellow chickens, and black chickens is\uff0e"}, {"key": "1499", "content": "A solid square formation, with each side of the outer layer having $$10$$ pieces, the second layer from the outside in total has pieces."}, {"key": "1500", "content": "The older brother and younger brother study at the same school. The older brother walks 65 meters per minute, and the younger brother walks 40 meters per minute. One day, the younger brother starts walking 5 minutes earlier than the older brother, who then leaves home. When the younger brother reaches the school, the older brother catches up exactly at the same time, then how far is their home from the school in meters."}, {"key": "1501", "content": "Hua Hua went to the store and bought $$2$$ pencils, $$2$$ erasers, and a number of rulers, paying a total of $$55$$ yuan. Knowing that a ruler costs $$3$$ yuan each, is the number of rulers Hua Hua bought odd or even ( )"}, {"key": "1502", "content": "When Sisi left the school, she saw that the lights in the first grade four classroom were not turned off, so she went to help turn them off. In her haste, she couldn't remember how many times she pressed the switch, only that the lights were off in the end. Which of the following numbers could not possibly be the number of times she pressed the switch?"}, {"key": "1503", "content": "Among the following numbers, there are those that can be divided by $$2$$; those that can be divided by $$5$$; those that can be divided by $$4$$; and those that can be divided by $$8$$.\n$$234$$  $$789$$  $$7756$$  $$8865$$  $$3728$$  $$8064$$"}, {"key": "1504", "content": "Six natural numbers: $$234$$, $$530$$, $$658$$, $$54367$$, $$90816$$, $$342125$$ among them. ($$1$$) The number of them divisible by $$2$$ is , and the number divisible by $$5$$ is . ($$2$$) The number of them divisible by $$4$$ is , and the number divisible by $$25$$ is ."}, {"key": "1505", "content": "6 natural numbers: 234, 530, 658, 54367, 90816, 342125. The number of them that can be divided by 8 is . The number of them that can be divided by 125 is "}, {"key": "1506", "content": "Among the following four-digit numbers, there are a few that can be divided by $$9$$.\n$$2304\uff0c 4389\uff0c 9801\uff0c 4728 \uff0c 3205 \uff0c 4090\uff0c 2358\uff0c 1108$$"}, {"key": "1507", "content": "Fill in the appropriate number in the \"$$\\square$$\" of the multiplication vertical form below to make the vertical form valid, the product is.\n question_1507-image_0"}, {"key": "1508", "content": "In the number puzzle shown below, the dividend is.\n22\n\n\n\n\n\u25a1\n\u25a1\n\n\n\u25a1\n\u25a1\n\u25a1\n\n\n6\n\u25a1\n\n\n\n\u25a1\n\u25a1\n2\n\n\n\u25a1\n\u25a1\n\u25a1\n\n\n\n\n0"}, {"key": "1509", "content": "As shown in the diagram, fill in the appropriate numbers in the boxes in the diagram to make the division long division correct. Then, the obtained quotient is.\n question_1509-image_0"}, {"key": "1510", "content": "Calculate: $$9+99+999+9999+99999=$$."}, {"key": "1511", "content": "Calculate: $$201620162016\\div 6300630063=$$\uff0e"}, {"key": "1512", "content": "Calculate $$13+103+1003+10003+100003$$=\uff0e"}, {"key": "1513", "content": "$$999999\\times 444444$$=\uff0e"}, {"key": "1514", "content": "Calculate: $$1987+9871+7198+8719=$$."}, {"key": "1515", "content": "Please circle three adjacent numbers in a row in the table, so that the sum of the three numbers is $$60$$.\n\n\n\n$$1$$\n$$2$$\n$$3$$\n$$4$$\n\n\n$$5$$\n$$6$$\n$$7$$\n$$8$$\n\n\n$$9$$\n$$10$$\n$$11$$\n$$12$$\n\n\n\n$$\\cdots $$\n\n$$\\cdots $$\n\n$$\\cdots $$\n\n$$\\cdots $$"}, {"key": "1516", "content": "As shown in the figure, natural numbers starting from $$7$$ are arranged according to a certain rule, please answer: \n($$1$$) $$72$$ is in row , column ;\n($$2$$) The number in the $$4$$th row and $$22$$nd column is.\n question_1516-image_0"}, {"key": "1517", "content": "In a residential area, there are $$5$$ cars needing to refuel at the gas station, and the time they take to refuel are respectively $$6$$, $$2$$, $$8$$, $$9$$, $$5$$ minutes. Currently, there is only one pump available at the gas station, so the shortest total time for these five cars to refuel and wait is minutes."}, {"key": "1518", "content": "It is known that Xiao Ming walks $$70$$ meters per minute, and Xiao Hong walks $$55$$ meters per minute. Both start from locations $$A$$ and $$B$$ at the same time. If they walk towards each other, they meet after $$6$$ minutes; if they walk in the same direction, Xiao Ming catches up with Xiao Hong after a certain number of minutes."}, {"key": "1519", "content": "Multiple choice question: Cars A and B start from two locations 1912 kilometers apart and head towards each other. Car A travels at 64 kilometers per hour, and Car B travels at 56 kilometers per hour. Car B departs 2 hours before Car A. After how many hours of travel does Car A meet Car B? ( )"}, {"key": "1520", "content": "Locations A and B are $$120$$ kilometers apart. A car from location A departs, traveling at $$20$$ kilometers per hour. At the same time, a car from location B departs, traveling at $$30$$ kilometers per hour. Both cars travel in the same direction, with the B car behind the A car. After how many hours can the B car catch up with the A car?"}, {"key": "1521", "content": "The Fat Sheep School organized the little sheep to line up and walk to the outing, with the queue being a total length of 630 meters, walking at a speed of 60 meters per minute. Fei Yangyang, at the end of the line, caught up to the front with a speed of 150 meters per minute, then immediately returned to the back of the line, using a total of minutes."}, {"key": "1522", "content": "Location A and B are $$520$$ km apart, a passenger train and a freight train leave from the two locations at the same time and meet after $$4$$ hours. The freight train travels $$48$$ km per hour, and by the time they meet, the passenger train has traveled more kilometers than the freight train."}, {"key": "1523", "content": "The equation that has the same answer as $$6\\times \u25a1-15=43$$ is ( )."}, {"key": "1524", "content": "Find the value represented by the symbol below.$$5\\times( \\blacksquare+1) =29 -\\blacksquare$$, then $$ \\blacksquare=$$"}, {"key": "1525", "content": "The equation that has the same answer as $$7a-6=43$$ is ( )."}, {"key": "1526", "content": "Subtract twice a certain number from $$42$$, the difference is $$24$$, find this number."}, {"key": "1527", "content": "This year, the age difference between father and son is $$25$$ years, the father's age is $$6$$ times the son's age, the father's age this year is."}, {"key": "1528", "content": "The perimeter of a rectangle is $$60$$ cm, the length is $$23$$ cm, and the width is cm."}, {"key": "1529", "content": "The image below shows a $$6\\times 6$$ area with $$7$$ trees planted. It is now required to set up tents on the unoccupied ground next to the trees, and the tents must be set up adjacent to a tree. No two tents can share a common point, and the number of tents in each row is as shown on the far left, with the number of tents in each column as shown at the top. There are a total of tents.\n question_1529-image_0"}, {"key": "1530", "content": "Loop puzzles, also known as number loops, involve connecting lines between adjacent grid points to form a single continuous loop without crossings or breaks. The numbers in the cells indicate the number of lines that should be drawn on the four sides of that cell; cells without numbers have no restrictions on the number of lines. Question: In the diagram, is there a line connecting the two points encircled ( )?\n question_1530-image_0"}, {"key": "1531", "content": "Setting up tents: The picture below shows a $$5\\times 5$$ area with $$5$$ trees. Now, it's required to set up tents on empty land not occupied by trees, and the tents must be set up beside a tree. No two tents can share a common point, and the number of tents in each row and each column is shown on the far right and bottom, respectively. Is there a tent in the 3rd row and 3rd column? ( )\n question_1531-image_0"}, {"key": "1532", "content": "In the picture, there are various ways to form the sentence 'Celebrating Macao's return.'\n question_1532-image_0"}, {"key": "1533", "content": "The shortest route from $$A$$ to $$B$$ has several lines.\n question_1533-image_0"}, {"key": "1534", "content": "A spider is at point $$A$$ on the top of a rectangular wooden block. It is known that the length of the rectangular block is $$80$$ cm, width $$40$$ cm, and height $$80$$ cm. The spider can only crawl on the edges, and cannot crawl the same edge twice. How far can the spider crawl at most in centimeters. question_1534-image_0"}, {"key": "1535", "content": "Divide $$14$$ identical exercise books into $$3$$ piles of different amounts, there are several different ways to do this."}, {"key": "1536", "content": "Split $$18$$ into the sum of three different non-zero natural numbers, but the three natural numbers can only be chosen from $$1\\sim 9$$. How many different ways of splitting are there, please list them all."}, {"key": "1537", "content": "Divide $10$ identical rulers among $3$ children, with each child getting at least one ruler, and there are different ways to divide them."}, {"key": "1538", "content": "The diagram below contains $$6$$ points and $$9$$ line segments. An ant starts from point $$A$$ and crawls to point $$C$$, following some of the line segments. If an ant can pass through the same point or the same line segment at most once, how many different ways can the ant crawl from point $$A$$ to point $$C$$? question_1538-image_0"}, {"key": "1539", "content": "Answer the following questions: Fill in the appropriate numbers in the blanks to make the vertical operations in the diagram correct, then the sum of the additions is. question_1539-image_0"}, {"key": "1540", "content": "Answer the following question: In the following equation, the same symbol represents the same digit and different symbols represent different digits. According to this equation, it can be inferred that: $$\\square +\\bigcirc +\\triangle +$$\u2606$$=$$. question_1540-image_0"}, {"key": "1541", "content": "Answer the following questions: In the subtraction equation below, each shape represents a number, with different shapes representing different numbers. What is the value of \u25b3? question_1541-image_0"}, {"key": "1542", "content": "As shown in the diagram, the numbers in the spaces are digits from $$3$$ to $$8$$ (which can be reused). Therefore, the sum of the numbers in these $$6$$ spaces is. question_1542-image_0"}, {"key": "1543", "content": "Mingming, Honghong, and Tiantian have a total of $$60$$ apples. Mingming has $$3$$ times the number of apples that Tiantian has, and Honghong has $$2$$ times the number of apples that Tiantian has minus $$6$$. How many apples does Tiantian have?."}, {"key": "1544", "content": "Damao's age $$5$$ years ago was equal to Ermao's age $$7$$ years from now. The sum of Damao's age $$4$$ years from now and Ermao's age $$3$$ years ago is $$35$$ years. Thus, Damao's age this year is $$23$$ years old, and Ermao's age this year is $$11$$ years old"}, {"key": "1545", "content": "It is known that the father is $$6$$ years older than the mother. $$2$$ years ago, the sum of the ages of the father and the mother was $$7$$ times the age of their son. In $$3$$ years, the sum of their ages will be $$9$$ years more than $$5$$ times the age of their son. Another year later, the mother's age will be twice the age of their son."}, {"key": "1546", "content": "The combined age of the two brothers this year is $$30$$ years old. When the older brother was as old as the younger brother is now, the younger brother's age was exactly half that of the older brother's age at that time. The older brother is years old this year."}, {"key": "1547", "content": "In the same plane, $$200$$ lines have at most how many different intersection points."}, {"key": "1548", "content": "A class of students went rowing. They calculated that by adding one more boat, each boat would fit exactly $$4$$ people; if one boat was removed, each boat would fit exactly $$5$$ people. Question: How many students are there in the class. question_1548-image_0"}, {"key": "1549", "content": "As shown in the diagram, color the five sections $$ABCDE$$ with $$4$$ different colors, where adjacent sections cannot be colored with the same color, and non-adjacent sections can be colored with the same color. How many different coloring methods are there for this drawing? question_1549-image_0"}, {"key": "1550", "content": "Using $$5$$ different colors to color the figure below, requiring adjacent areas (two areas with a common edge are called adjacent) to be colored differently. If colors can be reused, there are a total of different coloring methods. question_1550-image_0"}, {"key": "1551", "content": "Vera went to the flower shop to buy flowers to decorate the living room. The flower shop had $$5$$ pots of yellow flowers, $$7$$ pots of red flowers, and $$6$$ pots of pink flowers. Vera wanted to choose $$2$$ pots of flowers of different colors. Thus, she had several different ways to choose."}, {"key": "1552", "content": "At the sports meet, there are four running events: $$50$$ meters, $$100$$ meters, $$200$$ meters, and $$400$$ meters. It is stipulated that each participant can only participate in one of them. If A, B, C, and D four students register for these four events, please answer:\n(1) If each student can freely register for any of these four events, there are a total of types of registration methods;\n(2) If the four students register for different events from each other, there are a total of types of registration methods."}, {"key": "1553", "content": "There are $$5$$ buildings, with the number of floors ranging from $$2-6$$ floors. Taller buildings will block the view of shorter buildings. For example, in the figure, looking from the left arrow, you can only see $$2$$ buildings ($$3$$-story and $$6$$-story buildings), and from the right arrow, you can see $$3$$ buildings (4-story, $$5$$-story, and $$6$$-story buildings). If you want to see $$1$$ building from the left and $$3$$ buildings from the right, there are different possible situations. question_1553-image_0"}, {"key": "1554", "content": "The English word for \"\u6570\u5b66\" is \"$$MATH$$\". Color the letters with five different colors: red, yellow, blue, green, and purple, ensuring each letter is painted a different color. There are a total of different combinations of these colors."}, {"key": "1555", "content": "From the digits $$2$$, $$4$$, $$6$$, $$8$$, you can form numbers without repeating any digit."}, {"key": "1556", "content": "Xiaohua together with his father, mother, grandfather, and grandmother took a family portrait. It is known that Xiaohua cannot sit in the middle position. How many different arrangements are there?"}, {"key": "1557", "content": "Olympic venues implement garbage sorting. Five trash bins are placed at each location, marked from left to right: batteries, plastic, waste paper, cans, non-recyclable, as shown in the figure. Now, it is planned to paint the five trash bins in one of the three colors: red, green, or blue, with the requirement that adjacent bins must be different colors, and the bin for recycling waste paper cannot be painted red. There are a total of $$32$$ ways to paint them.\n question_1557-image_0"}, {"key": "1558", "content": "Color the figure below with $$5$$ different colors, requiring adjacent areas (two areas with a common edge are considered adjacent) to be colored differently. If colors can be reused, there are a total of different coloring methods. question_1558-image_0"}, {"key": "1559", "content": "As shown in the diagram, there are four countries on the map: $$A$$, $$B$$, $$C$$, and $$D$$. Now, using five different colors to color the map, in order to make the colors of adjacent countries different, there are several different coloring methods. question_1559-image_0"}, {"key": "1560", "content": "Using the digits $$0$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, how many unique five-digit even numbers can be formed without repeating any digit."}, {"key": "1561", "content": "Dongdong has $$9$$ cards, among which $$4$$ cards have the number $$2$$, $$2$$ cards have the number $$3$$, and $$3$$ cards have the number $$5$$. By randomly selecting any number of cards and calculating the product of the numbers on the cards (you can take just $$1$$ card or all $$9$$ cards), you can get a total of different products."}, {"key": "1562", "content": "If you are to choose 2 books from 15 different language books, 20 different math books, and 10 different foreign language books, ensuring they are from different subjects, then there are a total of different choices."}, {"key": "1563", "content": "Calculate: $$(12\\times 5)\\div (5\\div 3)\\div (4\\div 6)\\times (4\\div 3)=$$."}, {"key": "1564", "content": "Calculate: $$(4\\times 5\\times 6\\times 9\\times 11\\times 17)\\div (36\\times 66\\times 85)$$=."}, {"key": "1565", "content": "It is stipulated that the operation represented by $$\\odot$$ is as follows, $$a\\odot b=8\\times a-b$$. Calculate: (1) $$\\left( 4\\odot 2 \\right)\\odot 3$$=; (2) $$x\\odot 7=65$$, find $$x=$$."}, {"key": "1566", "content": "If $$4\\Delta 2=4+44=48$$, $$2\\Delta 3=2+22+222=246$$, $$1\\Delta 4=1+11+111+1111=1234$$, then $$1\\Delta 9=$$."}, {"key": "1567", "content": "Calculate: (1) $$1326\\div 34\\div 13=$$\uff0e(2) $$527\\times 15\\div 5=$$\uff0e(3) $$7600\\div 25\\div 4=$$\uff0e(4) $$39000\\div 125\\div 4\\div 26=$$\uff0e"}, {"key": "1568", "content": "Calculate: \n(1) $$(1300+26)\\div 13=$$.\n(2) $$(1100-77-88)\\div 11=$$.\n(3) $$13\\div 10+117\\div 10= $$.\n(4) $$981\\div 50+19\\div 50=$$."}, {"key": "1569", "content": "Calculate: $$29\\times (1008\\div 8-49\\times 18\\div 7\\div 6)\\div 40\\times 8=$$."}, {"key": "1570", "content": "Define $$a*b$$ as the average of all natural numbers between $$a$$ and $$b$$ (inclusive) that have the same parity (even or odd) as $$a$$. For example: $$7*14=(7+9+11+13)\\div 4=10$$, $$18*10=(18+16+14+12+10)\\div 5=14$$. To make the equation \u25a1$$*(19*99)=80$$ true by filling in the square with an appropriate natural number, what is the number to be filled in?"}, {"key": "1571", "content": "Calculation: $$12\\times 72\\times 162\\times 432\\div 2\\div 3\\div 4\\div 8\\div 9\\div 16\\div 27\\div 81$$=."}, {"key": "1572", "content": "Define \"$$\\odot $$\" as the operation: $$a\\odot b=3\\times a+2\\times b$$, compute: (1) $$4\\odot 5=$$\uff0e(2) $$4\\odot 2\\odot 3=$$\uff0e(3) $$4\\odot (2\\odot 3)=$$\uff0e"}, {"key": "1573", "content": "Calculate: $$1\\div 2017+2\\div 2017+3\\div 2017+4\\div 2017+\\cdots +2017\\div 2017=$$."}, {"key": "1574", "content": "Given $$a\\nabla b=b\\left( a+1 \\right)-a\\left( b-1 \\right)$$, calculate: $$\\left( 2\\nabla 1 \\right)+\\left( 4\\nabla 3 \\right)+\\left( 6\\nabla 5 \\right)+\\left( 8\\nabla 7 \\right)+\\left( 10\\nabla 9 \\right)=$$."}, {"key": "1575", "content": "During the festival, fairy lights were installed on a $$6$$-storey building, with a total of $$666$$ lights installed. It is known that starting from the second floor, each floor has $$6$$ fewer lights than the one below it. How many lights were installed on the top floor."}, {"key": "1576", "content": "There are five distinct non-zero natural numbers, the smallest of which is $$7$$. If one of them decreases by $$20$$ and the other four increase by $$5$$, the result will still be these five numbers. The sum of these five numbers is."}, {"key": "1577", "content": "$$n\\forall b$$ denotes $$n$$ times $$3$$ minus $$b$$. For example: $$1\\forall 2=1\\times 3-2=1$$, then $$10\\forall 6$$."}, {"key": "1578", "content": "Calculate: $$25\\div 7+24\\div 7=$$."}, {"key": "1579", "content": "Arithmetic sequence: $$7$$, $$11$$, $$15$$, $$\\ldots$$, the $$30th$$ term is."}, {"key": "1580", "content": "Calculate: $$6+12+18+24+\\cdots+96=$$."}, {"key": "1581", "content": "A train shuttles back and forth between Changsha and Wuhan, stopping at a total of $$4$$ stations, and needs to prepare different types of tickets."}, {"key": "1582", "content": "If the 4th number of an arithmetic sequence is 31, and the 7th number is 49, then its 10th number is."}, {"key": "1583", "content": "Calculate: $$11\\div 17+17\\div 19+20\\div 17+40\\div 19+37\\div 17$$=."}, {"key": "1584", "content": "Using $$4$$ different colors of watercolor pens to color the letters \u201c$$ABCD$$\u201d, requiring that different letters be colored with different pens, there are a total of different combinations of colors available."}, {"key": "1585", "content": "In an arithmetic sequence, the first term is $$11$$, and the $$11$$th term is $$51$$. Find the common difference."}, {"key": "1586", "content": "The map has four countries: $$A$$, $$B$$, $$C$$, and $$D$$ (as shown below). Now there are five colors available for coloring the map: red, yellow, blue, green, and purple, to ensure that adjacent countries have different colors. Not every color must be used, resulting in a number of coloring methods.\n question_1586-image_0"}, {"key": "1587", "content": "Sum: $$6+10+14+\\cdots +50+54$$=."}, {"key": "1588", "content": "Calculate: $$105+107+109+111+113+115+117=$$."}, {"key": "1589", "content": "The diameters of five pulleys form an arithmetic sequence. It is known that the smallest and the largest diameters of the pulleys are $$120$$ mm and $$216$$ mm, respectively. Thus, the diameter of the second pulley is ____ mm, the diameter of the third pulley is ____ mm, and the diameter of the fourth pulley is ____ mm."}, {"key": "1590", "content": "In a kindergarten, $$378$$ children form several circles (one circle within another) for a game. It is known that the innermost circle has $$22$$ people and the outermost circle has $$62$$ people. If the difference in the number of people between two adjacent circles is the same, then the difference in the number of people between two adjacent circles is."}, {"key": "1591", "content": "There is a pile of logs with uniform thickness, arranged in a trapezoid shape. Starting from the top, each layer going down adds one log, with a total of $$28$$ layers. The bottom layer has $$32$$ logs, so there are a total of $$x$$ logs in this pile."}, {"key": "1592", "content": "There is a piece of paper, the first time it is cut into $$7$$ pieces; the second time, pick any one of the pieces from the first cut, and cut it into $$7$$ pieces again; the third time, again pick any piece from all the pieces obtained before, and cut it into $$7$$ pieces $$\\cdots \\cdots$$ and so on. After the $$10th$$ cut, the total number of pieces cut out is, and is it possible that after a certain cut, the total number of pieces is exactly $$2019$$: . (Fill in Yes or No)"}, {"key": "1593", "content": "A natural number can be expressed as the sum of $$5$$ consecutive natural numbers, and can also be expressed as the sum of $$7$$ consecutive natural numbers. Therefore, listing such natural numbers from smallest to largest, the first $$3$$ numbers are , , ."}, {"key": "1594", "content": "If the fourth number of an arithmetic sequence is $$21$$, and the sixth number is $$33$$, then the eighth number is."}, {"key": "1595", "content": "The sum of all the numbers that are multiples of $$3$$ from $$10\\sim 90$$ is."}, {"key": "1596", "content": "Calculate: $$3+4+5+\\cdots +99+100$$=."}, {"key": "1597", "content": "For the series of numbers $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$19$$ $$\\cdots$$, the $$10$$th number is, $$49$$ is which number in this series, the difference between the $$100$$th number and the $$50$$th number is."}, {"key": "1598", "content": "Viola first wrote an arithmetic sequence on the blackboard. As soon as she finished, Eddie rushed to the podium and erased most of the numbers, leaving only the fourth number $$31$$ and the tenth number $$73$$. The difference between two consecutive numbers in this arithmetic sequence is, and the first number is."}, {"key": "1599", "content": "A series of numbers consists of $$13$$ numbers, each number is $$7$$ more than its predecessor, and the $$13$$th number is $$125$$, the first number is."}, {"key": "1600", "content": "To celebrate the 16th anniversary of its founding, Siyuan School organized a sports meet. During the opening ceremony, the representative teams of each grade entered the arena in sequence. The first-grade students formed a solid square formation to perform gymnastics, with $$18$$ people on each side of the outermost layer. How many people are there in the entire square formation?"}, {"key": "1601", "content": "After the sports meeting ended, all the students went to the gymnasium for the closing ceremony. The volunteers congratulated the athletes with beautiful flowers, and arranged a five-layer hollow square formation of flower beds in the open space in front of the gymnasium, using a total of $$240$$ pots of flowers. How many pots of flowers are there in the middle layer? How many in the outermost layer? How many in the innermost layer?"}, {"key": "1602", "content": "A group of students are arrayed in a three-tier hollow square, with an additional $$9$$ people. If the hollow center were to increase by two tiers, there would be $$15$$ fewer people. There are students."}, {"key": "1603", "content": "To prepare for the school's group dance competition, the third-grade students are lining up in formation. If they arrange themselves into a 3-layer hollow square, there are 10 more people than needed. If they add another layer in the hollow middle part, there are 6 fewer people. Thus, a total number of students participating in the rehearsal is."}, {"key": "1604", "content": "If there is a 3-layer hollow triangular array with each side of the outer layer having 17 chess pieces, then there are a total of chess pieces."}, {"key": "1605", "content": "The students of Class 1, Grade 4 participated in a broadcast gymnastics competition, forming a square formation with each row and each column having $$8$$ people. How many students are there in the square formation, and how many would remain if a row and a column are removed?"}, {"key": "1606", "content": "The new semester begins, and the Young Pioneers holding flowers have formed a square formation with two layers on each side around a float, with the outermost layer having $$13$$ people on each side, and there are people from the Young Pioneers around the float."}, {"key": "1607", "content": "A square wall is tiled with small square tiles in two colors: red and green. Starting from the outside and moving inward, the outermost layer of tiles is red, the second layer is green, the third layer is red, the fourth layer is green, and so on, alternating colors layer by layer, using a total of $$400$$ tiles. The difference in the number of the two colors of tiles is __."}, {"key": "1608", "content": "The school is going to have a gymnastics performance where participants stand in a triangle formation of $$10$$ rows.\uff08\uff11\uff09A total of people participate in the performance.\uff08\uff12\uff09If the people on the outermost layer hold ribbons, then people are holding ribbons. question_1608-image_0"}, {"key": "1609", "content": "There are $$196$$ Go pieces, arranged into a solid $$14\\times 14$$ square matrix. Players A and B take turns removing all the pieces from the outermost layer until all pieces are taken, with player A taking more pieces than player B."}, {"key": "1610", "content": "The students of Sunshine Elementary School are arranged in a solid square formation on the playground. It is known that the outermost circle consists of boys and the next inner circle is made up of girls, followed by boys $$\\cdots \\cdots $$ and so on until the very center. If the total number of boys is $$52$$ more than the total number of girls, how many students are there in total?"}, {"key": "1611", "content": "A certain troop's soldiers are arranged in a solid square formation during a march. An additional group of $$31$$ people joins their formation, resulting in an increase of one row both horizontally and vertically, now totaling a certain number of soldiers."}, {"key": "1612", "content": "Eddie used some chess pieces to form a two-layer hollow square matrix. Later, he added $$28$$ chess pieces to make the figure into a three-layer hollow square matrix. At the beginning, the maximum number of chess pieces Eddie could have placed is , and the minimum possible number of chess pieces he could have placed is ."}, {"key": "1613", "content": "Students in the fourth grade at Hope Primary School were arranged in a solid square formation, with 5 people left over. If one row was added both horizontally and vertically, forming a slightly larger solid square, then 26 people would be missing. There are people in the fourth grade at Hope Primary School."}, {"key": "1614", "content": "$$120$$ chess pieces are arranged in a three-layer hollow square matrix, with each side of the innermost layer having one chess piece."}, {"key": "1615", "content": "A fourth grade class at a certain school is arranged in a square formation, with the number of people on the outermost layer being $$40$$ people. Thus, each side of the outermost layer of the square has people, and the entire square has people in total."}, {"key": "1616", "content": "In a certain barbershop, there is only one barber, but five customers arrived at the same time. Based on the hairstyles they want, it respectively takes $$10$$, $$12$$, $$15$$, $$20$$, and $$24$$ minutes. Arrange their haircut order in a way that minimizes the total time spent on haircuts and waiting. The minimum total time is in minutes."}, {"key": "1617", "content": "There are two barbers in the barbershop now, and $$6$$ customers have arrived at the same time. Based on the hairstyles they want, it respectively takes $$8$$, $$10$$, $$12$$, $$15$$, $$20$$, and $$24$$ minutes. Arrange their haircut order rationally, so the total waiting time (including haircut time) for the $$6$$ people is minimized. What is the minimum time in minutes."}, {"key": "1618", "content": "There are $$8$$ people each holding a bucket and going to the tap to get water at the same time. It takes $$1$$ minute to fill the first person's bucket, $$2$$ minutes to fill the second person's bucket, and so on. (1) When there is only one tap, arrange the $$8$$ people to fetch water so that their total fetching and waiting time is minimized, then the minimum time is minutes."}, {"key": "1619", "content": "There are $$8$$ people each holding a bucket and going to the tap to fetch water at the same time. It takes $$1$$ minute to fill the first person's bucket, $$2$$ minutes for the second person's bucket, and so on. (2) When there are two taps, arranging the $$8$$ people to fetch water in such a way that their total fetching and waiting time is minimized, the least amount of time needed is minutes."}, {"key": "1620", "content": "The maintenance station of the Sunshine Electric Vehicle Company has $$7$$ electric vehicles needing repairs. If a single worker repairs these $$7$$ electric vehicles, the respective repair times are $$12$$, $$17$$, $$8$$, $$18$$, $$23$$, $$30$$, $$14$$ minutes. The loss for each electric vehicle for every $$1$$ minute of downtime is $$11$$ yuan. Now, with $$3$$ maintenance workers of the same efficiency working independently: (1) A rational arrangement can minimize the economic loss, so the minimum loss is yuan."}, {"key": "1621", "content": "Answer the following questions: As shown in the diagram, there are five residential buildings $$A$$, $$B$$, $$C$$, $$D$$, $$E$$ on the street, each with the same number of residents. Now, a bus stop is to be established. In order for the sum of the distances from the five buildings to the bus stop to be the shortest, where should the bus stop be located? question_1621-image_0"}, {"key": "1622", "content": "Answer the following questions: As shown in the figure, there are six residential buildings $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, $$F$$ on the street, each with the same number of people. Now, if a bus stop is to be established to minimize the total distance residents need to walk to reach the stop, where should the bus stop be located? question_1622-image_0"}, {"key": "1623", "content": "Answer the following questions: As shown in the diagram, there is a road running from west to east with schools $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, having $$200$$, $$300$$, $$400$$, $$500$$, and $$600$$ people respectively. The distance between any two adjacent schools is $$100$$ meters. Now, a public bus station is to be built at the entrance of one of the schools to minimize the total distance for everyone to reach the station. Where should the bus station be built? question_1623-image_0"}, {"key": "1624", "content": "The figure shows the schematic diagram of the roads between five villages $$A$$, $$B$$, $$C$$, $$D$$, $$E$$. The number in $$\\bigcirc$$ represents the number of students who need to go to school from each village, and the number on the roads represents the distance between two villages (in kilometers). Now, a primary school needs to be built in one of the five villages. To minimize the total distance traveled by all students to the school, the primary school should be built in ( ). question_1624-image_0"}, {"key": "1625", "content": "There is a water tower to provide water for $$6$$ residential points beside a certain highway (as shown in the picture, unit: kilometers). There are two types of water pipes to be installed: thick pipes can supply water to $$6$$ residential points, and thin pipes can only supply water to $$1$$ residential point. The cost of thick pipes is $$7000$$ yuan per kilogram, and the cost of thin pipes is $$2000$$ yuan per kilometer. Arrange this project reasonably to minimize the cost, the cost should be yuan. question_1625-image_0"}, {"key": "1626", "content": "Answer the question as required. (1) Beijing and Shenzhen have $$10$$ and $$6$$ identical machines, respectively, preparing to give $$11$$ to Wuhan and $$5$$ to Xi'an. The freight for each machine is shown in the table. To minimize the total freight cost, the minimum freight cost is yuan. question_1626-image_0"}, {"key": "1627", "content": "Answer the question as required. (2) Beijing and Shanghai have $$10$$ and $$6$$ identical machines, respectively, prepared to send $$11$$ to Wuhan and $$5$$ to Xi'an. The freight for each machine is shown in the table. If the goal is to minimize the total shipping cost, the minimum total shipping cost is yuan. question_1627-image_0"}, {"key": "1628", "content": "It is known that a pack of 5 red pens is 61 yuan, blue pens 70 yuan; a pack of 3 red pens is 40 yuan, blue pens 47 yuan; purchases must be made by the pack. If at least 47 red and blue pens each must be purchased, the minimum cost is yuan."}, {"key": "1629", "content": "There are ten villages located on a road departing from a large county town (as shown in the diagram below, with the distance unit being kilometers). In order to install water pipes to supply tap water from the county to each village, two types of water pipes can be used: thick pipes that can supply all the villages, and thin pipes that can only supply one village. The cost for thick pipes is $$8000$$ RMB per kilometer, and for thin pipes, it is $$2000$$ RMB per kilometer. By appropriately matching and connecting thick and thin pipes, the total project cost can be reduced. According to what you think is the most cost-saving method, the cost should be RMB. question_1629-image_0"}, {"key": "1630", "content": "On a road, there is a warehouse every $$100$$ kilometers (as shown in the figure), there are a total of $$5$$ warehouses. Warehouse number one contains $$10$$ tons of goods, warehouse number two has $$20$$ tons of goods, and warehouse number five contains $$40$$ tons of goods, the other two warehouses are empty. Now, if we want to consolidate all the goods into one warehouse, and it costs $$1$$ yuan to transport one ton of goods for one kilometer, then the minimum amount of transportation fees required is. question_1630-image_0"}, {"key": "1631", "content": "There are eight lathes in the workshop that malfunctioned at the same time. It is known that the repair time for the first to the eighth lathe is $$4$$, $$8$$, $$9$$, $$12$$, $$13$$, $$16$$, $$15$$, $$14$$ minutes respectively. There are two repairmen with the same efficiency available. The task is to arrange the repairs so that the duration from the start to the end of the repair is the shortest. This shortest time is in minutes."}, {"key": "1632", "content": "The southern and northern warehouses have 30 tons and 20 tons of goods respectively, preparing to deliver 15 tons to Warehouse A, 25 tons to Warehouse B, and 10 tons to Warehouse C. The freight cost per ton of goods is as shown in the table below (unit: Yuan). Therefore, the minimum freight cost required is.\n\n\n\n\nA\nB\nC\n\n\nSouthern Warehouse\n$$12$$\n$$5$$\n$$10$$\n\n\nNorthern Warehouse\n$$10$$\n$$6$$\n$$13$$"}, {"key": "1633", "content": "As shown: the numbers labeled on the left of each row and on the top of each column represent the count of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_1633-image_0"}, {"key": "1634", "content": "As shown in the figure: the numbers marked on the left side of each row and on the top side of each column represent the number of consecutive black blocks in that row or column. Kids, based on these numbers, can you mark all the black blocks? question_1634-image_0"}, {"key": "1635", "content": "As shown in the picture: The numbers on the left side of each row and the top side of each column represent the sequence of continuous black blocks in that row or column. Can you, kids, mark all the black blocks based on these numbers? question_1635-image_0"}, {"key": "1636", "content": "As shown in the diagram: the numbers marked on the left side of each row and on the top side of each column represent the number of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? ( ) question_1636-image_0"}, {"key": "1637", "content": "As shown: The numbers marked on the left of each row and on the top of each column represent the quantity of continuous black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? ( ) question_1637-image_0"}, {"key": "1638", "content": "Driving $$125$$ sheep into $$6$$ pens, the pen with the most sheep has at least sheep."}, {"key": "1639", "content": "Some students went to the administrator to borrow $$50$$ basketballs. The administrator said: If you take them all at once, there will definitely be one person who has to take at least $$8$$. So, what is the maximum number of students? ( )."}, {"key": "1640", "content": "A deck of playing cards has a total of $$54$$ cards, including $$2$$ jokers, and $$13$$ cards each of the four suits: spades, hearts, clubs, and diamonds. (2) At least how many cards must be drawn to ensure that cards of all four suits have been drawn."}, {"key": "1641", "content": "A standard deck of playing cards has $$54$$ cards in total, including $$2$$ jokers, and also has four suits: spades, hearts, clubs, and diamonds, each with $$13$$ cards. (4) At least how many cards must be drawn to guarantee that there is a \"pair\" (two jokers count as a pair) among the drawn cards."}, {"key": "1642", "content": "A deck of poker cards has $$52$$ cards after removing the two jokers, including four suits: spades, hearts, clubs, and diamonds. Each suit has $$13$$ cards with point values from $$1$$ to $$13$$. What is the minimum number of cards one must draw to ensure drawing a spade? ( )"}, {"key": "1643", "content": "There are $$9$$ yellow socks, $$7$$ green socks, $$4$$ white socks, $$2$$ red socks, $$1$$ black sock. Eddie, with his eyes closed, feels for socks: (3) At least how many socks must he grab to ensure he can form $$2$$ pairs of socks of the same color."}, {"key": "1644", "content": "Place $$17$$ apples into $$3$$ drawers, the drawer with the most apples has at least $$6$$ apples."}, {"key": "1645", "content": "To distribute $$31$$ ping pong balls into $$5$$ ping pong ball boxes, with each box having at least $$1$$ ball, the box with the most balls must have at least $$7$$ balls."}, {"key": "1646", "content": "There are four different colors of cards in the box, $$100$$, $$90$$, $$80$$, and $$70$$ pieces. Using $$59$$ cards of the same color can be exchanged for a pencil case of the same color, using $$46$$ cards of the same color can be exchanged for a notebook of the same color, and using $$24$$ cards of the same color can be exchanged for a mechanical pencil of the same color. Therefore, the maximum possible number of cards taken out at one time still cannot guarantee that the extracted cards can be exchanged for one item of each of the three types of stationery with different colors."}, {"key": "1647", "content": "There are $$5$$ black balls, $$6$$ white balls, $$7$$ red balls on the table. How many balls must be drawn blindly at minimum to ensure that all three colors of balls are drawn?"}, {"key": "1648", "content": "Drive $$50$$ cows into $$7$$ cow pens, the cow pen with the most cows will have at least $$8$$ cows."}, {"key": "1649", "content": "Every day at noon, 25 apples are distributed in the class. No matter how they are distributed, there is always someone who gets at least 3 apples. This means there can be at most people in the class."}, {"key": "1650", "content": "Among any $$40$$ people, there are at least $$4$$ people belonging to the same zodiac sign."}, {"key": "1651", "content": "The kindergarten aunt has $$72$$ candies to distribute to a number of kids at most, ensuring that no matter how they are distributed, there will always be a child who gets at least $$3$$ candies."}, {"key": "1652", "content": "45 students in class 3 of grade 3 were all born in the same year. The following statement is correct ( )."}, {"key": "1653", "content": "Students have three kinds of number cards: $$1$$, $$2$$, $$3$$, each kind with many cards. The teacher asks each student to select two or three cards to form a two-digit or three-digit number. If at least three students form the exact same number, then there must be at least a certain number of students."}, {"key": "1654", "content": "A deck of playing cards contains a total of 54 cards, including four suits: spades, clubs, hearts, and diamonds. Each suit has one card for each point value from 1 to 13, plus there are 2 joker cards. How many cards must be drawn from the deck at minimum to ensure that two cards drawn have the same point value and suit? (Assuming jokers do not have a point value)"}, {"key": "1655", "content": "A signalman has many signal flags in three colors: red, yellow, and blue. They can be taken out one at a time, or two or three at a time, and arranged in a line to represent various signals. Therefore, among $$300$$ signals, there are at least some signals that are exactly the same."}, {"key": "1656", "content": "There are some balls of the same size and shape in the pocket: there are $$8$$ red balls, $$10$$ green balls, $$12$$ yellow balls, and $$15$$ white balls. At least how many balls must be drawn to ensure that there are at least $$3$$, $$6$$, and $$9$$ balls of three different colors respectively."}, {"key": "1657", "content": "There are $$211$$ students and four different types of chocolates, with the quantity of each type of chocolate exceeding $$633$$ pieces. It is stipulated that each student can take up to three pieces of chocolate, or none at all. If grouped according to whether the type and quantity of chocolates taken are the same, then the group with the most students will have at least $$7$$ students."}, {"key": "1658", "content": "As shown in the diagram: the numbers labeled on the left side of each row and the top side of each column represent the number of continuous black squares in that row or column. Kids, can you mark all the black squares based on these numbers? question_1658-image_0"}, {"key": "1659", "content": "As shown in the picture: The numbers labeled on the left side of each row and the top of each column represent the count of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? The black block represented by the number \"1\" in the $$10^{th}$$ row is located in the $$nth$$ position (from left to right). question_1659-image_0"}, {"key": "1660", "content": "As shown in the diagram: The numbers marked on the left side of each row and the top of each column represent the amount of consecutive black squares in that row or column. Kids, can you mark all the black squares based on these numbers? question_1660-image_0"}, {"key": "1661", "content": "As shown: The numbers marked on the left of each row and the top of each column represent the number of consecutive black blocks in that row or column. Kids, based on these numbers, can you mark all the black blocks? question_1661-image_0"}, {"key": "1662", "content": "As shown in the figure: the numbers marked on the left side of each row and the top side of each column represent the count of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_1662-image_0"}, {"key": "1663", "content": "As shown in the picture: The numbers on the left of each row and the top of each column represent the amount of consecutive black blocks in that row or column. Kids, can you mark all the black blocks according to these numbers? question_1663-image_0"}, {"key": "1664", "content": "As shown in the picture: The numbers marked on the left side of each row and the top of each column represent the number of consecutive black squares in that row or column. Kids, based on these numbers, can you identify all the black squares? question_1664-image_0"}, {"key": "1665", "content": "As shown in the figure: the numbers marked on the left side of each row and on the top side of each column represent the count of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_1665-image_0"}, {"key": "1666", "content": "As shown in the diagram: the numbers marked on the left side of each row and the top of each column represent the number of consecutive black blocks in that row or column. Kids, based on these numbers, can you mark all the black blocks? question_1666-image_0"}, {"key": "1667", "content": "Transporting $$78$$ tons of goods from City A to City B, if using a truck with a capacity of $$5$$ tons for a single trip, the freight cost is $$110$$ yuan. Using a small truck with a capacity of $$2$$ tons for a single trip costs $$50$$ yuan. If it is possible to rent both large and small trucks simultaneously, the minimum freight cost needed is yuan."}, {"key": "1668", "content": "Chief Zhao went down to the village to convene a meeting of village cadres from four villages: A, B, C, D. Each pair of adjacent villages is 5 kilometers apart (as shown in the figure). The number of people attending the meeting is 8 from village A, 5 from village B, 3 from village C, and 7 from village D. Which village should Chief Zhao choose for the meeting to minimize the total distance traveled by all attendees? ( ) question_1668-image_0"}, {"key": "1669", "content": "There are $$100$$ Young Pioneers participating in a radio calisthenics competition, forming a solid square formation. The question is, how many Young Pioneers are standing around the four sides of this square."}, {"key": "1670", "content": "Fourth-grade students at Xinhua Elementary School form a solid square formation, and there are extra $$9$$ people. If one row is added both horizontally and vertically to form a slightly larger solid square, they are short of $$24$$ people. Find the total number of fourth-grade students."}, {"key": "1671", "content": "During the gymnastics performance, the sixth-grade students formed a solid square formation (with an equal number of people in each row and column). It is known that there are $$72$$ people on the outermost layer, so there are a total of people in this square formation."}, {"key": "1672", "content": "Aunt Wang needs to photocopy $$5$$ manuscripts, both front and back, if the copier can only do single-sided copying and can hold up to $$2$$ sheets at a time, then the minimum number of times she needs to copy to finish."}, {"key": "1673", "content": "Zhao, Sun, and Li, three students, went to the school clinic for treatment at the same time. Sun needed an injection, which took $$5$$ minutes; Li needed a change of dressing in surgery, which took $$3$$ minutes; Zhao only needed to apply eye drops, taking $$1$$ minute. There is only one doctor, Dr. Zhang, in the clinic. To minimize the total time the three students spend in the clinic, the shortest total time would be in minutes."}, {"key": "1674", "content": "There are $$120$$ students in the third grade of primary school, who are arranged into a three-layer hollow square matrix. If another layer is added inside, it would require additional people."}, {"key": "1675", "content": "At the carnival, there were $$100$$ students who drew tickets with numbers ranging from $$1$$ to $$100$$. The rules for awarding prizes based on ticket numbers were as follows: ($$1$$) For a ticket number that is a multiple of $$2$$, award $$2$$ pencils. ($$2$$) For a ticket number that is a multiple of $$3$$, award $$3$$ pencils. ($$3$$) Ticket numbers that are multiples of both $$2$$ and $$3$$ can receive rewards repeatedly. ($$4$$) All other ticket numbers will be awarded $$1$$ pencil. Based on this, the total number of pencils prepared for this activity at the carnival was."}, {"key": "1676", "content": "There are 30 coins with numbers $$1\\sim 30$$ facing up on a table. First, flip the coins numbered as multiples of $$3$$, then flip the coins numbered as multiples of $$4$$. In the end, there are still coins facing up."}, {"key": "1677", "content": "Students in a certain class each hold flags of three colors: red, yellow, and blue. It is known that there are a total of $$34$$ people holding red flags, $$26$$ people holding yellow flags, and $$18$$ people holding blue flags; $$9$$ people are holding both red and yellow flags, $$4$$ people are holding both yellow and blue flags, and $$3$$ people are holding both red and blue flags; $$1$$ person is holding red, yellow, and blue flags. How many people are there in this class."}, {"key": "1678", "content": "A class has $$45$$ students, many of whom joined extracurricular interest groups. $$22$$ students joined the music interest group, $$26$$ students joined the art interest group, and $$6$$ students did not join any interest groups. How many students joined both the music and art interest groups?"}, {"key": "1679", "content": "The experimental primary school features calligraphy and mathematical thinking training. There are a total of $$245$$ students in the fifth grade, among which more students participated in calligraphy training than in mathematical thinking training by $$82$$ people. There were $$44$$ students who participated in both calligraphy and mathematical thinking training, and $$63$$ students did not participate in either, so, the number of fifth-grade students at the experimental primary school who participated in mathematical thinking training is."}, {"key": "1680", "content": "The school's arts group has a total of $$45$$ members, among which $$22$$ students can play the piano, $$27$$ students can play the violin, and the number of students who can do both is exactly $$3$$ times the number of students who can do neither. Therefore, the minimum number of students who can do at least one of them is ."}, {"key": "1681", "content": "In the math interest group, there are $$35$$ people subscribing to publication $$A$$, $$21$$ people subscribing to publication $$B$$, among them $$14$$ people subscribe to both, and only $$5$$ people do not subscribe to either, so in total the math interest group has people."}, {"key": "1682", "content": "There are $$2006$$ lamps lit up, each controlled by a switch, numbered in order as $$1$$, $$2$$, $$3$$, \u2026, $$2006$$. First, turn off the lamps numbered with multiples of $$2$$ by pressing their switches once; then turn off the lamps numbered with multiples of $$3$$ by pressing their switches once, and finally, turn off the lamps numbered with multiples of $$5$$ by pressing their switches once. After these steps, the lamps that are still lit up are."}, {"key": "1683", "content": "A wooden stick that is $$180$$ centimeters long, starting from the left end, make a mark every $$2$$ centimeters, after marking, start from the left end again and make a mark every $$3$$ centimeters, then start from the left end and make a mark every $$5$$ centimeters, and then start from the left end and make a mark every $$7$$ centimeters, finally cut the wooden stick at these marks, in total, the stick can be cut into pieces of small wooden sticks."}, {"key": "1684", "content": "(1) When numbering the pages of a book, a total of $$11$$ number \"$$6$$\" was used, this book has pages."}, {"key": "1685", "content": "One page in the middle of a book was torn out, and the sum of the remaining page numbers is $$5027$$. The two page numbers on the torn sheet are the page and the page. (Fill in from smallest to largest)"}, {"key": "1686", "content": "A dictionary has a total of $$400$$ pages, the digit \u201c$$0$$\u201d appears $$ times."}, {"key": "1687", "content": "The page numbers of a novel use a total of $$127$$ digits. This book has pages."}, {"key": "1688", "content": "A book has a total of $$200$$ pages, and the page numbers from $$1$$ to $$200$$ use a total of several digits."}, {"key": "1689", "content": "Arrange the natural numbers in ascending order without gaps into one large number: $$123456789101112\\cdots$$ Question: What is the digit in the $$200$$th position from the left."}, {"key": "1690", "content": "When assigning page numbers to a book, a total of $$81$$ number \u201c$$7$$\u201ds were used. How many pages does the book have at minimum? And at maximum? ( )"}, {"key": "1691", "content": "(2) 8 players participate in a round-robin tennis tournament, where every pair of players competes in one match, so a total number of matches held is."}, {"key": "1692", "content": "(3) A number of players participated in a tennis round-robin tournament, with a total of $$45$$ matches played among the players."}, {"key": "1693", "content": "The national teams that participate in the World Cup football tournament total $$32$$, known as the top $$32$$. Among them, every $$4$$ national teams are grouped into one group. In the round-robin tournament, each national team must and can only play one match against the other teams in their group. The top two teams from each group enter the knockout stages; in the knockout stages, every two teams play one match to decide the winner, producing the top $$8$$, top $$4$$, until finally deciding the champion (first place), runner-up (second place), third place, and fourth place. (The two losers of the semi-finals will participate in the third and fourth place playoff, and the other losers in the knockout stages will no longer participate.) With this, all the matches of this World Cup will have concluded. Based on the information above, calculate the total number of matches in the whole World Cup football tournament."}, {"key": "1694", "content": "$$A$$, $$B$$, $$C$$, $$D$$, $$E$$, and Eddie participate in a round-robin tournament, and part of the matches have already been played. It is known that $$A$$ has played $$5$$ matches, $$B$$ has played $$4$$ matches, $$C$$ has played $$3$$ matches, $$D$$ has played $$2$$ matches, and $$E$$ has played $$1$$ match, so how many matches has Eddie played?"}, {"key": "1695", "content": "Four students in the class participate in a checkers competition, where every pair of students play a match. The winner of each match receives $$2$$ points, a draw awards each $$1$$ points, and the loser receives $$0$$ points. (1) The total points of the four students is points."}, {"key": "1696", "content": "Five students named A, B, C, D, and E compete in a competition, where every pair of students play one match. The winner of each match earns $$2$$ points, each gets $$1$$ point for a draw, and the loser gets $$0$$ point$$. It is known that students A, B, C, and D scored $$8$$ points, $$5$$ points, $$2$$ points, and $$2$$ points respectively. Therefore, student E's score is points."}, {"key": "1697", "content": "The average of three numbers is $$120$$. After adding another number, the average of the four numbers becomes $$150$$. What is the newly added number?"}, {"key": "1698", "content": "Given the average of five natural numbers $$A$$, $$B$$, $$C$$, $$D$$, $$E$$ is $$15$$, the average of $$A$$, $$B$$, and $$C$$ is $$13$$, and the average of $$C$$, $$D$$, and $$E$$ is $$17$$. Find $$C$$."}, {"key": "1699", "content": "Divide $$20$$ apples evenly between Mingming and his $$4$$ friends, on average each person can get apples."}, {"key": "1700", "content": "Huanhuan walks to school from home every morning. If he walks at $$50$$ meters per minute, he will be $$5$$ minutes late. If he walks at $$70$$ meters per minute, he can arrive $$5$$ minutes early. The distance from Huanhuan's home to the school is meters."}, {"key": "1701", "content": "The Monkey King distributes peaches to the little monkeys. If each little monkey gets 10 peaches, there would be 100 peaches left; if the total number of little monkeys doubled, and still, each little monkey got 10 peaches, there would be 200 peaches short. So, how many peaches did the Monkey King prepare in total."}, {"key": "1702", "content": "A school has $$100$$ students participating in a mathematics competition, with an average score of $$63$$ points. The average score for male students is $$60$$ points, and the average score for female students is $$70$$ points. Therefore, there are more male students participating in the competition than female students."}, {"key": "1703", "content": "Class A has $$33$$ students, and Class B has $$22$$ students. In one exam, the average score of Class A is $$80$$ points, and the overall average score of Class A and B is $$82$$ points. Calculate the average score of Class B. ( )"}, {"key": "1704", "content": "Teacher Lele originally planned to select 15 first prize winners and 20 second prize winners. Now, by adjusting the last 5 of the first prize winners to second prize, the average score of the first prize winners increased by 8 points, and the average score of the second prize winners increased by 6 points. Then, the original average score of the first prize was how many points more than that of the second prize."}, {"key": "1705", "content": "Four teams play in a single round-robin tournament, where a win yields $$3$$ points, a draw $$1$$ point to each, and a loss $$0$$ points. It is known that the champion has the least goal difference among the four teams and not all matches are drawn. Points for the champion. (Goal difference = Goals scored $$-$$ Goals conceded; teams with equal points are ranked by goal difference.)"}, {"key": "1706", "content": "Six people participate in a table tennis tournament, where every two players have to play a match against each other. The winner gets $$2$$ points, and the loser gets $$0$$ points. According to the results, the second and the fifth places are tied between two people. Therefore, the first place scored points, and the fourth place scored points."}, {"key": "1707", "content": "In a round-robin chess tournament with $$5$$ players, each pair of players plays one game against each other. It is stipulated that winning a game earns $$2$$ points, drawing earns each $$1$$ point, and losing earns $$0$$ points. It is known that after the tournament, $$4$$ of the players together scored $$16$$ points, then the $$5$$th player scored points."}, {"key": "1708", "content": "In the NBA playoffs, 16 teams compete in elimination matches, but each pair of teams must play a 'best of seven' series, where the first to win four games advances. To determine an overall champion, at least $$60$$ games to as many as $$105$$ games must be held."}, {"key": "1709", "content": "Four people, A, B, C, and D, participate in a round-robin tournament. A win scores $$3$$ points, a draw scores $$1$$ point, and a loss scores $$0$$ points. It is known that A, B, and C have scored $$7$$, $$3$$, and $$2$$ points respectively, and B has no draws. Therefore, D scored points."}, {"key": "1710", "content": "Four soccer teams play a round-robin tournament. The rules are that a win earns $$3$$ points, a draw earns $$1$$ point, and a loss earns $$0$$ points. There is one team that hasn't lost any match but still ranks last, and the situation where all matches are drawn didn't occur. Do you think this is possible? If yes, please give an example. If not, please explain why."}, {"key": "1711", "content": "$$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ five teams play in a round-robin tournament, where a win scores $$3$$ points, a loss scores $$0$$ points, and a tie scores $$1$$ point each. After the competition is over, it was found that Team $$A$$ won 2 and lost 2, Team $$B$$ scored $$8$$ points, Team $$C$$ scored $$9$$ points, and $$E$$ won against $$D$$. Then, $$D$$ scored points, $$E$$ scored points."}, {"key": "1712", "content": "There are four soccer teams $$A$$, $$B$$, $$C$$, and $$D$$ participating in a round-robin tournament, with the rule: win a game for $$2$$ points, draw for $$1$$ point, and lose for $$0$$ points. After all the games are finished, teams $$A$$ and $$B$$ tie for the first place in total points, team $$C$$ is in second place, and team $$D$$ is in third place. Thus, the highest possible points team $$C$$ can earn."}, {"key": "1713", "content": "Badminton has always been a strong sport in our country. In an international competition, our famous player Bao Chunlai $$2:1$$ reversed the match against Indonesian player Taufik (badminton is to $$21$$ points), after calculation, the total score of both players in three games was astonishingly $$59$$ points each, and the points difference in each game did not exceed $$4$$ points (when someone scores $$21$$ points or more, leading by $$2$$ points to win), then the scores of the three games respectively are, . (Bao Chunlai's score is listed first)"}, {"key": "1714", "content": "A, B, C, D, four people play a round-robin table tennis tournament, resulting in three people having the same number of wins (no draws). Another person won some matches."}, {"key": "1715", "content": "The squares of non-zero natural numbers arranged in ascending order: $$14916253649\\cdots \\cdots $$, then the digit at the $$100$$th position from the left is."}, {"key": "1716", "content": "When numbering the pages of a book, a total of $$24$$ '8's were used, and the last page contains the digit '8'. The book has pages."}, {"key": "1717", "content": "A dictionary has a total of $$1755$$ pages. The number $$0$$ appears in the page numbers $$times$$."}, {"key": "1718", "content": "Mao Mao has a book, with one sheet (containing two adjacent pages) torn out from the middle by Dou Dou. By adding together the page numbers of the remaining pages, Mao Mao got a total of $$777$$. Please, what was the original number of pages in Mao Mao's book?"}, {"key": "1719", "content": "To paginate a student dictionary, $$2925$$ digits were used. This dictionary has a total of pages."}, {"key": "1720", "content": "A page in the middle of a book was torn out, and the sum of the remaining page numbers is $$1133$$. The two page numbers on the torn out sheet are the sum."}, {"key": "1721", "content": "A science fiction novel has a total of $$1320$$ pages. The number of digits used in the page numbers for this science fiction novel is."}, {"key": "1722", "content": "Arrange numbers from $$1\\sim 1000$$ in ascending order without spaces into one large number: $$1234567891011121314$$...$$9991000$$. How many times does the number segment \"$$123$$\" appear in this multi-digit number?"}, {"key": "1723", "content": "In a math textbook, the number $$0$$ appears $$123$$ times, this math textbook has at least this many pages."}, {"key": "1724", "content": "Three classmates went on a picnic, and for lunch, they bought a total of eight loaves of bread, which the three of them shared equally. When buying the bread, one person paid for five loaves of bread, and another paid for three loaves of bread. After eating, the third person calculated that he should pay $$2$$ yuan and $$4$$ jiao in total, so how much should he give to the first and second person?"}, {"key": "1725", "content": "Xiao Ming walks from home to school. If he walks at a speed of $$40$$ meters per minute, he will be $$2$$ minutes late. If he walks at a speed of $$50$$ meters per minute, he will arrive $$4$$ minutes early. The distance from Xiao Ming's home to school in meters."}, {"key": "1726", "content": "35 numbers are arranged into 5 rows and 7 columns, with the average of the 7 columns being 39, 41, 40, 45, 42, 39, and 41, respectively. The averages of the first 4 rows are 42, 39, 44, and 41, respectively. The average of the last row is."}, {"key": "1727", "content": "Xueersi School has prepared a redeem-gifts-with-Xueersi-coins event for students who achieve excellent results. If each outstanding student is given $$10$$ Xueersi coins, there will be $$1000$$ coins left. If the number of outstanding students is doubled (with the number of coins given to each student remaining the same), there will be $$200$$ coins short. Then, the total number of Xueersi coins prepared is ( )."}, {"key": "1728", "content": "Originally, the plan for the Xueersi Cup was to have $$10$$ people win the first prize and $$20$$ people win the second prize. Now, the last $$4$$ people in the first prize category have been adjusted to the second prize category, resulting in an increase in the average score of the students who won the second prize by $$2$$ points, and the average score of the students who won the first prize also increased by $$2$$ points. Thus, the average score of the originally planned first prize was more than that of the second prize by several points."}, {"key": "1729", "content": "Baobao wrote a manuscript, having dinner after writing half of it. After dinner, the typing speed increased by 32 characters per minute. It took a total of 50 minutes to finish the article, and the first 25 minutes had 640 characters less than the last 25 minutes. Thus, the manuscript has a total number of characters of."}, {"key": "1730", "content": "In an entrance examination, there are $$50$$ students who took the test, where the average score of the top $$10$$ students is $$8$$ points higher than the average score of all the students in the test. Therefore, the average score of the remaining $$40$$ students is lower than the average score of all the students in the test."}, {"key": "1731", "content": "The clothing store is about to produce a batch of dresses. If they only make $$5$$ pieces a day, after the specified period, there will still be $$9$$ pieces not completed; but if they make $$3$$ more pieces a day, they can not only finish on time but also only need to make $$5$$ pieces on the last day. So, the specified period is days, and this batch of dresses totals pieces."}, {"key": "1732", "content": "The little white rabbit and the little gray rabbit each have a certain number of individuals. If $$6$$ little white rabbits and $$3$$ little gray rabbits are placed in a cage, there are $$4$$ more little white rabbits, and the little gray rabbits exactly fit; if $$7$$ little white rabbits and $$3$$ little gray rabbits are placed in a cage, the little white rabbits exactly fit, and there are $$12$$ more little gray rabbits. Then, the total number of little white rabbits and little gray rabbits is ."}, {"key": "1733", "content": "Measure the depth of a well with a rope. When the rope is folded in three and measured, it extends $$2$$ feet above the well; when the rope is folded in four and measured, the upper end of the rope is $$1$$ foot from the well's mouth. Find the depth of the well and the length of the rope. (Ignore the length of the bent parts, and assume each fold is of equal length.)"}, {"key": "1734", "content": "There was a pile of peaches, the first monkey took half of them and then put back $$1$$ peach; the second monkey took half of the remaining ones and put back $$1$$ peach; the third monkey also took half of the remaining ones and put back $$1$$ peach$$\\cdots \\cdots$$ continuing in this manner, the $$2018$$th monkey took half of the remaining ones and put back one, leaving $$2$$ peaches. Calculate how many peaches there were originally."}, {"key": "1735", "content": "The doctor allocates his monthly salary in the following way: half of the monthly salary is deposited into the bank, half of the remaining money minus $$300$$ is used to pay the mortgage, and then half of the money left over plus $$300$$ is used for meal expenses, leaving $$800$$. How much is the doctor's monthly salary in yuan?"}, {"key": "1736", "content": "A bird pecks at the rice, the first time it ate more than half of the amount of millet by $$10$$ grains, the second time it ate less than half of the remaining by $$12$$ grains, the third time it ate $$14$$ grains, and finally, there were $$15$$ grains of millet left.$$ How many grains of millet were there originally?"}, {"key": "1737", "content": "There is a pile of chess pieces. After dividing it into three equal parts, one piece remains. Taking away two parts and another piece, and then dividing the remaining chess pieces into three equal parts again, there is still one piece remaining. After taking away two parts and another piece, finally, dividing the remaining chess pieces into three equal parts again, there is still one piece remaining. The question is, how many chess pieces were there originally at least."}, {"key": "1738", "content": "Classes A, B, and C have a total of 144 students. First, a number of students equal to the number in class B are transferred from class A to class B. Then, a number of students equal to the number in class C are transferred from class B to class C. Finally, a number of students equal to the number now in class A are transferred from class C to class A. In this way, the numbers of students in classes A, B, and C become equal. Originally, class A had more students than class B."}, {"key": "1739", "content": "There are $$24$$ birds on three trees, $$3$$ birds flew from the first tree to the second tree, and $$5$$ birds flew from the second tree to the third tree. Eventually, the number of birds on the three trees became the same. How many birds were there originally on the first, second, and third trees respectively?"}, {"key": "1740", "content": "Three monkeys divided a pile of peaches. The biggest monkey first took half of the pile minus $$1$$ peach; the second monkey took half of the remaining peaches plus $$1$$ peach; the little monkey got the remaining $$8$$ peaches, and then there were no peaches left. The total number of peaches in this pile was $$34$$ peaches."}, {"key": "1741", "content": "$$48$$ kilograms of water are divided into three bottles. The first time, some water from bottle $$A$$ is poured into bottles $$B$$ and $$C$$, doubling the amount of water in bottles $$B$$ and $$C$$ from their original amount; the second time, some water from bottle $$B$$ is poured into bottles $$A$$ and $$C$$, also doubling the water in bottles $$A$$ and $$C$$ compared to the water already in them; the third time, some water from bottle $$C$$ is poured into bottles $$A$$ and $$B$$, doubling the water in bottles $$A$$ and $$B$$ compared to the water already in them. After these three transfers, the three bottles have the same amount of water. How much water did bottles $$A$$, $$B$$, and $$C$$ originally have?"}, {"key": "1742", "content": "An elderly person said: 'If you add $$14$$ to my age, divide by $$3$$, then subtract $$26$$, and finally multiply by $$25$$, it happens to be $$100$$ years old.' The age of this elderly person this year is\uff0e"}, {"key": "1743", "content": "The doctor asked Dakuan to plant a row of trees on one side of the road. Initially, Dakuan planted $$5$$ poplar trees in succession, and then the doctor said, 'It\u2019s not right to plant them like this. You need to follow the sequence of planting $$3$$ willow trees, $$2$$ pine trees, $$1$$ poplar tree, and then $$3$$ willow trees, $$2$$ pine trees, $$1$$ poplar tree $$\\cdots \\cdots$$ in order.' After that, Dakuan continued to plant following this pattern. In the end, Dakuan planted a total of $$200$$ trees. Please answer: How many willow trees, pine trees, and poplar trees did Dakuan plant? question_1743-image_0"}, {"key": "1744", "content": "This year's September 29 is Wei'er's 6th birthday. It is known that this day is Sunday, then the day Wei'er was born was"}, {"key": "1745", "content": "There are a total of $$50$$ large and small oil bottles, each large bottle can hold $$4$$ kilograms of oil, and each small bottle can hold $$2$$ kilograms of oil, with the large bottles together holding $$20$$ kilograms more oil than the small bottles (every oil bottle is filled). The number of large bottles is ___, and the number of small bottles is ___."}, {"key": "1746", "content": "Chickens and rabbits are in the same cage, there are $$26$$ more chickens than rabbits, and there are a total of $$274$$ legs. The number of chickens and rabbits are."}, {"key": "1747", "content": "Person A and Person B each write articles for a journal. For each article published, Person A earns a net profit of $400, and Person B earns $500. If an article is not accepted, Person A loses $200 in costs, and Person B loses $300. Each person writes 10 articles, and a total of 14 articles are published. At settlement, Person A earns $1000 more than Person B. Number of articles published by Person A and Person B."}, {"key": "1748", "content": "\nA person went hunting in the jungle and encountered a pack of wolves among which there were some mutant wolves. It is known that the person has one head and two legs, a normal wolf has one head and four legs, and a mutant wolf has two heads and three legs. The total number of heads and legs of all the people and wolves combined is $$21$$ heads and $$57$$ legs, then the total number of wolves (including mutant wolves) is."}, {"key": "1749", "content": "In a pond, there are some turtles, each of which sleeps for half a day; some sleep in the morning, and others in the afternoon. While sleeping, some turtles only retract their four legs into the shell, while others retract both their head and legs into the shell. One day, a total of $$20$$ heads and $$60$$ legs could be counted in the morning, and $$17$$ heads and $$40$$ legs could be counted in the afternoon. Therefore, the number of turtles that only retract their four legs into the shell while sleeping is $$12$$."}, {"key": "1750", "content": "In ancient legends, there were four magical types of birds: the two-tailed bird ($$1$$ head $$2$$ tails), the three-tailed bird ($$1$$ head $$3$$ tails), the six-tailed bird ($$1$$ head $$6$$ tails), and the eight-tailed bird ($$2$$ heads $$8$$ tails). One day, the four types of birds happened to gather together. A two-tailed bird said: 'I found that the number of our kind of birds is exactly $$2$$ times more than the eight-tailed birds plus $$5$$.' A three-tailed bird said: 'Our number is not many, only more than half of the six-tailed birds by $$2$$.' Given that the total number of tails of the four types of birds is $$2$$ less than $$4$$ times the total number of heads, and the total number of heads is $$241$$ less than the total number of tails, then how many three-tailed birds are there in total."}, {"key": "1751", "content": "Chickens and rabbits are kept in the same cage. It is known that there are $$5$$ more chickens than rabbits, and the number of legs of the rabbits is $$24$$ more than that of the chickens. So, there are chickens, and rabbits."}, {"key": "1752", "content": "The teacher from Xueersi distributed cards to the students in the class, with each boy receiving $$4$$ zodiac points cards and $$2$$ note-taking expert cards, and each girl receiving $$6$$ zodiac points cards and $$2$$ note-taking expert cards. It is known that the teacher distributed a total of $$88$$ zodiac points cards and $$40$$ note-taking expert cards, so the number of girls in this class is."}, {"key": "1753", "content": "A test paper consists of $$21$$ questions, with each correct answer scoring $$8$$ points and each incorrect answer deducting $$6$$ points. Xiaoming completed all the questions and scored $$98$$ points. Thus, he answered a total of correct questions."}, {"key": "1754", "content": "Ms. Wei Wei is a stamp collector, she has stamps of both 50 cents and 1 RMB, totaling 50 stamps, and the total face value of 1 RMB stamps is 17 RMB more than that of the 50 cents stamps. How many stamps of 1 RMB and 50 cents does she have respectively?"}, {"key": "1755", "content": "The little monkeys in the Huaguo Mountain are eating peaches. If $$6$$ little monkeys eat $$180$$ peaches in $$3$$ days, according to this calculation, $$5$$ days would allow for $$400$$ peaches to be eaten by a single little monkey."}, {"key": "1756", "content": "The little monkeys in the Flower Fruit Mountain are eating peaches. If $$6$$ little monkeys eat $$180$$ peaches in $$3$$ days, according to this, $$10$$ little monkeys need $$days$$ to eat $$200$$ peaches."}, {"key": "1757", "content": "A basket of peaches can feed $$10$$ monkeys for $$5$$ days. After $$2$$ days, $$4$$ monkeys leave. The remaining peaches can feed the remaining monkeys for days. (Assuming each monkey eats the same amount of peaches every day)"}, {"key": "1758", "content": "The total distance from home to the supermarket is $$720$$ meters. The elder sister walks at $$60$$ meters per minute, taking minutes to complete the whole journey. The younger sister takes $$3$$ minutes more than the elder sister to complete the whole journey, walking meters per minute."}, {"key": "1759", "content": "The greening team planted $$201$$ trees in $$3$$ days and needs to plant another $$737$$ trees. Given this work efficiency, the number of days needed to complete the task is ."}, {"key": "1760", "content": "$$3$$ mice ate $$45$$ ears of corn in $$5$$ days, at this rate, $$288$$ ears of corn would be enough for one mouse for $$8$$ days."}, {"key": "1761", "content": "Eddie rides his bicycle at a speed of $$15$$ kilometers per hour,\n(1) In $$4$$ hours, he can travel kilometers;\n(2) At the same speed, he rode for $$90$$ kilometers, it took hours."}, {"key": "1762", "content": "Please identify and fill in the pattern for each term in the following sequences: (1) The first term is $$11$$, the second term is $$14$$, the third term is $$17$$, $$ \\cdots $$ then the nth term is."}, {"key": "1763", "content": "A certain city has several straight roads, none of which are parallel; every two roads intersect, but no more than 3 roads intersect at any crossroad. If a traffic policeman is stationed at each intersection, and a total of 45 traffic policemen are needed, how many roads does this city have?"}, {"key": "1764", "content": "Four triangles and two circles can divide a plane into at most how many parts."}, {"key": "1765", "content": "As shown in the figure, there are a total of line segments in a rectangular grid made up of small squares.\n question_1765-image_0"}, {"key": "1766", "content": "The figure below contains a parallelogram.\n question_1766-image_0"}, {"key": "1767", "content": "The figure below is a half square, divided into small isosceles right triangles. There are square(s) and triangle(s) in the figure.\n question_1767-image_0"}, {"key": "1768", "content": "There are a total number of squares in the picture.\n question_1768-image_0"}, {"key": "1769", "content": "$$3$$ straight lines can divide a plane into at most several planes."}, {"key": "1770", "content": "$$15$$ triangles can divide a plane into a maximum of parts."}, {"key": "1771", "content": "There are $$100$$ straight lines on a plane, they have at most different intersections."}, {"key": "1772", "content": "A pancake (thickness not considered), cut with $$6$$ cuts (the cuts are straight lines), can be divided into a maximum number of parts."}, {"key": "1773", "content": "Draw two concave quadrilaterals on a plane (a quadrilateral with one reentrant angle, whose sides do not intersect each other except at the vertices, as shown in the schematic below), at most, the plane can be divided into several parts.\n question_1773-image_0"}, {"key": "1774", "content": "On a plane, 4 rectangles and 2 lines can divide the plane into a maximum number of parts."}, {"key": "1775", "content": "Fill in the appropriate numbers on the horizontal lines in the list below, and write down the nth term of the series.\n$$13$$, $$17$$, $$23$$, $$31$$, $$41$$, the nth term of the series is."}, {"key": "1776", "content": "The three numbers in each of the following figures follow the same pattern. According to this pattern, the value of $$a$$ is.\n question_1776-image_0"}, {"key": "1777", "content": "As shown in the figure, rectangle $$ABCD$$ is a park, with a length of $$30$$ meters and a width of $$15$$ meters. The shaded area represents a path that is $$4$$ meters wide. The area of the path is in square meters.\n question_1777-image_0"}, {"key": "1778", "content": "As shown in the figure, two identical parallelograms are placed horizontally and vertically, overlapping each other. It is known that the overlapping part is exactly a square with a side length of $$8$$ centimeters, the length of $$AH$$ is $$3$$ centimeters, then the area covered by these two parallelograms is square centimeters.\n question_1778-image_0"}, {"key": "1779", "content": "As shown in the figure, the area of square $$ABCD$$ is $$16$$ square centimeters, $$ED=CH=4$$ centimeters, $$EF=2$$ centimeters, the quadrilateral $$EFGH$$ is a rectangle, and the area of trapezoid $$ABGF$$ is square centimeters.\n question_1779-image_0"}, {"key": "1780", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$DE$$ is vertical to $$AB$$ at $$E$$, $$DF$$ is vertical to $$BC$$ at $$F$$. It is known that $$AB=12$$, $$DE=5$$, $$DF=10$$. Calculate $$BC=$$.\n question_1780-image_0"}, {"key": "1781", "content": "As shown in the diagram, in parallelogram $$ABCD$$, the length of $$AB$$ is $$10$$ centimeters, the distance from point $$E$$ to side $$CD$$ is $$8$$ centimeters, then the area of parallelogram $$ABEF$$ is larger than the area of parallelogram $$ABCD$$ by square centimeters. question_1781-image_0"}, {"key": "1782", "content": "$$A$$ and $$B$$ are $$780$$ kilometers apart, a truck travels at $$56$$ kilometers per hour, and a passenger car travels at $$74$$ kilometers per hour. Both vehicles leave from point $$A$$ towards point $$B$$ at the same time, and immediately return upon reaching $$B$$. After hours, the two vehicles meet for the first time. The meeting point is kilometers away from point $$B$$."}, {"key": "1783", "content": "Places $$AB$$ are $$60$$ kilometers apart, Xiaomu and Xiaowang depart from location $$A$$ towards location $$B$$, and immediately return to location $$A$$ upon reaching location $$B$$, then continuously going back and forth. Xiaobei departs from location $$B$$ towards location $$A$$, and upon reaching location $$A$$, returns to location $$B$$, then continuously going back and forth. It is known that the three of them set off at the same time, $$2$$ hours later Xiaomu meets Xiaobei, $$3$$ hours later Xiaowang meets Xiaobei, $$6$$ hours later, Xiaomu meets Xiaowang. When Xiaowang first reaches location $$B$$, Xiaobei is $$0$$ kilometers away from location $$A$$."}, {"key": "1784", "content": "Calculate a number in the following way: $$+2$$, $$\\times 2$$, $$-2$$, $$\\div 2$$, $$+2$$, $$\\times 2$$, $$-2$$, $$\\div 2$$, $$\\cdots \\cdots $$\uff0e(2) If a number after $$2015$$ calculations results in $$1012$$, this number is."}, {"key": "1785", "content": "Two groups of students participate in voluntary labor, the number of students in Group A is 3 times that of Group B, and the number of students in Group B is 40 less than 3 times that of Group A. How many students are there in total participating in voluntary labor?"}, {"key": "1786", "content": "Xiaoming and his dad made dumplings together. His dad made 5 times as many dumplings as Xiaoming did. During dinner, the two of them finished all the dumplings. Xiaoming ate 8 more dumplings than his dad. If Xiaoming had eaten 6 more dumplings, then he would have eaten 4 times the amount of dumplings he made. So, how many dumplings did his dad eat?"}, {"key": "1787", "content": "One day, there was a power outage, and two candles of the same length were lit in the room at the same time. These two candles had different masses, one could last for $$6$$ hours, and the other could last for $$10$$ hours. When the electricity was restored and the candles were blown out, it was found that the remaining length of one candle was $$3$$ times the remaining length of the other. The duration of the power outage was hours."}, {"key": "1788", "content": "Using $$14$$ matchsticks, place a number in each square inside a box, forming three numbers with all digits being different, to make an addition equation with the smallest possible result. question_1788-image_0"}, {"key": "1789", "content": "Below are all the cases of numbers made up of matchsticks. Please form a number using matchsticks. If this number is $$361$$ more than the number of matchsticks it requires, what is the number? (For example: Forming $$18$$ requires $$9$$ matchsticks, and $$18-9=9$$, so $$18$$ is $$9$$ more than the number of matchsticks it uses.) question_1789-image_0"}, {"key": "1790", "content": "Using $$16$$ matchsticks, place a number in each square within a frame so that the two numbers formed have all different digits, and compose an addition equation with the smallest possible result. question_1790-image_0"}, {"key": "1791", "content": "Using $$13$$ matchsticks, place a number in each square frame. You can place a single-digit number or a multi-digit number. The numbers placed can be the same or different. The goal is to form an addition equation with the largest possible result and the smallest possible result. question_1791-image_0"}, {"key": "1792", "content": "You can arrange all the numbers using matchsticks, and the arrangement for each number is shown in the following illustration:\n question_1792-image_0 \nJianjian arranged the number $$20161203$$ using $$37$$ matchsticks as shown below. Afterwards, Jianjian rearranged the matchsticks of one of the numbers to another number (using all the matchsticks), thus forming a new eight-digit number. There are several possibilities.\n question_1792-image_1"}, {"key": "1793", "content": "With $$18$$ matchsticks (exactly used up), what's the largest and the smallest number that can be formed? question_1793-image_0"}, {"key": "1794", "content": "Using $$11$$ matchsticks (exactly), the largest and smallest numbers that can be formed with all distinct digits are. question_1794-image_0"}, {"key": "1795", "content": "The figure below (unit: cm) shows two identical right trapezoids overlapping each other, then the area of the shaded part is in square centimeters. question_1795-image_0"}, {"key": "1796", "content": "As shown in the figure, quadrilateral $$ABDE$$ is a square with a side length of $$6$$ cm, and quadrilateral $$ABCF$$ is a trapezoid. Given that the line segment $$EF=2$$ cm, and $$CD=4$$ cm. Then, the area of the trapezoid $$ABCF$$ is square centimeters.\n question_1796-image_0"}, {"key": "1797", "content": "As shown in the figure, quadrilateral $$ABFE$$ is a rectangle with an area of $$48$$ square centimeters, and quadrilateral $$EFDC$$ is a trapezoid with an area of $$88$$ square centimeters. Given $$AB=8$$ cm, $$CD=14$$ cm, then the area of quadrilateral $$ABCD$$ is square centimeters. question_1797-image_0"}, {"key": "1798", "content": "As shown in the figure, quadrilateral $$ABCD$$ is a trapezoid, quadrilateral $$ABED$$ is a parallelogram, quadrilateral $$FGHI$$ is a rectangle, $$E$$, $$F$$, $$G$$ are respectively the midpoints of sides $$CD$$, $$AD$$, $$BC$$. If the area of the parallelogram $$ABED$$ is $$48$$ square centimeters, then, the area of the rectangle $$FGHI$$ is square centimeters. question_1798-image_0"}, {"key": "1799", "content": "The shaded area in the diagram is composed of four trapezoids. It is known that the distance from point $$C$$ to $$HG$$ and $$GF$$, and the distance from point $$A$$ to $$HE$$ and $$EF$$, are both $$6$$ centimeters. The area of the shaded part is $$240$$ square centimeters. The perimeter of the quadrilateral $$ABCD$$ is $$25$$ centimeters. Then, the perimeter of the quadrilateral $$EFGH$$ is centimeters. question_1799-image_0"}, {"key": "1800", "content": "As shown in the diagram, two parallelograms $$ABEF$$ and $$CDFG$$ are divided from trapezoid $$ABCD$$. The area of parallelogram $$ABEF$$ is $$60$$ square meters, and the length of $$AF$$ is $$10$$ meters, the length of $$FD$$ is $$4$$ meters, the length of $$EG$$ is twice the length of $$BE$$. The area of the trapezoid $$ABCD$$ is square meters.\n question_1800-image_0"}, {"key": "1801", "content": "As shown in the figure, in the right-angle trapezoid $$ABCD$$, triangle $$ABE$$ and triangle $$CDE$$ are both isosceles right triangles, and $$BC=20$$ cm. Then, the area of the right-angle trapezoid $$ABCD$$ is square centimeters. question_1801-image_0"}, {"key": "1802", "content": "As shown in the figure, it is known that the area of trapezoid $$ABCD$$ is $$50$$ square centimeters, the height $$AE$$ measures $$5$$ centimeters, and the line segment $$CD$$ is $$4$$ centimeters longer than $$AB$$. Then, the lengths of $$AB$$ and $$CD$$ are centimeters and centimeters respectively. question_1802-image_0"}, {"key": "1803", "content": "Doctor and Da Kuan started from two places $$2300$$ meters apart at the same time, moving towards each other. Doctor walks $$60$$ meters per minute, and Da Kuan walks $$45$$ meters per minute. The first time the distance between them is $$200$$ meters."}, {"key": "1804", "content": "Xiao Dong and Xiao Xi set off from City A at the same time, driving towards Destination B, which is 480 kilometers away. Xiao Dong's car travels at 53 kilometers per hour, while Xiao Xi's car travels at 27 kilometers per hour. After Xiao Dong arrives at City B, he immediately returns. They meet on the way, some hours after setting off."}, {"key": "1805", "content": "Eddie is on his way home, 1000 meters away from the door. Wier and the dog run towards him together. Eddie's speed is 60 meters per minute, Wier's speed is 40 meters per minute, and the dog's speed is 250 meters per minute. The dog runs back and forth at the same speed between Eddie and Wier. When Eddie meets Wier, the total distance run by the dog is meters."}, {"key": "1806", "content": "Car A and Car B start from two locations 1912 kilometers apart and head towards each other. Car A travels at 64 kilometers per hour, and Car B travels at 56 kilometers per hour. Car B starts 2 hours before Car A. Car A travels for hours before meeting Car B."}, {"key": "1807", "content": "Xiao Zhang and Xiao Wang started from Place A to Place B at exactly $$8$$ am. Xiao Zhang drove at a speed of $$60$$ kilometers per hour. Xiao Wang walked at a speed of $$4$$ kilometers per hour. If Xiao Zhang reached Place B and then immediately returned along the same route after staying for $$1$$ hour, and happened to meet Xiao Wang, who was still on his way to Place B, at exactly $$10$$ am. Then, the distance between Place A and Place B is in kilometers."}, {"key": "1808", "content": "A and B start from point $$A$$, while C starts from point $$B$$, moving towards each other and returning immediately upon reaching their destinations. When A meets C, B is exactly at the midpoint between $$AB$$; when B meets C, A has just reached $$B$$. When A meets B, C has walked $$2014$$ meters, and the distance between $$AB$$ in meters."}, {"key": "1809", "content": "Eddy and Vi started at the same time from two places $$120$$ kilometers apart, Eddy's speed is $$47$$ kilometers per hour, Vi's speed is $$13$$ kilometers per hour, they meet after hours of departure."}, {"key": "1810", "content": "A motorcycle and a bicycle set off at the same time from two places, A and B, which are $$365$$ kilometers apart, heading towards each other. The motorcycle travels at $$55$$ kilometers per hour, and the bicycle travels at $$15$$ kilometers per hour. Along the way, the motorcycle breaks down and is repaired for $$1$$ hour before continuing. When the two meet, the motorcycle has traveled kilometers."}, {"key": "1811", "content": "The distance between the two locations is $$100$$ meters. Person A and Person B start walking from the same place in the same direction at the same time, with Person A walking $$6$$ meters per second and Person B walking $$4$$ meters per second. When one of them reaches the opposite side, they immediately return and meet the other person. The time from departure to meeting is in seconds."}, {"key": "1812", "content": "Mengmeng and Yangyang agreed to meet at a certain point between them, Mengmeng walks $$68$$ meters per minute, and Yangyang walks $$35$$ meters per minute, they both set off at the same time and after $$8$$ minutes have not yet met, at this point they are $$342$$ meters apart, therefore the distance between Mengmeng and Yangyang is meters."}, {"key": "1813", "content": "Person A and Person B start from two places at the same time, walking towards each other. Person A walks at $$68$$ meters per minute, while Person B walks at $$62$$ meters per minute. After $$15$$ minutes, they cross paths and then are $$150$$ meters apart. The distance between the two places is meters."}, {"key": "1814", "content": "Following a 4-step operation sequence of 'first add $$12$$, then subtract $$9$$, next add $$6$$, and then subtract $$4$$', repeat the calculation in sequence. After some steps, the result is exactly $$1988$$; after some steps, the result is exactly $$2005$$."}, {"key": "1815", "content": "Location A and Location B are $$480$$ kilometers apart. Teacher Wang started his journey from Location A on a motorcycle, and $$1$$ hour later, Teacher Li started from Location A in a car, both arriving at Location B at the same time. The initial speed of the motorcycle was $$80$$ kilometers per hour, which was later reduced to $$60$$ kilometers per hour. The speed of the car was $$80$$ kilometers per hour. So, the question is, after how many hours did Teacher Wang decelerate his motorcycle."}, {"key": "1816", "content": "During the festival celebration, Person A and B simultaneously lit two sparkler fuse lines of the same length. These two fuse lines have different qualities, one can last for $$10$$ seconds, and the other can last for $$30$$ seconds. When A and B ran back to the safety zone, they found that the remaining length of one was $$2$$ times the remaining length of the other. Therefore, the time it took for A and B to run back to the safety zone was $$6$$ seconds."}, {"key": "1817", "content": "Eddie and Will discussed the number of points, Eddie said: 'Three times my number of points is still 50 less than yours.' Will said: 'In fact, twice my number of points is 600 more than yours.' So, the two of them have a total number of points."}, {"key": "1818", "content": "Originally, A had 6 times as many story books as B. Each of them bought 20 more books, then A had 2 times as many books as B. How many story books did A and B originally have, respectively?"}, {"key": "1819", "content": "Lingling needs to cross a small steep slope from the library to the stadium. She walks up the slope at $$40$$ meters per minute and down the slope at $$60$$ meters per minute. The distance from the library to the stadium is $$600$$ meters, and it takes $$12$$ minutes to cover the distance. It takes Lingling minutes to return."}, {"key": "1820", "content": "Person A and B participated in a burger eating contest together. Within the time limit of 30 minutes, the number of burgers eaten by A is half of that by B, while the number of burgers B ate is 12 less than 5 times that of A. Therefore, the total number of burgers eaten by A and B is ."}, {"key": "1821", "content": "Calculate a number in the following way: $$+3$$, $$\\times 3$$, $$-3$$, $$\\div 3$$, $$+3$$, $$\\times 3$$, $$-3$$, $$\\div 3$$, $$\\cdots \\cdots $$\uff0e(1) If $$5$$ is calculated $$100$$ times, the result is\uff0e(2) If a number is calculated $$2021$$ times and the result is $$1015$$, then this number is\uff0e"}, {"key": "1822", "content": "In the school, the number of boxes of white chalk is $$4$$ times the number of boxes of colored chalk. If $$12$$ boxes of white chalk and $$12$$ boxes of colored chalk are purchased respectively, then the number of boxes of white chalk is $$3$$ times the number of boxes of colored chalk. Originally, there were boxes of white chalk."}, {"key": "1823", "content": "The total distance from point A to point B is $$80$$ kilometers, including uphill, flat, and downhill roads. Lili's speed going uphill is $$3$$ kilometers per hour, on flat roads is $$5$$ kilometers per hour, and going downhill is $$6$$ kilometers per hour. It took Lili $$18$$ hours from point A to point B, and $$20$$ hours from point B back to point A. Thus, the uphill distance from point A to point B is kilometers."}, {"key": "1824", "content": "One day, there was a power outage, and two candles of the same length were lit in the room at the same time. The two candles had different masses, one could last for $$4$$ hours, and the other could last for $$12$$ hours. When the power was restored, and the candles were blown out, it was found that the remaining length of one candle was $$3$$ times the remaining length of the other one. Therefore, the duration of this power outage was hours."}, {"key": "1825", "content": "The reading corner is divided into Area A and Area B. The number of books in Area A is 3 times plus 4 books more than in Area B. If one book is moved from Area B to Area A, then the number of books in Area A becomes 5 times that of Area B. Originally, Area A has books."}, {"key": "1826", "content": "There is a $$7\\times 7$$ matrix as follows, according to the rule, the matrix is expanded to a $$50\\times 50$$ matrix. Which letter will be in the bottom right corner of the matrix? $$C$$$$B$$$$A$$$$E$$$$D$$$$C$$$$B$$$$D$$$$A$$$$E$$$$D$$$$C$$$$B$$$$A$$$$E$$$$B$$$$B$$$$A$$$$E$$$$A$$$$E$$$$A$$$$C$$$$C$$$$A$$$$D$$$$E$$$$D$$$$B$$$$D$$$$D$$$$B$$$$C$$$$D$$$$C$$$$C$$$$E$$$$E$$$$A$$$$B$$$$C$$$$B$$$$D$$$$A$$$$B$$$$C$$$$D$$$$E$$$$A$$"}, {"key": "1827", "content": "The doctor and Eddie made egg tarts together, with the doctor making 7 times the number Eddie did. They ate half of the egg tarts during afternoon tea, and Eddie ate 6 more than the doctor. If Eddie ate one more, then he would have eaten 3 times what he made. So, how many egg tarts did the doctor eat?"}, {"key": "1828", "content": "Chef A and Chef B discussed the number of their specialty dishes. A said, 'My specialty dishes are 60 less than 4 times yours.' B said, 'Actually, twice the number of my specialty dishes is 540 more than yours.' Therefore, the two have a total of specialty dishes."}, {"key": "1829", "content": "After the exam results came out, the Doctor had a paper with $$98$$ in one hand and a paper with $$89$$ in the other, and said: 'If I multiply the number in my left hand by $$3$$ and the number in my right hand by $$2$$, and then add these two products together, the sum is an odd number', please guess, which score is in the Doctor's left hand."}, {"key": "1830", "content": "Place the numbers $$1$$ to $$6$$ on the six vertices of a triangular prism, and then write the average of the numbers at the two vertices at the midpoint of each edge. If the numbers written at the midpoints of the three edges of the upper base (\\(\\triangle ABC\\)) and the lower base (\\(\\triangle DEF\\)) are all integers, then among the numbers written at the other three midpoints, there is one that is not an integer.\n question_1830-image_0"}, {"key": "1831", "content": "Sequence: $$1$$, $$1$$, $$6$$, $$21$$, $$81$$, $$306$$, ..., starting from the third number, each number is three times the sum of its previous two numbers. Among the first $$2018$$ numbers of this sequence, there is a certain number of even numbers."}, {"key": "1832", "content": "Find two integers such that their sum is $$264$$ and their difference is $$57$$. Do such numbers exist? ( )"}, {"key": "1833", "content": "There are enough apples, pears, and oranges mixed together. If they are divided into 9 piles at random, does it always exist that two piles can be merged so that the number of fruits of all three kinds is even?"}, {"key": "1834", "content": "There are $$400$$ chess pieces in a box, including $$200$$ black pieces and $$200$$ white pieces. The following operation is performed on these pieces: each time $$2$$ pieces are taken out, if they are of the same color, add $$1$$ black piece back; if they are of different colors, add $$1$$ white piece back. This operation effectively reduces the number of pieces by $$1$$ each time. Then, after $$399$$ operations, what color is the last remaining piece?"}, {"key": "1835", "content": "There are $$5$$ coins on the table. Flip one of them for the first time, two for the second time, three for the third time, four for the fourth time, and five for the fifth time. Is there a way to flip the coins such that all of them are turned over? If there are $$6$$ coins on the table, and you flip them six times in a similar manner, can you find a way to flip all the coins over?"}, {"key": "1836", "content": "There are $$9$$ chess pieces placed at the bottom left corner of an $$8\\times 8$$ chessboard, forming a $$3\\times 3$$ square (as shown in the bottom-left image). It is stipulated that each chess piece can jump over another piece next to it to an empty square, that is, it can move symmetrically centered on the piece next to it, being able to jump horizontally, vertically, or along the diagonal (as shown in the bottom-right image, the $$1$$st piece can jump to positions $$2$$, $$3$$, $$4$$). The question is: Can these pieces jump to fill the $$3\\times 3$$ square at the top right corner of the chessboard? question_1836-image_0"}, {"key": "1837", "content": "As shown in the figure, starting from point $$0$$, a tree is planted every $$3$$ meters. If $$3$$ 'Protect Trees' signs are hung on $$3$$ trees separately, then no matter how they are hung, the distance between at least two of the trees with signs will be an even number (in meters). Please explain the reason. question_1837-image_0"}, {"key": "1838", "content": "In a math test consisting of $$20$$ questions, it is stipulated that answering a question correctly scores $$2$$ points, answering incorrectly deducts $$1$$ point, and unanswered questions do not receive any points. After the test, Xiao Ming scored a total of $$23$$ points. He wants to know how many questions he answered incorrectly, but he only remembers that the number of unanswered questions is an even number. Please help Xiao Yuan calculate how many questions he answered incorrectly."}, {"key": "1839", "content": "School resumed after the New Year, and some students needed to buy new uniforms. Wei Er collected the uniform fees from $$9$$ classmates (each person paid the same amount) and handed them to the teacher. The teacher gave Wei Er a note, which read 'The fee for the uniforms is $$\\overline{2\\square 38}$$ yuan,' but a drop of ink made the number in the square unclear. Eddie looked at it and quickly figured out the number in the square. Smart kids, this number is."}, {"key": "1840", "content": "There are five numbers: $$0$$, $$1$$, $$4$$, $$7$$, $$9$$. Select four numbers to form a four-digit number. Arrange the four-digit numbers that can be divided by $$3$$ from smallest to largest, the fifth number is."}, {"key": "1841", "content": "Given a six-digit number $$\\overline{20\\square 279}$$ that is divisible by $$11$$, the digit in $$\\square $$ is."}, {"key": "1842", "content": "Change one digit in $$54679$$ so that the five-digit number can be divided by $$5$$, the largest modified five-digit number is."}, {"key": "1843", "content": "If the four-digit number $$\\overline{9a8a}$$ is divisible by both $$3$$ and $$5$$, then the number represented by $$a$$ is."}, {"key": "1844", "content": "Change one digit in $$3255$$ so that this four-digit number is divisible by $$8$$, then the modified four-digit number is."}, {"key": "1845", "content": "We can use matchsticks to arrange the numbers $$0\\sim 9$$. Please tell, among the arranged numbers, which one uses the maximum number of matchsticks. question_1845-image_0"}, {"key": "1846", "content": "Dividing $$8$$ identical peaches into $$3$$ piles, there are a total of different ways."}, {"key": "1847", "content": "As shown in the diagram, a little ant starts from the apex $$A$$ of a tetrahedron and travels along the edges of the tetrahedron, visiting the $$4$$ vertices sequentially without repetition, and then returns to the vertex $$A$$. How many different paths can the little ant take in total? \n question_1847-image_0"}, {"key": "1848", "content": "A and B play table tennis, whoever wins two consecutive games first wins. If no one wins the first two consecutive games, then whoever wins three games first wins. Continue until a winner is determined. Question: How many possible outcomes are there in total?"}, {"key": "1849", "content": "XueXue had some apples, which were evenly distributed among $$5$$ kids, with each kid receiving $$4$$ apples. After distribution, XueXue was left with $$2$$ apples. How many apples did XueXue originally have?"}, {"key": "1850", "content": "Pea is $$10$$ years old this year, Potato is $$20$$ years old this year, when the sum of their ages is $$60$$ years old, Pea is __ years old, Potato is __ years old."}, {"key": "1851", "content": "The elder brother said to the younger brother: \"When I was your age, you were only $$5$$ years old.\" The younger brother said to the elder brother: \"When I am your age, you will already be $$35$$ years old.\" Thus, this year the younger brother is $$15$$ years old."}, {"key": "1852", "content": "This year, Xue Xue is $$6$$ years old, dad is $$30$$ years old. After a certain number of years, dad's age will be $$4$$ times Xue Xue's age."}, {"key": "1853", "content": "13 lines on the same plane can have at most how many points of intersection."}, {"key": "1854", "content": "There are a total of $$5$$ lines and $$7$$ intersections in the figure. If only line $${{l}_{1}}$$ is removed, there remain intersections. If only line $${{l}_{2}}$$ is removed, there remain intersections. If only line $${{l}_{3}}$$ is removed, there remain intersections. If only line $${{l}_{4}}$$ is removed, there remain intersections. If only line $${{l}_{5}}$$ is removed, there remain intersections.\n question_1854-image_0"}, {"key": "1855", "content": "There are a total of $$4$$ lines and $$3$$ intersections in the figure. Remove line number, and the intersections remain unchanged.\n question_1855-image_0"}, {"key": "1856", "content": "On the same plane, there can be up to $$30$$ lines with a maximum number of intersection points."}, {"key": "1857", "content": "There is a city street map constructed from rectangles as shown below. A police officer starts patrolling from point $$A$$ and needs to pass through each road segment at least once before returning to point $$A$$. How many meters does he need to walk at least? question_1857-image_0"}, {"key": "1858", "content": "The figure below is a plan view of a park's road system, where the numbers indicate the lengths of the roads (unit: meters), $$A$$ and $$B$$ are respectively the entrance and exit of the park. Entering from the entrance, traversing all the roads, and then exiting from the exit, the shortest distance is meters. question_1858-image_0"}, {"key": "1859", "content": "To distribute $$12$$ pieces of candy among three kids, with each person getting at least $$2$$ pieces and each person getting a different number of pieces, there are a total of ways to do this."}, {"key": "1860", "content": "Xinhua Elementary School arranges $$4$$ extracurricular activities per week, including sports, arts, and technology. If it is required that each type of activity occurs at least once a week, and the same activity cannot be arranged consecutively, how many different arrangements are there?"}, {"key": "1861", "content": "As shown in the figure, walk from the starting point to the endpoint along the line, with the requirement to pick up the flag at each station, and each station is only allowed to be passed through once. There are several different ways to walk.\n question_1861-image_0"}, {"key": "1862", "content": "A three-digit number whose digits sum to $$6$$, the number of such three-digit numbers is."}, {"key": "1863", "content": "The natural numbers $$21$$, $$654$$, $$7521$$ have one thing in common, they all have at least two digits, and for any two adjacent digits, the left digit is greater than the right digit. We name these numbers 'Descending Numbers'. Using the four numbers $$4$$, $$6$$, $$7$$, $$9$$, we can form some 'Descending Numbers'."}, {"key": "1864", "content": "Distributing $$10$$ identical balls into $$3$$ identical boxes (it's possible for some boxes to be empty) results in a total of different methods."}, {"key": "1865", "content": "As shown in the figure, an ant starts from the vertex $$P$$ of a pyramid and walks along the edges of the pyramid, visiting each of the $$5$$ vertices exactly once before stopping. How many different paths can the ant take? question_1865-image_0"}, {"key": "1866", "content": "Schools distribute dormitories. If each dormitory houses $$8$$ people, there will be $$2$$ extra dormitories left. If each dormitory houses $$6$$ people, there will be $$12$$ people without housing. There are a total of dormitories."}, {"key": "1867", "content": "A teacher takes a few students to eat ice cream. If buying each student a slush and a $2 cone, there is a total shortage of $15; if only buying each student a slush, there is still a shortage of $5. How many students are there in total?"}, {"key": "1868", "content": "Teacher Tang distributes candies to the classmates. If one student gets $$12$$ candies and the rest each get $$10$$ candies, then all the candies are exactly distributed. But if two students each get $$5$$ candies and the rest each get $$12$$ candies, then all the candies are exactly distributed again. So, how many students are there in the class? And how many candies does Teacher Tang have?"}, {"key": "1869", "content": "A tailor received an order to sew buttons on a batch of jackets. If they sew $$5$$ pieces a day, they will finish $$2$$ days after the scheduled deadline; if they sew $$9$$ pieces a day, they can finish $$2$$ days ahead of schedule. The total number of jackets in this batch is pieces."}, {"key": "1870", "content": "The teacher distributed apples and peaches to the children, the total number of apples bought was $$2$$ times that of peaches. After each child received $$5$$ peaches, there were still $$15$$ peaches left; if each person received $$14$$ apples, there was a shortfall of $$30$$ apples in total. The teacher bought a total of peaches and apples."}, {"key": "1871", "content": "Young Pioneers go to arrange flower pots. If each person arranges $$5$$ pots, there are $$3$$ pots left unarranged; if among them $$2$$ people arrange $$4$$ pots each, and the rest arrange $$6$$ pots each, the flower pots are just enough. Ask how many Young Pioneers participated in the flower pot arranging activity, and how many flower pots in total were arranged."}, {"key": "1872", "content": "Teacher Peach took the children out for a spring outing and was responsible for allocating the accommodation rooms. It is known that if each room accommodates 3 people, there will be 23 people left over; if each room accommodates 5 people, 1 room will be vacant. Therefore, there are rooms and children."}, {"key": "1873", "content": "Mother rabbit divides carrots among the baby rabbits, each baby rabbit gets $$2$$ and there are $$8$$ extra, for each baby rabbit to get $$5$$ there are $$4$$ short, then there are rabbits."}, {"key": "1874", "content": "The area of the shape in the picture is square meters.\n question_1874-image_0"}, {"key": "1875", "content": "(1) The area of a rectangle is $$42$$ square meters, the length is $$7$$ meters, the width is meters;\n(2) The area of a square is $$144$$ square meters, the side length is meters."}, {"key": "1876", "content": "As shown in the figure, the large rectangle is divided into four smaller rectangles, three of which have areas of: $$4$$ square centimeters, $$6$$ square centimeters, $$10$$ square centimeters, then the area of the shaded part is square centimeters. question_1876-image_0 \u200b"}, {"key": "1877", "content": "Eddie has an $$\"L\"$$-shaped swimming pool as shown in the figure below. He plans to buy some blue tiles to lay at the bottom of the pool (sides not considered). Eddie needs to buy tiles in square meters. question_1877-image_0"}, {"key": "1878", "content": "As shown in the figure, in a square garden with a side length of $$8$$ meters, there are $$4$$ shaded walkways with a width of $$1$$ meter (the shaded part in the diagram), and the area of the garden (the blank part) is in square meters. question_1878-image_0"}, {"key": "1879", "content": "Below is a rectangular garden with an area of $$42$$ square meters, it is known that the width of the garden is $$6$$ meters, the length of the garden is meters. question_1879-image_0"}, {"key": "1880", "content": "As shown in the diagram, one large rectangle is divided into 9 smaller rectangles, among which the areas of the 3 small rectangles located at the corners are 9, 15, and 12, respectively. The area of the 4th corner's small rectangle equals. question_1880-image_0"}, {"key": "1881", "content": "A rectangle is divided into four smaller rectangles by two lines. Given the area of three of the rectangles, find the area of the rectangle at the $$?$$ in square centimeters. question_1881-image_0"}, {"key": "1882", "content": "As shown in the picture, in a square vegetable garden there are $$2$$ paths each with a width of $$1$$ meter. It is known that the area of the shaded part is $$35$$ square meters, and the area of the vegetable garden (the blank part) is in square meters. question_1882-image_0"}, {"key": "1883", "content": "There is a rectangular flower bed that is $$8$$ meters long and $$5$$ meters wide, with a $$1$$ meter wide path laid around the perimeter. Calculate the area of the path in square meters.\n question_1883-image_0"}, {"key": "1884", "content": "Delegations from two companies are meeting together, with 10 representatives from Company A and 12 from Company B. A meeting now requires the selection of one recorder from each of Company A and Company B, as well as a chairman from Company A. Therefore, there are a total of methods of selection."}, {"key": "1885", "content": "The figure below is a plan view of a school playground. It is known that segment $$a=120$$ meters, $$b=130$$ meters, $$c=70$$ meters, $$d=60$$ meters, $$l=250$$ meters. Teacher Wang runs around the school $$3$$ times every morning, so Teacher Wang runs meters every day.\n question_1885-image_0"}, {"key": "1886", "content": "The postman has $$3$$ routes from $$A$$ village to $$B$$ village, and $$2$$ routes from $$B$$ village to $$C$$ village. Therefore, the postman has a total of different ways to go from $$A$$ village through $$B$$ village to $$C$$ village.\n question_1886-image_0"}, {"key": "1887", "content": "As shown in the figure, the side length of square $$ABCD$$ is $$6$$ centimeters. Parallel lines are drawn through any two non-coincident points within the square, dividing the square into $$9$$ smaller rectangles. The total perimeter of these $$9$$ smaller rectangles is in centimeters.\n question_1887-image_0"}, {"key": "1888", "content": "How many distinct three-digit even numbers can be formed using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$?"}, {"key": "1889", "content": "There is a rectangular vegetable plot, as shown in the figure. The area of the vegetable plot is more square meters than the area of the radish plot.\n question_1889-image_0"}, {"key": "1890", "content": "As shown in the figure, a large rectangle is divided into $$4$$ smaller rectangles, among which three of the smaller rectangles have areas of $$28\\text{cm}^{2}$$, $$8\\text{cm}^{2}$$, and $$42\\text{cm}^{2}$$, respectively. The area represented by rectangle $$A$$ is in $$\\text{cm}^{2}$$. \n question_1890-image_0"}, {"key": "1891", "content": "In the figure below, the adjacent edges are perpendicular to each other, so the perimeter of this figure is.\n question_1891-image_0"}, {"key": "1892", "content": "Write 'I love math' with $$4$$ different colors of pens, with each adjacent character in a different color, there are in total ways."}, {"key": "1893", "content": "A community built a rectangular leisure square (as shown in the figure), with a perimeter of $$300$$ meters and a length of $$90$$ meters. It is known that the activity area is a square, and the rest is used as a fountain, with the area of the fountain in square meters.\n question_1893-image_0"}, {"key": "1894", "content": "There is a square flowerbed with a side length of $$15$$ meters, and a $$2$$ meters wide path is laid around the perimeter. The area of the path is square meters.\n question_1894-image_0"}, {"key": "1895", "content": "Compute $$\\left( 4800-240+720 \\right)\\div 12=$$."}, {"key": "1896", "content": "Let $$a\\oplus b=\\left( a+2b \\right)-\\left( a+b \\right)$$, where $$a$$ and $$b$$ are natural numbers. Then, $$\\left( 1\\oplus 2 \\right)+\\left( 2\\oplus 3 \\right)+\\left( 3\\oplus 4 \\right)+\\left( 4\\oplus 5 \\right)=$$."}, {"key": "1897", "content": "Given that the first term of the arithmetic sequence is $$4$$, and the $$8$$th term is $$298$$, then the common difference of this sequence is."}, {"key": "1898", "content": "A theater has $$20$$ rows of seats, with each row having $$2$$ more seats than the row in front of it. The last row has $$70$$ seats. The total number of seats in the theater is."}, {"key": "1899", "content": "As shown in the figure: The numbers marked on the left side of each row and the top side of each column represent the count of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_1899-image_0"}, {"key": "1900", "content": "As shown in the picture: The numbers on the left side of each row and the top side of each column represent the count of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_1900-image_0"}, {"key": "1901", "content": "A solid square formation, with a total of $$56$$ people on the outermost layer. Thus, the number of people on each side of the outer layer is."}, {"key": "1902", "content": "A $$3$$-layer hollow square matrix, with each side of the outer layer having $$9$$ people, this $$3$$-layer hollow square matrix has a total of people."}, {"key": "1903", "content": "A total of $$200$$ people are arranged in a $$5$$-layer hollow square formation, with each side of the outermost layer having people. To add one more row and one more column to the outside, the number of people needed to be added is ."}, {"key": "1904", "content": "Xiaoming arranged a solid square array, using $$40$$ pieces for the outermost layer, for a total of pieces."}, {"key": "1905", "content": "Students in the third grade of a school are arranged in a square formation, with 80 people forming the outermost layer. How many people are there on each side of the outermost layer? How many students are there in total in the third grade in this square formation?"}, {"key": "1906", "content": "During military training, the students formed a three-layer hollow square formation consisting of $$204$$ people. How many people are there on each outside edge? ( )"}, {"key": "1907", "content": "A solid square array, with each side of the outermost layer having $$14$$ people, then the total number of people in this square array is."}, {"key": "1908", "content": "Four grade 4 classes participated in a tug-of-war competition, with each pair of classes competing once. Each class has to compete in matches, and there will be a total of matches."}, {"key": "1909", "content": "An old man said: \"If you add $$14$$ to my age, divide by $$3$$, then subtract $$26$$, and finally multiply by $$25$$, it happens to be $$100$$ years old.\" The age of this old man this year is."}, {"key": "1910", "content": "Vera and Eddie were practicing running on the playground, after a period of time, the distance Eddie ran was 3 times that of Vera's plus 80 meters, Eddie ran 280 meters more than Vera, Vera ran meters."}, {"key": "1911", "content": "Third grade has $$7$$ classes participating in a soccer competition, with each pair of classes playing a match against each other. It is stipulated that the winner gets $$2$$ points, the loser gets $$0$$ points, and in the case of a draw, each gets $$1$$ point. Therefore, the total points for the $$7$$ classes are points."}, {"key": "1912", "content": "Hope Elementary School's fourth-grade group organized a soccer competition, in which teams were paired to play in a single round-robin. A total of $$45$$ matches were played. How many teams participated in the competition?"}, {"key": "1913", "content": "$$9$$ students participate in the competition, each pair of students must compete once, a total of $$\\text{competitions}$$."}, {"key": "1914", "content": "Mingming, Honghong, and Tiantian together have $$60$$ apples, Mingming has $$3$$ times the number of apples as Tiantian, Honghong has $$2$$ times the number of apples as Tiantian minus $$6$$ apples, then Tiantian has apples."}, {"key": "1915", "content": "Congcong's family raises chickens, ducks, and rabbits for a total of $$88$$ animals. The number of chickens is $$3$$ times that of ducks, and the number of rabbits is $$4$$ times that of ducks. So, how many rabbits does Congcong's family raise?"}, {"key": "1916", "content": "The store has grapes, strawberries, and bananas totaling $$51$$ kilograms. The weight of the grapes is $$3$$ times the strawberries minus $$3$$ kilograms, and the weight of the bananas is $$2$$ times the grapes. The grapes weigh kilograms."}, {"key": "1917", "content": "Person A and person B compare the number of point cards they have. If person A gives B $$20$$ cards, and then B gives A $$30$$ cards from his current point cards, at this time both have exactly $$100$$ cards, how many point cards did person A originally have."}, {"key": "1918", "content": "During the New Year, mom sent red envelopes with lucky money to the children through WeChat, Jiajia was the first to claim, taking half of the money in the red envelope, Jianjian was the second to claim, taking $$5$$ yuan, and in the end, $$6$$ yuan was all claimed by Chengcheng. Mom totally sent out yuan in red envelopes."}, {"key": "1919", "content": "There are $$48$$ books divided among two groups of children, with the second group having $$5$$ more people than the first group. If all the books are given to the first group, some children can get $$5$$ books each, and the rest can get $$4$$ books each; if all the books are distributed to the second group, some children can get $$4$$ books each, and the rest can get $$3$$ books each. The question is: how many people are there in total in the two groups."}, {"key": "1920", "content": "There are several pieces of milk candy and chocolate candy each. If $$6$$ pieces of milk candy and $$4$$ pieces of chocolate candy are put into a bag, there are $$4$$ more pieces of milk candy left, and the chocolate candies just fit: if $$8$$ pieces of milk candy and $$4$$ pieces of chocolate candy are put into a bag, the milk candies just fit, and there are $$8$$ more pieces of chocolate candy. There are pieces of milk candy, and pieces of chocolate candy."}, {"key": "1921", "content": "The Monkey King led a group of monkeys to pick peaches. After finishing work in the afternoon, the Monkey King began to distribute them. If each small monkey gets $$3$$, there will be $$10$$ left. If each small monkey gets $$4$$, there will be $$1$$ monkey that can only get $$3$$. Among these monkeys (not including the Monkey King), there are some monkeys."}, {"key": "1922", "content": "Students from a choir went to the conference room for a meeting. If each bench seats $$3$$ people, there are $$9$$ people left over. If each bench seats $$4$$ people, there is one bench left over. Question: How many people are in the choir?"}, {"key": "1923", "content": "The teacher plans to distribute candies to the students. If each person receives $$14$$ candies, there will be $$19$$ candies left; if the number of students doubles, and each person receives $$9$$ candies, there will be $$17$$ candies short. So, how many candies does the teacher have in total."}, {"key": "1924", "content": "The kindergarten distributes a basket of apples among the children. If they are given to the older children, with each child receiving $$5$$ apples, there will be $$6$$ apples short; if given to the younger children, with each child receiving $$4$$ apples, there will be $$4$$ apples left. Knowing that there are $$2$$ fewer older children than younger children, how many apples are in the basket?"}, {"key": "1925", "content": "A worker needs to grind $$200$$ kg of flour, and grinds $$60$$ kg in $$3$$ hours. Based on this calculation, the remaining flour will take hours to finish grinding."}, {"key": "1926", "content": "Grandpa hired several identical robots to help him plow a field of $$1800$$ square meters. After calculation, if $$12$$ robots are hired, it takes $$18$$ hours to plow all the fields. If grandpa hires $$24$$ robots to work for $$15$$ hours, they can plow square meters of field."}, {"key": "1927", "content": "In the \"Celebration of the 70th Anniversary of the Founding of the Nation\" knowledge quiz, answering a question correctly earns $$10$$ points, while answering incorrectly deducts $$5$$ points. Congcong attempted $$10$$ questions in total and finally scored $$85$$ points. He got questions right and questions wrong."}, {"key": "1928", "content": "As shown in the diagram, the length of $$AB$$ is $$8$$ cm, the length of $$AD$$ is $$5$$ cm, and the length of $$BE$$ is $$4$$ cm, then the area of the parallelogram is square centimeters.\n question_1928-image_0"}, {"key": "1929", "content": "As shown in the figure, quadrilateral $$ABCD$$ is a rhombus, given that $$AC=20$$, $$BD=11$$, then the area of the rhombus is."}, {"key": "1930", "content": "Master Wang processed $$60$$ parts in $$2$$ hours. Based on this calculation, he can process parts for $$8$$ hours a day. If he needs to process $$360$$ parts, it requires hours."}, {"key": "1931", "content": "Xingxing and Yaoyao agreed to meet at the peach store between their two homes. Xingxing walks $$52$$ meters per minute, and Yaoyao walks $$44$$ meters per minute. They both set off and after $$12$$ minutes, they are still $$208$$ meters apart before they can meet. Can you calculate the distance between Xingxing and Yaoyao\u2019s homes in meters?"}, {"key": "1932", "content": "Place natural numbers into the following table according to a certain rule, then number $$26$$ is in the row and column of the table.\n question_1932-image_0"}, {"key": "1933", "content": "As shown in the figure below, if positive integers are arranged according to a certain pattern, then the number in row $$9$$ and column $$2$$ is.\n question_1933-image_0"}, {"key": "1934", "content": "Arrange the consecutive odd numbers $$1$$, $$3$$, $$5$$, $$7$$, $$9$$, $$11$$, $$\\cdots$$, $$\\cdots$$ in a table, five per row. If a cross frame is moved up, down, left, or right, it can enclose another five numbers, and the sum of these five numbers equals $$2015$$. The largest of these five numbers is.\n question_1934-image_0"}, {"key": "1935", "content": "The image below shows a part of a math puzzle. Please answer: Is there a line connecting the two encircled points? ( )\n question_1935-image_0"}, {"key": "1936", "content": "The triangle in the picture below is.\n question_1936-image_0"}, {"key": "1937", "content": "In the following equation, the same Chinese characters represent the same digits, and different Chinese characters represent different digits, where \"\u7231\" represents , \"\u5b66\" represents , \"\u4e60\" represents .\n question_1937-image_0"}, {"key": "1938", "content": "$$60\\div 12$$=."}, {"key": "1939", "content": "$$75\\div 25$$=."}, {"key": "1940", "content": "$$72\\div 18$$=."}, {"key": "1941", "content": "3 mice eat 12 kilograms of rice in 2 days, then 1 mouse eats kilograms of rice in 1 day."}, {"key": "1942", "content": "Teacher Zhang needs to plant a flag every $$5$$ meters along a $$200$$ meters circular track, the total number of flags needed is ( )."}, {"key": "1943", "content": "As shown in the figure, a frog jumps among four lotus leaves, each time from one leaf to another adjacent leaf. If the frog starts on leaf $$B$$ and then jumps continuously $$4$$ times, there are a total of different ways to jump. question_1943-image_0"}, {"key": "1944", "content": "There are some four-digit numbers that have this characteristic: the difference between two adjacent digits is $$1$$, such as $$1210$$, $$3454$$, etc. Then, the total number of four-digit numbers that meet this requirement and have each digit less than $$3$$ is."}, {"key": "1945", "content": "$$A$$, $$B$$, $$C$$, $$D$$ four people are passing the ball to each other, starting with $$A$$ for the first pass, after $4$ passes, the ball just happens to return to $$A$$'s hands, then the total number of different passing methods is."}, {"key": "1946", "content": "Mao Mao likes to eat three kinds of snacks: chocolate, lollipops, and chips. She will not eat the same kind on two consecutive days. If she eats chocolate on the first day and also on the fourth day, then there are several different arrangements for her menu in these four days."}, {"key": "1947", "content": "There are $10$ cards, among which there are two with $1$, three with $3$, three with $5$, and two with $9$ written on them. Question: Is it possible to select five cards such that the sum of the numbers on them is $28$ (cards cannot be rotated)? (Fill in \"$\\text{A}$\" or \"$\\text{B}$\")\n$\\text{A}$. Yes $\\text{B}$. No"}, {"key": "1948", "content": "The school organized a spring outing, and Xiao Ming went to the supermarket to buy food for the trip. He bought two bottles of Coke, two bags of biscuits, a few sausages, and paid a total of $$101$$ yuan. Given that the price of one sausage is $$1$$ yuan, think about whether the number of sausages Xiao Ming bought is odd or even."}, {"key": "1949", "content": "Black pearls and white balls total $$101$$ in number, strung together in the following arrangement: ... In this string of pearls, the last pearl should be of color, and there are a total of pearls of this color in this string."}, {"key": "1950", "content": "A string of beads, arranged in the order of $$3$$ black beads, $$2$$ white beads, $$3$$ black beads, $$2$$ white beads... Then, the color of the $$38$$th bead is."}, {"key": "1951", "content": "Calculate: $$37\\times 1001001001=$$"}, {"key": "1952", "content": "Calculate: (1) $$19\\times 999=$$\uff0e(2) $$87\\times 9999=$$\uff0e"}, {"key": "1953", "content": "Calculate: $$131\\times 64+131\\times 35+131=$$\uff0e"}, {"key": "1954", "content": "Calculate: (1) $$25\\times 124=$$\uff0e(2) $$808\\times 125=$$\uff0e(3) $$37\\times 9\\times 2=$$\uff0e"}, {"key": "1955", "content": "(1) $65 \\times 31 + 130 + 65 \\times 67 = $;\n(2) $132 \\times 36 + 132 \\times 63 = $."}, {"key": "1956", "content": "$$3000\\div (125\\times 3)=$$."}, {"key": "1957", "content": "The perimeter of a square is $$24$$ cm, its side length is cm, and its area is square cm."}, {"key": "1958", "content": "Groups A, B, and C have a total of $$600$$ people. Group B is twice the size of Group A; Group C is three times the size of Group A. Then, Group A has ____ people."}, {"key": "1959", "content": "In a mental arithmetic competition, it was stipulated that: $$8$$ points would be awarded for each correct answer, and $$5$$ points would be deducted for each wrong answer. Xiao Hua answered $$18$$ questions and scored $$92$$ points. Xiao Hua got $$X$$ questions wrong in this competition."}, {"key": "1960", "content": "There are a total of $$20$$ chickens and rabbits with a total of $$50$$ legs. How many chickens and rabbits are there?"}, {"key": "1961", "content": "The school organized a boating trip for 44 children from the third-grade class ($$1$$), with each small boat seating $$4$$ people and each large boat seating $$6$$ people. A total of $$10$$ boats were exactly needed. Please ask how many large boats and how many small boats there were."}, {"key": "1962", "content": "At the end of the semester, Teacher Yu gave a total of $$20$$ questions to the students. The scoring principle was: for each correct answer, $$5$$ points were awarded, for each unanswered or incorrect answer, not only no points were awarded but also $$1$$ point was deducted. Xiaohua scored $$64$$ points in this test, please ask: How many questions did Xiaohua not attempt or get wrong in this test."}, {"key": "1963", "content": "Among 1 to 20, there are numbers that are multiples of 2 or 3."}, {"key": "1964", "content": "The following diagram must be completed with at least how many strokes. question_1964-image_0"}, {"key": "1965", "content": "The figure below shows the layout of a children's park. The entrance and exit should be located at point or point to traverse every path without repetition. question_1965-image_0"}, {"key": "1966", "content": "The figure below has an odd number of points. question_1966-image_0"}, {"key": "1967", "content": "The image below is a part of the third-order magic square, $$A=$$\uff0e question_1967-image_0"}, {"key": "1968", "content": "$$15\u00d734-14\u00d715=$$\uff0e"}, {"key": "1969", "content": "In the decimal $$5.0893$$, $$5$$ is in the unit's place, representing $$5$$ ones; $$8$$ is in the place, representing tens; $$9$$ is in the place, representing hundredths; $$3$$ is in the place, representing thousandths."}, {"key": "1970", "content": "Remove the \"$$0$$\" from the decimals below, the one whose value remains unchanged is ( )."}, {"key": "1971", "content": "Which two decimals have the same fractional part ( )."}, {"key": "1972", "content": "A number is made up of $$6$$ ones, $$8$$ $$0.1$$s, and $$4$$ $$0.01$$s, this number is, read as."}, {"key": "1973", "content": "Using decimal point movement, calculate: $$0.3343\\times 10=$$; $$80.8\\div 100=$$."}, {"key": "1974", "content": "In the 100m sprint race, the results for the 5 competitors in group 4 are as follows:\n\n\n\n\nCompetitor Number\n\n$$1$$\n\n$$2$$\n\n$$3$$\n\n$$4$$\n\n$$5$$\n\n\n\nTime$$/$$Seconds\n\n$$16.08$$\n\n$$15.98$$\n\n$$16.80$$\n\n$$15.89$$\n\n$$18.06$$\n\n\n\nThe top three competitors in this group are the numbers ,,, competitors.\n question_1974-image_0"}, {"key": "1975", "content": "There are $$8$$ different novels and $$10$$ different comics on the bookshelf, and Star wants to take $$1$$ novel and $$1$$ comic book from the bookshelf, there are different ways to do so."}, {"key": "1976", "content": "As shown in the diagram, quadrilateral $$ABCD$$ is a rhombus, given $$AC=9$$ and $$BD=6$$. The area of the rhombus is. (Hint: The diagonals of a rhombus are perpendicular to each other.) question_1976-image_0"}, {"key": "1977", "content": "The elder brother and the younger brother each have a number of scorecards, with the elder brother having $$5$$ times the amount of the younger brother. If the elder brother gives $$12$$ cards to the younger brother, the elder brother would still have $$4$$ more cards than the younger. Find the original number of scorecards the elder brother had."}, {"key": "1978", "content": "Basket A and Basket B have the same number of apples. If $$12$$ apples are taken from Basket B and put into Basket A, at this time the number of apples in Basket A is $$4$$ times that of Basket B. How many apples were originally in Basket A? question_1978-image_0"}, {"key": "1979", "content": "Xiaomin has $$15$$ dolls, Xiaohua has $$9$$ dolls. If Xiaohua gives Xiaomin a doll, then Xiaomin will have twice as many dolls as Xiaohua."}, {"key": "1980", "content": "A large rectangle is divided into four smaller rectangles by two lines parallel to its sides, with the areas of three of the rectangles as shown in the figure, and the area of the fourth rectangle is.\n question_1980-image_0"}, {"key": "1981", "content": "There are different kinds of books: $$6$$ detective novels, $$4$$ picture books, $$3$$ magazines, and $$2$$ storybooks, making a total of various methods to choose one book."}, {"key": "1982", "content": "Mr. Zhang and Mr. Li have a total of $$100$$ yuan. If Mr. Zhang is given another $$20$$ yuan, then Mr. Zhang will have double the amount of money as Mr. Li. How much money did Mr. Zhang originally have?"}, {"key": "1983", "content": "As shown in the diagram, a rectangle is divided into four rectangles of different sizes by two line segments. The areas of three of the rectangles are $$36$$ square meters, $$8$$ square meters, and $$2$$ square meters, respectively. The area of the other rectangle is square meters.\n question_1983-image_0"}, {"key": "1984", "content": "Mingming, Junjun, Lili, and Fangfang are at the medical office to get vaccinated. There is only one school doctor in the office, so they can only be vaccinated one by one in sequence. Therefore, there are $$4$$ people getting vaccinated with different queuing methods."}, {"key": "1985", "content": "As shown in the figure below, there are four islands A, B, C, D, connected by a total of nine bridges. At least how many additional bridges need to be built to allow tourists to walk across all bridges without repeating any bridge and return to the starting point. question_1985-image_0"}, {"key": "1986", "content": "A cleaning vehicle sweeps the streets, each section of the street is $$1$$ kilometer long, the cleaning vehicle starts from $$A$$, covers all the streets and then returns to $$A$$. What is the shortest path it can take for the entire journey in kilometers. question_1986-image_0 \u200b"}, {"key": "1987", "content": "The diagram below is a street layout of a community, showing the lengths of streets as indicated (unit: kilometers), with different letters representing different building codes. A courier starts from the central courier point (located between buildings $$C$$ and $$D$$ at point $$P$$) and has to walk all the streets and return to the central point. What is the shortest path the courier can take? The shortest path is kilometers. question_1987-image_0"}, {"key": "1988", "content": "The following image is a route map of a maze. If you enter from point $$A$$, you can pass through every point without repeating any route and finally exit from a point.\n question_1988-image_0"}, {"key": "1989", "content": "Can the following figures be drawn with one stroke? If yes, please try to draw it. If not, please add the minimum lines to make it a single stroke figure.\n question_1989-image_0"}, {"key": "1990", "content": "Can the figure below be drawn in one stroke? If not, simply remove a line between ( ) two points to make it a one-stroke figure.\n question_1990-image_0"}, {"key": "1991", "content": "Distribute $$8$$ identical rulers to $$3$$ children, each child gets at least one and the quantities they get are all different, there are several different ways of distribution."}, {"key": "1992", "content": "Divide $$6$$ identical erasers among $$3$$ children, such that each child gets at least one eraser and no two children get the same number of erasers. How many different ways are there to do this?"}, {"key": "1993", "content": "The Little Rabbit's family planted three kinds of vegetables: carrots, cabbages, and spinach. They eat only one type of vegetable per day, and do not eat the same vegetable on two consecutive days. If carrots are eaten on the first day, then there can be a total of different arrangements for the continuous 4-day menu."}, {"key": "1994", "content": "Natural numbers $$12$$, $$135$$, $$1349$$ share a common feature, having at least two digits, and for any two adjacent digits, the digit on the left is less than the digit on the right. We name such numbers \"increasing numbers\". Using the four digits $$4$$, $$6$$, $$7$$, $$9$$, you can form several \"increasing numbers\"."}, {"key": "1995", "content": "Divide $$12$$ eggs into $$3$$ piles, how many ways of division are there?"}, {"key": "1996", "content": "$$\\text{A}$$, $$\\text{B}$$, $$\\text{C}$$ three people practice passing the ball, starting with the ball in $$\\text{A}$$'s hands, after $$3$$ passes, the number of passing methods where the ball is not in $$\\text{A}$$'s hands is."}, {"key": "1997", "content": "There are currently $$14$$ matchsticks, used to form numbers, exactly using all of them.$$.$$ The largest three-digit number that can be formed is, the smallest three-digit number that can be formed is\uff0e question_1997-image_0"}, {"key": "1998", "content": "There are now $$12$$ matchsticks, used to arrange numbers, using exactly all of them.$$.$$ The largest three-digit number that can be formed is, and the smallest three-digit number that can be formed is\uff0e question_1998-image_0"}, {"key": "1999", "content": "Using $$19$$ matchsticks (all used up), the greatest and smallest numbers that can be formed with each digit being distinct are. question_1999-image_0"}, {"key": "2000", "content": "Using $$9$$ matchsticks, place a number in each box within a square. The numbers can be single or multiple digits, can be the same or different. The final addition equation formed has the largest result being and the smallest result being. question_2000-image_0"}, {"key": "2001", "content": "We can use matchsticks to arrange the numbers $$0\\sim 9$$. If you are given $$11$$ matchsticks and have to use them all, what is the largest three-digit number you can form?"}, {"key": "2002", "content": "We can use matchsticks to layout the numbers $$0\\sim 9$$. If you are given $$11$$ matchsticks and have to use them all exactly: question_2002-image_0 (2) What is the smallest three-digit number that can be formed?"}, {"key": "2003", "content": "Using $$10$$ matchsticks (using them all up), the smallest number that can be formed with each digit being different is. question_2003-image_0"}, {"key": "2004", "content": "We can use matchsticks to form the numbers $$0\\sim 9$$. If you are given $$10$$ matchsticks (all to be used), the largest possible number that can be formed is, and the smallest possible number that can be formed is. question_2004-image_0"}, {"key": "2005", "content": "In the equation below, different Chinese characters represent different digits, and the same Chinese characters represent the same digit, making the equation valid. Thus, the four-digit number \"$$\\overline{{\u7f8e\u597d\u672a\u6765}}$$\" is. $$\\begin{matrix}&& &&\u6765 \\\\& &&\u672a & \u6765 \\\\&& \u597d&\u672a&\u6765\\\\+&\u7f8e&\u597d&\u672a&\u6765\\\\\\hline &8&1&0&2\\end{matrix}$$"}, {"key": "2006", "content": "In the following addition problem, the same Chinese character represents the same digit, and different Chinese characters represent different digits. Then, the digit represented by '\u597d' is."}, {"key": "2007", "content": "As shown in the figure below, the numbers in the spaces are all digits from $$2\\sim6$$ (which can be used repeatedly). Therefore, the sum of the numbers in these $$9$$ spaces is. question_2007-image_0"}, {"key": "2008", "content": "The following vertical addition problem consists of $$10$$ digits, exactly one of each from $$0$$ to $$9$$. The position of $$3$$ is already given, please count: How many different vertical addition problems satisfying the conditions exist. question_2008-image_0"}, {"key": "2009", "content": "Place the numbers $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, and $$5$$ in the boxes $$\\square$$ below in the equation, totaling to.\n question_2009-image_0"}, {"key": "2010", "content": "In the provided vertical arithmetic problem, the same shape represents the same digit, and different shapes represent different digits, then \u2606=\uff0c\u25cb=\uff0c\u25b3=.\n\n\n\n\n\u2606\n\u25cb\n\n\n+\n\u2606\n\u25cb\n\n\n\n\u25b3\n6\n\n\n-\n\n\u25b3\n\n\n\n4\n2"}, {"key": "2011", "content": "Complete the following arithmetic operation.\n\n\n\n\n\n$$6$$\n\n\n\n$$+$$\n\n\n$$2$$\n\n\n\n\n$$4$$\n$$8$$"}, {"key": "2012", "content": "Calculate $$\\left( 625\\times 3 \\right)\\times16 $$="}, {"key": "2013", "content": "Calculate: $$125\\times 16\\times 5$$="}, {"key": "2014", "content": "Calculate: $$46\\times 99$$=\uff0e"}, {"key": "2015", "content": "Calculate: $$67\\times 139-67\\times 39$$=\uff0e"}, {"key": "2016", "content": "Calculate: $$35\\times 19+35\\times 82-35$$=."}, {"key": "2017", "content": "Calculate: $$57\\times 36+64\\times 32+64\\times 25$$=\uff0e"}, {"key": "2018", "content": "Compute: $$29\\times 33+76\\times 53+29\\times 43+76\\times 18$$=\uff0e"}, {"key": "2019", "content": "Calculate: (1) $$4\\times 666\\times 25=$$ (2) $$88\\times 125=$$"}, {"key": "2020", "content": "Calculate: $$125\\times (100-8)=$$\uff0e"}, {"key": "2021", "content": "Calculate: $$45\\times 21+45\\times 2+45\\times 77=$$."}, {"key": "2022", "content": "Please answer the following questions: If you put $$32$$ chocolates into two boxes and then take $$4$$ chocolates from the first box and put them into the second box, the number of chocolates in both boxes becomes equal. How many chocolates were originally in the first box?"}, {"key": "2023", "content": "Please answer the following questions: Eddie and Vi agreed to go to the amusement park for fun. Together, they brought $$170$$ dollars. After Eddie gave Vi $$30$$ dollars, he still had $$10$$ dollars more than Vi. Calculate how much money Eddie and Vi originally had."}, {"key": "2024", "content": "Please answer the following questions: Class A and Class B together have $$105$$ books. The number of books in Class A is $$3$$ times that of Class B minus $$15$$ books. How many books does Class B have, and how many books does Class A have?"}, {"key": "2025", "content": "There are $$470$$ kilograms of oil in barrel A, and $$190$$ kilograms of oil in barrel B. How many kilograms of oil need to be transferred from barrel A to barrel B to make the oil in barrel A twice as much as the oil in barrel B?"}, {"key": "2026", "content": "There are a total of $$75$$ trees in the park, with poplars being $$5$$ times the number of willows, and pines being $$2$$ times the number of willows plus $$3$$ trees. How many poplars and pines are there?"}, {"key": "2027", "content": "Please answer the following questions. A bookshelf has $$2$$ shelves, the number of books on the upper shelf is $$3$$ times plus $$8$$ more than that on the lower shelf, and it is known that the difference between the two shelves is $$48$$ books. How many books are there on the upper shelf?"}, {"key": "2028", "content": "Please answer the following questions. There are $$2$$ shelves on a bookshelf, with the number of books on the upper shelf being $$3$$ times less than $$4$$ books compared to the lower shelf, and it is known that the difference between the two shelves is $$66$$ books. How many books are there in total on the two shelves?"}, {"key": "2029", "content": "Calculate the following problem where a monkey and a rooster share milk candies. The number of milk candies shared by the rooster is 3 less than 3 times the number shared by the monkey, and the rooster got 27 more milk candies than the monkey. Please answer: How many milk candies did the monkey and the rooster get respectively?"}, {"key": "2030", "content": "There are two barrels of oil, the first barrel weighs $$55$$ kilograms, the second barrel weighs $$35$$ kilograms. After pouring out the same amount of oil from both barrels, the remainder in the first barrel is $$3$$ times that of the second barrel. How many kilograms of oil are left in the first barrel?"}, {"key": "2031", "content": "The first class of the third grade is going to participate in the sports meet! All the students are actively signing up, and Qian Qian, Yang Yang, and Xi Xi all want to sign up. There are 5 events including running, high jump, long jump, shot put, and skipping rope. Each person can only participate in one event. (1) If everyone can participate in the same event, there are a total of different options for which event to participate in."}, {"key": "2032", "content": "The first-grade class is going to participate in the sports meet! Everyone is actively signing up. Qianqian, Yangyang, and Xixi all want to sign up. There are 5 events: running, high jump, long jump, shot put, and skipping rope. Each person can only participate in one event. (2) If everyone participates in different events, there are a total of different choices for participation."}, {"key": "2033", "content": "In the sports meeting, there are four running events, which are $$50$$ meters, $$100$$ meters, $$200$$ meters, and $$400$$ meters. It is stipulated that each participant can only participate in one of them. Four students, A, B, C, and D, registered for these four events. Question: (2) If these four students registered for different events, how many different registration methods are there in total."}, {"key": "2034", "content": "With the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$. (1) It is possible to form different two-digit numbers."}, {"key": "2035", "content": "Using the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, you can form different three-digit numbers with no repeating digits."}, {"key": "2036", "content": "Using the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$. (3) you can form a different four-digit even number without repeated digits."}, {"key": "2037", "content": "Using the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$\uff0e(4) it is possible to form different four-digit numbers without repeating digits and this number is a multiple of $$5$$."}, {"key": "2038", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, it is possible to form different three-digit numbers with no repeating digits."}, {"key": "2039", "content": "Using digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, you can form different four-digit odd numbers without repeating any digit."}, {"key": "2040", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, one can form different four-digit even numbers without repeating digits."}, {"key": "2041", "content": "Color the following figure with $$5$$ different colors, requiring that adjacent areas (two areas with a common edge are considered adjacent) are colored differently. If colors can be reused, then there are a total of different coloring methods.\n question_2041-image_0"}, {"key": "2042", "content": "Using the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, you can form a three-digit even number without repeating digits."}, {"key": "2043", "content": "Eddie, before attending the party, has to choose a suitable combination from $$2$$ hats, $$4$$ different pairs of trousers, $$3$$ different suits, and $$2$$ different pairs of leather shoes, where choosing a hat is optional. Therefore, he has a total of different combinations. question_2043-image_0"}, {"key": "2044", "content": "As shown in the diagram, a map consists of five countries $$A$$, $$B$$, $$C$$, $$D$$, $$E$$. It is now required to use $$5$$ different colors to distinguish these countries, with the condition that adjacent countries cannot use the same color, while non-adjacent countries can use the same color. Therefore, the number of ways to color this map is.\n question_2044-image_0"}, {"key": "2045", "content": "The perimeter of the figure below is in centimeters. question_2045-image_0"}, {"key": "2046", "content": "The perimeter of the figure below is. question_2046-image_0"}, {"key": "2047", "content": "As shown in the figure, two rectangles form a square. If the perimeter of the square is $$6$$ centimeters less than the sum of the perimeters of the two rectangles, then the perimeter of the square is ____ centimeters.\n question_2047-image_0"}, {"key": "2048", "content": "As shown in the diagram, a square with a side length of $$6$$ cm is cut twice, turning it into $$3$$ rectangles. What is the total perimeter of these $$3$$ rectangles in centimeters?\n question_2048-image_0"}, {"key": "2049", "content": "There is a rectangular piece of paper with a length of $$10$$ cm and a width of $$8$$ cm. Cut vertically with scissors (as shown below), the sum of the perimeters of these $$2$$ rectangles is cm. question_2049-image_0"}, {"key": "2050", "content": "There is a rectangular piece of paper, the length is $$10$$ cm, and the width is $$8$$ cm, cut horizontally with scissors (see the figure below), the sum of the perimeters of these $$2$$ rectangles is in centimeters. question_2050-image_0"}, {"key": "2051", "content": "There is a rectangular piece of paper, its length is $$2$$ cm more than its width, and its perimeter is $$36$$ cm. Cut it with scissors $$3$$ times (as shown in the figure), the total perimeter of these $$6$$ rectangles is centimeters.\n question_2051-image_0"}, {"key": "2052", "content": "The diagram below shows the plan of a garden with the side lengths as shown. Calculate the perimeter of this garden in meters.\n question_2052-image_0"}, {"key": "2053", "content": "To protect the instruments safely, the doctor wants to build a metal protective fence. The perimeter of the fence is in decimeters. (Unit: decimeters)\n question_2053-image_0"}, {"key": "2054", "content": "As shown in the figure, there is a rectangular piece of paper with a length of $$10$$ cm and a width of $$6$$ cm. Using scissors to cut $$3$$ times, the sum of the perimeters of these $$6$$ small rectangles is in centimeters.\n question_2054-image_0"}, {"key": "2055", "content": "As shown in the figure: (1) Figure \u2460 is a square with an area of $$25{{\\text{m}}^{2}}$$, its side length is meters. question_2055-image_0"}, {"key": "2056", "content": "The area of the given figure $$2$$ is square centimeters. question_2056-image_0 question_2056-image_1"}, {"key": "2057", "content": "There is a flower garden that happens to be a square with a side length of $$10$$ meters, as shown in the following figure. There are three paths with a width of $$1$$ meter in the garden, as shown in the shaded part of the following figure. The area of the blank part is in square meters. question_2057-image_0"}, {"key": "2058", "content": "In the diagram, two squares of different sizes overlap, and the area of the red shaded part is larger than the area of the green shaded part by square centimeters. question_2058-image_0"}, {"key": "2059", "content": "(1) The area of a rectangle is $$108$$ square meters, the width is $$9$$ meters, and the length is meters;\n(2) The area of a square is $$625$$ square decimeters, and the side length is decimeters."}, {"key": "2060", "content": "A country has four generals, who have respectively made first, second, third, and fourth class contributions in campaigns to defend the nation\u2019s security. The king plans to reward them with land based on their contributions. The size of the land to be awarded is as follows, the area of land $$B$$ is in square kilometers.\n question_2060-image_0"}, {"key": "2061", "content": "Calculate: (1) $$67000\\div 25=$$."}, {"key": "2062", "content": "First observe, then calculate the following expressions: (1) $$(130+39)\\div 13=$$."}, {"key": "2063", "content": "$$70\\div 12+74\\div 12=$$\uff0e"}, {"key": "2064", "content": "Compute: \n$$(830+83)\\div 83=$$"}, {"key": "2065", "content": "A new operation is defined as $$m\\Omega n=2\\times m+3\\times n$$.\nCalculate: $$4\\Omega 5+5\\Omega 6=$$\uff0e"}, {"key": "2066", "content": "Fill in the blanks as required. (2) $$8+10+12+14+16= $$."}, {"key": "2067", "content": "In an arithmetic sequence with $$15$$ numbers, it is known that the first number is $$9$$ and the eighth number is $$30$$. Calculate the sum of the sequence."}, {"key": "2068", "content": "There are $$7$$ consecutive natural numbers with a sum of $$70$$, then the middle number is."}, {"key": "2069", "content": "Calculate: $$1+3+5+7+9+$$$$\\cdots \\cdots $$+$$19+21$$=\uff0e"}, {"key": "2070", "content": "Calculate: $$7+11+15+\\cdots \\cdots +83=$$."}, {"key": "2071", "content": "The given sequence is $$2$$, $$5$$, $$8$$, $$11$$, $$\u2026\u2026$$, the $$50th$$ number is."}, {"key": "2072", "content": "A movie theater auditorium has a total of $$11$$ rows of seats, with each subsequent row having $$2$$ more seats than the row in front of it. The first row has $$10$$ seats. (1) The last row has ____ seats."}, {"key": "2073", "content": "A cinema has a total of $$11$$ rows of seats, with each row having $$2$$ more seats than the row in front of it. The first row has $$10$$ seats. (2) The total number of seats in this cinema is ____."}, {"key": "2074", "content": "Sum: $$103+104+105+106+107+108+109$$=\uff0e"}, {"key": "2075", "content": "Sum: $$5+8+11+\\cdots +128=$$\uff0e"}, {"key": "2076", "content": "Xiaotie collects candies. On day $$1$$, he collected $$3$$ candies, and each day he collected $$2$$ more candies than the previous day. So, on day $$59$$, he collected $$\\_\\_\\_\\_$$ candies."}, {"key": "2077", "content": "The fourth grade forms two solid squares for the dance performance. (2) The square formation of Class 2 of the fourth grade has 10 people on each side at the outermost layer, and the outermost layer has in total people."}, {"key": "2078", "content": "The solid square formation of the 5th grade, class 1, has a total of $$36$$ people on the outermost layer. (1) How many people are there on each side of the outermost layer of this square formation?"}, {"key": "2079", "content": "Students in sixth grade are arranged in a solid square formation, with 5 people left over. If one row is added both horizontally and vertically to form a slightly larger solid square formation, then there will be 26 people missing. (1) The number of people in the sixth grade is."}, {"key": "2080", "content": "A solid square formation, the outermost layer has $$40$$ people, asking how many people there are on each side of the outermost layer."}, {"key": "2081", "content": "After the sports meet, all students went to the gymnasium for the closing ceremony. Volunteers congratulated the athletes with beautiful flowers. They arranged a five-layer hollow square flower bed in the open space in front of the gymnasium, using a total of $$240$$ flower pots. How many flower pots were there in the very middle layer?"}, {"key": "2082", "content": "After the sports meeting, all the students went to the gymnasium to participate in the closing ceremony. Volunteers congratulated the athletes with beautiful flowers and arranged a five-layer hollow square flower bed in the open space in front of the gymnasium, using a total of $$240$$ pots of flowers. So, the number of flower pots in the most inner layer is."}, {"key": "2083", "content": "After the sports meeting ended, all the students went to the gymnasium to participate in the closing ceremony. Volunteers used beautiful flowers to congratulate the athletes, arranging a five-layer hollow square formation of flower beds on the open ground in front of the gymnasium, using a total of $$240$$ pots of flowers. Then, how many pots of flowers are there in the outermost layer."}, {"key": "2084", "content": "The third grade of the primary school has $$120$$ students. They form a three-layer hollow square formation. Question: (1) How many people are on the outer layer."}, {"key": "2085", "content": "There are $$120$$ students in the third grade of elementary school. They are arranged in a three-layer hollow square formation. Question: (3) If one layer is added on the outside, turning it into a four-layer hollow square formation, how many more people should be added?"}, {"key": "2086", "content": "With $$336$$ chess pieces arranged into a six-layer hollow square matrix, the number of chess pieces in the outermost layer is."}, {"key": "2087", "content": "Using $$336$$ chess pieces to form a six-layer hollow square matrix, then the innermost layer has chess pieces."}, {"key": "2088", "content": "20 badminton players participate in a singles competition, paired up for a round-robin tournament, so one of the players, Xiao Hong, has to compete with ( ) other players."}, {"key": "2089", "content": "The students participated in a radio gymnastics competition, forming a solid square formation with each row and each column having $$9$$ people. How many people need to be added to add an additional layer on the outermost part?"}, {"key": "2090", "content": "Lingling is fond of Go, and she arranged a double-layer hollow square formation with chess pieces on the board, with each side of the outer layer having $$14$$ chess pieces. The question is: How many chess pieces did she use in total?"}, {"key": "2091", "content": "A total of $$200$$ people are arranged into a $$5$$-layer hollow square formation, with the outermost layer of the formation having people on each side."}, {"key": "2092", "content": "Students $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ are participating in a chess competition, where each pair has to play one game against each other. Up to now, $$A$$ has played $$4$$ games, $$B$$ has played $$3$$ games, $$C$$ has played $$2$$ games, and $$D$$ has played $$1$$ game. Question: How many games has student $$E$$ played so far."}, {"key": "2093", "content": "The school is going to hold a table tennis competition, with $$5$$ academic groups participating in the competition, each academic group sending $$2$$ representative teams. Each team will play a match against each of the other teams, so each team will play matches, and in total, matches will be played."}, {"key": "2094", "content": "Four soccer teams play in a round-robin tournament, where each pair of teams plays one match. If a match is drawn, each team gets $$1$$ point, otherwise, the winning team gets $$3$$ points and the losing team gets $$0$$ points. It is known that teams A, B, C, and D scored $$7$$ points, $$4$$ points, $$4$$ points, and $$1$$ point respectively. Then, the total number of drawn matches in all games is ( )."}, {"key": "2095", "content": "Five basketball teams play in a round-robin tournament, meaning each pair of teams plays against each other once, with the winner scoring $$2$$ points, the loser scoring $$0$$ points, and a tie resulting in $$1$$ point for each. The final scores of all teams are different. It is known that: the first-place team had no ties; the second-place team had no losses; the fourth-place team had no wins. Then, the total number of draws in all matches was ."}, {"key": "2096", "content": "There are a total of $$32$$ national teams participating in the World Cup, known as the top $$32$$. Among them, every $$4$$ national teams are grouped into $$1$$ group, and in the round-robin competitions, each national team must and can only play a match against each of the other teams in the same group. The top $$2$$ teams from each group enter the knockout stage; the knockout stage determines the winners and losers in one match between every two countries, producing the top $$8$$, top $$4$$, until finally determining the champion (first place), runner-up (second place), third place, and fourth place. (The two losers from the semi-finals participate in the third and fourth place match, while the other losers from the knockout stage do not participate in further matches.) With this, all the matches of this World Cup come to an end. Based on the information above, calculate the total number of matches in the entire World Cup."}, {"key": "2097", "content": "There are $$128$$ children participating in the '10th I Can Eat the Most' competition. The competition is conducted in a knockout manner until a champion is decided. A total of ( ) competitions need to be arranged."}, {"key": "2098", "content": "$$12$$ players participate in a round-robin tennis tournament, where the rule is that each person has to play a match against every other person. How many matches in total will be held?"}, {"key": "2099", "content": "Eight people participate in a round-robin Chinese chess tournament. It is stipulated that the winner gets $$2$$ points, the loser gets $$0$$ points, and in the event of a draw, both sides get $$1$$ point each. After the competition is over, the total points accumulated by the eight participants must be points."}, {"key": "2100", "content": "Eddie and Will arrive at the tourist rest area, where they find: chrysanthemums, camellias, and roses totaling $$109$$ pots, with the chrysanthemums being $$3$$ times the camellias plus $$1$$ pot, and the camellias are twice the roses. Then, how many more pots are there of chrysanthemums than roses?"}, {"key": "2101", "content": "Dividing two numbers, the quotient is $$3$$ with a remainder of $$2$$. It is known that the sum of the dividend, divisor, quotient, and remainder is $$115$$. The dividend is, and the divisor is"}, {"key": "2102", "content": "Eddie has $$1$$ yuan more than double the money that Dengdeng has, Vee has $$11$$ yuan less than five times the money that Dengdeng has, and moreover, Vee has $$24$$ yuan more than Eddie. Eddie brought yuan, Dengdeng brought yuan, Vee brought yuan."}, {"key": "2103", "content": "Among three people, A, B, and C, eating steamed buns, A ate 3 more than twice as many as B, B ate twice as many as C, and together they ate a total of 73 steamed buns. How many steamed buns did A eat?"}, {"key": "2104", "content": "Zhu Bajie leads McDull, Peppa Pig, Zhu Jianqiang, and other little pigs to play games together, totaling $$20$$ little pigs. Zhu Bajie divides the little pigs into three groups. The number of pigs in the first group is $$4$$ less than the total number of pigs in the other two groups, and the second group has $$2$$ more pigs than the third group. So, the first group has pigs, the second group has pigs, and the third group has pigs. (Zhu Bajie is not a little pig)"}, {"key": "2105", "content": "Students A, B, C, and D divide up homework, totaling $$60$$ books. A said: 'I have the least amount of homework, $$2$$ less than B, $$2$$ less than D, $$4$$ less than C,' then A gets this number of homework books. C gets this number of homework books."}, {"key": "2106", "content": "There was a money-grubber always wanting to increase his wealth. One day, he encountered an elderly man on a bridge. The man said to him: 'If you walk across this bridge and then come back, the money on you will double. However, as a reward, you need to give me $$32$$ copper coins for each round trip.' The money-grubber did the math and found it reasonable, so he agreed. After walking to the other side of the bridge and back, his money indeed doubled, and he happily gave $$32$$ copper coins to the elderly man. By the end of the third round trip, the last $$32$$ copper coins were given to the elderly man, leaving him with not a single coin. Question: How many copper coins did the money-grubber originally have?"}, {"key": "2107", "content": "The doctor allocates his monthly salary in the following way: Half of his monthly salary is saved in the bank, half of the remaining money minus $$300$$ is for mortgage payments, then half of the rest plus $$300$$ is for dining expenses, leaving him with $$800$$. What is the doctor's monthly salary?"}, {"key": "2108", "content": "There are three piles of apples, labeled A, B, and C, with a total of $$96$$ apples. In the first move, the same number of apples as there are in pile B are taken from pile A and put into pile B; in the second move, the same number of apples as there are in pile C are taken from pile B and put into pile C; in the third move, apples equivalent to the remaining number of apples in pile A are taken from pile C and put into pile A, making the number of apples in the three piles equal. Initially, pile A had apples, pile B had apples, and pile C had apples."}, {"key": "2109", "content": "While solving a subtraction problem, Eddie mistakenly wrote the units digit of the minuend as $$5$$ instead of $$3$$, the tens digit as $$0$$ instead of $$6$$, and the hundreds digit of the subtrahend as $$2$$ instead of $$7$$. As a result, he got the difference as $$1994$$. What is the correct difference?"}, {"key": "2110", "content": "When doing a subtraction problem, if the units place of the minuend is mistaken for $$8$$ instead of $$4$$, and the tens place is mistaken for $$4$$ instead of $$8$$, the difference turned out to be $$125$$. Then, the correct result should be."}, {"key": "2111", "content": "A group of ants moving house, originally stored a pile of food, the first day they moved out more than half of the total plus $$10$$ grams, the second day they moved out less than half of the remaining minus $$12$$ grams, as a result, there are still $$32$$ grams left in the nest, so, the ants moved out a total of grams of food."}, {"key": "2112", "content": "The doctor asked Da Kuan to plant a row of trees on one side of the road. Initially, Da Kuan planted $$5$$ poplar trees in a row. Then the doctor said, \"This isn't the correct way to plant. You need to plant following this sequence: $$3$$ willow trees, $$2$$ pine trees, $$1$$ poplar tree, and then repeat with $$3$$ willow trees, $$2$$ pine trees, $$1$$ poplar tree $$\\cdots \\cdots$$.\" After that, Da Kuan continued planting trees according to this sequence. In total, Da Kuan planted $$200$$ trees. Please answer: how many willow trees, pine trees, and poplar trees did Da Kuan plant? question_2112-image_0"}, {"key": "2113", "content": "October 1, 2018, was a Monday. After another 27 days it would be Sunday."}, {"key": "2114", "content": "January 1, 2015, was Thursday, February 5, 2017, is on a Sunday"}, {"key": "2115", "content": "The professor continues to distribute mineral water to Class 3-2. If each group is given $$4$$ boxes, there will be $$17$$ boxes extra; if each group is given $$7$$ boxes, there will be $$10$$ boxes short. Thus, how many groups are there in Class 3-2? The professor prepared boxes of mineral water. question_2115-image_0"}, {"key": "2116", "content": "The fourth grade class one of Max Primary School distributed Band-Aids. If each person gets $$2$$ Band-Aids, there would be $$20$$ Band-Aids left after distribution. If each person gets $$3$$ Band-Aids, $$10$$ people would not get any Band-Aids. How many Band-Aids does the fourth grade class one have in total?"}, {"key": "2117", "content": "The fifth-grade is responsible for transporting fruit. If each student in class one transports $$7$$ boxes, then there are $$10$$ boxes left over; if each student in class two transports $$8$$ boxes, then there are $$2$$ boxes short. It is known that class one has $$3$$ more students than class two. There are a total of boxes of fruit, class one has students, and class two has students."}, {"key": "2118", "content": "Wei'er distributes chocolates. If each person gets 12 pieces, there will be 14 pieces left; if the number of students doubles and each one gets 7 pieces, there will be a shortage of 8 pieces. Wei'er has a total of chocolates."}, {"key": "2119", "content": "The owner of a flower shop plans to put some roses into vases. If each vase contains 6 roses, then the remaining roses will exactly fill 3 vases; if each vase contains 8 roses, there will be 3 empty vases. Therefore, there is a total of roses."}, {"key": "2120", "content": "Daming and Xiaobai live in the same building. Their speed of climbing stairs is the same, and the time it takes to climb each floor is also the same. It takes $$180$$ seconds to climb to the $$6th$$ floor. If the speed remains unchanged, Daming takes $$3$$ minutes to get home. Can you tell which floor do they live on?"}, {"key": "2121", "content": "$$5$$ workers can manufacture $$80$$ parts in $$2$$ hours, at this rate, $$4$$ people can manufacture how many parts in $$7$$ hours."}, {"key": "2122", "content": "Grandma Wang has $$5$$ dairy cows that produce $$630$$ kilograms of milk in $$7$$ days, according to this calculation, $$10$$ dairy cows can produce kilograms of milk in $$14$$ days."}, {"key": "2123", "content": "The image is a hollow square made up of \"funny face\" emojis. Draw one layer outside of it, and it requires some funny face emojis. Add another layer outside, and it requires some funny face emojis. question_2123-image_0"}, {"key": "2124", "content": "A math test with only $$20$$ questions, for each correct answer $$5$$ points are awarded, and for each wrong answer or unanswered question $$3$$ points are deducted. This time, Wei'er failed to pass the test (passing is $$60$$ points), but she found that if she had made one less mistake, she would have exactly passed. How many questions did she answer correctly."}, {"key": "2125", "content": "A certain restaurant has $$39$$ signature dishes, Eddie has tried $$15$$ of them, Vi has tried $$9$$ of them, and there are $$4$$ dishes that both have tried. There is a signature dish that neither has tried."}, {"key": "2126", "content": "The third grade had $$50$$ students go to the cafeteria for lunch, where many dishes were prepared. Of these, $$26$$ students chose tomato and scrambled eggs, $$21$$ students chose braised pork, $$17$$ people did not choose either of these two dishes, and there were people who chose both dishes."}, {"key": "2127", "content": "Class 3 ($$1$$) has $$55$$ students participating in the sports meeting, with each person participating in at least one of the running or rope skipping competitions. It is known that $$36$$ people participated in the running and $$38$$ people participated in the rope skipping. There are people who only participated in rope skipping."}, {"key": "2128", "content": "Class 3 ($$2$$) has $$50$$ students. Some can ride bikes, others can swim. There are $$35$$ who can ride bikes, $$15$$ are good at both, and there is no student who can\u2019t do either. Thus, the number of people who can swim is."}, {"key": "2129", "content": "Among the natural numbers from $$1\\sim 100$$: (1) There are ____ multiples of $$2$$."}, {"key": "2130", "content": "Among the natural numbers from $$1\\sim 100$$: (2) There are ____ multiples of $$5$$."}, {"key": "2131", "content": "Among these natural numbers from $$1\\sim 100$$: (3) The number that is both a multiple of $$2$$ and a multiple of $$5$$ is."}, {"key": "2132", "content": "Among these natural numbers from $$1\\sim 100$$: (4) The number of multiples of $$2$$ or $$5$$ is."}, {"key": "2133", "content": "Among these natural numbers from $$1\\sim 100$$: (5) those that are neither multiples of $$2$$ nor multiples of $$5$$ have ."}, {"key": "2134", "content": "Among the natural numbers from $$1$$ to $$60$$: (3) The number of numbers that are multiples of both $$3$$ and $$5$$."}, {"key": "2135", "content": "Among these natural numbers from $$1$$ to $$60$$: (2) The number of multiples of $$5$$ is."}, {"key": "2136", "content": "Among these natural numbers from $$1$$ to $$60$$: (1)The number of multiples of $$3$$ is."}, {"key": "2137", "content": "Among these natural numbers from $$1$$ to $$60$$: (4) the number of multiples of $$3$$ or $$5$$ is."}, {"key": "2138", "content": "Among natural numbers from $$1$$ to $$60$$: (5) The number of numbers that are neither multiples of $$3$$ nor multiples of $$5$$ is."}, {"key": "2139", "content": "The school organizes chess competitions in three groups: Go, Chinese chess, and international chess. There are 42 people participating in the Go competition, 55 in the Chinese chess competition, and 33 in the international chess competition. There are 18 people participating in both Go and Chinese chess competitions, 10 people in both Go and international chess competitions, and 9 people in both Chinese chess and international chess competitions. There are 5 people who participated in all three chess competitions. The question asks how many people participated in the chess competitions in total."}, {"key": "2140", "content": "A certain company\u2019s annual meeting requires a performance program. There are $$40$$ people performing a square dance, $$60$$ people performing eye exercises, $$99$$ people performing sleeping in public. There are $$15$$ people participating in both square dancing and eye exercises; there are $$20$$ people participating in both square dancing and sleeping in public; there are $$24$$ people participating in both eye exercises and sleeping in public. There are $$6$$ people participating in all three programs. Those who do not perform are happily eating and drinking below the stage. The company has a total of $$1024$$ employees. People are happily eating and drinking below the stage."}, {"key": "2141", "content": "Students in a certain class each hold flags of three different colors: red, yellow, and blue. Each student has at least one flag. It is known that there are a total of $$34$$ students with red flags, $$26$$ with yellow flags, and $$18$$ with blue flags. Amongst them, there are $$6$$ students who have all three colors of flags. Moreover, there are $$9$$ students who have only red and yellow flags, $$4$$ students who have only yellow and blue flags, and $$3$$ students who have only red and blue flags. So, how many students are there in the class in total? question_2141-image_0"}, {"key": "2142", "content": "The Youth Palace's spring calligraphy class, fine arts class, and instrumental music class are enrolling students. The calligraphy class enrolled $$29$$ students, fine arts enrolled $$28$$ students, and the instrumental music class enrolled $$27$$ students. Among these students, there are $$13$$ who enrolled in both calligraphy and fine arts, $$12$$ who enrolled in both calligraphy and instrumental music, $$11$$ who enrolled in both fine arts and instrumental music, and $$5$$ who enrolled in all three subjects. Therefore, the number of students who enrolled in only one subject is ."}, {"key": "2143", "content": "The length of a towel is $$48$$ cm, and the width is $$20$$ cm, what is the area of this towel in square centimeters?"}, {"key": "2144", "content": "Use parity analysis to determine whether the result of $$34+51+422\\times 8$$ is ( )."}, {"key": "2145", "content": "As shown in the diagram, there is a white rectangle inside the trapezoid. The width of the rectangle is $$2$$ meters. Please calculate the area of the gray shadow in square meters. question_2145-image_0"}, {"key": "2146", "content": "Xiao Ming's pocket money is just enough to buy $$4$$ erasers. How many pencils can he buy with this money? question_2146-image_0"}, {"key": "2147", "content": "Below is the production statistics chart of Factory 1 and Factory 2. question_2147-image_0 The production volume of Factory 1 in May is 10,000 units more than the production volume of Factory 2 in March."}, {"key": "2148", "content": "$$174\\div (2\\times 3)$$="}, {"key": "2149", "content": "Calculate: $$240\\times 2\\div 6$$="}, {"key": "2150", "content": "As shown in the diagram, please fill in the blanks with suitable numbers to make the multiplication vertical method valid. The result of the multiplication is. question_2150-image_0"}, {"key": "2151", "content": "In the multiplication vertical problem shown in the figure, question_2151-image_0 represent different numbers. Question: What is the three-digit number in question_2151-image_1. question_2151-image_2"}, {"key": "2152", "content": "The picture below shows an incomplete vertical multiplication equation, the result of this equation is. question_2152-image_0"}, {"key": "2153", "content": "As shown in the figure, there is an incomplete vertical multiplication equation. Now it is known that one of the numbers is $$8$$. The result of this multiplication is. question_2153-image_0"}, {"key": "2154", "content": "In the multiplication vertical expression shown in the figure, some numbers are covered by triangular pieces of paper. The result of the calculation is. question_2154-image_0"}, {"key": "2155", "content": "Complete the multiplication equation in the diagram below, the sum of the two factors is.\n question_2155-image_0"}, {"key": "2156", "content": "The picture below is an incomplete division problem, the dividend in this problem is. question_2156-image_0"}, {"key": "2157", "content": "As shown in the diagram, fill in the blank with the appropriate number to make the division long division correct. Then, the divisor is. question_2157-image_0"}, {"key": "2158", "content": "[Thinking Expansion] Fill in the $$\\square$$ with an appropriate number so that the three-digit number $$\\overline{76\\square}$$ can be divided by both $$2$$ and $$3$$. List all possible three-digit numbers in ascending order."}, {"key": "2159", "content": "[Campus Knowledge] The experimental primary school has two rectangular playgrounds with equal areas. The East playground is $$6$$ meters long and $$5$$ meters wide; the West playground is $$2$$ meters wide and its length is meters."}, {"key": "2160", "content": "[Campus Knowledge] The teacher assigned $$112$$ math problems to be completed in $$8$$ days. Qingqing does $$11$$ problems each day, leaving ___ left."}, {"key": "2161", "content": "[Thinking Expansion] Calculate: $$21\\times 101+27\\times 99=$$"}, {"key": "2162", "content": "[Thinking Expansion] As shown in the figure, in the parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$BC=12$$ cm, $$AF=8$$ cm, $$CD=6$$ cm. Then the length of the line segment $$AE$$ is in centimeters. question_2162-image_0"}, {"key": "2163", "content": "[Campus Knowledge] Calculation: $231\\times 7=$"}, {"key": "2164", "content": "[Campus Knowledge] In the dessert shop, one Swiss roll costs $$7$$ yuan, one box contains $$4$$ rolls, buying $$16$$ boxes of Swiss rolls costs yuan."}, {"key": "2165", "content": "[Thinking Expansion] Places A and B are $$980$$ kilometers apart. A fire truck starts from place A and heads towards place B at a speed of $$40$$ kilometers per hour. $$2$$ hours later, a sedan starts from place B and heads towards place A at a speed of $$60$$ kilometers per hour. Then, starting from the departure of the fire truck, the two vehicles meet on the way after $$11$$ hours."}, {"key": "2166", "content": "[Thinking Expansion] Calculate: $(1947+9471+4719+7194)\\div 7=$"}, {"key": "2167", "content": "[School Knowledge] Da Kuan wants to evenly distribute $$279$$ roses among $$9$$ teachers. Then, each teacher will get roses."}, {"key": "2168", "content": "In a certain barber shop, there is only one barber, but at the same time five customers come in. Depending on the haircuts they want, they respectively need 10, 12, 15, 20, and 24 minutes. Arrange their haircut order reasonably so that the total of their haircut and waiting time is the minimum. Then, the minimum time in minutes is."}, {"key": "2169", "content": "There are $$8$$ people each holding a bucket and going to the tap to get water at the same time. It takes $$1$$ minute to fill the first person's bucket, $$2$$ minutes for the second person's bucket, and so on. (1) When there's only one tap, how should these $$8$$ people be arranged to fetch water so that their total water fetching and waiting time is the minimum. The shortest time is minutes."}, {"key": "2170", "content": "There are $$8$$ people each holding a bucket going to the tap to fetch water at the same time. It takes $$1$$ minute to fill the first person's bucket at the tap, $$2$$ minutes for the second person's bucket, and so on. (2) When there are two taps, how should these $$8$$ people be arranged to fetch water so that their total fetching and waiting time is minimized. The shortest time is minutes."}, {"key": "2171", "content": "(1) As shown in the figure, there are five residential buildings $$A$$, $$B$$, $$C$$, $$D$$, $$E$$ on the street, each with the same number of residents. Now a bus stop is to be established. In order for the sum of distances from the five buildings to the bus stop to be the shortest, where should the bus stop be located? question_2171-image_0"}, {"key": "2172", "content": "As shown in the diagram, there are five schools along a road from west to east named $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, with 200, 300, 400, 500, and 600 people respectively. The distance between any two adjacent schools is 100 meters. Now, a public bus station is to be built at the entrance of one of the schools to minimize the total distance for everyone to reach the station. Where should the station be built? question_2172-image_0"}, {"key": "2173", "content": "Along a highway, every $$10$$ kilometers, there is a warehouse (as shown in the diagram) for a total of $$5$$ warehouses. Warehouse $$A$$ contains $$13$$ tons of goods, warehouse $$B$$ contains $$23$$ tons of goods, warehouse $$C$$ contains $$35$$ tons of goods, warehouse $$D$$ contains $$30$$ tons of goods, warehouse $$E$$ contains $$37$$ tons of goods. Now, we want to concentrate all the goods in one warehouse. If the transportation cost for each ton of goods per kilometer is $$2$$ yuan, then the warehouse where the goods are stored with the least transportation cost, the least cost is yuan. question_2173-image_0"}, {"key": "2174", "content": "A certain village has six sugarcane fields, with yields as shown in the figure below. Now planning to build a sugar factory, where should the sugar factory be built to minimize total transportation costs? question_2174-image_0"}, {"key": "2175", "content": "Beijing and Shenzhen each have $$10$$ and $$6$$ identical machines respectively, ready to give $$11$$ to Wuhan and $$5$$ to Xi'an, the shipping cost per machine is as shown in the table. The redistribution can minimize the total shipping cost, the minimum shipping cost is yuan. question_2175-image_0"}, {"key": "2176", "content": "Beijing and Shanghai have $$10$$ and $$6$$ identical machines, respectively, prepared to give Wuhan $$11$$ machines and Xi'an $$5$$ machines. The freight for each machine is shown in the table. The shipment can minimize the total freight cost, and the least freight cost is yuan. question_2176-image_0"}, {"key": "2177", "content": "There is only one barber in the barbershop, but at the same time, five customers arrived. According to the hairstyle they want, it takes $$8$$, $$10$$, $$13$$, $$15$$, and $$20$$ minutes respectively. How should their haircut order be arranged so that the total time spent on haircuts and waiting for these five people is minimized? The minimum time is."}, {"key": "2178", "content": "On a highway, there is a warehouse every $$10$$ kilometers, totaling $$4$$ warehouses. The figures in the diagram represent the mass of the goods stored in each warehouse (in tons). Now, if all the goods are to be concentrated in one of the warehouses, and transporting each ton of goods for $$1$$ kilometer costs $$1$$ yuan, then the minimum transportation cost needed is.\n question_2178-image_0"}, {"key": "2179", "content": "$12+102+1002+10002=$"}, {"key": "2180", "content": "In a barbershop, there are two barbers, A and B, and six customers arrive at the same time. Based on the hairstyles they wish to have, the required times are $$8$$, $$14$$, $$13$$, $$9$$, $$23$$ and $$28$$ minutes, respectively. How should the order of haircuts be arranged to minimize the total time spent on haircuts and waiting for these six people? The shortest total time is in minutes."}, {"key": "2181", "content": "As shown in the diagram, arranging continuous natural numbers starting from $$1$$ according to the following pattern, the number in the $$100$$th row and $$6$$th column is. question_2181-image_0"}, {"key": "2182", "content": "As shown in the diagram, the natural numbers starting from $$7$$ are arranged in a certain pattern. Please answer:\n($$1$$) $$102$$ is in the row, column;\n($$2$$) The number in the $$4$$th row and $$25$$th column is.\n question_2182-image_0"}, {"key": "2183", "content": "As shown in the figure, a residential area consists of five households: Zhang, Wang, Li, Sun, and Liu, with equal distances between each household. The government plans to establish a water collection station in the area to facilitate water usage for the residents. In order to minimize the total distance traveled by all five households to the water station, next to which household should the station be located? question_2183-image_0"}, {"key": "2184", "content": "Calculate: $$\uff081987+9871+7198+8719\uff09\\div1111=$$."}, {"key": "2185", "content": "Starting from $$1$$, natural numbers are arranged according to the rule shown in the diagram, and a parallelogram frames nine numbers. If the sum of the nine numbers is $$99$$, then the largest number in the frame is.\n question_2185-image_0"}, {"key": "2186", "content": "$$123123123=123\\times $$; $$12341234=1234\\times $$."}, {"key": "2187", "content": "As shown in the figure, arrange the positive integers in a pattern, and connect $$4$$ numbers with a triangle. The triangle cannot be rotated, and the sum of these four numbers equals $$91$$. The largest number among these four numbers is.\n question_2187-image_0"}, {"key": "2188", "content": "Calculate the value of the following expression.\n$$2018+182+1820+8201=$$"}, {"key": "2189", "content": "Egg Bro bought $$24$$ eggs, the number he bought was $$2$$ times plus $$6$$ more than what Egg Sis bought, how many eggs did Egg Sis buy."}, {"key": "2190", "content": "A certain advance team of the People's Liberation Army set out from the camp, moving toward a certain place at a speed of $$4$$ kilometers per hour. $$7$$ hours later, due to an urgent matter, a courier was sent on a motorcycle at a speed of $$18$$ kilometers per hour to make contact. After a certain number of hours, the courier was able to catch up with the advance team."}, {"key": "2191", "content": "$$a\\times b\\times c+d=$$ ( )."}, {"key": "2192", "content": "The age difference between the father and son is $$27$$ years, the father's age is $$10$$ times that of the son's age, how old is the child in five years."}, {"key": "2193", "content": "Locations A and B are $$476$$ kilometers apart. A passenger train and a freight train start from the two locations at the same time and meet after $$4$$ hours. The freight train travels at $$52$$ kilometers per hour. By the time they meet, the passenger train has traveled $$60$$ kilometers more than the freight train."}, {"key": "2194", "content": "If the lengths of all three sides of a triangle are integers, and two of the sides are $$7$$ and $$10$$, then the minimum and maximum lengths of the other side are."}, {"key": "2195", "content": "An isosceles triangle, with two of its sides measuring $$5$$ cm and $$8$$ cm, respectively, means that the length of the third side of the triangle could be cm or cm, and the perimeter of this triangle could be cm or cm. (Fill in the blanks in ascending order)"}, {"key": "2196", "content": "An equilateral triangle has three equal interior angles. The triangle in Figure $$1$$ is an equilateral triangle, therefore $$\\angle A=$$ degrees, $$\\angle B=$$ degrees, $$\\angle C=$$ degrees. question_2196-image_0"}, {"key": "2197", "content": "An isosceles triangle has a base angle of $$80\u00b0$$. What is the vertex angle in degrees?"}, {"key": "2198", "content": "An isosceles triangle has a vertex angle of $$80\u00b0$$. What are the base angles in degrees?"}, {"key": "2199", "content": "The two base angles of an isosceles triangle are equal, the triangle in figure $$2$$ is an isosceles right triangle, thus $$\\angle A=$$ degrees, $$\\angle B=$$ degrees, $$\\angle C=$$ degrees. question_2199-image_0"}, {"key": "2200", "content": "Answer the question based on the requirements. As shown in figure $$1$$, $$\\angle 1+\\angle 2+\\angle 3+\\angle 4 =$$ degrees. question_2200-image_0"}, {"key": "2201", "content": "What is the sum of the interior angles of a heptagon in degrees?"}, {"key": "2202", "content": "Using two equally long pieces of wire, one is shaped into a square and the other into a rectangle. Compared to the perimeter of the rectangle, the perimeter of the square is ( )."}, {"key": "2203", "content": "As shown in the figure, the perimeter of the polygon is in centimeters. question_2203-image_0"}, {"key": "2204", "content": "Calculate: $$23\\times50=$$."}, {"key": "2205", "content": "$$2$$ people plant $$60$$ trees in $$3$$ hours, $$1$$ person plants ( ) trees in $$1$$ hour."}, {"key": "2206", "content": "Four cats caught $$32$$ mice in four days. Eight cats in eight days caught mice."}, {"key": "2207", "content": "Given a set of numbers $$2$$, $$5$$, $$4$$, $$5$$, $$A$$, to make their average $$4$$, $$A$$ is ()."}, {"key": "2208", "content": "Xiao Ming decides to travel to three places: Hong Kong, Macao, and Taiwan, and wants to visit each place once without repetition. He has a total of different order of visits."}, {"key": "2209", "content": "$$A$$, $$B$$, $$C$$, and $$D$$ pass the ball to each other, starting with $$A$$ making the first pass. After $$3$$ passes, the ball just happens to return to $$A$$'s hands. Thus, there are a total of different passing methods."}, {"key": "2210", "content": "As shown in the figure, an ant starts from the vertex $$A$$ of a regular tetrahedron, walks along the edges of this regular tetrahedron, sequentially visits $$4$$ vertices and then returns to vertex $$A$$. The question is: how many different ways can this little ant walk in total.\n question_2210-image_0"}, {"key": "2211", "content": "Toss a coin once, and the side facing up can be either heads or tails. Please enumerate the outcomes of tossing a coin three times using a tree diagram, with the side facing up in each scenario."}, {"key": "2212", "content": "Xiaoming has three kinds of fruits: apples, bananas, and oranges, and he has enough of each kind. He plans to eat one kind a day for a total of 4 days. It is known that Xiaoming ate an apple on the first day, and he will not eat the same fruit on two consecutive days. Therefore, there are a total of $$8$$ different ways of eating."}, {"key": "2213", "content": "In the diagram, there are $$6$$ points and $$8$$ line segments. A beetle starts from point $$A$$ and must crawl to point $$F$$ (it stops moving once it reaches point $$F$$) along some of the line segments. It can pass through the same point or the same line segment only once. The beetle has a maximum number of different ways to reach point $$F$$. question_2213-image_0"}, {"key": "2214", "content": "There is a bunch of Go pieces, and Wei er arranges them according to a certain pattern (see below), with a total of $$79$$ pieces. What color is the last piece?"}, {"key": "2215", "content": "Four students form a circle to play a passing game, as shown in the figure below. Starting with student number 1, the ball is passed clockwise 46 times, and the ball should be in hand.\n question_2215-image_0"}, {"key": "2216", "content": "There is a string of beads in two colors, black and white, arranged according to the following pattern: $$\\cdots \\cdots $$ Among the statements below regarding the color of the 36th bead, the correct one is ( )."}, {"key": "2217", "content": "There is a bunch of Go pieces, arranged by Wei as 'four black and five white,' see the figure below. 77 pieces were arranged. How many white pieces are there in total? question_2217-image_0"}, {"key": "2218", "content": "A series of numbers is arranged in the order $$1$$, $$3$$, $$5$$, $$7$$, $$9$$, $$1$$, $$3$$, $$5$$, $$7$$, $$9$$, $$1$$, $$3$$, $$5$$, $$7$$, $$9$$, $$\\cdots \\cdots$$. A total of $$48$$ numbers appear, what is the sum of these $$48$$ numbers?"}, {"key": "2219", "content": "35 apples are to be distributed among 3 kids, without the requirement for equal amounts, but each person must receive an even number of apples. Is it possible? ( )."}, {"key": "2220", "content": "Is the result of $$1+ 2+ 3+ 4+5+6+7+8+9$$ odd or even?"}, {"key": "2221", "content": "In the evening, Lanlan was doing homework at home with the light on when suddenly the room went dark. Lanlan pressed the switch $$2$$ times, and her mother pressed it $$4$$ times, realizing there was a power outage. When the power came back, was the light switch on or off? If the switch was pressed a total of $$65$$ times, then was the switch on or off? ( )"}, {"key": "2222", "content": "The simple calculation of $25\\times3\\times4$ is ( )."}, {"key": "2223", "content": "Calculate: $$300\\times 13\\div 4\\div 25=$$\uff0e"}, {"key": "2224", "content": "Complete the following calculations: \n$$230\\times 8\\div 23=$$\uff0e$$320\\times 25\\div 8=$$\uff0e"}, {"key": "2225", "content": "Calculate: (1) $$2400\\div 15\\div 4=$$. (2) $$11000\\div 125\\div 11=$$."}, {"key": "2226", "content": "Calculate: $$14\\div \\left( 3\\div 2 \\right)\\times \\left( 6\\div 7 \\right)=$$."}, {"key": "2227", "content": "$$2870\\div35$$="}, {"key": "2228", "content": "A ballpoint pen costs $$8$$ yuan, and a box of colored pencils costs three times the price of a ballpoint pen minus $$2$$ yuan. How much money does Xiao Hua need to buy a box of colored pencils and a ballpoint pen? ( )"}, {"key": "2229", "content": "A family of three, the sum of their ages is $$72$$ years, the mother and father are the same age, the mother's age is $$4$$ times the child's age, mother's age, child's age."}, {"key": "2230", "content": "There are a total of $$180$$ customers in the store, consisting of female and male customers. The number of female customers is $$3$$ times plus $$20$$ more than the number of male customers. There are male customers and female customers."}, {"key": "2231", "content": "Eddy has $$5$$ reward cards, Vi's amount is $$2$$ times of Eddy's, and Xiaoming's amount is $$3$$ times of Eddy's. The three people have a total of cards."}, {"key": "2232", "content": "The school plans to plant a total of $$300$$ trees, including poplar trees, willow trees, and locust trees. The number of poplar trees is $$3$$ times the number of willow trees, and the number of locust trees is $$2$$ times the number of poplar trees. So, in total, there will be willow trees, poplar trees, and locust trees."}, {"key": "2233", "content": "Huanhuan has $$12$$ more glass marbles than Lele, if both of them buy $$3$$ more each, then Huanhuan now has $$4$$ times the number of glass marbles as Lele, how many glass marbles did Huanhuan originally have."}, {"key": "2234", "content": "Eddie and Dengdeng were practicing running on the playground, after a period of time, the distance Eddie ran was 3 times more than Dengdeng's plus an extra 80 meters. If Dengdeng ran 500 meters less than Eddie, the distance Eddie ran was meters."}, {"key": "2235", "content": "Children A and B have the same quantity of chocolates. After giving B $$64$$ more pieces, B's quantity of chocolates becomes $$3$$ times that of A. How many pieces of chocolate does B have now."}, {"key": "2236", "content": "Xiaoxuan has some colored pencils and crayons, the number of colored pencils is 18 more than the crayons, and the number of colored pencils is 4 more than 3 times the number of crayons."}, {"key": "2237", "content": "$$2016$$ year $$11$$ month $$25$$ day is Friday, so the $$2017$$ year's $$11$$ month $$25$$ day is on a ( ) ."}, {"key": "2238", "content": "$$2016$$ year $$1$$ month $$1$$ day is Friday, then what day of the week is $$2$$ month $$7$$ day of $$2016$$? (Represent the answer with numbers $$1\\sim 7$$)"}, {"key": "2239", "content": "Xuexue and Sisi have a total of $$21$$ candies, Xuexue has $$2$$ times more candies than Sisi, so how many candies does Sisi have?"}, {"key": "2240", "content": "There are $$32$$ red flowers and $$7$$ yellow flowers. To make the number of red flowers four times the number of yellow flowers, if the number of red flowers remains unchanged, the number of yellow flowers that need to be added is."}, {"key": "2241", "content": "Please fill each cell of a $$3\\times 3$$ grid with the numbers $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, $$10$$, $$11$$, $$12$$, $$13$$ without repetition, such that the sum of each row, each column, and each diagonal line are equal. Then, the magic constant of this magic square is. question_2241-image_0"}, {"key": "2242", "content": "Fill in the appropriate numbers in the grid shown in the picture below, so that the sum of the three numbers in each row, each column, and each diagonal is equal. Then, the number that should be filled in the box marked with a \u201c\u2606\u201d is.\n question_2242-image_0"}, {"key": "2243", "content": "As shown in the figure, fill in the appropriate numbers in the diagram to make it a third-order magic square, then $$A+B+C+D+E=$$.\n question_2243-image_0"}, {"key": "2244", "content": "The image below is a 3x3 magic square, please fill in the blank ( ) with the correct number.\n question_2244-image_0"}, {"key": "2245", "content": "Fill in the squares below with appropriate numbers so that the sum of the three numbers on each row, each column, and each diagonal equals $$24$$ (three numbers have already been filled in). The number that should be filled in the square with a red circle is ( ).\n question_2245-image_0"}, {"key": "2246", "content": "The statistics of interest groups liked by primary school students are as follows, among which ( ) interest group has the highest number of people. question_2246-image_0"}, {"key": "2247", "content": "Below is the statistical table of the number of students in the third grade of a school, fill in the appropriate numbers in the table.\n\n\n\nThird Grade Student Number Statistics Table\n\n\n\nGender\nNumber of People\nClass\nMale\nFemale\nTotal\n\n\nThird ($$1$$)\n\n$$23$$\n\n\n\nThird ($$2$$)\n$$24$$\n\n$$41$$\n\n\nTotal\n$$50$$\n\n$$90$$"}, {"key": "2248", "content": "The lines in the image below represent paths. Please observe carefully and think seriously, the one who can crawl all over the paths without repetition is the ant. (A, B) question_2248-image_0"}, {"key": "2249", "content": "The figure below shows the apple sales situation of supermarket A and supermarket B from January to March. In March, supermarket A sold ( ) boxes more than supermarket B. question_2249-image_0"}, {"key": "2250", "content": "At least how many lines need to be added below to transform the figure into a one-stroke drawing.\n question_2250-image_0"}, {"key": "2251", "content": "The minimum number of paintbrushes needed to draw the figure below.\n question_2251-image_0"}, {"key": "2252", "content": "The image below is a floor plan of a children's playground. The entrance and exit should be set at point or point to be able to walk all the paths without repeating. question_2252-image_0"}, {"key": "2253", "content": "There are $$20$$ bicycles and tricycles in total, with $$56$$ wheels altogether. The number of bicycles and tricycles are respectively."}, {"key": "2254", "content": "There are in total $$20$$ chickens and rabbits in a cage, with a total of $$48$$ legs, then there are $$ chickens."}, {"key": "2255", "content": "A Chinese language test consists of $$10$$ questions, with each correct answer adding $$10$$ points, and each wrong answer or unanswered question deducting $$5$$ points. Eddie scored $$55$$ points in this test, how many questions did he answer correctly?"}, {"key": "2256", "content": "In a parking lot, there are a total of $$24$$ vehicles consisting of cars and motorcycles. Cars have $$4$$ wheels each, and motorcycles have $$3$$ wheels each. Together, these vehicles have a total of $$86$$ wheels. Then, there are motorcycles and cars."}, {"key": "2257", "content": "A bicycle has $$2$$ wheels, a car has $$4$$ wheels, now there are a total of $$30$$ vehicles, with a total of $$100$$ wheels, the question is how many cars are there in total."}, {"key": "2258", "content": "In a science knowledge contest, there were a total of $$10$$ questions. Each correct answer was awarded $$6$$ points, and each wrong answer deducted $$2$$ points. Eddie completed all the questions and finally scored $$44$$ points, getting questions correct."}, {"key": "2259", "content": "Eddy has a total of $$30$$ coins consisting of $$2$$-cent and $$5$$-cent coins, with a total amount of $$10$$ Yuan and $$2$$ cents. There are some $$2$$-cent coins and some $$5$$-cent coins."}, {"key": "2260", "content": "In a cage, there are a total of $$12$$ chickens and rabbits, with $$30$$ feet in all. Therefore, there are a total of $$9$$ chickens and $$3$$ rabbits."}, {"key": "2261", "content": "Zebras and ostriches live on the savannah, and now there are zebras (four legs) and ostriches (two legs) totaling $$18$$ animals on the savannah, they have together $$60$$ legs, so there are zebras ."}, {"key": "2262", "content": "There are tricycles and bicycles in the parking lot totaling $$23$$ vehicles, with a total of $$60$$ wheels. So, the number of bicycles in the parking lot is ."}, {"key": "2263", "content": "The children in Teacher Xu's class all love to eat very much. There are $$12$$ children who love to eat apples, $$15$$ children who love to eat cakes, and $$5$$ children who love both. There are none who don't love either. So, the total number of children in the class is ."}, {"key": "2264", "content": "There is an oil pot filled with oil. Half of the oil was poured out, and then half of the remaining oil was poured out again, leaving $$3$$ liters of oil in the pot. How many liters of oil were there in the pot originally?"}, {"key": "2265", "content": "Wei wants to go from home to XueErSi. Please help Wei to count, in total there are several different shortest routes. question_2265-image_0"}, {"key": "2266", "content": "The picture below shows a spider web of a mutated spider. It is known that spiders can only crawl upwards or to the right. If a spider crawls from point $$A$$ to point $$B$$, there are a total of different possible routes. question_2266-image_0"}, {"key": "2267", "content": "Distribute some apples among several children, giving each $$3$$ apples, and it's just enough. If each was given $$5$$ apples, there would be $$14$$ less. There are children, and there are apples."}, {"key": "2268", "content": "Vera stores her collected stamps in several envelopes. If each envelope contains $$20$$ stamps, she is short of $$10$$ stamps; if each envelope contains $$18$$ stamps, she is short of $$2$$ stamps. Therefore, Vera has envelopes and stamps."}, {"key": "2269", "content": "Dad and Xiao Ming together ate $7$ ice creams, each ate at least $1$, then there are several distribution methods."}, {"key": "2270", "content": "A rectangle has a perimeter of $$18$$ cm and a width of $$3$$ cm. Its length is ( ) cm."}, {"key": "2271", "content": "A rectangle with a length of $$25$$ cm and a width of $$8$$ cm is cut into two rectangles along the line segment between the midpoints of the two long sides. The total perimeter of these two rectangles is how many centimeters more than the perimeter of the original rectangle."}, {"key": "2272", "content": "Cut a square piece of paper with a side length of $$20$$ cm into $$4$$ rectangular pieces of the same size (as shown in the figure below), the total perimeter of the $$4$$ rectangular pieces is longer than the perimeter of the square piece by cm\uff0e question_2272-image_0"}, {"key": "2273", "content": "The simplified calculation of $$275+29+25$$ is ( )."}, {"key": "2274", "content": "There is a rectangular piece of paper, the length is $$8$$ cm, and the width is $$4$$ cm. If you cut it once horizontally and once vertically (as shown in the picture), then the sum of the perimeters of these $$4$$ small rectangles is in centimeters. question_2274-image_0"}, {"key": "2275", "content": "Cut a rectangular paper that is $$12$$ cm long and $$8$$ cm wide into $$4$$ identical small rectangles. Among the following three cutting methods, the small rectangle cut out in figure ( ) has the shortest perimeter.\n\n\n\n question_2275-image_0 \n question_2275-image_1 \n question_2275-image_2 \n\n\nFigure \u2460\nFigure \u2461\nFigure \u2462"}, {"key": "2276", "content": "Xiao Hong and Xiao Lan have a total of $$80$$ stamps. If Xiao Hong adds $$10$$ more stamps and Xiao Lan takes out $$6$$ stamps, then Xiao Hong will have $$3$$ times the number of stamps as Xiao Lan. How many stamps does Xiao Hong currently have?"}, {"key": "2277", "content": "Child A and Child B have the same amount of chocolates. If A gives B $$6$$ chocolates, then B will have $$3$$ times as many chocolates as A had originally."}, {"key": "2278", "content": "Xiaolin has $$30$$ pictures, after giving $$5$$ pictures to Xiao Jun, both have the same number of pictures. Originally, Xiaolin had more ( ) pictures than Xiao Jun."}, {"key": "2279", "content": "Dad, mom, grandpa, and grandma stand in a row to take a photo, with grandpa only able to stand at the most right position. They can take a total of ( ) different photos."}, {"key": "2280", "content": "As shown in the diagram, a large rectangle is divided into four smaller rectangles, three of which have areas of $$48$$, $$24$$, and $$30$$ square decimeters respectively. What is the area of the shaded rectangle in square decimeters? question_2280-image_0"}, {"key": "2281", "content": "As shown in the figure, in a quadrilateral, the diagonals are perpendicular to each other. It is known that $$AC=10$$ cm, $$BD=6$$ cm, then the area of the quadrilateral $$ABCD$$ is ( ) square centimeters.\n question_2281-image_0"}, {"key": "2282", "content": "For the parallelogram shown below, based on the given conditions, the correct area equation listed is ( )\uff0e\n question_2282-image_0"}, {"key": "2283", "content": "The area of a parallelogram is $$48$$ square centimeters, and its height is $$4$$ centimeters, the corresponding base is ( ) centimeters."}, {"key": "2284", "content": "Given the length of $$AB$$ is $$20$$ centimeters, $$AF$$ is $$18$$ centimeters, and $$BC$$ is $$12$$ centimeters, what is the area of the parallelogram $$ABCD$$? ( ) question_2284-image_0"}, {"key": "2285", "content": "A number divided by $$7$$, the quotient is $$15$$, and the remainder is $$6$$, then this number is. $$\\square\\div 7=15\\cdots 6$$"}, {"key": "2286", "content": "A number divided by $$5$$, with a quotient of $$9$$ and a remainder, then the maximum possible dividend is."}, {"key": "2287", "content": "$$137$$ divided by a certain number, the quotient is $$22$$ with a remainder of $$5$$, then the certain number equals."}, {"key": "2288", "content": "A natural number is divided by another natural number, yielding a quotient of $$49$$ and a remainder of $$19$$. The sum of the dividend and divisor is $$2019$$. The dividend is."}, {"key": "2289", "content": "When two numbers are divided, the quotient is $$3$$ and the remainder is $$5$$. If the dividend and the divisor are both tripled, then the quotient will be , and the remainder will be ."}, {"key": "2290", "content": "If a number is divided by $$24$$, the quotient is $$18$$, and the remainder is $$13$$, then this number is."}, {"key": "2291", "content": "Dividing two numbers, with the divisor being $$17$$ and the quotient being $$49$$, there is a remainder, then the largest possible dividend is."}, {"key": "2292", "content": "Divide two numbers, where the dividend is $$16$$, the quotient is $$3$$, and the remainder is $$1$$. Thus, the divisor is $$16\\div\\square=3\\cdots 1$$"}, {"key": "2293", "content": "Divide two numbers, the quotient is $$4$$ without remainder. The sum of the dividend and divisor equals $$75$$. The dividend is a multiple of the divisor, the dividend is."}, {"key": "2294", "content": "Dividing two numbers results in a quotient of $$25$$ with no remainder. The sum of the dividend and divisor is $$520$$. The divisor is."}, {"key": "2295", "content": "There is a class with more than 10 students, on the first day, the teacher evenly distributed 80 point cards among the students, with 5 remaining, in total there were students."}, {"key": "2296", "content": "A large rectangle is divided into $$9$$ smaller rectangles, where the perimeter of $$4$$ pieces has been marked, so the perimeter of the large rectangle is in centimeters. (Unit: centimeters)\n question_2296-image_0"}, {"key": "2297", "content": "How many different natural numbers without repeated digits can be formed using the digits $$0$$, $$2$$, $$4$$? ( )"}, {"key": "2298", "content": "Using the numbers $$1$$, $$2$$, $$3$$, how many unique odd numbers can be formed."}, {"key": "2299", "content": "There are five kinds of gifts priced at $$2$$ yuan, $$5$$ yuan, $$8$$ yuan, $$11$$ yuan, $$14$$ yuan respectively, and five kinds of boxes priced at $$1$$ yuan, $$3$$ yuan, $$5$$ yuan, $$7$$ yuan, $$9$$ yuan respectively. Each gift comes with a box, making a total of different prices."}, {"key": "2300", "content": "In the addition problem below, the same Chinese characters represent the same digit, and different Chinese characters represent different digits. What number does \"$$\\overline{good future}$$\" represent?\n\n\n\n\n\n\nFuture\n\n\n\n\nNot\nFuture\n\n\n+\nGood\nNot\nFuture\n\n\n\n3\n2\n1"}, {"key": "2301", "content": "In the following equation, different Chinese characters represent different digits, and the same Chinese characters represent the same digit, making the equation valid. Then, the four-digit number \"$$\\overline{Hope Child Becomes Dragon}$$\" is.\n$$\\begin{matrix}&&&&Dragon \\\\&&&Becomes&Dragon\\\\&&Child&Becomes&Dragon\\\\ +&Hope& Child&Becomes&Dragon \\\\ \\hline &2 & 0&1&2 \\end{matrix}$$"}, {"key": "2302", "content": "9 individual(s) can complete 12 pieces of work in 6 days, at this rate, 3 individuals can complete how many pieces of work in 3 days? 21 individuals can complete how many pieces of work in 12 days."}, {"key": "2303", "content": "Eddie bought a storybook, reading $$25$$ pages for the first $$4$$ days and then $$40$$ pages for the next $$6$$ days, finishing the book exactly. Then, his daily average number of pages read is. question_2303-image_0"}, {"key": "2304", "content": "Four students each have an average of $$40$$ scorecards. The fifth student has $$10$$ more cards than the average number of cards of these four students. The average number of cards among these five students is."}, {"key": "2305", "content": "The average of seven numbers is $$11$$, the average of the first four numbers is $$8$$, the average of the last four numbers is $$13$$, the fourth number is."}, {"key": "2306", "content": "$$\\frac{12}{23}-\\left( \\frac{5}{23}-\\frac{7}{16} \\right)-\\frac{7}{23}$$=\uff0e$$\\frac{7}{92}-\\left( \\frac{5}{89}+\\frac{7}{92} \\right)+\\frac{6}{89}=$$\uff0e"}, {"key": "2307", "content": "Cinderella was invited to attend the ball at Max's Magic School. The clock in the hall struck 3 times at 3 o'clock, completing the strikes in 6 seconds. It struck 12 times at 12 o'clock. Cinderella must leave the ball before the 12th strike is completed. Starting from the first strike at 12 o'clock, Cinderella has seconds left to leave (ignoring the time it takes to strike the clock)."}, {"key": "2308", "content": "A train carrying wood has a total length of $$532$$ meters, of which the locomotive is $$12$$ meters long, and the length of each of the remaining carriages is $$25$$ meters. It is also known that the distance between each two carriages is $$1$$ meter. This train has a total number of carriages. (including the locomotive)"}, {"key": "2309", "content": "The length around a closed figure is its."}, {"key": "2310", "content": "The diagram below is the plan view of DingDing's school playground, with a length of $$150$$ meters and a width of $$50$$ meters. DingDing walks around the playground for a total distance of meters.\n question_2310-image_0"}, {"key": "2311", "content": "The perimeter of the image on the left is in centimeters, and the perimeter of the image on the right is in meters.\n question_2311-image_0"}, {"key": "2312", "content": "In figure \u2460, the perimeter of the rectangle = meters; in figure \u2461, the perimeter of the square = meters.\n question_2312-image_0"}, {"key": "2313", "content": "Using the numbers $$3$$, $$6$$, $$9$$, a different three-digit number with non-repeating digits can be formed."}, {"key": "2314", "content": "Given the perimeter of a square is $$64$$ meters, its side length is meters."}, {"key": "2315", "content": "Fill in each blank of the equation in the picture with a suitable number to make the vertical operation correct. Question: What is the sum?\n question_2315-image_0"}, {"key": "2316", "content": "Viola collected one coin of each of four different denominations, as shown in the figures, in total, different amounts of money can be formed. question_2316-image_0 question_2316-image_1 question_2316-image_2 question_2316-image_3"}, {"key": "2317", "content": "In the vertical arithmetic problem below, the same Chinese character represents the same digit, while different Chinese characters represent different digits. Then, the three-digit number represented by \"\u6570\u5b66\u4e66\" is.\n question_2317-image_0"}, {"key": "2318", "content": "Fill in the boxes in the following vertical formulas with appropriate numbers to make the equations valid. Calculate: $$A+B=$$.\n question_2318-image_0 question_2318-image_1"}, {"key": "2319", "content": "Can you calculate what number each Chinese character represents in the equation? The same Chinese characters represent the same number, and different Chinese characters represent different numbers. Three$$+$$good$$+$$study$$+$$student=.\n$$\\begin{matrix}&&& study & student \\\\&&good&study&student\\\\ +&three & good&study&student \\\\ \\hline&3 & 0&2&2 \\end{matrix}$$"}, {"key": "2320", "content": "Calculate, $$\u25b3=$$, heart $$=$$, $$\u25a1=$$.\n$$\\begin{matrix} {}& \\Delta& 0 &\\square \\\\ - &2&heart& 8 \\\\ \\hline {}& 3& 5& 9 \\\\\\end{matrix}$$"}, {"key": "2321", "content": "Playful Eddy accidentally spilled the ink, blackening the numbers in the column on the paper.$$ Mom told Eddy that the result of the column on the left is exactly one of the addends of the column on the right.$$ Smart kids, can you help Eddy restore these two columns? The result of the addition column you get is.\n question_2321-image_0"}, {"key": "2322", "content": "Fill in a number in each square below, there are several ways to do it.\n question_2322-image_0"}, {"key": "2323", "content": "According to the given equation, $$\\bigstar$$ represents, $$\u25b3$$ represents.\n question_2323-image_0"}, {"key": "2324", "content": "Vertical calculation: $$57\\times 70=$$"}, {"key": "2325", "content": "Calculate: $$204\\times 5-24\\times 13+500\\times 2=$$."}, {"key": "2326", "content": "Set up the calculation vertically: (1) $$40\\times 32=$$ (2) $$21\\times 30=$$"}, {"key": "2327", "content": "Fill in the appropriate numbers in the box below so that the equation holds true, the result of the equation is -.\n question_2327-image_0"}, {"key": "2328", "content": "In division, $$0$$ cannot act as ( )."}, {"key": "2329", "content": "Calculate:\n$$624\u00f76=$$.\n$$728\u00f78= $$\u200b."}, {"key": "2330", "content": "Calculate: $$51000\\div 300=$$."}, {"key": "2331", "content": "$$480\\div 70=6\\cdots\\cdots$$ ( )."}, {"key": "2332", "content": "Xiao Li ate $$\\frac{4}{5}$$ of a packet of candy, and Xiao Hua ate $$\\frac{4}{5}$$ of another packet of candy, both of them definitely ate the same amount of candy."}, {"key": "2333", "content": "Junjun has three homework assignments in Chinese, Mathematics, and foreign language, and plans to do one each day, without doing the same one on two consecutive days. If he does Chinese on Monday, he can do ."}, {"key": "2334", "content": "$$A$$, $$B$$, and $$C$$ are three kids passing a ball to each other, starting with $$A$$ as the first to pass the ball. After $$2$$ passes, there are a total of different ways to pass the ball."}, {"key": "2335", "content": "There is a string of beads arranged in black and white colors according to the following pattern: ......The color of the 45th bead is ( )."}, {"key": "2336", "content": "Distribute $$100$$ apples among $$7$$ kids. The number of apples given to each kid does not have to be the same. However, the number of apples each receives must be odd. Think about it, is it possible?"}, {"key": "2337", "content": "$$142857\\times 7\\times 15\\times 13$$ Is the result odd or even? ( )\uff0e"}, {"key": "2338", "content": "Calculate (1) $$8\\times 5\\times 125=$$ (2) $$125\\times 16=$$"}, {"key": "2339", "content": "Calculate ($$1$$) $$25\\times (10-4)=$$ ($$2$$) $$35\\times (100-1)=$$"}, {"key": "2340", "content": "A rectangle with an area of $$\\text{160c}{{\\text{m}}^{2}}$$ and a width of $$\\text{10cm}$$, its length is $$\\text{cm}$$, and its perimeter is $$\\text{cm}$$."}, {"key": "2341", "content": "If the side length of square $$A$$ is $$3$$ times the side length of square $$B$$, then the perimeter of square $$A$$ is $$3$$ times the perimeter of square $$B$$, and the area of square $$A$$ is $$9$$ times the area of square $$B$$."}, {"key": "2342", "content": "There is $$470$$ kilograms of oil in barrel A and $$190$$ kilograms of oil in barrel B. How many kilograms of oil should be poured from barrel A into barrel B to make the oil in barrel A twice as much as in barrel B?"}, {"key": "2343", "content": "Xiao Ming divided 100 chess pieces into three piles. It is known that the second pile has 5 more pieces than the first pile, and the third pile is exactly 5 times the size of the second pile. The first pile has pieces, the second pile has pieces, the third pile has pieces."}, {"key": "2344", "content": "A certain TV factory produces 500 TVs every day. In a quality competition, producing one qualified TV scores 5 points, while producing one unqualified TV deducts 18 points. If they scored 9931 points in four days, then how many qualified TVs were produced in these four days."}, {"key": "2345", "content": "There are $$48$$ students in a self-study class. Among them, $$30$$ have finished their Chinese homework, $$20$$ have finished their mathematics homework, and $$8$$ have finished both Chinese and mathematics homework. How many students have not finished either Chinese or mathematics homework?"}, {"key": "2346", "content": "There are a total of $$20$$ chickens and rabbits in a cage, with a total of $$52$$ legs. The number of rabbits is ."}, {"key": "2347", "content": "Class 2 ($$3$$) has $$60$$ children divided into $$3$$ groups. From group one, $$5$$ people went to group two; from group two, $$6$$ people went to group three; from group three, $$4$$ people went to group one. Now, each group has the same number of people. Originally, group $$2$$ had people."}, {"key": "2348", "content": "In a certain school's Grade 4 Class 1, 20 students joined the technology interest group, 17 students joined the English interest group, and 9 students joined both interest groups. Therefore, there were people who only joined the technology group without joining the English group."}, {"key": "2349", "content": "Xiao Yu participated in a math contest, which had a total of $$20$$ questions. For each correct answer, he would earn $$5$$ points, and for each wrong answer, he would lose $$2$$ points. Xiao Yu completed all the questions and scored a total of $$65$$ points. How many questions did he answer correctly?"}, {"key": "2350", "content": "A bamboo shoot grows from sprouting to getting bigger. If it grows twice its height every day, it reaches $$40$$ centimeters after $$8$$ days. Then, to reach $$10$$ centimeters, it takes days."}, {"key": "2351", "content": "Xiao Ming is a child who really likes to do calculations. One day, he opened a page of calculation problems, first did 5 questions, then did half of the remaining ones, and finally, he did half of the remaining ones plus 3 more, totaling 38 questions. How many questions were there on this page in total?"}, {"key": "2352", "content": "Move the decimal point of $$21.045$$ two places to the left, shrinking it to the original, becoming. question_2352-image_0"}, {"key": "2353", "content": "Fill in the blanks with numbers $$1\\sim 6$$ so that each row, column, and palace contains no repeated numbers. There are two sets of \"TAL Education Group\", where the same Chinese character represents the same number, and different Chinese characters represent different numbers. Thus, the six-digit number represented by \u201c\u597d\u672a\u6765\u5b66\u800c\u601d\u201d is.\n question_2353-image_0"}, {"key": "2354", "content": "In the $$6\\times 6$$ grid shown in the figure, each square can only be filled with one of the letters $$A,B,C,D,E,F$$, and it is required that the six letters in each row, each column, and each $$2\\times 3$$ rectangle marked with a bold line must all be different. Then, except for the first and last squares, the order of the letters filled in from left to right in the middle four squares of the fourth row is ( ).\n question_2354-image_0"}, {"key": "2355", "content": "Fill in the blanks below with $$1\\sim 6$$, so that each row, each column, and each region does not have repeating numbers. Then, $$A=$$. question_2355-image_0"}, {"key": "2356", "content": "Fill in the numbers $$1\\sim 4$$ such that no row or column contains any repeat numbers. The number in the top left corner indicates the total sum of the numbers filled within the bold frame. The first number from the left in the last row is. question_2356-image_0"}, {"key": "2357", "content": "After folding a rectangular paper $$ABCD$$ as shown in the figure and pressing it flat so that the triangle $$DCF$$ falls onto the position of triangle $$DEF$$ with the vertex $$E$$ exactly on $$AB$$, it is known that $$\\angle 2=50{}^\\circ$$, $$\\angle 1 +\\angle 3 =90\u00b0$$. (1) The degree of $$\\angle DEF$$ is. (2) The degree of $$\\angle 1$$ is. question_2357-image_0 \u200b"}, {"key": "2358", "content": "Count, there are a total of rectangles in the following diagram.\n question_2358-image_0"}, {"key": "2359", "content": "(1) There is a line segment in the following figure. question_2359-image_0 (2) There are a total of line segments in the following figure. question_2359-image_1"}, {"key": "2360", "content": "There is a square in the picture.\n question_2360-image_0"}, {"key": "2361", "content": "The picture has a total of squares.\n question_2361-image_0"}, {"key": "2362", "content": "The first-grade second class is performing martial arts, with a total of $$121$$ participants. They are arranged in a square formation. question_2362-image_0"}, {"key": "2363", "content": "The third grade class 1 forms a solid square formation to perform a group dance, with each side of the outermost layer of the square having $$5$$ people. In total, there are people in the outermost layer.\n question_2363-image_0"}, {"key": "2364", "content": "The third grade's second class formed a solid square formation, with $$36$$ people on the outermost layer, and people on each side of the outermost layer.\n question_2364-image_0"}, {"key": "2365", "content": "Arrange $$36$$ chess pieces into a solid square, how many chess pieces are there in the outermost layer of the square."}, {"key": "2366", "content": "As shown in the figure, the outermost layer has more dots than the second layer (from the outside in), the second layer has more dots than the third layer (from the outside in), the third layer has more dots than the fourth layer (from the outside in).\n question_2366-image_0"}, {"key": "2367", "content": "Insert \"$$+$$\" in the appropriate places to make the equation valid (adjacent numbers can form one number). question_2367-image_0"}, {"key": "2368", "content": "What results can be computed using the two digits $$6$$ and operation symbols? question_2368-image_0 \u200b$$6+ 6=12$$ $$6- 6$$ =$$6\\times 6=36$$ $$6\\div 6$$= question_2368-image_1 \u200bDo you have any other methods?"}, {"key": "2369", "content": "The final result of simplifying the following expression is ( ). $$a\\times3+6\\times(a+b)=$$"}, {"key": "2370", "content": "Calculate: $$1+3+5+7+\\ldots +51+53=$$."}, {"key": "2371", "content": "Son and mother calculate ages, the sum of their ages two years ago was $$36$$ years, this year the mother's age is $$4$$ times the child's age. So this year the son is ____ years old."}, {"key": "2372", "content": "Students of class 1, grade 3 participated in the radio calisthenics competition, forming a square formation with $$9$$ people in each row and $$9$$ people in each column, originally having a total number of students in the formation; if one row and one column are removed, a number of students were removed."}, {"key": "2373", "content": "Given the arithmetic sequence $$2$$, $$7$$, $$12$$, $$17$$, $$\\cdots$$, then $$77$$ is the term number of this sequence."}, {"key": "2374", "content": "Xiao Lin is $$3$$ years old this year, and his father is $$31$$ years old. When Xiao Lin is a certain age, his father's age is exactly $$5$$ times that of Xiao Lin."}, {"key": "2375", "content": "Given an arithmetic sequence $$2$$, $$5$$, $$8$$, $$11$$, $$\\cdots$$, then the $$20$$th number in the sequence is."}, {"key": "2376", "content": "A solid square array, with $$32$$ people on the outermost layer, and people on each side of the outermost layer."}, {"key": "2377", "content": "Please use the four numbers $$2$$, $$3$$, $$4$$, $$6$$, fill in $$+$$, $$-$$, $$\\times $$, $$\\div $$ and ( ) between them arbitrarily, and each number can only be used once, to make their result equal to $$24$$. Which of the following options makes the equation correct?"}, {"key": "2378", "content": "Add the proper operation symbols (without adding parentheses) to the box to make the equation valid. The correct option is ( ).\n$$17$$\u25a1$$3$$\u25a1$$4$$\u25a1$$9$$\u25a1$$7$$\u25a1$$6$$\u25a1$$4=20$$"}, {"key": "2379", "content": "Fill in the appropriate operator signs or parentheses in the equation below, the option that makes the equation correct is ( ).\n$$5$$ $$5$$ $$5$$ $$=30$$."}, {"key": "2380", "content": "Wei'er wants to go from home to Xueersi, please help Wei'er count, there are a total of different shortest routes. question_2380-image_0"}, {"key": "2381", "content": "The diagram illustrates various unique pathways from 'spring' to 'dawn' in the sequence of 'unaware of the arrival of spring' (a phrase from a poem meaning sleeping soundly without noticing the dawn). question_2381-image_0"}, {"key": "2382", "content": "The Monkey King distributes peaches to the little monkeys. If each little monkey gets $$4$$ peaches, there will be an excess of $$5$$ peaches; if each little monkey gets $$5$$ peaches, then the peaches will be distributed exactly. So, in total, there are little monkeys. \u200b question_2382-image_0 \u200b"}, {"key": "2383", "content": "A fleet bought back some new tires. Xiaoming counted and found that if the $$2$$ front tires of each vehicle were replaced, there would still be $$20$$ new tires left; if all $$4$$ tires of each vehicle were replaced, there would only be $$6$$ new tires left. (1) The total number of vehicles in the fleet. (2) The number of tires bought back by the fleet. question_2383-image_0"}, {"key": "2384", "content": "At the end of the month, the boss calculates the salaries for everyone. If each person is given $$1000$$, there will be $$10000$$ left over; if each person is given $$1500$$, there will be $$5000$$ short. (1) The total difference in the distribution results of the two salary distribution methods is $$.$$ (2) The company has employees, and the boss has prepared $$.$$ for salaries."}, {"key": "2385", "content": "Eddie is responsible for distributing bottled water to class three of the third year. He prepared less bottled water than needed. If each group is given 4 boxes, there will be 2 boxes short; if each group is given 6 boxes, there will be 14 boxes short. How many groups are there in class three of the third year, and how many boxes of bottled water did Eddie prepare?"}, {"key": "2386", "content": "The school allocates dormitories for new students. If each room houses $$3$$ people, then there are $$22$$ people left over; if each room houses $$8$$ people, then $$1$$ room is empty. (1) Having $$1$$ room empty means there are fewer people. (2) There are rooms in the dormitory, and there are people among the new students. question_2386-image_0"}, {"key": "2387", "content": "The expansion task for the young pioneers is tree planting. If each young pioneer digs $$5$$ tree holes, there are still $$3$$ tree holes left undug; if two of them each dig $$4$$ tree holes, and the rest each dig $$6$$ tree holes, then all the tree holes can be exactly completed. There are altogether young pioneers, and a total of tree holes need to be dug. question_2387-image_0"}, {"key": "2388", "content": "Using $$3$$ rectangles that are $$4$$ cm wide and of the same size, to form a larger rectangle (as shown in the diagram below), the perimeter of this large rectangle is in centimeters. question_2388-image_0"}, {"key": "2389", "content": "There is a rectangular piece of paper with a length of $$6$$ cm and a width of $$3$$ cm. If you make a horizontal cut with scissors (as shown in the picture), then the sum of the perimeters of these $$2$$ rectangles is cm. question_2389-image_0"}, {"key": "2390", "content": "Calculate: $$568+(24-68)+(19-24)=$$."}, {"key": "2391", "content": "Dividing $$11$$ identical pieces of candy into $$3$$ piles of different quantities, there are a total of different methods."}, {"key": "2392", "content": "As shown in the diagram, two adjacent edges are perpendicular to each other, and the segment lengths are as follows, the perimeter of the shape is in centimeters.\n question_2392-image_0"}, {"key": "2393", "content": "$$24\\times 5+76\\times 5=$$."}, {"key": "2394", "content": "Using $$3$$ squares with a side length of $$1$$ cm to form a rectangle, the perimeter of this rectangle is in centimeters."}, {"key": "2395", "content": "$$78\\times 24+78\\times 35+59\\times 22=$$;"}, {"key": "2396", "content": "Distributing $10$ apples among $3$ kids, with each kid getting at least one apple, there are different methods of distribution."}, {"key": "2397", "content": "Calculate: $$305+296+310+297$$=."}, {"key": "2398", "content": "Two buckets of the same size contain the same amount of oil. If $$9$$ kilograms of oil are poured from the smaller bucket into the larger one, then the oil in the larger bucket is $$4$$ times that in the smaller bucket. How many kilograms of oil did the smaller bucket originally have?"}, {"key": "2399", "content": "Lulu arrives at the destination ready to have lunch and finds that there are $$9$$ Chinese restaurants, $$5$$ Western restaurants, and $$3$$ fast food restaurants nearby. They plan to choose one of these restaurants to eat at, resulting in a total of different choices.\n question_2399-image_0"}, {"key": "2400", "content": "Below is a fast food restaurant's menu, Lulu prepares to order one main dish, one snack, and one drink, she has a variety of different combination plans. question_2400-image_0"}, {"key": "2401", "content": "Max's Hotel has a total of $$4$$ rooms to choose from, with Eddie, Vi, Da Kuan, and Doctor each picking one room, there are a total of different selection schemes question_2401-image_0"}, {"key": "2402", "content": "There are $$5$$ students standing in a row for a photo, where student A can only stand on either end. Thus, there are a total of different ways to queue."}, {"key": "2403", "content": "A, B, C, D, and E are five people standing in a row for a photo. If A must stand as the second from the left, and B cannot stand as the first from the right, then there are a total of ways to stand."}, {"key": "2404", "content": "Wei Er has a square handkerchief, the length of the diagonal $$AC$$ is $$8$$ cm. Then the area of the handkerchief is square centimeters. question_2404-image_0"}, {"key": "2405", "content": "As shown in the figure, quadrilateral $$ABCD$$ has its two diagonals perpendicular to each other. Given: $$AC=5$$, $$BD=8$$, then the area of quadrilateral $$ABCD$$ is.\n question_2405-image_0"}, {"key": "2406", "content": "Given that the diagonals of quadrilateral $$ABCD$$ are perpendicular to each other, and the area of the quadrilateral is $$80$$ square centimeters, given $$AC=10$$ centimeters, the length of $$BD$$ is in centimeters. question_2406-image_0"}, {"key": "2407", "content": "As shown in the figure, the area of quadrilateral $$ABCD$$ with perpendicular diagonals is $$24$$ square centimeters. The length of $$AC$$ is $$2$$ centimeters shorter than $$BD$$. Then the length of $$BD$$ is centimeters. question_2407-image_0"}, {"key": "2408", "content": "A rectangular piece of land is divided into $$4$$ smaller rectangles, with the area of three pieces shown in the diagram (unit: square meters), the area of the remaining piece should be square meters.\n question_2408-image_0"}, {"key": "2409", "content": "As shown in the diagram, a rectangle is divided into four rectangles of unequal sizes by two line segments. The areas of three of the rectangles are respectively $$20$$ square meters, $$30$$ square meters, $$36$$ square meters. The area of the other rectangle is in square meters. question_2409-image_0"}, {"key": "2410", "content": "As shown in the figure, a large rectangle is divided into $$6$$ smaller rectangles, among which the area of $$4$$ small rectangles is shown in the figure (unit: square centimeters) (1) The area of the rectangle represented by $$A$$ is square centimeters. (2) The area of the large rectangle is square centimeters. question_2410-image_0"}, {"key": "2411", "content": "The area of the polygon in the shaded part of the figure below is square centimeters.\n question_2411-image_0"}, {"key": "2412", "content": "The following figure is a parallelogram, with the length of $$AE$$ being $$6$$ centimeters, the length of $$AF$$ being $$8$$ centimeters, and the length of $$DC$$ being $$10$$ centimeters, then the area of this parallelogram is square centimeters. question_2412-image_0"}, {"key": "2413", "content": "As shown in the figure, the area of the parallelogram is square centimeters. question_2413-image_0"}, {"key": "2414", "content": "As shown in the parallelogram $$ABCD$$, $$CD=18$$ cm, $$AE$$ is perpendicular to $$CD$$ at point $$E$$, $$AF$$ is perpendicular to $$BC$$ at point $$F$$, $$AE=10$$ cm, $$BC=12$$ cm, then the length of the line segment $$AF$$ is cm. question_2414-image_0"}, {"key": "2415", "content": "As shown in the figure, there is a small square and a shaded parallelogram inside a larger square. If the side length of the larger square is $$20$$ cm, and the side length of the smaller square is $$8$$ cm. Then, the area of the shaded parallelogram in the figure is square centimeters. question_2415-image_0"}, {"key": "2416", "content": "The area of the parallelogram in the figure below is $$\\text{c}{{\\text{m}}^{2}}$$. question_2416-image_0"}, {"key": "2417", "content": "As shown in the diagram, in parallelogram $$ABCD$$, it is known that $$AB=24$$, $$DF=20$$, $$DE=10$$, $$BC$$=\uff0e question_2417-image_0"}, {"key": "2418", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$, given that $$AB=10$$ cm, $$AE=5$$ cm, the area of parallelogram $$ABCD$$ is square centimeters.\n question_2418-image_0"}, {"key": "2419", "content": "As shown in the picture, the side length of the large square is $$12$$, and the side length of the small square is $$4$$. Then, the area of the shaded parallelogram is. question_2419-image_0"}, {"key": "2420", "content": "As shown in the figure, the sides of the two squares are respectively $$3$$ cm and $$7$$ cm. If the shaded part is a parallelogram, then the area of the shaded part is. question_2420-image_0"}, {"key": "2421", "content": "Given the length of $$AB$$ is $$30$$ cm, $$AF$$ is $$25$$ cm, and $$BC$$ is $$12$$ cm, what is the length of $$AE$$? ( ) question_2421-image_0"}, {"key": "2422", "content": "When dividing two numbers, the quotient is $$20$$ and the remainder is $$8$$. The minimum possible dividend is."}, {"key": "2423", "content": "Divide one natural number by another natural number, the quotient is $$7$$, exactly divisible, the sum of the dividend and the divisor is $$48$$. Therefore, the dividend is a multiple of the divisor, the dividend equals."}, {"key": "2424", "content": "Dividing two numbers gives a quotient of $$49$$ and a remainder of $$8$$. The sum of the dividend and divisor is $$2408$$. Find the dividend."}, {"key": "2425", "content": "When two numbers are divided, the quotient is $$9$$, and the remainder is $$7$$. The minimum dividend is."}, {"key": "2426", "content": "A number divided by $$7$$, the quotient is $$15$$, and the remainder is $$6$$, then this number is."}, {"key": "2427", "content": "When two numbers are divided, the quotient is $$3$$, and the remainder is $$5$$. If both the dividend and divisor are tripled, the new quotient and remainder will be as follows:"}, {"key": "2428", "content": "There is a class with more than $$10$$ students. On the first day, the teacher distributed $$80$$ reward cards evenly among the students, with $$5$$ cards left over; on the second day, the teacher distributed $$71$$ reward cards evenly among the students, with some cards left over."}, {"key": "2429", "content": "When dividing two numbers, if the dividend is $$16$$, the quotient is $$3$$, and the remainder is $$1$$, then the divisor is."}, {"key": "2430", "content": "When dividing two numbers, the quotient is $$49$$, and the remainder is $$16$$. The minimum dividend is."}, {"key": "2431", "content": "When dividing two numbers, the quotient is $$6$$ with a remainder of $$3$$, and the sum of the dividend, divisor, quotient, and remainder is $$68$$. What is the dividend?"}, {"key": "2432", "content": "$$1597\\div 27=59\\cdots\\cdots 4$$, after multiplying both the dividend and the divisor by $$5$$, $$7985\\div 135=$$$$\\cdots\\cdots$$\uff0e"}, {"key": "2433", "content": "Dividing two numbers, the quotient is $$25$$, and there is no remainder. The sum of the dividend and divisor is $$520$$. Therefore, the divisor is."}, {"key": "2434", "content": "Little rabbit Lele likes to eat three kinds of food: carrots, pumpkins, and spinach. She will not eat the same kind on two consecutive days. If she eats a carrot on the first day and also a carrot on the fourth day, how many different meal arrangement plans are there for these four days? ( )\n question_2434-image_0"}, {"key": "2435", "content": "Can you try to see how many different ways there are to pair meals?\nMeal pairing requirements: Each set meal must contain a meat dish and a vegetarian dish, plus a drink.\nMeat dishes: Stir-fried onion with meat, Braised beef brisket with sweet potato\nVegetarian dishes: Stir-fried radish, Dry-fried green beans\nDrinks: Soy milk, Coca-Cola"}, {"key": "2436", "content": "The snowman wants to buy buns because he is too hungry to move, please help the snowman count how many shortest paths are there in the figure below ( ).\n question_2436-image_0"}, {"key": "2437", "content": "$$100$$ students lined up in a row, the first time they count from left to right in a cycle of $$1\\tilde{\\ }4$$, the second time they count from right to left in a cycle of $$1\\tilde{\\ }5$$. Question: How many students called out both $$1$$ and $$5$$."}, {"key": "2438", "content": "There is a series of numbers: $$9286\\cdots \\cdots $$ Starting from the third digit, every digit is the unit digit of the product of its previous two digits, then the sum of the first $$100$$ digits is."}, {"key": "2439", "content": "Stringing $$7$$ white beads and $$4$$ black beads on a rope in turn, and repeat this pattern.$$.$$ If a total of $$120$$ beads are strung from the beginning, then among these $$120$$ beads, there are more white beads than black beads."}, {"key": "2440", "content": "In our Chinese lunar calendar, the years are represented in rotation by these 12 animals in order: Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, and Pig. For example, the year 1986 is the Year of the Tiger, 1987 the Year of the Rabbit, and 1988 the Year of the Dragon. So, the year 2049 will be the Year of the ( ) ."}, {"key": "2441", "content": "Olympic Mathematics Olympic Mathematics Olympic Mathematics$$\\cdots \\cdots $$The $$24$$th Chinese character is ( )."}, {"key": "2442", "content": "Find two integers whose sum is $$351$$ and difference is $$96$$. Do such numbers exist? ( )"}, {"key": "2443", "content": "Determine the parity of the result of the following expression:\n$$87\\times 19\\times 20\\times 39\\times 26$$"}, {"key": "2444", "content": "$$3$$ cups are facing up, can they all be flipped to face down after a finite number of moves if $$2$$ cups are flipped at a time?"}, {"key": "2445", "content": "Along the riverbank, there are $$8$$ types of plants, with the number of fruits produced by two adjacent types of plants differing by $$1$$. Question: Is it possible for the $$8$$ types of plants to produce a total of $$225$$ fruits? Explain your reasoning."}, {"key": "2446", "content": "There are $$6$$ people attending a party, and each person shakes hands with all the others. Therefore, these $$6$$ people shake hands ( ) times."}, {"key": "2447", "content": "Calculate $$7485+343\\times 141-17\\times 232-119\\times 120+2014$$, Eddie got the result as $$39639$$. Can you judge whether his calculation is correct?"}, {"key": "2448", "content": "There are four distinct natural numbers, the difference between the maximum and the minimum number is $$4$$, the product of the maximum and the minimum number is an odd number, and the sum of these four numbers is the largest two-digit odd number, then these four numbers in ascending order are , , and ."}, {"key": "2449", "content": "There is an empty cup with its opening upwards. The first flip turns a cup with its opening upwards to downwards. The second flip turns a cup with its opening downwards back to upwards. Xiao Ming flipped back and forth a total of 66 times. In the end, is the cup's opening facing upwards or downwards ( )?"}, {"key": "2450", "content": "Distribute 20 apples among 3 kids. It's not required that each kid gets the same number of apples. However, the number of apples each gets must be odd. Think about it, is it possible?"}, {"key": "2451", "content": "Simplify $$25\\times 28=$$ ( )."}, {"key": "2452", "content": "$$25\\times 23\\times 4=$$\uff08 \uff09\uff0e"}, {"key": "2453", "content": "Compute: $$4900\\div 4\\div 25$$=."}, {"key": "2454", "content": "$$(36\\times 56)\\div (7\\times 18)=$$ ( )."}, {"key": "2455", "content": "The result of the following calculation is: $$34\\times3535\\div(3434\\times35)$$"}, {"key": "2456", "content": "Calculate: \n(1)$$\\left( 189+27 \\right)\\div 9=$$\uff0e\n(2)$$\\left( 110+77+88 \\right)\\div 11=$$\uff0e"}, {"key": "2457", "content": "Calculate: (1) $$325\\div 7+424\\div 7=$$.\n(2) $$215\\div 29+65\\div 29+300\\div 29=$$."}, {"key": "2458", "content": "Calculate: $$1+44\\times 34\\div 11\\div 17=$$ ()."}, {"key": "2459", "content": "$$32\\times 5\\div 32\\times 5=$$\uff08 \uff09\uff0e"}, {"key": "2460", "content": "The simplified method for $$420\\div 35$$ is ( )."}, {"key": "2461", "content": "There is a rectangular field, length $$15$$ meters, width $$6$$ meters. Increase the length by $$5$$ meters and the width by $$4$$ meters, the area increases by ( )."}, {"key": "2462", "content": "Wrap a $$60$$ cm long wire into a square, the area of this square is ( )."}, {"key": "2463", "content": "A square vegetable garden is bordered on one side by a wall and surrounded by a fence that is $$24$$ meters long. The area of this vegetable patch is in square meters."}, {"key": "2464", "content": "The figure below is a schematic diagram of Eddie's house room. Please calculate the area of the dining room and kitchen in square meters based on the data provided in the diagram.\n question_2464-image_0"}, {"key": "2465", "content": "A field, length $$60$$ meters, width $$45$$ meters, after expansion, the length increased by $$15$$ meters, the width increased by $$8$$ meters, find the increased area of this field in square meters."}, {"key": "2466", "content": "If the perimeter of square $$A$$ is 3 times the perimeter of square $$B$$, then the side length of square $$A$$ is ___ times the side length of square $$B$$, and the area of square $$A$$ is ___ times the area of square $$B$$."}, {"key": "2467", "content": "A square with a side length of $$2$$ meters, comparing its area and perimeter, ( )."}, {"key": "2468", "content": "As shown in the figure, an 'L'-shaped piece of paper with a perimeter of 52 cm can be divided along the dotted line into two identical rectangles. If the longest side is 16 cm, then the area of the 'L'-shaped piece of paper is in square centimeters.\n question_2468-image_0"}, {"key": "2469", "content": "The area of a square is $$64$$ square decimeters, its side length must be ( )."}, {"key": "2470", "content": "The little white rabbit and the little gray rabbit have a total of $$50$$ carrots, the little gray rabbit has $$2$$ times more carrots than the little white rabbit plus $$2$$ more. The little white rabbit has carrots, the little gray rabbit has carrots."}, {"key": "2471", "content": "There are peach trees and pear trees in the orchard, totaling $$348$$ trees. The number of peach trees is $$12$$ less than $$2$$ times the number of pear trees. How many pear trees and peach trees are there?"}, {"key": "2472", "content": "A set of books consists of three volumes: upper, middle, and lower. The upper volume is $$1$$ yuan more expensive than the middle volume, and the middle volume is $$2$$ yuan more expensive than the lower volume. The set is priced at $$32$$ yuan in total. Please calculate the price of the upper, middle, and lower volumes respectively."}, {"key": "2473", "content": "A certain school plans to plant a total of $$240$$ trees, including poplars, willows, and locust trees. The number of poplars is $$5$$ times that of willows, and the number of locust trees is $$2$$ times that of poplars. How many willows, poplars, and locust trees were originally planned to be planted?"}, {"key": "2474", "content": "The older brother has $$38$$ books, and the younger brother has $$34$$ books. After the older brother gives some books to the younger brother, the number of books the younger brother has becomes $$2$$ times the number of books the older brother has."}, {"key": "2475", "content": "There are a total of $$1000$$ kilograms of oil in two oil drums, A and B. If $$15$$ kilograms of oil are transferred from drum B to drum A, then the amount of oil in drum A becomes $$4$$ times that in drum B. How many more kilograms of oil were there in drum A compared to drum B originally?"}, {"key": "2476", "content": "In the book corner of class ($$1$$) of the third grade, there are a total of $$47$$ books, including storybooks and comic books. If $$7$$ storybooks are taken away, the number of storybooks will be $$4$$ times that of comic books. How many comic books and storybooks were there originally?"}, {"key": "2477", "content": "The sum of three numbers A, B, and C is $$183$$. B is $$4$$ less than $$2$$ times C, and A is $$7$$ more than $$3$$ times C. What is the value of A?"}, {"key": "2478", "content": "There are a total of $$110$$ apples and pears, the number of apples is $$20$$ more than double the number of pears. How many apples and pears are there? \uff08 \uff09"}, {"key": "2479", "content": "The music group has $$24$$ girls, the number of girls is $$4$$ times the number of boys, there are ( ) boys."}, {"key": "2480", "content": "Radish Head planted a total of $$126$$ radishes, the number of white radishes is twice that of green radishes, and the number of carrots is twice that of white radishes. How many green radishes are there? \uff08 \uff09"}, {"key": "2481", "content": "There are many chickens and ducks in the farm, among which the number of chickens exceeds ducks by $$100$$, and the number of chickens is $$20$$ less than $$3$$ times the number of ducks. So, there are chickens, and ducks in the farm."}, {"key": "2482", "content": "The day before Monday is Sunday\uff08 \uff09."}, {"key": "2483", "content": "Our country regained sovereignty over Hong Kong on July 1, 1997. That day was a Tuesday. So, what day of the week was the tenth anniversary on July 1, 2007?"}, {"key": "2484", "content": "January 1, 2012 was a Sunday, May 1, 2019 was a weekday."}, {"key": "2485", "content": "$$2013$$ year's $$6$$th of June is a Friday, then the $$10$$th of October of this year falls on what weekday. (Fill in the number)"}, {"key": "2486", "content": "Today is Wednesday, then starting from tomorrow, the $$365$$th day falls on a \uff0e"}, {"key": "2487", "content": "February 1, 2019, was a Friday. The third to last day of the month was a weekday."}, {"key": "2488", "content": "The International Children's Day in $$2013$$ was Saturday, the International Children's Day in $$2014$$ was on a Sunday ( )."}, {"key": "2489", "content": "$$2019$$ year $$6$$ month $$26$$ day is Wednesday, $$7$$ month $$10$$ day is Wednesday."}, {"key": "2490", "content": "Fill in $$5$$ numbers in the blank spaces of the magic square as shown in the figure, so that the sum of the numbers on each row, each column, and the two diagonals are all equal. Then, the first number of the second row is.\n question_2490-image_0"}, {"key": "2491", "content": "As shown in the figure, fill in appropriate numbers in the diagram to form a third-order magic square. Then, the sum of $$A+B+C+D+E=$$.\n question_2491-image_0"}, {"key": "2492", "content": "In the nine squares shown in the diagram, four numbers have already been filled in. Please fill in five more natural numbers so that the product of any three numbers in any row or column is equal. (Cannot fill in $$0$$, and the magic product must be less than 50). Fill in all the squares, magic product = .\n question_2492-image_0"}, {"key": "2493", "content": "In the magic square, all filled in numbers are integers greater than $$0$$, and the product of the three numbers in each row, each column, and each diagonal are equal. Therefore, the integer represented by $$A$$ in the figure equals.\n\n\n\n$$3$$\n\n\n\n\n$$4$$\n\n\n$$A$$\n\n\n\n\n$$1$$"}, {"key": "2494", "content": "To compile the temperature changes in Shenzhen in May, you can use ( ) statistical diagram."}, {"key": "2495", "content": "The number of plastic bags used by the Naughty family in ( ) months is less than that used by the Laughing family.\nquestion_2495-image_0"}, {"key": "2496", "content": "Among the statistical charts below, chart ( )'s horizontal line position can reflect the average level of these four data."}, {"key": "2497", "content": "Regarding the next four Olympic Games, the incorrect statement among the following is ().\n question_2497-image_0"}, {"key": "2498", "content": "The statistics graph of class ball games hobbies drawn by Xiao Xiao is shown on the right. The following statements are incorrect ( ).\n question_2498-image_0"}, {"key": "2499", "content": "Cai Lin investigated the heights of $$6$$ students in their group, the data is as follows:\n\n\n\n\nStudent Number\n\n$$1$$\n\n$$2$$\n\n$$3$$\n\n$$4$$\n\n$$5$$\n\n$$6$$\n\n\n\nHeight (cm)\n\n$$136$$\n\n$$138$$\n\n$$147$$\n\n$$151$$\n\n$$143$$\n\n$$145$$\n\n\n\nThe incorrect statement below is (\u3000\u3000)"}, {"key": "2500", "content": "Determine which of the following figures cannot be drawn with one stroke ( ).\n question_2500-image_0"}, {"key": "2501", "content": "The figure below can ( ) (fill in \u201ccan\u201d or \u201ccannot\u201d) be drawn in one stroke. If not, directly connect a line between ( ) two points to make it drawable in one stroke.\n question_2501-image_0"}, {"key": "2502", "content": "As shown in the diagram, the minimum number of strokes required to complete it is ( ).\n question_2502-image_0"}, {"key": "2503", "content": "Determine which of the following figures cannot be drawn with a single stroke ( )."}, {"key": "2504", "content": "The image shows the floor plan of a greenhouse, which is made up of $$6$$ showrooms, with each adjacent room connected by a door. We also need to add an exit (fill in the letter), allowing Eddie to enter from entrance $$A$$, pass through all the doors once without repeating, and finally exit the greenhouse through the exit.\n question_2504-image_0"}, {"key": "2505", "content": "In the diagram below, each small square has a side length of $$100$$ meters. Xiao Ming walks from point $$A$$ to point $$B$$ along the line segments without repeating any path, the maximum distance he can walk is meters.\n question_2505-image_0"}, {"key": "2506", "content": "The picture contains three squares of different sizes: large, medium, and small. The area of the large square is 32 more than the area of the medium square, and the perimeter of the large square is 16 more than the perimeter of the small square. What is the area of the large square? question_2506-image_0"}, {"key": "2507", "content": "As shown in the figure, $$E$$ is the trisection point on the side $$CD$$ of the square $$ABCD$$. $$BE$$ divides the square into a trapezoid and a triangle. The perimeter of the trapezoid is $$8$$ centimeters longer than that of the triangle. The area of the square $$ABCD$$ is in square centimeters. question_2507-image_0"}, {"key": "2508", "content": "It is known that the edge length of a larger square exceeds the smaller square's edge length by $$2$$ centimeters, and the area of the larger square is $$40$$ square centimeters greater than that of the smaller square. Find the area of both the larger and smaller squares in square centimeters."}, {"key": "2509", "content": "Each side in the figure is perpendicular to its adjacent sides, and the length of each side is equal. If the perimeter of this figure is $$56$$ cm, then, the area of this figure is square centimeters. question_2509-image_0"}, {"key": "2510", "content": "There is a square flowerbed with a side length of $$5$$ meters, surrounded by a $$1$$-meter-wide path on all four sides. The area of the path is in square meters. question_2510-image_0"}, {"key": "2511", "content": "There is a rectangle with a perimeter of $$72$$ cm, which is composed of three equally sized squares. The area of one square is in square centimeters."}, {"key": "2512", "content": "Grandma Li used a $$36$$ meter long fence to enclose $$3$$ square chicken coops, the first one in the middle of the field; the second one against a wall on one side; the third one in the corner, with two sides against the wall. Therefore, the respective areas of the three chicken coops are , , square meters."}, {"key": "2513", "content": "A square paddy field has an area of $$900$$ square meters. If each of its sides is increased by $$20$$ meters, the current area is square meters."}, {"key": "2514", "content": "As shown in the figure, three square pieces of paper of the same size in red, yellow, and green are placed inside a cubic box, overlapping each other. It is known that among the parts exposed on the outside, the area of the red color is $$20$$, the area of the yellow color is $$12$$, and the area of the green color is $$8$$. Then, the area of the bottom face of the cubic box is. question_2514-image_0"}, {"key": "2515", "content": "As shown in the picture, $$9$$ small rectangles form $$1$$ big rectangle. Following the numbering in the picture, the area of rectangle $$1$$ is $$2$$ square centimeters, rectangle $$2$$ is $$4$$ square centimeters, rectangle $$3$$ is $$6$$ square centimeters, rectangle $$4$$ is $$8$$ square centimeters, and rectangle $$5$$ is $$10$$ square centimeters. The area of rectangle $$6$$ is square centimeters. question_2515-image_0"}, {"key": "2516", "content": "The following image can be drawn in one stroke has ( )\uff0e\n question_2516-image_0"}, {"key": "2517", "content": "The lines in the diagram represent the paths of the park. Eddie and Chaos stand at points $$A$$ and $$B$$ respectively. They agree to start at their respective positions at the same time and walk through each path in the park, finally arriving at point $$C$$. Question: Who will arrive at $$C$$ first?\n question_2517-image_0"}, {"key": "2518", "content": "There is a group of chickens and rabbits in the zoo, they have a total of $$31$$ heads and $$94$$ feet, question: how many chickens are there\uff08 \uff09."}, {"key": "2519", "content": "There are a number of chickens and rabbits in a cage. Counting from above, there are $$8$$ heads, and counting from below, there are $$26$$ feet. The number of chickens and rabbits are ( )."}, {"key": "2520", "content": "During the school anniversary evening party, there are $$60$$ light bulbs lit, each controlled by a pull string switch. They are numbered in order $$1,$$ $$2,$$ $$3\\cdots ,$$ $$60.$$ Then, the pull strings of bulbs numbered with multiples of $$2$$ are pulled once, followed by those numbered with multiples of $$3,$$ and lastly, those numbered with multiples of $$5.$$ After pulling the strings $$3$$ times, the number of bulbs that remain lit is."}, {"key": "2521", "content": "Class three ($$1$$) has $$40$$ people, each person participates in at least one sport, $$27$$ people participate in running, $$28$$ people participate in jumping rope, and the number of people who participate in both is ( )."}, {"key": "2522", "content": "Every member of the school's literary and arts group can play at least one musical instrument. It is known that there are $$24$$ people who can play the violin, $$17$$ people who can play the keyboard, and among them, there are $$8$$ people who can play both instruments. The total number of people in this group is ( )."}, {"key": "2523", "content": "Class 4(1) has $$48$$ students. During a self-study class, $$30$$ students completed their Chinese homework, and $$20$$ students finished their math homework. There are $$6$$ students who did not finish either the Chinese or math homework. Both Chinese and math homework were completed by ( ) students."}, {"key": "2524", "content": "A number, from which $$2$$ is subtracted, then divided by $$2$$, added $$2$$, and finally multiplied by $$2$$, results in $$2014$$. The original number is ( )."}, {"key": "2525", "content": "Xue Xue solved such a problem: A number plus $$3$$, minus $$5$$, times $$4$$, divided by $$6$$ equals $$16$$. Find this number. ( )"}, {"key": "2526", "content": "There are $$24$$ birds on three trees, $$3$$ birds flew from the first tree to the second tree, and $$5$$ birds flew from the second tree to the third tree, finally, there were an equal number of birds on all three trees. How many birds were there originally on the first, second, and third trees respectively?"}, {"key": "2527", "content": "Three monkeys divided a pile of peaches among themselves. The biggest monkey took half of the pile minus $$1$$ peach; the second monkey took half of the remaining peaches plus $$1$$ peach; the smallest monkey got the remaining $$8$$ peaches, and then there were no peaches left. The pile originally had ____ peaches."}, {"key": "2528", "content": "Enter a number into the computer, and it will calculate according to given instructions: if the input is an even number, divide by $$2$$; if the input is an odd number, subtract $$5$$. After a number is input, the result is $$12$$. What could the original input number be? ( )."}, {"key": "2529", "content": "There is a number, add $$37$$ to it, then multiply by $$18$$, subtract $$323$$, and divide the result by $$23$$, the quotient is $$16$$, and the remainder is $$11$$. The original number was."}, {"key": "2530", "content": "There is a box of delicious dried fish. A greedy cat ate half of it, leaving 15 pieces. How many pieces of dried fish were originally in the box?"}, {"key": "2531", "content": "Originally, there were some apples stored in the bear cave. The big bear brought back another $$10$$ apples. Then, the little bear secretly ate half of them, leaving $$20$$ apples. The question is, how many apples were originally in the cave?"}, {"key": "2532", "content": "A number plus $$3$$, times $$7$$, minus $$6$$, and finally divided by $$5$$, results in $$10$$, what is the number ( )?"}, {"key": "2533", "content": "Adding $$6$$ instances of $$5.8$$, the incorrect expression is ( )."}, {"key": "2534", "content": "$$0.90$$ and $$0.900$$ compared ( )\uff0e"}, {"key": "2535", "content": "The result of simplifying $$30.030$$ is ( )."}, {"key": "2536", "content": "There are ( ) right angles in the figure below.\n question_2536-image_0"}, {"key": "2537", "content": "The size of an angle and the length of the two sides are ( )."}, {"key": "2538", "content": "The degree measure of $$\\angle A$$ in the figure is ( ) degrees.\n question_2538-image_0"}, {"key": "2539", "content": "As shown in the diagram, fold the rectangle paper along $$AC$$ so that point $$B$$ falls on $${{B}^{\\prime }}$$, $$CF$$ bisects $$\\angle {{B}^{\\prime }}CE$$, then $$\\angle ACF=$$$${}^\\circ $$.\n question_2539-image_0"}, {"key": "2540", "content": "Straight lines $$AB$$ and $$CD$$ intersect at point $$O$$, $$OE$$ bisects $$\\angle AOD$$, $$\\angle FOC=90{}^\\circ $$, $$\\angle 1=40{}^\\circ $$. Then $$\\angle 2$$=$${}^\\circ$$, $$\\angle 3$$=$${}^\\circ$$.\n question_2540-image_0"}, {"key": "2541", "content": "As shown in the figure, it is known that $$O$$ is a point on the line $$AD$$, the three angles $$\\angle AOB, \\angle BOC, \\angle COD$$ increase successively by $$25{}^\\circ$$. Then $$\\angle AOB$$ = $${}^\\circ$$, $$\\angle BOC$$ = $${}^\\circ$$, $$\\angle COD$$ = $${}^\\circ$$. \n question_2541-image_0"}, {"key": "2542", "content": "As shown in the figure, it is known that $$\\angle AOB=165{}^\\circ $$, $$\\angle AOC=\\angle BOD=90{}^\\circ $$, find $$\\angle COD$$=$$^\\circ $$.\n question_2542-image_0"}, {"key": "2543", "content": "Count and fill in the blanks. question_2543-image_0"}, {"key": "2544", "content": "Count the number of squares in the picture below.\n question_2544-image_0"}, {"key": "2545", "content": "There is a square in the picture, rectangles (including squares).\n question_2545-image_0"}, {"key": "2546", "content": "12 years ago, the father was 11 times older than his daughter; this year, the father is 3 times older than his daughter. How many years later will the father be twice as old as his daughter?"}, {"key": "2547", "content": "This year, the brother's age is $$3$$ times that of the younger brother. $$24$$ years later, the brother's age will be $$16$$ years less than double the younger brother's age. Calculate the ages of the brother and the younger brother this year."}, {"key": "2548", "content": "A family of three, the father is $$3$$ years older than the mother, and now the sum of their ages is $$80$$ years old, $$10$$ years ago the sum of their ages was $$51$$ years old, the father is years old this year."}, {"key": "2549", "content": "Xiao Zhi is $$9$$ years old this year, and the sum of his parents' ages is $$81$$ years. Question: What will the average age of the three be in a year if it's $$40$$ years old."}, {"key": "2550", "content": "The difference in the sum of the ages of the father and son $$4$$ years ago and $$4$$ years later is ()."}, {"key": "2551", "content": "Lingling is $$8$$ years old this year, her dad's age is $$4$$ times that of Lingling's. $$4$$ years ago, the age difference between Lingling and her dad was ( ) years."}, {"key": "2552", "content": "The sister is $$13$$ years old this year, and the brother is $$9$$ years old this year. When the sum of their ages is $$40$$ years old, how old should each of them be?"}, {"key": "2553", "content": "As shown in the figure, points $$B$$, $$O$$, $$D$$ are on the same line. If $$\\angle 1=15{}^\\circ $$ and $$\\angle 2=105{}^\\circ $$, then the degree of $$\\angle AOC$$ is (\u3000\u3000). \n question_2553-image_0"}, {"key": "2554", "content": "In the figure, $$AC$$ is a straight line. It satisfies the following relationship: the angle $$\\angle AOB$$ is $$3$$ times the degree of $$\\angle BOC$$. What is the degree of $$\\angle BOC$$?\n question_2554-image_0"}, {"key": "2555", "content": "Count, how many triangles are in the image below?\n question_2555-image_0"}, {"key": "2556", "content": "A set of set squares can combine to form an angle of ( )."}, {"key": "2557", "content": "$$0.05$$ and $$0.050$$ ( )."}, {"key": "2558", "content": "As shown in the figure, it is known that $$\\triangle ABC$$, $$\\angle B=70^{\\circ}$$, if along the dotted line in the figure $$\\angle B$$ is cut off, then $$\\angle 1+\\angle 2$$ equals to ( ).\n question_2558-image_0"}, {"key": "2559", "content": "How many triangles are there in the image below? ( )\n question_2559-image_0"}, {"key": "2560", "content": "Given the sequence $$2$$, $$6$$, $$10$$, $$14$$\u2026$$122$$.\n(I) How many terms does this sequence have?\n(II) What is the sum of this sequence?\n(III) What is the $$20$$th term of this sequence?"}, {"key": "2561", "content": "Among the following expressions, the correct shorthand for $$a\\times 3.3\\times b$$ is ( )."}, {"key": "2562", "content": "After removing the decimal point from a decimal, it is $$39.6$$ greater than the original number, this decimal is ( )."}, {"key": "2563", "content": "Count the total number of line segments in the figure below?\n question_2563-image_0"}, {"key": "2564", "content": "Xiaoling's family has three members. It is known that Xiaoling's dad is $$3$$ years older than her mom. This year, the total age of the three family members is $$71$$ years old. $$8$$ years ago, the total age of this family was $$49$$ years. How old is Xiaoling's mom this year?"}, {"key": "2565", "content": "Move the decimal point of a decimal two places to the left and then three places to the right, this decimal ( )."}, {"key": "2566", "content": "Calculate: $${{({{2}^{2}}\\times {{3}^{3}}\\times {{5}^{5}})}^{4}}=$$."}, {"key": "2567", "content": "Among the following, $$\\angle 1$$ and $$\\angle 2$$ are complementary angles ( )."}, {"key": "2568", "content": "A team of students are arranged in a hollow square formation, with $$52$$ people on the outermost layer and $$28$$ people on the innermost layer. The total number of students in this team is ( )."}, {"key": "2569", "content": "Fill in the appropriate arithmetic operators on the line below to make the equation true: $$1$$$$2$$$$3=0$$"}, {"key": "2570", "content": "Fill in the appropriate arithmetic operator on the underline below to make the equation valid: $$3$$$$8=24$$."}, {"key": "2571", "content": "Fill in the appropriate arithmetic operation on the line below to make the equation true: $$1998$$$$111=18$$."}, {"key": "2572", "content": "Based on the rules of the 24-point game, form 24 using the numbers 3, 5, 7, 9. Among the options below, the correct one is ( )."}, {"key": "2573", "content": "Fill in \"$$+$$\" or \"$$-$$\" in the $$\\square$$ below to make the equation valid: $$11$$$$9$$$$7$$$$5$$$$3$$$$1=0$$"}, {"key": "2574", "content": "A row of small flags is arranged in a sequence that cycles through 1 red flag, 2 green flags, and 3 yellow flags. Among the first 60 flags, there are some green flags"}, {"key": "2575", "content": "As shown in the figure, a frog jumps between points $$A$$, $$B$$, $$C$$, $$D$$ (not allowed to jump in place). If the frog starts jumping from point $$A$$ and jumps $$2$$ times, there are a total of different ways to jump.\n question_2575-image_0"}, {"key": "2576", "content": "The result of $1\\times 2+3\\times 4+5\\times 6+\\cdots +97\\times 98+99\\times 100$ is odd or even?"}, {"key": "2577", "content": "Person A, B, and C pass the ball to each other, with each pass necessarily going to another person. Starting with A, after $$2$$ passes, there is a possibility that the ball ends up with C."}, {"key": "2578", "content": "The result of $31\\times 23+15\\times 66+11\\times 17$ is. (Fill in 'odd' or 'even')"}, {"key": "2579", "content": "There is a sequence of numbers: $$2$$, $$3$$, $$4$$, $$5$$, $$2$$, $$3$$, $$4$$, $$5$$, $$2$$, $$3$$, $$4$$, $$5$$\u2026 The $$44$$th number is."}, {"key": "2580", "content": "Ultraman encounters a group of monsters, with the large monsters having $$2$$ heads and $$4$$ legs, and the small monsters having $$2$$ heads and $$2$$ legs. Together, there are a total of $$20$$ heads and $$32$$ legs. How many large monsters are there?"}, {"key": "2581", "content": "A certain school has $$30$$ dorms, with each large dorm housing $$6$$ people, and each small dorm housing $$4$$ people. It is known that there are a total of $$168$$ people living in these dorms, so there are large dorms among them."}, {"key": "2582", "content": "There are a total of triangles in the following figure. question_2582-image_0"}, {"key": "2583", "content": "The teacher said to Xiaoming: \"The age I was $$15$$ years ago is the same as the age you will be in $$6$$ years. $$7$$ years ago, my age was $$8$$ times your age.\", Xiaoming's age this year, the teacher's age this year."}, {"key": "2584", "content": "Xiaowen is $$7$$ years old this year, Xiaowen's dad is $$35$$ years old this year, when Xiaowen was at a certain age, his dad's age was $$8$$ times that of Xiaowen's."}, {"key": "2585", "content": "Fill in the $$\u25a1$$ in the following vertical operation with the appropriate number to make the equation true, then $$A=$$.\n question_2585-image_0"}, {"key": "2586", "content": "Fill in the $$\u25a1$$ in the following vertical calculation with the appropriate number so that the equation holds, then the minuend in this vertical calculation is. \n question_2586-image_0"}, {"key": "2587", "content": "Fill in the blanks with appropriate numbers in the diagram so that the addition vertical expression is valid. Find: the sum obtained by the addition vertical expression is.\n$$\\begin{matrix}& & &\\boxed{7} \\\\ +&&\\square & \\boxed{5} \\\\ \\hline &\\square&\\square & \\square \\end{matrix}$$"}, {"key": "2588", "content": "Fill in the box with the appropriate number to make the equation valid. The four-digit minuend is.\n question_2588-image_0"}, {"key": "2589", "content": "$3$ workers processed $90$ parts in $5$ hours, at this rate, $10$ workers will process parts in $10$ hours."}, {"key": "2590", "content": "There are $$300$$ portions of hay in the warehouse, enough to feed $$10$$ cows for $$30$$ days. $$1$$ cow can eat $$1$$ portion of hay per day."}, {"key": "2591", "content": "Perform vertical calculation:\n$$122\\div 2=$$; $$123\\div 3=$$."}, {"key": "2592", "content": "Xiaoming's average score for the first four math tests was $$89$$ points. After the fifth test, his average score rose to $$90$$ points. How many points did Xiaoming get in the fifth test?"}, {"key": "2593", "content": "In Carrefour supermarket, potatoes cost $$5$$ Yuan per jin, and chili costs $$10$$ Yuan per jin. Mom bought $$3$$ jin of potatoes and $$2$$ jin of chili, so the average cost per jin of vegetables spent by mom was Yuan."}, {"key": "2594", "content": "Wei'er plans to learn piano, dance, or singing over the next $$5$$ days, studying only one course per day, without repeating the same course on consecutive days. She plans to learn piano on the first day and also on the last day. Therefore, there are a total of several learning plans."}, {"key": "2595", "content": "The Doctor, Eddie, and Vi pass the ball to each other, starting with the Doctor. After $$4$$ passes, the ball returns to the Doctor's hands. There is a different way of passing the ball."}, {"key": "2596", "content": "As shown in the diagram, an ant starts from vertex $$P$$ of a pyramid, and it walks along the edges of the pyramid, visiting each of the $$5$$ vertices exactly once before stopping. How many different paths can the ant take? question_2596-image_0"}, {"key": "2597", "content": "Edi and Vi are participating in a table tennis match, where the first to win two games will be victorious. Thus, there are several possible outcomes for the match."}, {"key": "2598", "content": "A series of shapes are arranged according to the following pattern: \u2606\u2606\u25cb\u25cb\u2606\u25b3\u25b3\u25cb\u25cb\u2606\u25b3\u25b3\u25cb\u25cb\u2606\u25b3\u25b3\u2026\u2026 The 50th shape in this series is ( )\uff0e"}, {"key": "2599", "content": "Is the sum of $$1+2+3+\\cdots +2017$$ odd or even?"}, {"key": "2600", "content": "Below is a rectangular garden with an area of $$42$$ square meters. It is known that the length of this garden is $$7$$ meters, and the width of this garden is meters.\n question_2600-image_0"}, {"key": "2601", "content": "The area of a square is $$81$$ square meters, and the side length is meters. question_2601-image_0"}, {"key": "2602", "content": "If the side length of square $$A$$ is twice that of square $$B$$, then the perimeter of square $$A$$ is twice that of square $$B$$'s perimeter; the area of square $$A$$ is four times that of square $$B$$'s area.\n question_2602-image_0"}, {"key": "2603", "content": "The area of a rectangle is $$36$$ square centimeters, the width is $$4$$ centimeters, its length is in centimeters, and its perimeter is in centimeters."}, {"key": "2604", "content": "September 10th, 2018 (Teacher's Day) is Monday, and the same year's National Day (October 1st) is ( )."}, {"key": "2605", "content": "$$2017$$ year $$2$$ month $$1$$ day is Wednesday. Starting from this day, the $$25$$th day falls on a ."}, {"key": "2606", "content": "The picture below is an incomplete 4x4 magic square, please complete it. The first number in the first row is, the third number in the first row is, the second number in the second row is, the fourth number in the second row is, the second number in the fourth row is. question_2606-image_0"}, {"key": "2607", "content": "There is a river island in the center of a river, surrounded by four bridges connecting to the shore. Question: Is it possible to find a route that traverses all the bridges without repeating any? ().\n question_2607-image_0"}, {"key": "2608", "content": "The image is a floor plan of a supermarket, with six doors in total. Zhang Ming wants to walk through all the aisles without repeating any route. Can he do it? If yes, please design an entry and exit strategy for him. If not, please explain why. question_2608-image_0"}, {"key": "2609", "content": "There are $$45$$ chickens and rabbits in total, locked in the same cage, and there are $$100$$ legs in the cage. The cage contains chickens and rabbits."}, {"key": "2610", "content": "The school purchased a total of $$120$$ meat floss bread and ham bread for the students, spending a total of $$285$$ yuan. Knowing that each meat floss bread costs $$2$$ yuan and each ham bread costs $$3$$ yuan, then the school purchased meat floss bread and ham bread."}, {"key": "2611", "content": "Eddy participated in a fire safety knowledge contest with a total of $$10$$ questions. Scoring $$10$$ points for each correct answer and losing $$3$$ points for each unanswered or incorrect answer, (1) if Eddy answered all $$10$$ questions correctly, his score; (2) if Eddy left unanswered or answered incorrectly $$2$$ questions, his score; (3) if Eddy scored $$48$$ points, then he left unanswered or answered incorrectly questions."}, {"key": "2612", "content": "A worker delivers 200 celadon vases. For each intact vase delivered, a shipping fee of $20 is paid. For each damaged vase, a penalty of $100 is incurred. After delivery of these vases, the worker received a total of $3400. How many were damaged?"}, {"key": "2613", "content": "Class 4 ($$1$$) has $$30$$ students. Among them, $$15$$ students have watched the animated movie \"Lotus Lantern\", $$12$$ students have watched \"Journey to the West\", and $$6$$ students have watched both of these animated movies. Therefore, the number of students who have only watched one of these two animated movies is $$.$$ The number of students who have not watched either of these two animated movies is $$.$$"}, {"key": "2614", "content": "Weld two iron bars of $$23$$ centimeters and $$37$$ centimeters into one. Knowing the welding part is $$3$$ centimeters long, after welding this iron bar is ____ centimeters long."}, {"key": "2615", "content": "The fourth grade of Yuhong Primary School has $$35$$ students learning the piano, $$27$$ students learning to draw, and $$10$$ students learning both piano and drawing. The number of students learning only the piano and the number learning only drawing are."}, {"key": "2616", "content": "A class has $$46$$ students, $$12$$ of them participate in the art group, $$23$$ students participate in the music group, and $$5$$ students participate in both groups. Therefore, the number of students who haven't participated in either the art group or the music group is ."}, {"key": "2617", "content": "There are 30 coins numbered from $$1\\sim 30$$ with heads up on the table. First, flip the coins that are multiples of $$3$$, then flip the coins that are multiples of $$4$$. In the end, there are still some coins with heads up."}, {"key": "2618", "content": "The fourth-grade science activity group has a total of $$48$$ people. During a timed science activity competition involving cutting and pasting car models and assembling airplane models, the teacher found at the time of roll call: $$25$$ students had cut and pasted a car model, $$32$$ students had assembled an airplane model. Every student completed at least one activity. The number of students who completed both activities is $$9$$ people."}, {"key": "2619", "content": "Among the students from four third-grade classes who signed up for the sports meeting, there are $$74$$ students not from class one, $$92$$ students not from class four, and a total of $$46$$ students from class two and class three signed up. The total number of third-grade students participating in the competition is people."}, {"key": "2620", "content": "Experiment Elementary School, Fourth Grade, Class Two, has $$28$$ students participating in the Chinese language interest group, $$29$$ students participating in the mathematics interest group, and $$12$$ students participating in both groups. This class has students participating in either the Chinese or mathematics interest groups."}, {"key": "2621", "content": "There are $$96$$ goats on three mountains in total, with $$4$$ goats running from Mountain 1 to Mountain 2, and $$8$$ goats running from Mountain 2 to Mountain 3. After these movements, the number of goats on each of the three mountains is equal. How many goats were originally on each mountain?"}, {"key": "2622", "content": "At the award ceremony of the robot programming competition, Eddie asked the teacher: \"How many points did I get?\" The teacher said: \"After your score is subtracted by $$6$$, divided by $$2$$, then added by $$10$$, and finally multiplied by $$2$$, it is exactly $$100$$ points.\" Eddie scored in this competition."}, {"key": "2623", "content": "There were $$26$$ bricks, 2 brothers were vying to carry them. The younger brother rushed in front, just as he organized the bricks, the elder brother arrived. Seeing that the younger brother had picked too many, the elder brother took half from him for himself. The younger brother thought he could handle it and took half back from the elder brother. The elder brother thought he had taken too few, so the younger brother had to give the elder brother $$5$$ more bricks, this way the elder brother picked $$2$$ more bricks than the younger brother. Initially, the younger brother planned to pick up bricks."}, {"key": "2624", "content": "An old man takes a pot to buy wine. When encountering a shop, the amount doubles. Seeing flowers, he drinks eight taels. Encountering shops and flowers three times, he finishes the wine in the pot. There was originally two taels of wine in the pot."}, {"key": "2625", "content": "Please fill in $$1$$, $$2$$, $$3$$, $$4$$ in the grid respectively; such that each row and each column contains the numbers $$1$$, $$2$$, $$3$$, $$4$$ without any repetitions; the number in the upper-left corner represents the sum of the numbers filled in the bold-bordered area. question_2625-image_0 The first number in the first row is."}, {"key": "2626", "content": "In $$5246$$, the difference in value between $$2$$ and $$4$$ is ( )."}, {"key": "2627", "content": "Xiao Ming walks $$1.5$$ kilometers from school to home. One day after school, he walked $$0.3$$ kilometers from school, then went back to the school to pick up a math book, and then walked back home. This day, he walked an extra kilometer to get home. question_2627-image_0"}, {"key": "2628", "content": "The '$$6$$' in the decimal $$4.67$$ represents there are $$6$$ of ten-ths."}, {"key": "2629", "content": "In the 100m sprint, the results for the 5 participants in group 4 are as follows: Participant number 1 2 3 4 5 and their times in seconds are 16.08 15.98 16.80 15.89 18.06 respectively. The first place in this group goes to participant number. question_2629-image_0"}, {"key": "2630", "content": "As shown in the figure, $$\\angle 1=30^\\circ $$, then $$\\angle 2=$$$$^\\circ $$\uff0e question_2630-image_0"}, {"key": "2631", "content": "As shown in the figure, the correct name of the angle is \uff08 \uff09\n question_2631-image_0"}, {"key": "2632", "content": "The sum of two acute angles is ( )."}, {"key": "2633", "content": "As shown in the diagram, within the right angle $$AOB$$ there is a ray $$OC$$, and $$\\angle AOC$$ is $$30$$ degrees larger than $$\\angle BOC$$. Then $$\\angle BOC$$ is degrees. question_2633-image_0"}, {"key": "2634", "content": "Count, how many triangles are there in the figure in total.\n question_2634-image_0"}, {"key": "2635", "content": "(1) The number of diagonally placed squares in the image is ; (2) There are a total of squares in the image. question_2635-image_0"}, {"key": "2636", "content": "(1) The number of diagonally placed squares in the image is; (2) The total number of squares in the image is. question_2636-image_0 \u200b"}, {"key": "2637", "content": "There are a total of squares in the picture below.\n question_2637-image_0"}, {"key": "2638", "content": "The second class of the first grade performed martial arts, with a total of $$49$$ participants, who formed a solid square formation. question_2638-image_1"}, {"key": "2639", "content": "Third grade arranged into three solid squares to perform a group dance, with the outermost layer of each square having $$5$$ people on each side, and the outermost layer having a total of people. question_2639-image_0"}, {"key": "2640", "content": "During military training, the students formed a three-layer hollow square formation, with 60 people in the innermost layer. How many people were in the outermost layer?"}, {"key": "2641", "content": "Volunteers lined up to take a group photo in a three-tier hollow square formation, with a total of $$48$$ people on the outermost layer, and some people in the innermost layer."}, {"key": "2642", "content": "A solid square formation with each side of the outermost layer having $$11$$ people, then the outermost layer of this square formation has a total of people."}, {"key": "2643", "content": "Insert \"$$+$$\" at the appropriate places to make the equation valid (adjacent numbers can form one number). $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$=$$ $$42$$"}, {"key": "2644", "content": "Fill in \"$$+$$\" or \"$$-$$\" in the appropriate places to make the equation valid (adjacent numbers can form one number).$$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6=342$$"}, {"key": "2645", "content": "Wei Er distributed prizes to the customers, each customer got $$14$$ cups, resulting in $$10$$ cups left over. If each customer had got $$16$$ cups, then $$2$$ cups would be left over. Wei Er had a total of cups. $$10+2=12$$ (cups), $$16-14=2$$ (cups), thus there are $$12\\div2=6$$ (people) customers, having cups $$6\\times14-10=74$$ (cups)."}, {"key": "2646", "content": "The school bought a bunch of small soccer balls to distribute among the classes: if each class gets 4 balls, there are 66 balls short; if each class gets 2 balls, then it's just enough to distribute to all, the school has a total of classes."}, {"key": "2647", "content": "A teacher distributes strawberries to children in kindergarten. If every child gets $$5$$ strawberries, there are $$14$$ left; if every child gets $$7$$ strawberries, there are $$4$$ short. How many children are there, and how many strawberries in total?"}, {"key": "2648", "content": "Eddie is responsible for distributing mineral water to Class 3-3. He has prepared less mineral water. If each group is given $$4$$ boxes, there will be a shortage of $$2$$ boxes; if each group is given $$6$$ boxes, there will be a shortage of $$14$$ boxes. So, how many groups are there in Class 3-3 in total. question_2648-image_0"}, {"key": "2649", "content": "Divide 8 tanks among three children, Xiao Xiao, Zhong Zhong, and Da Da, with each getting at least one tank. There is a certain method."}, {"key": "2650", "content": "The prizes prepared by the teacher for the fun sports meeting are lollipops. The teacher wants to divide $$8$$ identical lollipops into $$3$$ piles, there are in total different methods."}, {"key": "2651", "content": "Divide 15 identical balls into three piles, with at least 3 in each pile, there are several ways to do it."}, {"key": "2652", "content": "There are $3$ identical candies, to be divided among two kids (it's possible that someone gets none), there can be several ways to divide them."}, {"key": "2653", "content": "Calculate: $$22\\times 8+42\\times 92+20\\times8=$$."}, {"key": "2654", "content": "Calculate: (1) $$33\\times 66+33\\times 34=$$\uff0e(2) $$16\\times 43+16\\times 31+16\\times 26=$$\uff0e"}, {"key": "2655", "content": "Calculate: $$14\\times 25+14\\times 76-14$$=."}, {"key": "2656", "content": "To cut a rectangle measuring $$12$$ cm in length and $$8$$ cm in width into $$4$$ identical small rectangles, among the following three cutting methods, the figure shows the small rectangle with the shortest perimeter. question_2656-image_0 question_2656-image_1 question_2656-image_2 Figure \u2460 Figure \u2461 Figure \u2462"}, {"key": "2657", "content": "Calculate: $$24\\times 5+18\\times 5=$$."}, {"key": "2658", "content": "$$391-98-102$$=\uff0e"}, {"key": "2659", "content": "Split $$8$$ into the sum of $$3$$ distinct natural numbers, there are a total of different methods."}, {"key": "2660", "content": "As shown in the diagram, two adjacent sides are perpendicular to each other, with line segment lengths as follows, the perimeter of the shape is in centimeters. question_2660-image_0"}, {"key": "2661", "content": "Distribute $$6$$ identical erasers among $$3$$ kids, with each kid getting at least one eraser. How many different distribution methods are there?"}, {"key": "2662", "content": "Place $$7$$ identical pears into three identical plates, each plate must contain some. There are a total of different methods of placing."}, {"key": "2663", "content": "Vehicles A and B originally had a total of $$43$$ passengers. Upon arriving at a certain location, $$5$$ passengers alighted from vehicle A, and $$2$$ passengers boarded vehicle B. At this point, the number of passengers in vehicle A was exactly $$3$$ times the number of passengers in vehicle B. The original number of passengers in vehicle A was , and the original number of passengers in vehicle B was . question_2663-image_0"}, {"key": "2664", "content": "Initially, tanks A and B contained the same amount of oil. Now, if $$9$$ kg of oil is poured from tank A to tank B, then the oil in tank B is $$4$$ times that in tank A. How much oil is now in tank A and in tank B, respectively? question_2664-image_0"}, {"key": "2665", "content": "Huanhuan has 3 times as many cards as Lele. If Huanhuan gives Lele 10 cards, their numbers of cards will be the same. How many cards did Huanhuan and Lele originally have?"}, {"key": "2666", "content": "Xiao Lin has $$30$$ pictures. After giving $$5$$ pictures to Xiao Jun, both of them have the same number of pictures. Originally, Xiao Lin had more pictures than Xiao Jun."}, {"key": "2667", "content": "Dad, mom, grandpa, and grandma line up to take a photo, where grandpa can only stand at the far right. They can take a total of different photos."}, {"key": "2668", "content": "The class organized a picnic in the park, and Teacher Deer wants to choose one each from $$2$$ tops, $$3$$ pairs of trousers, and $$1$$ hat for the outfit, where the hat is optional, making a total of combinations."}, {"key": "2669", "content": "Xiao Qi, Xiao Ling, and Xiao Jun, three classmates, line up for a photo. There are ( ) different ways to arrange them."}, {"key": "2670", "content": "Wei has a square handkerchief, the length of diagonal $$AC$$ is $$8$$ cm. Then, the area of the handkerchief is square centimeters. question_2670-image_0"}, {"key": "2671", "content": "As shown in the figure, in the quadrilateral $$ABCD$$, diagonals $$AC$$ and $$BD$$ are perpendicular to each other. Given that $$AC=26$$ cm and $$BD=24$$ cm, the area of quadrilateral $$ABCD$$ is square centimeters. question_2671-image_0"}, {"key": "2672", "content": "As shown in the figure, a large rectangle is divided into four smaller rectangles, with the areas of three of the rectangles being $$48$$, $$24$$, and $$30$$ square decimeters, respectively. The area of the shaded rectangle is in square decimeters question_2672-image_0"}, {"key": "2673", "content": "The description of the phenomenon 'by pulling a diagonal of a rectangular wooden frame, the frame becomes a parallelogram' is incorrect in the following statement ( )."}, {"key": "2674", "content": "As shown in the figure, the area of this parallelogram is ( ) square centimeters.\n question_2674-image_0"}, {"key": "2675", "content": "In the division formula $$\\square \\div 28 =13\\cdots \\cdots \\square$$, the maximum value of the dividend equals $$13\\times 28+28=392$$"}, {"key": "2676", "content": "Dividing one natural number by another, the quotient is $$7$$ and it divides exactly, the sum of the dividend and divisor is $$48$$. (1) The dividend is a multiple of the divisor. (2) Complete the following line diagram. question_2676-image_0 (3) The dividend is."}, {"key": "2677", "content": "When two numbers are divided, the quotient is $$6$$ with a remainder of $$3$$. The sum of the dividend, divisor, quotient, and remainder is $$68$$. (1) The dividend is multiple times the divisor. The sum of the dividend and divisor is. (2) The dividend is."}, {"key": "2678", "content": "A number divided by $$15$$, the quotient is $$30$$, with a remainder, the maximum value of the dividend is."}, {"key": "2679", "content": "When dividing two numbers, the quotient is $$5$$ with no remainder, and the sum of the dividend and divisor equals $$60$$. Therefore, the dividend is a multiple of the divisor, and the divisor equals $$10$$."}, {"key": "2680", "content": "As shown in the figure, the area of this parallelogram is ( ) square centimeters. question_2680-image_0"}, {"key": "2681", "content": "Calculate. (1)$$\\frac{1}{7}+\\frac{2}{7}=$$\uff0e(2)$$\\frac{2}{9}+\\frac{5}{9}=$$\uff0e"}, {"key": "2682", "content": "Insert $$10$$ colored flags at equal distances along one side of a $$90$$ meter long track (flags also at both ends), the distance between each neighboring pair of flags is ( )."}, {"key": "2683", "content": "There are a row of colored flags on the sports field, totaling $$34$$ flags, arranged in a sequence of $$3$$ red flags and $$1$$ yellow flag in turn. Among these colored flags, there are $$26$$ red flags."}, {"key": "2684", "content": "The distance between two buildings is $$28$$ meters, and a poplar tree is planted every $$4$$ meters, for a total of poplar trees that can be planted. (The width of the tree is negligible)"}, {"key": "2685", "content": "There is a string of beads in two colors, black and white, arranged according to the following pattern: \u2026\u2026 The $$15$$th bead in this string is of ( ) color."}, {"key": "2686", "content": "$$1$$, $$2$$, $$3$$, $$1$$, $$2$$, $$3$$, $$1$$,\u2026 so the 16th number is."}, {"key": "2687", "content": "There is a string of colored lights on the TV tower, arranged in the order of \"red, yellow, green, white\". Please calculate, the color of the $$11$$th light is ( )."}, {"key": "2688", "content": "Is the result of the calculation $$123+325-62\\times 101+33\\times 22$$ odd or even ( )\uff0e"}, {"key": "2689", "content": "$$57\\times 17\\times 15\\times 13$$ Is the result odd or even? ( )."}, {"key": "2690", "content": "A doctor repeats writing the phrase 'studying makes me happy' in order, totaling $$56$$ Chinese characters, the last one is the ( ) character."}, {"key": "2691", "content": "The result of $$15+23$$ is an"}, {"key": "2692", "content": "Calculate: $$25\\times 125\\times 4=$$."}, {"key": "2693", "content": "$$11\\times 4+11\\times 6=$$."}, {"key": "2694", "content": "Calculate: \n(1)$$2\\times 5=$$\uff0e\n(2)$$4\\times 25=$$\uff0e"}, {"key": "2695", "content": "$$32+24+68=$$"}, {"key": "2696", "content": "String beads sequentially in the order of $$2$$ red beads, $$2$$ white beads, $$5$$ black beads on a rope, and repeat this sequence. If counting from the beginning, the $$50$$th bead is of ( ) color."}, {"key": "2697", "content": "As shown in the figure, what is the $$21$$st figure? $$\\bigcirc \\square \\triangle \\bigcirc \\square \\triangle \\bigcirc \\square \\triangle \\cdots \\cdots $$"}, {"key": "2698", "content": "$$45\\div4+35\\div4=$$"}, {"key": "2699", "content": "$$25\\times32=$$"}, {"key": "2700", "content": "Determine the parity of the result for the following expression: $$27\\times 38-18\\times 71+39\\times 65-23\\times 14$$."}, {"key": "2701", "content": "The image below shows a rectangle and a square. Can you calculate their areas respectively? The area of the rectangle is, and the area of the square is.\n question_2701-image_0"}, {"key": "2702", "content": "$$7{{\\text{m}}^{2}}=$$$$\\text{d}{{\\text{m}}^{2}}=$$$$\\text{c}{{\\text{m}}^{2}}$$\uff0e"}, {"key": "2703", "content": "(1) The area of the rectangle is $$20$$ square centimeters, the length is $$5$$ centimeters, and the width is centimeters.\n(2) The area of the square is $$36$$ square centimeters, and the side length is centimeters."}, {"key": "2704", "content": "The following image is a 3x3 magic square with a magic constant of $$33$$. Please complete the numbers in the blanks. The first number in the second row is. question_2704-image_0"}, {"key": "2705", "content": "Fill in the numbers $$2$$, $$4$$, $$6$$, $$8$$, $$10$$, $$12$$, $$14$$, $$16$$, $$18$$ into each cell of the following $$3\\times 3$$ grid so that the sum of the numbers in every row, every column, and both diagonals are the same. What number should be filled in the middle cell?"}, {"key": "2706", "content": "As shown in the figure, there is a third-order magic square. According to the given numbers, fill in the $$A$$ position.\n question_2706-image_0"}, {"key": "2707", "content": "Four girls participated in a high jump competition, with the results as shown in the table below. The third place is ( ).\n\n\n\n\nName\n\nXiao Yue\n\nXiao Ying\n\nXiao Tian\n\nXiao Li\n\n\n\nResult/meters\n\n$$1.3$$\n\n$$0.9$$\n\n$$0.7$$\n\n$$1.2$$"}, {"key": "2708", "content": "The picture below is of a countryside river with six bridges built over it. Can you start from one of the villages and traverse all the bridges without repeating any? (You can only cross each bridge once, but you may walk back and forth on land) question_2708-image_0"}, {"key": "2709", "content": "The picture below needs at least a few lines added to transform it into a one-stroke figure.\n question_2709-image_0"}, {"key": "2710", "content": "Among the following figures, which cannot be drawn with a single stroke is figure.\n question_2710-image_0"}, {"key": "2711", "content": "Using $$11$$, $$13$$, $$15$$, $$17$$, $$19$$, $$21$$, $$23$$, $$25$$, $$27$$ to create a 3x3 magic square, the middle number should be."}, {"key": "2712", "content": "A cricket has $$6$$ legs, a spider has $$8$$ legs, together there are $$8$$ crickets and spiders with a total of $$54$$ legs, number of crickets, number of spiders."}, {"key": "2713", "content": "Eddie put chickens and rabbits in the same cage, counted them, and there were $$10$$ rabbits, $$8$$ chickens, and a certain number of legs in the cage."}, {"key": "2714", "content": "A bicycle has two wheels, and a tricycle has three wheels. There are a total of $$10$$ bicycles and tricycles in the shed, and counting all the wheels together there are $$26$$ wheels. Therefore, there are $$6$$ tricycles."}, {"key": "2715", "content": "There are tigers and peacocks in the zoo totaling $$45$$ animals. Together, they have $$136$$ legs. The number of tigers is, and the number of peacocks is."}, {"key": "2716", "content": "There are $$30$$ people in the third grade, class three, who joined the Chinese interest group, and $$45$$ people who joined the Math interest group, with $$20$$ people participating in both groups. This class has people who joined either the Chinese or Math interest groups."}, {"key": "2717", "content": "Grade 3 Class 4 has a total of $$32$$ students, each student participated in at least one of the math interest group or English interest group, $$19$$ students participated in the math interest group, $$21$$ students participated in the English interest group, some students participated in both interest groups."}, {"key": "2718", "content": "Count the number of triangles in the figure below.\n question_2718-image_0"}, {"key": "2719", "content": "Use an expression containing letters to represent the \u201c?\u201d at the place. question_2719-image_0"}, {"key": "2720", "content": "Among the following options, which can be represented by $$2N$$ + $$4$$ ( )."}, {"key": "2721", "content": "In the school's instrumental group, the number of boys is 2 less than 3 times the number of girls, there are $$a$$ girls, and together, boys and girls sum up to $$30$$ people. Represent the quantity relationship with an algebraic expression:"}, {"key": "2722", "content": "Find the pattern: $$1$$, $$3$$, $$5$$, $$7$$, $$\\cdots $$, the $$7$$th number is."}, {"key": "2723", "content": "$$1+2+3+\\cdots +10=$$."}, {"key": "2724", "content": "In each small cell of a board divided into $$64$$ small cells, stones are placed. If $$2$$ stones are placed in the first cell, $$4$$ stones in the second cell, $$6$$ stones in the third cell, $$8$$ stones in the fourth cell, and so on until all $$64$$ cells are filled, how many stones are placed in total?"}, {"key": "2725", "content": "For the sequence of numbers $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$19$$, $$\\cdots$$, the $$10$$th number is, $$49$$ is the nth number of this sequence."}, {"key": "2726", "content": "The figure is a square dot matrix, this square dot matrix has a total of . question_2726-image_0"}, {"key": "2727", "content": "As shown is a square dot matrix, the outermost layer has a total of dots; question_2727-image_0"}, {"key": "2728", "content": "Divide $$24$$ apples evenly among $$6$$ people, each person gets number of apples."}, {"key": "2729", "content": "The older brother has $$95$$ books, and the younger brother has $$155$$ books. After the older brother gave some books to the younger brother, the total number of books the younger brother had became exactly $$4$$ times that of the older brother's. (1) After the older brother gave some books to the younger brother, how many books do the older brother and the younger brother have in total? (2) How many books do the older brother and the younger brother each have at this time? question_2729-image_0"}, {"key": "2730", "content": "Below is a fast food restaurant's menu, Lulu plans to order a main dish, a snack, and a beverage, one of each. How many different combinations can she have? question_2730-image_0"}, {"key": "2731", "content": "There are $$21$$ female students and $$23$$ male students in Class 1, Grade 3 of Sunshine Primary School, (1) how many different ways are there to choose one person to be the flag bearer? (2) how many different ways are there to choose a boy to be the flag bearer and a girl to be the flag guard?"}, {"key": "2732", "content": "Eddie is preparing clothes for a seaside trip. He has prepared $$2$$ different tops, $$4$$ different pants, $$3$$ different pairs of shoes, and $$2$$ different hats. (1) How many different matching schemes are there if no hats are chosen? (2) How many different matching schemes are there if hats are chosen? (3) How many different matching schemes are there in total if hats can be chosen or not chosen?"}, {"key": "2733", "content": "There are a total of $$3$$ rooms available in the hotel for selection, Eddie, Vi, and Da Kuan each choose one room, how many different selection schemes are there in total? question_2733-image_0"}, {"key": "2734", "content": "As shown in the diagram, in parallelogram $$ABCD$$, line $$AE$$ is drawn perpendicular to $$BC$$ at point $$E$$ from point $$A$$. It is known that the area of parallelogram $$ABCD$$ is $$48$$ square centimeters and $$AE=8$$ centimeters. What is the length of $$AD$$ in centimeters? question_2734-image_0"}, {"key": "2735", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$ from point $$A$$. Given $$AB=5$$ cm, and $$AE=3$$ cm, then the area of parallelogram $$ABCD$$ is square centimeters. question_2735-image_0"}, {"key": "2736", "content": "A number divided by $$7$$ gives a quotient of $$19$$ with a remainder. $$\\bigcirc \\div 7=19\\ldots \\ldots \\square $$, the maximum remainder is, at this time the dividend is."}, {"key": "2737", "content": "Eddy took out his precious collection of $$35$$ pieces of chocolate to share with everyone, but he didn't eat any. The chocolates were distributed equally among the third-grade students who participated in the contest, fewer than $$10$$ people, and there were $$5$$ pieces left, which couldn't be divided further. How many third-grade students participated in the contest?"}, {"key": "2738", "content": "Kids, have you ever played Minesweeper? In the sudoku grid below, the \"$$3$$\" indicates that there are a total of mines in the $$8$$ cells surrounding \u201c$$3$$\u201d.\n question_2738-image_0"}, {"key": "2739", "content": "Xueersi School organized a tree planting activity. It is known that $$5$$ people plant $$80$$ trees in $$2$$ hours. If each person plants the same number of trees per hour, then $$1$$ person plants $$1$$ hour tree plants."}, {"key": "2740", "content": "$$2$$ people plant $$60$$ trees in $$3$$ hours, $$1$$ person plants trees in $$1$$ hour."}, {"key": "2741", "content": "What numbers do the following letters represent?\n question_2741-image_0 \n$$A=$$\uff0e\n$$B=$$\uff0e\n$$C=$$\uff0e"}, {"key": "2742", "content": "(1) $$\\frac{3}{5}$$ means dividing the unit \"$$1$$\" evenly into parts, taking of those parts, its fraction unit is ;\n(2) $$\\frac{20}{20}$$ means dividing the unit \"$$1$$\" evenly into parts, taking of those parts, its fraction unit is ."}, {"key": "2743", "content": "In the squares shaded with shadows, mark the ones which are mines with an \"X\", and those that are safe zones with an \"O\". Question: What about the square in the $$7$$th row and the $$4$$th column?\n question_2743-image_0"}, {"key": "2744", "content": "The following image shows a $$4\\times 4$$ area with $$3$$ trees planted. Now it's required to set up tents on the vacant land where no trees are planted, and the tents must be adjacent to a tree. No two tents can occupy squares that share a common point, and the number of tents in each row and each column is shown on the rightmost side and the bottom, respectively. Please draw the location of the tents. Is there a tent in the 2nd row and 4th column?\n question_2744-image_0"}, {"key": "2745", "content": "In a cattle farm, $$3$$ cows can finish $$24$$ bales of hay in $$2$$ days. Now, $$5$$ cows can finish $$140$$ bales of hay a day."}, {"key": "2746", "content": "Class A has $$33$$ students, and Class B has $$22$$ students. In an examination, the average score of Class A is $$80$$ points, and the combined average score of Class A and Class B is $$82$$ points. Find the average score of Class B."}, {"key": "2747", "content": "Using the digits $$1$$, $$3$$, $$6$$, you can form different natural numbers without repeating digits."}, {"key": "2748", "content": "Uncle worker planted trees on one side of the road. He planted a total of $$10$$ trees from one end to the other (trees planted at both ends), with each pair of trees spaced $$10$$ meters apart. Calculate the length of this section of the road in meters."}, {"key": "2749", "content": "Calculate: $$\\frac{19}{21}+\\frac{10}{21}=$$, $$\\frac{9}{13}-\\frac{2}{13}=$$."}, {"key": "2750", "content": "Column subtraction calculation: $$17\\times 32\\times 125\\times 25=$$."}, {"key": "2751", "content": "Calculate: $$7\\times 22\\times 26\\times 2$$=\uff0e"}, {"key": "2752", "content": "A little grasshopper is hopping around, it can only jump from one point to either of its two adjacent points at each time. It starts from point $$A$$ and jumps $$3$$ times, please draw a tree diagram to show all the different ways it can jump.\n question_2752-image_0"}, {"key": "2753", "content": "Quickly decide, $$11$$, $$17$$, $$20$$, $$39$$, $$24$$, is the sum odd or even?"}, {"key": "2754", "content": "The side length of a square is $$5\\text{cm}$$, its perimeter is $$\\text{cm}$$, and its area is $$\\text{cm}^2$$."}, {"key": "2755", "content": "A rectangle and a square have the same perimeter. The rectangle is $$10$$ meters long and its width is $$2$$ meters less than its length. The area of the rectangle and the area of the square are."}, {"key": "2756", "content": "The library has a total of $$420$$ books, including mathematics books, science books, and comic books. The number of mathematics books is $$2$$ times that of comic books, and the number of science books is $$3$$ times that of comic books. So, there are comic books, mathematics books, and science books respectively."}, {"key": "2757", "content": "Calculate: $$10\\times 3\\times 19\\div 3=$$."}, {"key": "2758", "content": "(1) The area of the rectangle is $$20\\text{c}{{\\text{m}}^{2}}$$, the length is $$5$$ cm, and the width is in cm.\n(2) The area of the square is $$25\\text{c}{{\\text{m}}^{2}}$$, with the side length in cm."}, {"key": "2759", "content": "$$\\left( 90+18+36 \\right)\\div 9=$$."}, {"key": "2760", "content": "Calculate: $$77\\times 47+77\\times 53=$$\uff0e"}, {"key": "2761", "content": "$$125\\times (8\\div 10)=$$."}, {"key": "2762", "content": "As shown in the diagram, the area of the square is square centimeters, and the area of the rectangle is square centimeters.\n question_2762-image_0"}, {"key": "2763", "content": "Eddie did such a problem: a number plus $$3$$, minus $$5$$, multiplied by $$4$$, divided by $$6$$ equals $$16$$, this number is."}, {"key": "2764", "content": "As shown in the diagram, it is known that $$\\angle AOB=60{}^\\circ $$, $$OC$$ is the angle bisector of $$\\angle AOB$$ ($$OC$$ divides $$\\angle AOB$$ equally into two identical angles), then the degree of $$\\angle AOC$$ is degrees.\n question_2764-image_0"}, {"key": "2765", "content": "A four-digit number composed of $$1$$ and $$2$$ without consecutive $$2$$s (for example: $$2112$$) has a total of."}, {"key": "2766", "content": "As shown, $$ABCDEF$$ is a regular hexagon, a frog starts at vertex $$A$$, and it can jump to one of the two adjacent vertices each time. If it can jump to point $$C$$ within $3$ moves, it stops jumping (for example: $$A-B-C$$); if it cannot reach point $$C$$ within $3$ moves, it also stops after making $3$ moves (for example: $$A-F-E-F$$). Then, the total number of different possible jumping paths the frog can take from start to stop is .\n question_2766-image_0"}, {"key": "2767", "content": "$$ABCD$$ four people passing the ball to each other, starting with $$A$$ for the first pass, after $4$ passes, the ball just happens to return to $$A$$'s hands, then the total number of different passing methods is."}, {"key": "2768", "content": "Dakuan and Eddie plan to go to the library, stadium, and amusement park. The doctor stipulates they can only play for five days, changing places each day, starting from the library closest to home. Moreover, after playing for $$4$$ days, they must return to the library on the fifth day. In total, Dakuan and Eddie have several ways to play."}, {"key": "2769", "content": "As shown in the diagram, an ant needs to walk from one vertex $$A$$ of a triangular prism to another vertex $$B$$ along its edges, visiting each point at most once. There are different routes for the ant to take.\n question_2769-image_0"}, {"key": "2770", "content": "$$A$$, $$B$$, $$C$$, $$D$$ four children pass the ball to each other, starting with $$A$$ for the 1st pass. After 3 passes, the ball just happens to return to $$A$$'s hands. How many different ways of passing the ball are there? ( )"}, {"key": "2771", "content": "Eddie repeatedly writes 'I love the motherland' in sequence, totaling $$76$$ Chinese characters, the last one is ( ) character."}, {"key": "2772", "content": "Xiao Ding arranges beads of the same size in red, white, and black in a pattern: first $$2$$ reds, then $$1$$ white, followed by $$3$$ blacks. Can you calculate what color the $$152$$nd bead is?"}, {"key": "2773", "content": "Calculate: (1) $$23\\times 4\\times 25$$=\n(2) $$125\\times 13\\times 8$$=\n(3) $$48\\times 125$$=\n(4) $$45\\times \\left( 100+2 \\right)$$ =\n(5) $$125\\times (80+4)$$=\n(6) $$24\\times \\left( 50-5 \\right)$$="}, {"key": "2774", "content": "Calculate: $$49\\times 772+51\\times 775=$$."}, {"key": "2775", "content": "Calculate: $$78\\times 1994+22\\times 1996=$$"}, {"key": "2776", "content": "Calculate: (1) $$78\\times 75+75\\times 22$$ = (2) $$56\\times 778+56\\times 222$$ ="}, {"key": "2777", "content": "Compute:\n$$99\\times 78+33\\times 66=$$.\n$$25\\times 22+50\\times 21+75\\times 12=$$."}, {"key": "2778", "content": "Calculate: \n(1) $$23\\times 67+23\\times 32+23$$=\uff0e\n(2) $$34\\times 25+87\\times 22+34\\times 62+87\\times 44$$=\uff0e"}, {"key": "2779", "content": "Calculate: $$\\left( 12\\times 5 \\right)\\div \\left( 5\\div 3 \\right)\\div \\left( 4\\div 6 \\right)\\times \\left( 4\\div 3 \\right)=$$"}, {"key": "2780", "content": "A, B, and C have a total of $$100$$ extracurricular books. The quotient of A's books divided by B's books, and C's books divided by A's books, is $$5$$, and the remainder is also $$1$$ in both divisions. Then, how many books does B have?"}, {"key": "2781", "content": "Using a wire that is $$64$$ cm in length to form a rectangle with a length of $$20$$ cm, the width of this rectangle is ( )."}, {"key": "2782", "content": "$$125\\times 365\\times 8=$$( )\uff0e"}, {"key": "2783", "content": "Compute: (1) $$4900\\div 4\\div 25$$ (2) $$21\\times 15\\div 5$$"}, {"key": "2784", "content": "Square A and square B, it is known that the perimeter of square A is $$36$$ cm, then the perimeter of square B is ( ) cm.\n question_2784-image_0"}, {"key": "2785", "content": "The number of male and female workers in the textile factory is the same. If $$40$$ male workers are transferred out and $$60$$ female workers are transferred in, at this time, the number of female workers is $$5$$ times the number of male workers. How many male workers were there originally in the textile factory?"}, {"key": "2786", "content": "A certain month has five Saturdays, the date of the last Saturday is an even number, the day of the $$1$$st of this month is."}, {"key": "2787", "content": "On the eve of the Mid-Autumn Festival, the company distributed shopping vouchers to the employees. Each person in the marketing department received $$3$$ mooncake vouchers and $$2$$ fruit vouchers, while each person in the technical department received $$2$$ mooncake vouchers and $$3$$ fruit vouchers. It is known that a total of $$110$$ mooncake vouchers and $$90$$ fruit vouchers were distributed. Thus, there are people in the marketing department and people in the technical department."}, {"key": "2788", "content": "There are two kinds of strange animals in the cage, a two-headed bird and a two-headed deer. Each two-headed bird has $$2$$ legs, and each two-headed deer has $$4$$ legs. It is known that they have a total of $$40$$ heads and $$68$$ legs in total. There are two-headed birds and two-headed deer."}, {"key": "2789", "content": "Li Ming and Zhang Liang take turns typing a document, with Li Ming typing $$15$$ pages a day and Zhang Liang typing $$10$$ pages a day. They typed for $$25$$ days in a row, averaging $$12$$ pages a day. How many days did Zhang Liang type?"}, {"key": "2790", "content": "In the zoo, there are some sika deer and ostriches, with a total of $$208$$ legs. There are $$20$$ more ostriches than sika deer, and the number of sika deer is ( )."}, {"key": "2791", "content": "Chickens and rabbits in the same cage, there are a total of $$30$$ heads, $$100$$ feet, there are ( ) chickens."}, {"key": "2792", "content": "In Grade 4 Class A, there are $$12$$ people who like oranges, $$10$$ people who like tangerines, and $$2$$ people who like both oranges and tangerines. Thus, the total number of people in Grade 4 Class A who like either oranges or tangerines is ( ) people."}, {"key": "2793", "content": "Class 5-1 has a total of $$52$$ people, each person knows at least one of two games: chess or checkers. Among them, there are $$32$$ people who can play chess and $$28$$ people who can play checkers. There are ( ) people who can play both games."}, {"key": "2794", "content": "Class 4(2) has $$48$$ students. During a self-study class, $$30$$ students finished their Chinese homework, $$20$$ students finished their Math homework, and $$6$$ students did not finish either Chinese or Math homework.\n($$1$$) How many students finished both Chinese and Math homework?\n($$2$$) How many students finished only the Chinese homework?"}, {"key": "2795", "content": "Guangming Primary School's fifth-grade extracurricular activities include groups for sports, music, and calligraphy, with participation numbers of $$54$$, $$46$$, and $$36$$ respectively. There are $$4$$ students who participate in both sports and music groups, $$7$$ students who participate in both sports and calligraphy groups, and $$10$$ students who participate in both music and calligraphy groups. There are $$2$$ students who participate in all three groups. The total number of fifth-grade students at Guangming Primary School participating in extracurricular activities is ."}, {"key": "2796", "content": "A class has $$56$$ students, $$28$$ students participated in the English competition, $$27$$ participated in the Math competition, if there are $$25$$ students who did not participate in both, then the number of students who participated in both English and Math competition is ."}, {"key": "2797", "content": "Grade 3 class 3 has $$45$$ students participating in a subject competition. After the results were announced, there were $$10$$ students who got full marks in mathematics, $$3$$ students who got full marks in both mathematics and Chinese, and there were $$29$$ students who didn't get full marks in these two subjects. How many students got full marks in Chinese?"}, {"key": "2798", "content": "\nSecond graders in class 3 are having a crisp noodle showdown. There are $$17$$ children who chose Little Raccoon crisp noodles, $$19$$ children did not choose Magician crisp noodles, if there are $$7$$ children who neither chose Magician nor Little Raccoon, then, there are children who chose both Magician and Little Raccoon."}, {"key": "2799", "content": "The clothes below belong to the little squirrel. How many different combinations can the little squirrel make to form a set of clothes?\n question_2799-image_0"}, {"key": "2800", "content": "Three people, A, B, and C, pass the ball to each other, and each time the ball must be passed on. Starting with A for the first pass, how many ways can the ball be passed to A for the fourth time?"}, {"key": "2801", "content": "Monday's menu: Meat dishes: Braised Beef, Meatballs; Vegetarian dishes: Cold Mixed Tomatoes, Stir-fried Mustard Greens, Stir-fried Bean Sprouts. Meal requirement: Each set meal should include one meat dish and one vegetarian dish. How many different meal combinations are there? \uff08 \uff09"}, {"key": "2802", "content": "Split the unit \u201c$$1$$\u201d into $$10$$ equal parts, take $$7$$ out of them, represented by the fraction (    ), its fractional unit is (    ), and the number of fractional units is (    ) pieces."}, {"key": "2803", "content": "Which of the following ribbons is the longest ()?"}, {"key": "2804", "content": "Convert the following fractions to decimals, and decimals to fractions: $$0.7=$$, $$1.9=$$, $$3.26=$$;$$\\frac{4}{10}=$$, $$3\\frac{3}{5}=$$, $$\\frac{21}{20}=$$."}, {"key": "2805", "content": "Compare the size of the following two numbers:\n$$5.99$$$$6.1$$;\n$$12.02$$$$12.20$$;\n$$0.044$$$$0.0433$$;\n$$22.75$$$$22.750$$."}, {"key": "2806", "content": "Compare the size: $$0.75$$ and $$\\frac{7}{10}$$."}, {"key": "2807", "content": "A certain two-digit decimal, when rounded and truncated to one decimal place, results in the sum of the two one-digit decimals being $$50.8$$. Therefore, the original two-digit decimal is at least."}, {"key": "2808", "content": "Compute: $$2020.20-1006.674-(1000.326-652.8)=$$."}, {"key": "2809", "content": "Calculate: $$9.7+9.97+9.997+9.9997+9.99997=$$\uff0e"}, {"key": "2810", "content": "At exactly $$10$$ o'clock, the angle formed by the hour and minute hands on the clock that does not exceed $$180$$ degrees is degrees."}, {"key": "2811", "content": "Judging right from wrong.\n(1) The larger the angle, the longer its two sides.\n(2) An angle greater than $$90^\\circ$$ is called an obtuse angle.\n(3) Subtracting an acute angle from a right angle always results in an acute angle.\n(4) An angle of $$20^\\circ$$ viewed through a magnifying glass that magnifies 5 times is still $$20^\\circ$$."}, {"key": "2812", "content": "acute angle$$+$$acute angle$$=$$( )\uff0e"}, {"key": "2813", "content": "The right image contains ( ) angles.\n question_2813-image_0"}, {"key": "2814", "content": "There are a total of ______ squares in the picture.\n question_2814-image_0"}, {"key": "2815", "content": "How many triangles are there in the picture? \n question_2815-image_0"}, {"key": "2816", "content": "After dividing each side of an equilateral triangle into four equal parts and then connecting the corresponding segments, the figure below is obtained. How many upright triangles are there in the figure?\n question_2816-image_0"}, {"key": "2817", "content": "In the figure below, there are a total of triangles. question_2817-image_0"}, {"key": "2818", "content": "There are a total of squares in the picture.\n question_2818-image_0"}, {"key": "2819", "content": "As shown in the picture, there are $$7$$ nails on a wooden board, and a total of different triangles can be formed using rubber bands.\n question_2819-image_0"}, {"key": "2820", "content": "In the picture, there are a total of triangles, line segments.\n question_2820-image_0"}, {"key": "2821", "content": "When the father was the age the daughter is now, she was just four years old; when the father is $$79$$ years old, the daughter's age is exactly what the father's age is now, then the daughter's current age is ( )."}, {"key": "2822", "content": "The little elephant asked the big elephant: \"Mom, how old are you this year?\" The big elephant answered: \"When I was your age, you were only $$3$$ years old; when you reach my age, I will be $$39$$ years old.\" So, their ages this year are ()."}, {"key": "2823", "content": "The combined current age of father and mother is $$72$$ years. In five years, the father will be $$6$$ years older than the mother. The age of the father this year is ( ) years old, and the mother is ( ) years old."}, {"key": "2824", "content": "When $$x=3$$, $$y=2$$, $${{x}^{2}}+4y=$$."}, {"key": "2825", "content": "Given $$7^{m}=10$$, then the value of $$({7^{m}})^{3}$$ is."}, {"key": "2826", "content": "Given $$M=2a+b-3$$, $$N=7b-3a+10$$, if $$a+b=27$$, $$b-a=3$$, then $$2N+M=$$."}, {"key": "2827", "content": "If $${{3}^{m}}={{3}^{1}}\\times {{3}^{3}}\\times {{3}^{5}}\\times {{3}^{7}}\\times {{3}^{9}}$$, then $$m=$$."}, {"key": "2828", "content": "Which of the following expressions is equal to $${{a}^{2}}$$? ( )"}, {"key": "2829", "content": "In the schematic map of the street below, area $$C$$ is not passable due to construction, and there is a shortest route from $$A$$ to $$B$$.\n question_2829-image_0"}, {"key": "2830", "content": "As shown in the figure, starting from point $$A$$ to point $$B$$, there are a total of different shortest routes.\n question_2830-image_0"}, {"key": "2831", "content": "As shown in the diagram, to go from point $$A$$ to point $$B$$, one must pass through segment $$CD$$ and must not pass through segment $$EF$$. There are a total of different shortest routes.\n question_2831-image_0"}, {"key": "2832", "content": "A bee starts from $$A$$ and returns to $$B$$. It can only crawl to the adjacent beehive on the right side in each move and is not allowed to go backwards. There are a total of different methods.\n question_2832-image_0"}, {"key": "2833", "content": "As shown in the diagram, starting from point $$A$$ to point $$B$$, there are a total of different shortest routes.\n question_2833-image_0"}, {"key": "2834", "content": "As shown in the diagram, there are paths from point $$A$$ to point $$B$$ that represent the shortest route.\n question_2834-image_0"}, {"key": "2835", "content": "As shown in the street map, starting from $$A$$ and passing through the crossroad $$B$$, but not through $$C$$ to $$D$$, there are different shortest routes. question_2835-image_0"}, {"key": "2836", "content": "As shown in the diagram, point $$D$$ is under construction and cannot be passed through, so to go from $$A$$ to $$B$$, the total number of different paths to take the shortest route is ( ). question_2836-image_0"}, {"key": "2837", "content": "The 'Hope Learning' in the figure below has a different way of reading.\n question_2837-image_0"}, {"key": "2838", "content": "Teacher Xiao Si distributes exercise books to the students, giving $$6$$ books per student and still lacking $$20$$ books. If each student is given $$4$$ books, there still lacks $$2$$ books. How many exercise books are there in total? How many students are there? ( )"}, {"key": "2839", "content": "Distribute a bag of sugar to the children in the kindergarten. If each child gets $$4$$ candies, there would be $$5$$ candies left; if each child gets $$5$$ candies, there would be $$1$$ child who only gets $$1$$ candy. How many candies are in this bag? ( )"}, {"key": "2840", "content": "Jelly Teacher distributes candies to the students. If each person gets $$7$$ candies, there are $$6$$ candies left; if each person gets $$8$$ candies, then it exactly runs out. So, how many students are there in total? ( )"}, {"key": "2841", "content": "Xiaoqiao reads a novel. If she reads $$30$$ pages every day, she will finish the whole book one day later than the scheduled date; if she reads $$35$$ pages every day, she will read $$5$$ pages less on the last day; if she reads $$33$$ pages every day, she needs to read pages on the last day to finish the book according to the scheduled date."}, {"key": "2842", "content": "The teacher distributes reward cards to the new students, giving each child the same amount. If each child receives $$10$$ cards, there are $$30$$ cards short; if each child receives $$8$$ cards, there are still $$8$$ cards short. Question: How many students are there in total, and how many reward cards are there?"}, {"key": "2843", "content": "The new students at school are going to move into the dormitory, and each dormitory has the same number of residents. If each room houses $$4$$ people, there will be $$20$$ people left over; if each room houses $$8$$ people, there will be $$4$$ people left over. There are dormitory rooms, little friends."}, {"key": "2844", "content": "A school organized a group of teachers and students to attend a conference in another city and reserved some rooms in advance. If each room houses 3 people, there would be 20 people without a place to stay; if each room houses 6 people, the last 2 people could each have their own room. So, the total number of teachers and students attending the conference is."}, {"key": "2845", "content": "Students from the Happy Elementary School Young Pioneers went to the meeting room for a meeting. If each bench seats $$3$$ people, there are $$7$$ extra people; if each bench seats $$4$$ more people, there are $$3$$ extra benches. There are people from the Young Pioneers attending the meeting in the meeting room."}, {"key": "2846", "content": "The kindergarten gives candies to the award-winning children. If each child is given $$6$$ pieces, there would be $$12$$ pieces short. If each child is given $$9$$ pieces, there would be $$24$$ pieces short. How many pieces of candy are there in total? \uff08 \uff09"}, {"key": "2847", "content": "The school allocates dormitories for new students. If each room houses $$3$$ people, then there are $$22$$ extra people; if each room houses $$5$$ more people, then there is $$1$$ room left over. How many rooms are there in the dormitory?"}, {"key": "2848", "content": "The administrator evenly distributes a pile of peaches to all monkeys. If each monkey gets 4 peaches, there are 6 peaches left; if each monkey gets 6 peaches, there are 2 monkeys who do not get any peaches. How many monkeys are there in the group?"}, {"key": "2849", "content": "Distributing $$6$$ identical exercise books to $$2$$ people, with each person getting at least $$1$$ book, there are ( ) different ways to do this."}, {"key": "2850", "content": "Break $$6$$ into the sum of two natural numbers. How many possibilities are there? (Different orders of the same addends are considered the same combination)"}, {"key": "2851", "content": "Grandma Zhang went to the supermarket and bought $$12$$ boxes of Guangming milk. She found that these milks need to be packed into $$2$$ identical bags, and each bag can only hold up to $$10$$ boxes.$$ Grandma Zhang has a total of different methods to pack them."}, {"key": "2852", "content": "Among the 10 positive integers from $$1$$ to $$10$$, each time two distinct numbers are taken out so that their sum is a multiple of $$4$$, there are different methods to do this."}, {"key": "2853", "content": "Express $$8$$ as the sum of several (two or more) non-$$0$$ natural numbers, there are different ways to do so."}, {"key": "2854", "content": "$${{1876}^{2}}-2\\times 1876\\times 376+{{376}^{2}}=$$."}, {"key": "2855", "content": "$$(123+231+312)\\div 6=$$."}, {"key": "2856", "content": "Given $${{a}^{2}}+{{b}^{2}}=10$$ and $$ab=4$$, then $${{(a+b)}^{2}}=$$."}, {"key": "2857", "content": "Instantly solve the algebraic expression $${{54}^{2}}-2\\times 54\\times 46+{{46}^{2}}$$, the calculation result is:"}, {"key": "2858", "content": "Calculate using the difference of squares formula: $$416\\times 384=\uff08 \uff09$$ ."}, {"key": "2859", "content": "The perimeter of a rectangle with a length of $$10\\text{cm}$$ and a width of $$2\\text{cm}$$ is ( )."}, {"key": "2860", "content": "The correct result of calculating $${{(x+2)}^{2}}$$ is ( )."}, {"key": "2861", "content": "Compute: $$2009\\times 2009-2008\\times 2008=$$ ( )."}, {"key": "2862", "content": "Calculate: $$2014 \\times 20132012 - 2012 \\times 20132014$$"}, {"key": "2863", "content": "In the picture below, 9 identical rectangles form a large rectangle. The perimeter of the large rectangle is 90. What is the perimeter of each small rectangle? question_2863-image_0"}, {"key": "2864", "content": "In the bedroom, the floor tiles are laid out in the following dense manner. Five identical small rectangles are combined to form a large rectangle. If the perimeter of a small rectangle is $$40$$ cm, then the perimeter of the large rectangle is in cm. question_2864-image_0"}, {"key": "2865", "content": "As shown in the figure, use identical small rectangles to piece together the following shape. It is known that the total area of the shaded part is $$648$$, and the perimeter of the small rectangle is.\n question_2865-image_0"}, {"key": "2866", "content": "As shown in the diagram, a large rectangle is divided into $$9$$ smaller rectangles, with the perimeters of $$5$$ of them already marked. The perimeter of the large rectangle is in centimeters.\n question_2866-image_0"}, {"key": "2867", "content": "As shown in the diagram, a square paper piece with a side length of $$5\\text{cm}$$ is divided into $$5$$ rectangles along the dotted line. Then, by moving four of these rectangles in the direction and length indicated by the arrows, the perimeter of the resulting shape is $$\\text{cm}$$\uff0e question_2867-image_0"}, {"key": "2868", "content": "In the figure below, the shaded area $$BCGF$$ is a square, the length of segment $$FH$$ is $$18$$ cm, the length of segment $$AC$$ is $$24$$ cm, then the perimeter of rectangle $$ADHE$$ is cm.\n question_2868-image_0"}, {"key": "2869", "content": "Using four identical rectangles to form a large square with an area of $$100$$ square centimeters (as shown in the picture below), the perimeter of each rectangle is in centimeters.\n question_2869-image_0"}, {"key": "2870", "content": "As shown in the figure, a square is divided into $$4$$ identical rectangles, each with a perimeter of $$20$$ centimeters. Then the area of this square is square centimeters. ( )\n question_2870-image_0"}, {"key": "2871", "content": "Two squares, each with a side length of $$6$$ centimeters, are joined together to form a large rectangle. The perimeter of the resulting rectangle is less than the combined perimeters of the original two squares by centimeters.\n question_2871-image_0"}, {"key": "2872", "content": "As shown in the figure, the shaded part is a square. What is the perimeter of the largest rectangle in the picture? (Unit: decimeters)\n question_2872-image_0"}, {"key": "2873", "content": "It is known that the total weight of Xiao Su and Xiao Hei is $$200$$ kilograms, among which the weight of Xiao Su is $$3$$ times that of Xiao Hei. Then, the weight of Xiao Hei is ( ) kilograms."}, {"key": "2874", "content": "Assemble 5 squares, each with a side length of 1 cm, which of the following does not have the same perimeter as question_2874-image_0? ( )"}, {"key": "2875", "content": "Divide $$100$$ apples into two groups, where one group has exactly $$10$$ more than $$5$$ times the other group. Then, the smaller group has apples, and the larger group has apples."}, {"key": "2876", "content": "Three students, A, B, and C, each wrote a number on a card.\nA showed their number to B, and B said, \"The number I wrote is $$2$$ times less than yours minus $$3$$.\" \nB showed their number to C, and C said, \"The number I wrote is $$6$$ times more than yours plus $$10$$.\" \nC showed their number to A, and A said, \"The number you wrote is $$11$$ times more than mine plus $$1$$.\" \nSo the sum of the numbers written by the three people is."}, {"key": "2877", "content": "There are a total of 350 people consisting of the elderly, youths, and children in the park, among them, the number of youths is double that of the elderly, and the number of children is double that of the youths. Therefore, there are \\_\\_ elderly, \\_\\_ youths, and \\_\\_ children."}, {"key": "2878", "content": "The total number of apples in the large basket is $$7$$ times that in the small basket. If $$2$$ apples are added to each basket at the same time, then the number of apples in the large basket will become $$6$$ times that in the small basket. Then, originally, there were several apples in the large basket, and several apples in the small basket."}, {"key": "2879", "content": "The teacher bought the same number of square notebooks, ruled notebooks, and exercise books. He distributed $$1$$ square notebook, $$3$$ ruled notebooks, and $$5$$ exercise books to each student. At this time, there are $$24$$ ruled notebooks left, so how many square notebooks and exercise books are left in total?"}, {"key": "2880", "content": "The sum of two consecutive natural numbers is $$99$$, so the smaller number is, and the larger number is."}, {"key": "2881", "content": "Assuming the number of technology books and story books is the same as the number of literature books, then the total number of these three types of books is ( ) volumes.\n question_2881-image_0"}, {"key": "2882", "content": "Eddy has $$5$$ reward cards, Vi's amount is twice that of Eddy's. After Vi gives Eddy $$8$$ reward cards, the total number of reward cards the two have is ( ) cards."}, {"key": "2883", "content": "$$5$$ persons line up to take a photo, how many arrangements are possible? ( )"}, {"key": "2884", "content": "There are $$2$$ types of chocolate candies in the store: milk flavor and hazelnut flavor; there are $$3$$ types of fruit candies: apple flavor, pear flavor, and orange flavor. Xiao Ming wants to buy some candies for his friend. If Xiao Ming wants to buy $$1$$ kind of fruit candy and $$1$$ kind of chocolate candy, he has several different choices."}, {"key": "2885", "content": "From $$5$$ regular script, $$3$$ clerical script, and $$2$$ cursive script calligraphy pieces, select two pieces of different types of calligraphy works, there are a total of different selection methods."}, {"key": "2886", "content": "There are $$5$$ people standing in a row for a photo, among them, A must stand in the very center, there is a total of different ways."}, {"key": "2887", "content": "How many different ways are there for Da Kuan to visit the doctor? ( ) question_2887-image_0"}, {"key": "2888", "content": "Xiao Hua together with dad, mom, grandpa, and grandma take a family portrait. It is known that Xiao Hua cannot sit in the very middle position. How many different arrangements are possible?"}, {"key": "2889", "content": "If from $$13$$ different meat dishes, $$10$$ different vegetarian dishes, and $$12$$ different kinds of soup, two different types of dishes are to be chosen to pair for lunch, then how many different choices are there?"}, {"key": "2890", "content": "The incorrect equation is ()."}, {"key": "2891", "content": "How many different ways are there for Da Kuan to visit the doctor? ( )\n question_2891-image_0"}, {"key": "2892", "content": "If you select 2 books of different subjects from 15 different Chinese books, 20 different math books, and 10 different foreign language books, how many different choices are there?"}, {"key": "2893", "content": "There are three types of questions in the question bank, with $$30$$, $$40$$, and $$45$$ questions respectively. Each exam requires selecting one question from each of these three types to form a test paper. How many different test papers can be formed from this question bank?"}, {"key": "2894", "content": "As shown in the diagram, a frog is hopping among five lily pads, jumping from one lily pad to an adjacent one each time. If the frog starts on lily pad $$A$$ and then jumps continuously $$4$$ times, then there are a total of different ways to jump.\n question_2894-image_0"}, {"key": "2895", "content": "Along the riverbank, there are $$8$$ clumps of plants, with the number of berries on each pair of adjacent clumps differing by $$1$$. The question is: Is it possible for there to be a total of $$225$$ berries on the $$8$$ clumps of plants? Explain your reasoning."}, {"key": "2896", "content": "Calculate: (1) $$12200\\div 25=$$\uff0e(2) $$20100\\div 804=$$\uff0e"}, {"key": "2897", "content": "There is a square flower bed with a side length of $$5$$ meters, surrounded by a $$1$$ meter wide path on all sides. The area of the path is square meters. question_2897-image_0"}, {"key": "2898", "content": "A rectangular lawn covers an area of $$150$$ square meters, with a width of $$5$$ meters. Grandpa Zhang walks around the lawn for $$3$$ laps every afternoon. He walks meters every day."}, {"key": "2899", "content": "A square rice field has an area of $$900$$ square meters. If each side is increased by $$20$$ meters, the new area is square meters."}, {"key": "2900", "content": "This year, XinXin is $$6$$ years older than PengPeng. $$3$$ years ago, the sum of their ages was $$48$$ years old. This year, XinXin is __ years old, PengPeng is __ years old."}, {"key": "2901", "content": "(10 points) Mr. Zhang and Mr. Li together have $$100$$ yuan. If Mr. Zhang is given another $$20$$ yuan, then he will have twice the amount of money as Mr. Li. Originally, Mr. Zhang had yuan."}, {"key": "2902", "content": "The image contains a parallelogram. question_2902-image_0"}, {"key": "2903", "content": "Given the vertical puzzle as shown: $$\u2606=$$, $$\u25b3=$$?\n question_2903-image_0"}, {"key": "2904", "content": "In the addition formula shown in the figure below, each letter represents a number, and different letters represent different numbers. What is the four-digit number represented by $$\\overline{EFFC}$$ ( )\uff0e\n question_2904-image_0"}, {"key": "2905", "content": "What is the second addend in the following vertical addition? ( ).\n question_2905-image_0"}, {"key": "2906", "content": "Calculate: $$32+103\\times 13+210\\times 50=$$"}, {"key": "2907", "content": "Calculate: $$32\\times 8+23\\times 250+123\\times 601=$$"}, {"key": "2908", "content": "In the vertical multiplication question_2908-image_0, when calculating $$4\\times 3$$, what is actually being calculated is ( )."}, {"key": "2909", "content": "In the vertical equation shown in the figure below, $$64$$ represents ( ) .\n question_2909-image_0"}, {"key": "2910", "content": "The divisor is $$6$$, and the dividend is $$30$$. The equation is ( )."}, {"key": "2911", "content": "In the following equations, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers. Find the numbers represented by the Chinese characters to make the equation valid, and find out: $$I$$+$$love$$+$$mathematics$$+$$=$$.\n question_2911-image_0"}, {"key": "2912", "content": "As shown in the diagram, different Chinese characters in the equation represent different numbers. It is known that: \"\u7ea7$$=5$$\", then the three-digit number represented by \"$$\\overline{{\u5b66\u800c\u601d}}$$\" is.\n question_2912-image_0"}, {"key": "2913", "content": "In the following problem, each Chinese character represents a number, different characters represent different numbers, and the same characters represent the same numbers. If the equation holds, then \u201c$$\\overline{{force to host the Olympic Games}}$$\u201d represents the six-digit number is.\n question_2913-image_0"}, {"key": "2914", "content": "In the vertical calculation below, the same letter represents the same number, and different letters represent different numbers. Then the four-digit number $$\\overline{tavs}=$$.\n question_2914-image_0"}, {"key": "2915", "content": "Natural numbers $$12$$, $$456$$, $$1256$$ share a common characteristic, they all have at least two digits, and for any two adjacent digits, the left digit is less than the right digit. We call these \"Ascending Numbers.\" Using the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, we can form several \"Ascending Numbers\"."}, {"key": "2916", "content": "A, B, and C, three kids line up to take a photo, there are a total of different ways they can arrange themselves."}, {"key": "2917", "content": "Eddie uses several RMB banknotes of \u00a51, \u00a55, and \u00a510 (enough of each denomination) to buy a \u00a520 cup. Eddie has a total of different payment methods."}, {"key": "2918", "content": "There are three different denominations of coins in a certain place, as shown in the picture, assuming you have the following four coins. How many different amounts of money can you make in total.\n question_2918-image_0"}, {"key": "2919", "content": "Each book costs $$35$$ yuan, Xiao Ming bought $$24$$ books. Calculate the total cost of buying the books using long multiplication, the step indicated by the arrow in the long multiplication represents ( ).\n question_2919-image_0"}, {"key": "2920", "content": "As shown in the diagram, in the $$23\\times 14$$ vertical calculation, the second $$23$$ represents ( ).\n\n\n\n\n2\n3\n\n\nX\n1\n4\n\n\n\n9\n2\n\n\n2\n3\n\n\n\n3\n2\n2"}, {"key": "2921", "content": "Complete the following vertical calculation so that it is correct.\n 7  9 +  5  4 4 3"}, {"key": "2922", "content": "Each vehicle uses $$4$$ wheels, with $$145$$ wheels, the maximum number of vehicles that can be equipped so that each vehicle has $$4$$ wheels."}, {"key": "2923", "content": "Set up in vertical format for calculation. $$3\\times 30=$$  $$2\\times 60=$$  $$4\\times 50=$$"}, {"key": "2924", "content": "In the vertical calculation below, the number indicated by the arrow represents ( ).\n question_2924-image_0"}, {"key": "2925", "content": "In the vertical calculation on the right, $$560$$ represents ( ) .\n question_2925-image_0"}, {"key": "2926", "content": "Xiaodong finished $$27$$ problems in $$3$$ hours. According to this speed, he can complete $$72$$ problems in $$8$$ hours, and to complete $$108$$ problems he would need $$12$$ hours."}, {"key": "2927", "content": "A basket of peaches can feed $$10$$ monkeys for $$5$$ days. After $$2$$ days, $$4$$ monkeys leave. How many days can the remaining peaches feed the remaining monkeys? (Assuming each monkey eats the same amount of peaches per day)"}, {"key": "2928", "content": "$$3$$ mice $$5$$ days to eat $$45$$ corns, at this rate, $$8$$ mice need days to eat $$288$$ corns."}, {"key": "2929", "content": "3 people plant 150 trees in 5 hours, if each person plants the same number of trees per hour, how many trees can 6 people plant in 7 hours."}, {"key": "2930", "content": "The greening team planted $$201$$ trees in $$3$$ days, and still needs to plant $$737$$ trees. Based on this work efficiency, the total number of days required to complete the task is\uff0e"}, {"key": "2931", "content": "A certain orchard harvested a total of $$240$$ pears. If each box contains $$3$$ layers and each layer holds $$8$$ pears, how many boxes can be filled in total? Formulate the expression as ( )."}, {"key": "2932", "content": "Three cats catch $$3$$ mice in $$1$$ hour. Based on this calculation, to catch $$100$$ mice in $$10$$ hours, you should send ( ) kittens."}, {"key": "2933", "content": "A worker needs to grind $$200$$ kilograms of flour, $$3$$ hours were spent grinding $$60$$ kilograms, given this rate, how many more hours are needed to grind the remaining flour? ( )"}, {"key": "2934", "content": "The average age of everyone in the classroom is $$11$$ years old. If excluding one $$30$$-year-old teacher, the average age of the rest is $$10$$ years old. How many people are in the classroom?"}, {"key": "2935", "content": "In the future, in Class 5, Grade 3 of the elementary school, Group 1 has $$5$$ girls and $$3$$ boys. It is known that in a math test, the average score of the girls was $$90$$, and the average score of the boys was $$82$$. Therefore, the average score of this group of students is points."}, {"key": "2936", "content": "The average of four numbers is $$98$$. Removing one number, the average of the three remaining numbers becomes $$89$$. The number removed is."}, {"key": "2937", "content": "The sum of two numbers, A and B, is $$620$$. If a third number, C, is added, the average of the three numbers is $$9$$ more than the average of numbers A and B alone. Find number C."}, {"key": "2938", "content": "Xiaochuan finished reading a storybook this week. On the first day, she read $$12$$ pages, for the next three days she averaged $$15$$ pages per day, and for the last three days, she read a total of $$20$$ pages. She read an average of ____ pages of the storybook per day."}, {"key": "2939", "content": "The third grade class ($$1$$) has $$40$$ students, it was found after a survey that the average height of the top $$10$$ tallest students is $$3$$ cm taller than the class average height. Then, the average height of the other students is lower than the average height of the top $$10$$ students by cm."}, {"key": "2940", "content": "The number of people in classes A and B are respectively $$40$$ and $$30$$. It is known that the average score of class A is $$93$$ points, and the overall average score of the two classes is $$90$$ points. The average score of class B is ____ points."}, {"key": "2941", "content": "It takes $$6$$ minutes to saw a wooden stick into $$4$$ parts, then it takes ( ) minutes to saw this wooden stick into $$8$$ parts."}, {"key": "2942", "content": "Xiao Tie begins to plant trees on both sides of a road that is $$120$$ meters long, planting one tree every $$5$$ meters, totaling the number of trees that can be planted. (Trees are planted at both ends)"}, {"key": "2943", "content": "To build a new circular fountain, if statues are placed every $$2$$ meters around the circumference of the fountain, exactly $$8$$ statues can fit. Question: What is the circumference of this circular fountain in meters? (The width of the statues is negligible)"}, {"key": "2944", "content": "An electronic flea jumps one step at a time, from one circle to the adjacent circle. Now, a red flea starting from the circle marked with the number \u201c0\u201d jumps 1991 steps in the clockwise direction and lands in a circle. A black flea also starts from the circle marked with the number \u201c0\u201d, but it jumps 1949 steps in the counterclockwise direction and lands in another circle. Question: What is the product of the numbers in these two circles.\n question_2944-image_0"}, {"key": "2945", "content": "Based on the pattern of the series below, determine the position of $$51$$ as a number in the series. $$1$$, $$2$$, $$3$$, $$4$$, $$6$$, $$7$$, $$8$$, $$9$$, $$11$$, $$12$$, $$13$$, $$14$$, $$16$$, $$17$$\u2026\u2026"}, {"key": "2946", "content": "If today is the $$30$$th of January, we first write $$130$$, and the rule for writing the numbers thereafter is as follows: if the most recently written number is even, divide it by $$2$$ and then add $$2$$ to write it after, if the most recently written number is odd, multiply it by $$2$$ and then subtract $$2$$ to write it after. So we get: $$130$$, $$67$$, $$132$$, $$68$$...; then, the $$2018$$th number in this series is."}, {"key": "2947", "content": "On a point $$A$$ of a regular hexagon, there is a frog. If each side is considered to be $$1$$ cell, and the frog jumps clockwise, with the number of cells jumped following the sequence $$1$$, $$3$$, $$5$$, $$7$$, $$9\\cdots \\cdots $$, then at the $$30$$th jump, the frog lands on point\uff0e\n question_2947-image_0"}, {"key": "2948", "content": "1999 students line up in a row from front to back, counting according to the rules below: If the number reported by a student is a single digit, then the next student should report the sum of this number and 9; if the number reported by a student is a two-digit number, then the next student should report the sum of the last digit of this number and 6. Now, let the first student report the number 1, then the number reported by the last student is."}, {"key": "2949", "content": "At a family gathering, each participating parent brought one child. It is known that every father shook hands with everyone except his own family; each mother did not shake hands with other mothers but did shake hands with every father and child except her own family; children did not shake hands with each other. If a total of $$10$$ families participated in the gathering, then how many handshakes occurred among these $$30$$ people in total."}, {"key": "2950", "content": "Starting from the year AD 1 up to the years 2, 3, all the way to 2013, among these years, please ask how many are odd years and how many are even years."}, {"key": "2951", "content": "Calculate: $$17\\times 4\\times 25$$, $$125\\times 19\\times 8$$, $$12\\times 4\\times 25$$ The correct result is ( )."}, {"key": "2952", "content": "Compute: $$41\\times 236+79\\times 236-236\\times 20$$ =."}, {"key": "2953", "content": "Calculate: $$9039030\\div 43043=$$."}, {"key": "2954", "content": "Calculate: $$40\\times 41\\times 42\\times 43\\times 44\\times 45\\div 28\\div 129\\div 225=$$\uff0e"}, {"key": "2955", "content": "Calculate: $$3752\\div \\left( 39\\times 2 \\right)+5030\\div \\left( 39\\times 10 \\right)=$$\uff0e"}, {"key": "2956", "content": "Calculate: $$999999\\times 444444\\div 666666=$$\uff0e"}, {"key": "2957", "content": "Calculate: $$168\\times 25\\div 14\\times 7\\div 5=$$."}, {"key": "2958", "content": "Viola's house has a special little table, as shown below. She plans to buy some tablecloths to perfectly fit on the tabletop (sides not considered). The area of the tabletop is in square decimeters. (Unit: decimeters)\n question_2958-image_0"}, {"key": "2959", "content": "The sum of three numbers A, B, and C is $$76$$. A is $$6$$ less than double of B, and B is $$4$$ more than triple of C. Find the value of C, B, and A."}, {"key": "2960", "content": "The school bought a total of $$240$$ ping pong balls and badminton shuttlecocks, with the number of ping pong balls being $$4$$ times the number of shuttlecocks. How many of each were bought? ( )"}, {"key": "2961", "content": "Class A and Class B have a total of $$100$$ books. The number of books in Class A is $$3$$ times that of Class B, Class A has ( ) books."}, {"key": "2962", "content": "Xiao Ming divided 100 chess pieces into 3 piles. It is known that the first pile has more than twice the second pile, and the second pile has more than twice the third pile. What is the maximum number of chess pieces in the third pile?"}, {"key": "2963", "content": "Pool A contains $$260$$ cubic meters of water, Pool B contains $$120$$ cubic meters of water. If water flows from Pool A to Pool B at a rate of $$4$$ cubic meters per minute, then after a certain number of minutes, the water in Pool B will be $$4$$ times that of Pool A."}, {"key": "2964", "content": "Three primary schools A, B, and C have a total of $$2999$$ students. It is known that double the number of students in school A, the number of students in school B minus $$3$$, and the number of students in school C plus $$4$$ are all equal. Question: How many students are there in school A, school B, and school C?"}, {"key": "2965", "content": "Xiaoming and his father made dumplings together, and the number of dumplings made by his father was $$5$$ times that of Xiaoming. At dinner, the two ate all the dumplings, and Xiaoming ate $$8$$ more dumplings than his father. If he had eaten $$6$$ more, then the number he ate would be $$4$$ times what he made. How many dumplings did the father eat?"}, {"key": "2966", "content": "The gym is hosting table tennis singles and doubles matches. There are 4 more athletes in the doubles matches than in the singles. There are a total of 13 table tennis tables for the competition. Therefore, the number of athletes in the doubles matches is."}, {"key": "2967", "content": "There are a total of $$140$$ black and white chess pieces, divided into $$5$$ piles, with the black pieces in each pile being $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ times the number of white pieces in sequence. Also, the number of white pieces in the second pile is $$2$$ times that in the first pile, the third pile has $$3$$ times the white pieces of the first pile, the fourth pile has $$4$$ times, and the fifth pile has $$5$$ times the white pieces of the first pile. Then, the total number of white pieces is."}, {"key": "2968", "content": "Harry Potter has a magical magic tree. Each magic tree will bear magical fruits. The first fruit will appear when the tree is planted, and another fruit will grow every night thereafter. If he plants a certain number of magic trees on the first day, the number of magic trees he plants on the second day is double the number of the first day plus 2 trees, and the number of magic trees planted on the third day is triple the number of the first day plus 3 trees. After planting on the third day (before nightfall), all magic trees together have produced 277 magical fruits in total. So, how many magic trees did he plant on the first day?"}, {"key": "2969", "content": "When two numbers are divided, the quotient is $$4$$ and the remainder is $$1$$. If the sum of the dividend, divisor, quotient, and remainder is $$56$$, then the dividend equals."}, {"key": "2970", "content": "Kaka and Rote each have some candies. If Kaka gives Rote $$8$$ candies, Kaka will have $$3$$ fewer candies than Rote. If Rote gives Kaka $$8$$ candies, Kaka will then have $$1$$ more candy than triple the amount of Rote\u2019s candies. How many candies do they have in total?"}, {"key": "2971", "content": "The number of fifth-grade students at a certain school is $$154$$ fewer than the sixth graders. If another $$46$$ students transfer to the sixth grade, the number of sixth-grade students will be $$3$$ times that of the fifth graders. How many students are there in the fifth and sixth grade?"}, {"key": "2972", "content": "Basket A and Basket B have an equal weight of apples. Now, 12 kg of apples are transferred from Basket A to Basket B, resulting in Basket B's apples weighing 2 kg less than triple the weight of Basket A's apples. The weight of apples in Basket A is __ kg, and the weight of apples in Basket B is __ kg."}, {"key": "2973", "content": "There are two strips of paper, one is $$21$$ cm long and the other is $$13$$ cm long. After cutting the same length from both strips, the remaining length of the longer strip is $$3$$ times the length of the shorter strip. How many centimeters is the cut length?"}, {"key": "2974", "content": "In the Asian Cup final, the number of Chinese reporters was 3 times the number of foreign reporters. After the match, 180 Chinese reporters left the venue, and 40 foreign reporters left. The remaining number of Chinese and foreign reporters was equal. The number of Chinese reporters was ___, and the number of foreign reporters was ___."}, {"key": "2975", "content": "The kindergarten aunt has many gummy candies and fruit candies, of which the number of fruit candy packages is $$4$$ times that of gummy candies. Now, she puts together $$2$$ packages of gummy candies and $$2$$ packages of fruit candies in a gift bag each time. After preparing $$120$$ gift bags, she finds that the remaining number of fruit candy packages is $$10$$ times that of gummy candies. Then, how many more gift bags can she prepare?"}, {"key": "2976", "content": "Master Li produced a batch of parts one day, which he divided into two piles: A and B. If 15 parts are taken from pile A and put into pile B, the number of parts in the two piles is equal; if 15 parts are taken from pile B and put into pile A, then the number of parts in pile A is 3 times that of pile B. Therefore, originally, pile A had parts, and Master Li produced parts in total that day."}, {"key": "2977", "content": "There are $$94$$ kilograms of flour and $$138$$ kilograms of rice in the cafeteria, every day $$9$$ kilograms of both flour and rice are used. Days later, the remaining rice is $$3$$ times the amount of the remaining flour."}, {"key": "2978", "content": "Eddy, Viola, and Da Kuan each had some points cards. Eddy gave Viola $$30$$ cards, and then they had the same amount. Next, Viola gave Da Kuan $$40$$ cards, and then Viola and Da Kuan had the same amount. Finally, Da Kuan gave Eddy $$50$$ cards, and at that moment, Eddy had $$3$$ times as many cards as Da Kuan. How many points cards did the three of them have together?"}, {"key": "2979", "content": "The store released two new digital cameras, one is a high-end professional camera, and the other is a regular household camera. The household camera is very cheap, $$4600$$ yuan cheaper than the professional camera. The money to buy $$1$$ professional camera is enough to buy $$4$$ household cameras, and you\u2019d still have $$100$$ yuan left. Then, this professional camera sells for yuan."}, {"key": "2980", "content": "In the library, there are $$150$$ more technology books than comic books. The number of technology books is $$4$$ times the number of comic books minus $$30$$ books. There are books for technology books, and books for comic books."}, {"key": "2981", "content": "Students A, B, and C take turns fetching milk for Grandma Li every morning. If Student A's first time fetching milk was on a Monday, then the $$100$$th time Student A fetches the milk will be on a.-"}, {"key": "2982", "content": "In a certain year, the month of October has five Wednesdays and four Thursdays. The 8th of October that year falls on a weekday."}, {"key": "2983", "content": "$$2018$$ year $$5$$ month $$21$$ day is Monday, then, $$2018$$ year $$9$$ month $$15$$ day is week."}, {"key": "2984", "content": "In the Gregorian calendar, each common year has $$365$$ days, and each leap year has $$366$$ days. The year $$2012$$ is a leap year, and New Year's Day is on Sunday. Therefore, the next year in which New Year's Day also falls on a Sunday is the year ."}, {"key": "2985", "content": "Within a certain month, there are three Saturdays that fall on even-numbered days. The $$18$$th of this month is a ."}, {"key": "2986", "content": "$$2019$$ year $$10$$ month $$1$$ day is Tuesday, what day of the week was $$1949$$ year $$10$$ month $$1$$ day?"}, {"key": "2987", "content": "There are $$7$$ stations between places $$A$$ and $$B$$, and a train travels back and forth between $$A$$ and $$B$$ without stopping. It leaves from $$A$$, reaches the next station each day, and then returns to station number $$7$$ the day after reaching $$B$$, and so on repeatedly - It is known that the $$4$$th time the train enters station number $$4$$ is a Saturday, so what day of the week is it the $$20$$th time the train enters station number $$5$$. question_2987-image_0"}, {"key": "2988", "content": "If April 13 is a Friday, then the number of days until the next 13th that is also a Friday is days."}, {"key": "2989", "content": "A school has scheduled a total of $$86$$ mathematics classes for a semester, with two classes each on Monday, Wednesday, and Friday of odd weeks, and two classes each on Tuesday and Thursday of even weeks. Since the opening ceremony on the first Monday meant no classes were held, classes began from Wednesday. Thus, the last math class falls on a Tuesday."}, {"key": "2990", "content": "The year $$2018$$ has $$53$$ Mondays, and October $$1$$, $$2019$$ is a Monday."}, {"key": "2991", "content": "A month can have up to $$5$$ Sundays, in the $$12$$ months of a year, the maximum number of months that can have $$5$$ Sundays is."}, {"key": "2992", "content": "Xiaosu's weight is $$60$$ kg more than Xiaohei's, where Xiaosu's weight is $$3$$ times that of Xiaohei, then the weight of Xiaohei is ( ) kg."}, {"key": "2993", "content": "For numbers A and B, if number A increases by $$50$$ it equals number B, and if number B increases by $$350$$ it equals three times number A. What are the values of A and B?"}, {"key": "2994", "content": "Eddie and Dengdeng were practicing running on the playground. After a while, Eddie ran 80 meters more than 3 times the distance of Dengdeng. If Dengdeng ran 500 meters less than Eddie, how many meters did Dengdeng and Eddie run together?"}, {"key": "2995", "content": "New Year's Day in $$2013$$ was on a Friday, based on this, do you know what day of the week New Year's Day of $$2017$$ was?"}, {"key": "2996", "content": "June has $$30$$ days, if this month has $$5$$ Mondays and $$5$$ Tuesdays, then Children's Day on June 1st falls on a ( )\uff0e"}, {"key": "2997", "content": "If today is Friday, then the 30th day from today is a Sunday ( )."}, {"key": "2998", "content": "Can the following figure be drawn with one stroke? If it cannot be drawn with one stroke, how many strokes are needed at least?\n question_2998-image_0"}, {"key": "2999", "content": "On the way to school, Xiao Ming heard two people discussing their ages. He heard one say, 'When my age was what yours is now, you were only $$4$$ years old.$$' The other one said, 'When my age is what yours is now, you will be $$61$$ years old.$$' Among them, the younger one is currently $$23$$ years old."}, {"key": "3000", "content": "It is known that among the three generations of grandfather, father, and grandson, the age difference between the grandfather and the father is the same as that between the father and the grandson. The sum of the ages of the grandfather and the grandson is 82 years old. Next year, the age of the grandfather will be exactly 5 times the age of the grandson. Therefore, the grandfather's age this year is, the father's age this year is, and the grandson's age this year is."}, {"key": "3001", "content": "The year before last, the father's age was $$4$$ times the son's age; the year after next, the father's age will be $$3$$ times the son's age. The father's age this year is ____. "}, {"key": "3002", "content": "When the elder brother was celebrating his 30th birthday, the younger brother said: 'By the time I reach the age my brother is at this year, the sum of my brother's age at that time and my age this year will equal our father's age this year.' So, how old is the father this year?"}, {"key": "3003", "content": "Given $${{3}^{m}}\\cdot {{9}^{3}}\\cdot {{27}^{3}}\\cdot 8{{1}^{m}}={{3}^{30}}$$, find $$m=$$."}, {"key": "3004", "content": "If $${{a}^{m}}=2$$, $${{a}^{n}}=3$$, find the value of $${{a}^{3m+2n}}$$."}, {"key": "3005", "content": "Given $$x^n=4$$ and $$y^n=5$$, then $${{\\left( x^2y \\right)}^{2n}}=$$."}, {"key": "3006", "content": "If $$a^{m+n} \\times (3a^{m} \\cdot b^{n+1}) = 3a^{8}b^{3}$$, then $$m=$$, $$n=$$."}, {"key": "3007", "content": "Given $$M=33+11(x+2)$$, $$N=15 (3x-6)+22$$, if $$x=89$$, then $$4M-N=$$."}, {"key": "3008", "content": "$$2\\times 4\\times 8 \\times 16 \\times32 \\times64=$$\uff0e"}, {"key": "3009", "content": "$${{r}^{2}}$$ represents ( )."}, {"key": "3010", "content": "$$a\\times a\\times 1$$ can be abbreviated as ( )."}, {"key": "3011", "content": "Arithmetic sequence: $$7$$, $$11$$, $$15$$, $$ \\ldots $$, the $$30$$th number is."}, {"key": "3012", "content": "There is an arithmetic sequence with $$12$$ numbers. The sum of the first $$3$$ numbers is $$21$$, and the sum of the first $$6$$ numbers is $$69$$. Thus, the total sum of this arithmetic sequence is."}, {"key": "3013", "content": "Given an arithmetic sequence where the 5th term is 34 and the 15th term is 104, then the 10th term of this arithmetic sequence is."}, {"key": "3014", "content": "Calculate: $$1+3+5+7+9+11+13+15+17+19=$$."}, {"key": "3015", "content": "What is the sum of $$1$$$$+4$$$$+5$$$$+8$$$$+9$$$$+12$$$$+\\cdots$$$$+33$$$$+36$$$$+37$$$$+40$$?"}, {"key": "3016", "content": "Xueersi School organized a sports meeting. During the opening ceremony, representative teams from each grade entered the stadium for performances in sequence. First-grade students formed a solid square formation to perform gymnastics, with the outermost layer having $$18$$ people on each side.\n(1) The total number of people in this solid square formation is;\n(2) The total number of children on the outermost layer is."}, {"key": "3017", "content": "Xiaoxiao likes playing Go, and he arranged the pieces on the board to form a two-layer hollow square matrix, with each side of the outer layer having $$14$$ pieces, using a total of pieces.\n question_3017-image_0"}, {"key": "3018", "content": "Some chess pieces were arranged into a four-layer hollow square formation (the diagram is a schematic of a four-layer hollow square formation). Later, Xiaolin added $$28$$ chess pieces, which exactly turned into a five-layer hollow square formation (without moving the original chess pieces). How many chess pieces were there at the very beginning at least.\n question_3018-image_0"}, {"key": "3019", "content": "Count the number of odd vertices in the figure below.\n question_3019-image_0"}, {"key": "3020", "content": "Observe the figure below, it is drawn with a single stroke.\n question_3020-image_0"}, {"key": "3021", "content": "The figure below is a plan view of a park's pathways. To allow visitors to walk through every path without repeating, where should the entrance and exit be respectively? ( ). question_3021-image_0"}, {"key": "3022", "content": "A cleaning vehicle sweeps the streets, with each street being $$1$$ kilometer long. The cleaning vehicle starts from point $$A$$, traverses all the streets, and then returns to $$A$$. What is the shortest path it can take to cover the whole distance in kilometers? Please provide a path for the cleaning. question_3022-image_0"}, {"key": "3023", "content": "The figure below is the street distribution map of a community, with the length of each street shown in the diagram (unit: kilometers), and the letters in the diagram represent the codes for different buildings. A courier departs from a central courier point (located at point $$P$$ between buildings $$C$$ and $$D$$) and must walk through all the streets and return to the courier point. What is the shortest path they can take? How long is the shortest route in kilometers? question_3023-image_0"}, {"key": "3024", "content": "Divide $$10$$ pieces of sugar into $$2$$ piles of unequal amounts, there are a total of different ways."}, {"key": "3025", "content": "Distributing 10 identical lollipops into 3 piles, there are a total of different ways to do so."}, {"key": "3026", "content": "Wei'er takes out three number cards with the numbers $$1$$, $$3$$, and $$8$$ written on them. Therefore, she can form different natural numbers without repeated digits."}, {"key": "3027", "content": "Finish eating $$8$$ pieces of sugar in three days, eat every day, and the amount eaten each day is different, there are a total of different ways to do so."}, {"key": "3028", "content": "Expressing $$10$$ as the sum of $$3$$ natural numbers, how many different ways are there?"}, {"key": "3029", "content": "How many different ways can a PhD divide 10 identical lollipops into 3 piles?"}, {"key": "3030", "content": "Summer has arrived again, and it\u2019s the season to eat watermelon again.$$ Eddie plans to divide $$12$$ identical watermelons into $$3$$ piles, there are several different ways to do so."}, {"key": "3031", "content": "With the digit cards $$0$$, $$1$$, $$9$$, it is possible to form different three-digit numbers. (The picture can be rotated)\n question_3031-image_0"}, {"key": "3032", "content": "$$98+49+2+51=$$\uff0e"}, {"key": "3033", "content": "Fill in the appropriate numbers in the blanks to make the addition vertical expression in the diagram correct, fill in the question mark.\n question_3033-image_0"}, {"key": "3034", "content": "In the following equation, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers. Solve for: I $$+$$ Love $$+$$ Math $$+$$ Learning = question_3034-image_0"}, {"key": "3035", "content": "Fill in the blanks with appropriate numbers to make the subtraction vertical form in the figure below valid. The result of the calculation is. question_3035-image_0"}, {"key": "3036", "content": "In the equation with shapes below, $$\\square $$, $$\\bigcirc $$, and $$\\triangle $$ each represent different numbers. Please calculate what number each shape represents? $$\\square $$ represents, $$\\triangle $$ represents, $$\\bigcirc $$ represents. question_3036-image_0"}, {"key": "3037", "content": "Fill in the blanks with appropriate numbers in the diagram so that the addition problem is correct.\nThe formula should be +=$$1089$$\n question_3037-image_0"}, {"key": "3038", "content": "Calculate: (1) $$45\\times (100+2)$$=\uff1b(2) $$25\\times (50-4)$$="}, {"key": "3039", "content": "Calculate: $$25\\times (100-4)=$$."}, {"key": "3040", "content": "Calculate: (1) $$23\\times 4\\times 25=$$.\n(2) $$125\\times 13\\times 8=$$."}, {"key": "3041", "content": "Calculate: $$13\\times 25+13\\times 75$$=."}, {"key": "3042", "content": "The brother and sister together have $$67$$ picture books, the brother has $$13$$ more books than the sister. The brother has picture books, the sister has picture books."}, {"key": "3043", "content": "Mom bought some lychees and grapes, spending a total of $$60$$ dollars. It is known that the money spent on lychees is $$2$$ times the money spent on grapes minus $$3$$ dollars. How much money was spent on lychees?"}, {"key": "3044", "content": "The strongman Achilles can carry 20 kilograms of goods with one hand, while Socrates can carry 10 kilograms of goods with both hands. The two collaborated to move 450 kilograms of wheat from place A to place B, aiming to complete the move in the shortest possible time. Achilles carried twice as many times as Socrates. So, how many kilograms of wheat did Achilles carry? How many kilograms of wheat did Socrates carry? (Both Achilles and Socrates used both hands to carry goods)"}, {"key": "3045", "content": "Car A and Car B originally had a total of 43 passengers. After arriving at a certain place, 5 passengers got off Car A, and 2 passengers got on Car B. At this time, the number of passengers in Car A was exactly 3 times the number of passengers in Car B. The original number of passengers in Car A was __."}, {"key": "3046", "content": "Students from the second grade of Chunlei Primary School donate books to students in the mountain area. Classes 1, 2, and 3 together donate a total of $$300$$ books. The total number of books donated by Classes 1 and 2 is $$60$$ more than that donated by Class 3. If Class 3 donates $$40$$ more books than Class 1, then: Class 1 donated ; Class 2 donated ; Class 3 donated books."}, {"key": "3047", "content": "There are $$100$$ chess pieces in total, black and white, on the desk, which need to be divided into $$3$$ groups from few to many. The number of black pieces in each group is $$1$$, $$2$$, and $$3$$ times the number of white pieces, respectively. At the same time, the number of white pieces in the second group is exactly $$2$$ times that of the first group, and the number of white pieces in the third group is exactly $$3$$ times that of the first group. How many white pieces are there in total?"}, {"key": "3048", "content": "The sum of two consecutive odd numbers is $$36$$, the smaller of these two numbers is, and the larger is."}, {"key": "3049", "content": "In the orchard, there are a total of 350 trees, including peach trees, pear trees, and apple trees. The number of pear trees is 2 times the number of peach trees plus 10 trees, and the number of apple trees is 3 times the number of peach trees plus 4 trees. Then, the number of pear trees is __ trees."}, {"key": "3050", "content": "The number of passengers on a bus is $$3$$ times that of a car, and there are $$20$$ more passengers on the bus than in the car, then the number of passengers in the car is people."}, {"key": "3051", "content": "The flower shop has a total of $$86$$ flowers including chrysanthemums, roses, and tulips. Among them, the number of chrysanthemums is $$2$$times that of roses, and the number of tulips is $$3$$ times that of roses minus $$4$$ flowers. Question: How many roses, chrysanthemums, and tulips are there?"}, {"key": "3052", "content": "There are a total of $$80$$ trees in the park. The number of poplar trees is $$2$$ times the number of willow trees, and the number of pine trees is $$5$$ times the number of willow trees. There are poplar trees, pine trees, willow trees."}, {"key": "3053", "content": "Big Fat, Medium Fat, and Little Fat ate buns together, consuming a total of $$37$$ buns. Big Fat ate $$10$$ more buns than Little Fat, and Medium Fat ate $$3$$ fewer buns than Little Fat. How many buns did Big Fat eat?"}, {"key": "3054", "content": "The apples in basket A are 3 times the apples in basket B. If 10 kilograms of apples are taken from basket A and given to basket B, at this point, the weight of the apples in the two baskets is equal. Originally, basket A had kilograms of apples."}, {"key": "3055", "content": "Under the banyan tree by the pond, there are a group of chickens, ducks, and geese. Counting them reveals that the number of chickens is 5 times the number of ducks, and the number of geese is 2 times the number of chickens plus 5. Knowing there are a total of 277 birds, how many geese are there?"}, {"key": "3056", "content": "Eddie's pocket money is $$2$$ times that of Dakuan's, Vi's pocket money is $$5$$ times that of Dakuan's, and Vi's pocket money is $$24$$ yuan more than Eddie's. So, Eddie has yuan, Vi has yuan, Dakuan has yuan."}, {"key": "3057", "content": "A certain school's fifth-grade student population is $$154$$ less than the sixth-grade. If $$46$$ more students join the sixth grade, then the number of students in the sixth grade will be three times that of the fifth grade. There are people in fifth grade, and people in sixth grade."}, {"key": "3058", "content": "The number of red balloons in the square is $$80$$ less than the number of yellow balloons, while the number of yellow balloons is $$20$$ more than twice the number of red balloons. So, there are red balloons and yellow balloons."}, {"key": "3059", "content": "There are two strips of paper, one is $$21$$ centimeters long, and the other is $$13$$ centimeters long. After cutting off the same segment from both strips, the remaining length of the longer strip is $$3$$ times that of the shorter strip. The length of the segment cut off is in centimeters."}, {"key": "3060", "content": "The father is $$28$$ years older than his daughter. It is known that in $$5$$ years, the father's age will be $$3$$ times the age of the daughter. Therefore, the father's age this year is $$37$$ years old, and the daughter's age is $$9$$ years old."}, {"key": "3061", "content": "Dad is 22 years older than Xiaoqiang, and together they are 46 years old. Find Dad's age this year."}, {"key": "3062", "content": "Last year, the combined age of the mother and daughter was $$50$$ years old. This year, the mother's age is $$3$$ times the daughter's age. So, how old is the daughter this year?"}, {"key": "3063", "content": "The sister is $$13$$ years old this year, and the brother is $$9$$ years old this year. When the sum of their ages is $$40$$ years old, the sister will be __ years old, and the brother will be __ years old."}, {"key": "3064", "content": "A family of three, the sum of their ages two years ago was $$66$$ years. The mother and father are the same age, and this year the mother's age is $$4$$ times the child's age. How old is each person this year? Answer: child years old, mother and father years old"}, {"key": "3065", "content": "A said to B: 'When I was your current age, you were only $$5$$ years old.' B said to A: 'When I am your current age, you will be $$50$$ years old.' So, A is currently years old, B is currently years old."}, {"key": "3066", "content": "7 years ago, the mother's age was 7 times that of her daughter; this year, the combined age of the mother and daughter is 62 years. Question: How old is the mother this year?"}, {"key": "3067", "content": "The age of the elder monk 10 years ago is the same as the age of the younger monk 10 years from now. The sum of the elder monk's age 5 years from now and the younger monk's age 5 years ago is 40 years old. Hence, the elder monk is years old this year, and the younger monk is years old this year."}, {"key": "3068", "content": "Daughter is $$9$$ years old this year, and her father says to her: 'When you are as old as Dad, Dad will be $$63$$ years old!' How old is the father this year?"}, {"key": "3069", "content": "15 lines on the same plane can have at most how many intersection points."}, {"key": "3070", "content": "10 lines on the same plane can have a maximum of points."}, {"key": "3071", "content": "The teacher distributed exercise books to the students, giving out $$6$$ books per person and still missing $$20$$ books. If each person were given $$4$$ books, it would still be short by $$2$$ books. Thus, there are books in total, and there are students."}, {"key": "3072", "content": "Teacher Lele has a bucket of chocolates, which he divides among the third-grade children. If each child gets $$9$$ chocolates, then $$40$$ chocolates are left over. If each child gets $$12$$ chocolates, then $$10$$ chocolates are left over. How many chocolates does Teacher Lele have in total, and how many children did he share these chocolates with?"}, {"key": "3073", "content": "If Mr. Zhang gives 3 exercise books to each student, he will be short of 10 books. If he gives 2 exercise books to each student, he will have 5 books left. How many students and exercise books are there?"}, {"key": "3074", "content": "Mr. Wang bought exercise books for the students. If he buys $$7$$ books, he will be short of $$3$$ yuan. If he buys $$10$$ books, he will be short of $$12$$ yuan. What is the price of one exercise book in yuan? How much money does Mr. Wang have in total?"}, {"key": "3075", "content": "The Monkey King is distributing peaches to the little monkeys. If he gives each little monkey $$14$$ peaches, there will be $$10$$ peaches left; if he gives each little monkey $$16$$ peaches, there will only be $$2$$ peaches left. So, how many little monkeys are there in total? How many peaches did the Monkey King prepare?"}, {"key": "3076", "content": "Elementary school students are going on a spring outing by bus. If each bus seats $$60$$ people, there will be $$15$$ people who can't get on a bus; if each bus seats $$5$$ more people, there will be exactly one more bus available. How many students are there in total? How many buses are there in total?"}, {"key": "3077", "content": "Among the classmates Xiao Hua, Xiao Li, and Xiao Lv, one of them helped the sick Xiao Hong to complete her notes. When Xiao Hong asked who did this good deed, Xiao Hua said: 'It was Xiao Li.' Xiao Li said: 'It wasn't me.' Xiao Lv said: 'It wasn't me either.' In fact, two people were lying and only one was telling the truth. So, who actually helped Xiao Hong complete her notes? ( )"}, {"key": "3078", "content": "Perform vertical calculation: (1) $$999\\div 27=$$\uff0e(2) $$2870\\div35=$$\uff0e(3) $$4400\\div 55=$$\uff0e"}, {"key": "3079", "content": "Calculate: $$\\left( 4\\times 5\\times 7\\times 9\\times 11\\times 13 \\right)\\div \\left( 36\\times 77 \\right)$$=\uff0e"}, {"key": "3080", "content": "Calculate: (1) $$215\\div 29+65\\div 29+300\\div 29=$$\uff0e(2) $$120\\div 6+120\\div 4+120\\div 2=$$\uff0e"}, {"key": "3081", "content": "Calculate: $$12\\div \\left( 3\\div 2 \\right)\\times \\left( 6\\div 7 \\right)\\div \\left( 8\\div 7\\div 5\\times 2 \\right)\\div 3=$$."}, {"key": "3082", "content": "In a sequence of numbers, starting from the second number, each number is 4 more than the previous one. The 10th number is 103. What is the first number?"}, {"key": "3083", "content": "There are a bunch of logs with uniform thickness, stacked in a trapezoidal shape. From top to bottom, the number of logs increases equally with each layer. There are a total of $$8$$ layers. The $$4$$th layer has $$21$$ logs, and the $$6$$th layer has $$33$$ logs. How many logs are there in total?"}, {"key": "3084", "content": "The park arranged $$7$$ rows of flowers for the festival celebration, totaling $$420$$ pots. As one moves from the front to the back, the number of flowers in each row increases, with each row's flower count forming an arithmetic sequence. The $$7$$th row from the front has $$90$$ pots of flowers. Then, the difference in the number of pots between two adjacent rows is\uff0e"}, {"key": "3085", "content": "A string of numbers has a total of $$11$$ numbers, each number is $$7$$ more than its previous one, and the $$11$$th number is $$125$$. Thus, the first number is."}, {"key": "3086", "content": "1) A five-layer bookshelf has a total of $$450$$ books, with any two adjacent layers having $$10$$ fewer books on the upper layer than the lower one. How many books are there on the top layer? 2) Another five-layer bookshelf has a total of $$350$$ books, with each upper layer having the same fewer number of books compared to the layer directly below it, with the top layer having only $$10$$ books. Find the difference in the number of books between two adjacent layers."}, {"key": "3087", "content": "As shown: The number marked on the left side of each row and the top of each column represents the number of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_3087-image_0"}, {"key": "3088", "content": "As shown: The numbers labeled on the left side of each row and the top of each column represent the number of consecutive black blocks in that row or column. Kids, can you, based on these numbers, mark all the black blocks? question_3088-image_0"}, {"key": "3089", "content": "As shown: The numbers marked on the left of each row and the top of each column represent the count of consecutive black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_3089-image_0"}, {"key": "3090", "content": "As shown in the diagram: The numbers on the left side of each row and the top of each column represent the number of consecutive black blocks in that row or column. Kids, based on these numbers, can you mark all the black blocks? question_3090-image_0"}, {"key": "3091", "content": "The figure below contains a line segment. question_3091-image_0"}, {"key": "3092", "content": "Planting trees along one side of a $$30$$ meters long road, planting one every $$10$$ meters, with trees at both ends, the total number of trees planted on this road is."}, {"key": "3093", "content": "A bus from the start to the end has to travel a total of $$36\\text{km}$$, if it stops every $$3\\text{km}$$ (not counting the starting point), then the total number of stops till the destination is."}, {"key": "3094", "content": "There is a straight road, with $$30$$ trees planted on one side of the road, and trees are also planted at both ends of the road. It is known that the distance between every two trees is $$6$$ meters, then the length of this road is meters."}, {"key": "3095", "content": "To saw a uniformly thick piece of wood into $$5$$ sections, it takes five minutes for each cut, requiring a total of minutes."}, {"key": "3096", "content": "There is a square in the picture.\n question_3096-image_0"}, {"key": "3097", "content": "Count the number of triangles in the picture below.\n question_3097-image_0"}, {"key": "3098", "content": "The scholar repetitively writes 'studying makes me happy' in order, for a total of $$56$$ characters, the last one is the ( ) character."}, {"key": "3099", "content": "A class has $$56$$ students, $$28$$ students participated in the English competition, $$27$$ students participated in the math competition, if there are $$25$$ students who did not participate in any competition, then the number of students who participated in both the English and math competitions is ."}, {"key": "3100", "content": "Among the $$30$$ consecutive integers from $$1$$ to $$30$$, there are some that are multiples of $$2$$ or multiples of $$3$$."}, {"key": "3101", "content": "Fill in the appropriate number in the $$\\square$$ of the division long division so that the operation is valid, where the dividend is.\n question_3101-image_0"}, {"key": "3102", "content": "One side of the rectangle is equal to $$2a+b$$, and the other side is $$a-b$$ smaller than it, then the perimeter of this rectangle is. question_3102-image_0"}, {"key": "3103", "content": "Calculate: $$47+86+53+14=$$."}, {"key": "3104", "content": "$$29+299+2999+29999=$$."}, {"key": "3105", "content": "$$77+82+79+80+78=$$."}, {"key": "3106", "content": "Calculate: $$364-(476-187)+213-\\left( 324-236 \\right)-150$$=\uff0e"}, {"key": "3107", "content": "Calculate: $$105+1005+\\cdots+1\\underbrace{00\\cdots0}_{20 zeros}5=$$ ( )."}, {"key": "3108", "content": "The units digit of the sum of the series $$3+33+333+\\cdots +\\underbrace{33\\cdot \\cdot \\cdot 3}_{25\\, threes}$$ is?"}, {"key": "3109", "content": "Calculate: $$96-97+98-99+100-101+102-103+104$$"}, {"key": "3110", "content": "Calculate: $$59+599+5999+59999+599999=$$."}, {"key": "3111", "content": "Calculate: $$1000-90-88-93-89-95=$$."}, {"key": "3112", "content": "The area of the shape given below is.\n question_3112-image_0"}, {"key": "3113", "content": "As shown in the diagram below, a large square is divided into four parts: $$A$$, $$B$$, $$C$$, and $$D$$. It is known that the perimeter of part $$A$$ is $$4$$ cm, the perimeter of part $$B$$ is $$10$$ cm, and the perimeter of part $$C$$ is $$7$$ cm. What is the perimeter of the large square in centimeters?\n question_3113-image_0"}, {"key": "3114", "content": "A rectangle is 42cm long and 30cm wide. The width of the two shaded parts in the picture is 6cm each. The area of the unshaded part is in square centimeters.\n question_3114-image_0"}, {"key": "3115", "content": "As shown in the figure, it is known that $$AE=7$$, $$BF=3$$, $$CF=3$$, $$DE=10$$. Then, the area of the figure below is.\n question_3115-image_0"}, {"key": "3116", "content": "There are ( ) different ways to mix and match the shoes and socks below.\n\n\n\n\n question_3116-image_0 \n\n question_3116-image_1 \n\n\n\n question_3116-image_2 \n\n question_3116-image_3 \n\n question_3116-image_4"}, {"key": "3117", "content": "The delegations of two companies hold a meeting together, with 15 people from company A and 12 people from company B attending. Now, to select one meeting recorder from each company, there are a total of ways to choose."}, {"key": "3118", "content": "Using the digits $$1$$, $$2$$, $$3$$, $$4$$, a three-digit number with non-repeating digits can be formed."}, {"key": "3119", "content": "As shown in the picture, it is known that the missing part of the picture is a square with a side length of $$5$$. Therefore, the area of the figure below is.\n question_3119-image_0"}, {"key": "3120", "content": "The area of a rectangle is $$280$$ square centimeters, the width is $$7$$ centimeters, and the length is centimeters."}, {"key": "3121", "content": "As shown in the diagram, there is a rectangular piece of paper, measuring $$7$$ cm in length and $$5$$ cm in width. If its top right corner is folded down and its bottom left corner is folded up, the area of the uncovered shaded portion is in square centimeters.\n question_3121-image_0"}, {"key": "3122", "content": "There is a flower garden that is exactly a square with a side length of $$10$$ meters, as shown in the figure below. There are three paths with a width of $$1$$ meter in the garden, as shown in the shaded area below. Calculate the area of the blank part in square meters. question_3122-image_0"}, {"key": "3123", "content": "There is a rectangular flowerbed with a perimeter of $$30$$ meters and a length of $$9$$ meters. A $$2$$-meter-wide path is laid around the outside perimeter. Calculate the area of the path in square meters. question_3123-image_0"}, {"key": "3124", "content": "As shown in the figure, the numbers in the figure represent the area of the small rectangles. What is the area of the rectangle marked with a question mark? question_3124-image_0"}, {"key": "3125", "content": "The area of the polygon in the figure is square centimeters. (Unit: cm) question_3125-image_0"}, {"key": "3126", "content": "There is a rectangular vegetable patch that is $$75$$ meters long and $$20$$ meters wide, with a square pond in the middle with a side length of $$4$$ meters. Calculate the planting area of the vegetable patch in square meters."}, {"key": "3127", "content": "A, B, C, and D are comparing their heights. A says, 'I am the tallest.' B says, 'I am not the shortest.' C says, 'I am not as tall as A, but someone is shorter than me.' D says, 'I am the shortest.' The actual measurement results show that only one person is wrong. So, the tallest person is."}, {"key": "3128", "content": "$$A$$, $$B$$, $$C$$, and $$D$$ are from China, Japan, the United States, and France, respectively, and each person has $$1$$ occupation. It is known that: ($$1$$) $$A$$ and the Chinese person are doctors; ($$2$$) $$B$$ and the French person are teachers; ($$3$$) $$C$$ and the Japanese person have different occupations; ($$4$$) $$D$$ is not a doctor. Therefore, $$A$$ is____, $$B$$ is____, $$C$$ is____, $$D$$ is____."}, {"key": "3129", "content": "There are three people, A, B, and C, who are members of the school's football team, table tennis team, and basketball team respectively. Only one of the following statements is true: (1) A is on the football team; (2) B is not on the football team; (3) C is not on the basketball team. Therefore, A is in the team, B is in the team, C is in the team."}, {"key": "3130", "content": "There are three people $$A$$, $$B$$, and $$C$$. One is a director, one is an editor, and one is a driver. It is known that $$A$$ is older than the editor, the driver is older than the director, and the editor is older than $$C$$. So, among these three people, who is the director, who is the editor, and who is the driver."}, {"key": "3131", "content": "Calculate: $$9+13+17+21+25+29+33=$$."}, {"key": "3132", "content": "Sum: $$1+5+9+\\cdots +33+37=$$."}, {"key": "3133", "content": "Divide a square board into $$12$$ small squares, and place pebbles in each small square. If the first square has $$2$$ pebbles, the second square has $$4$$ pebbles, the third square has $$6$$ pebbles, the fourth square has $$8$$ pebbles, and so on, until all $$12$$ squares are filled, the total number of pebbles placed is."}, {"key": "3134", "content": "Calculate: $$3+8+13+18+23+28+33+38=$$."}, {"key": "3135", "content": "In an arithmetic sequence, the first term is $$15$$, the $$7$$th term is $$57$$, the common difference is."}, {"key": "3136", "content": "In an arithmetic sequence, the difference between two consecutive terms is $$9$$. The $$9$$th term is $$98$$. Find the $$17$$th term."}, {"key": "3137", "content": "The Sugar Monk went to the Western Paradise to acquire the candy-making technology of the West. He had to eat sugar every day. Starting from the second day, he ate 5 more pieces of candy each day than the day before. On the 21st day, he ate 666 pieces of candy. On the 1st day, he ate pieces of candy."}, {"key": "3138", "content": "There is a triangle in the figure below.\n question_3138-image_0"}, {"key": "3139", "content": "There are several triangles in the picture below.\n question_3139-image_0"}, {"key": "3140", "content": "The picture below contains a total of rectangles (including squares). question_3140-image_0"}, {"key": "3141", "content": "Count, how many rectangles are there in total in the picture. question_3141-image_0"}, {"key": "3142", "content": "There is a line segment in the picture.\n question_3142-image_0"}, {"key": "3143", "content": "$$2018$$ year $$10$$ month $$25$$ day is Thursday, $$2019$$ year $$10$$ month $$25$$ day is a weekday."}, {"key": "3144", "content": "Car A and Car B set off from two places, A and B, which are $$280$$ kilometers apart, towards each other at the same time, and meet after $$8$$ hours. After the meeting, both cars continue to drive, and after another $$6$$ hours, Car A reaches B. At this point, how many kilometers is Car B from A?"}, {"key": "3145", "content": "As shown in the diagram, there are four islands: $$A$$, $$B$$, $$C$$, $$D$$, connected by nine bridges. If a tourist wants to cross all these nine bridges exactly once, it is not possible. question_3145-image_0"}, {"key": "3146", "content": "Eddy is tidying up his desk, dividing $$12$$ identical erasers into $$3$$ piles of different quantities, there are a total of different methods of division."}, {"key": "3147", "content": "The little rabbit's family planted three types of vegetables: carrots, cabbage, and spinach. They eat only one type of vegetable a day and do not eat the same variety on two consecutive days. If they eat carrots on day $$1$$ and cabbage on day $$6$$, then there are several different arrangements for the continuous $$6$$ days' meals."}, {"key": "3148", "content": "Compute: $$33\\times 66+33\\times 34$$=\uff0e"}, {"key": "3149", "content": "2 years ago, Mom's age was 6 times Zhou Zhou's age; 3 years later, the sum of Mom and Zhou Zhou's ages will be 45 years. So, Zhou Zhou's age this year is ____ years old."}, {"key": "3150", "content": "The father said to his son: \"When I was your age, you were only $$3$$ years old\", the son laughed and said to his father: \"When I get to be the same age as dad is now, dad will be $$75$$ years old.\" So, the father's age this year is ."}, {"key": "3151", "content": "Image ($$1$$) has a triangle, image ($$2$$) has a triangle, image ($$3$$) has a triangle. question_3151-image_0 question_3151-image_1 question_3151-image_2"}, {"key": "3152", "content": "The image contains a total number of triangles. question_3152-image_0"}, {"key": "3153", "content": "There are a total of rectangles (including squares) in the picture. question_3153-image_0"}, {"key": "3154", "content": "There is a square in the picture.\n question_3154-image_0"}, {"key": "3155", "content": "There is a triangle in the picture.\n question_3155-image_0"}, {"key": "3156", "content": "The diagram below contains a straight line and intersections question_3156-image_0"}, {"key": "3157", "content": "Please answer the following questions: In the same plane, $$3$$ straight lines can have at most how many intersection points. Each line has how many intersection points"}, {"key": "3158", "content": "Please answer the following questions: On the same plane, $$4$$ straight lines can have at most how many intersection points. Each line has how many intersection points."}, {"key": "3159", "content": "Please answer the following questions: On the same plane, $$101$$ straight lines can have at most intersections. There are intersections on each line."}, {"key": "3160", "content": "Zhu Bajie divides watermelons among his subordinates, if each person gets $$3$$ and there are $$40$$ left, if each person gets $$6$$ there are $$10$$ left, Zhu Bajie has several subordinates, and watermelons."}, {"key": "3161", "content": "Departing from $$A$$, passing through $$B$$ to $$C$$, how many routes are there in total?\n question_3161-image_0"}, {"key": "3162", "content": "With the numbers $$3$$, $$4$$, $$5$$, $$8$$\n(1) Different two-digit numbers can be formed.\n(2) Different three-digit numbers without repeated digits can be formed."}, {"key": "3163", "content": "There are $$2$$ books and $$5$$ newspapers. Xiao Ming takes out one book and one newspaper, there are ( ) different ways to do so."}, {"key": "3164", "content": "As shown in the figure, a large rectangle is divided into $$4$$ smaller rectangles, among which three of the smaller rectangles have areas of $$20\\text{cm}^{2}$$, $$8\\text{cm}^{2}$$, and $$40\\text{cm}^{2}$$ respectively. The area of the rectangle represented by $$A$$ is $$\\text{cm}^{2}$$.\n question_3164-image_0"}, {"key": "3165", "content": "The area of the figure below is.\n question_3165-image_0"}, {"key": "3166", "content": "A rectangle with an area of $$\\text{160c}{{\\text{m}}^{2}}$$ and a width of $$\\text{1dm}$$ has a length of $$\\text{cm}$$."}, {"key": "3167", "content": "Rule $$a$$\u203b$$b$$ denotes $$3$$ times $$a$$ minus $$2$$ times $$b$$, which means $$a$$\u203b$$b=3a-2b$$, for example: $$4$$\u203b$$4=3\\times 4-2\\times 4=4$$; likewise, $$a\\triangle b$$ denotes $$3$$ times $$a$$ plus $$2$$ times $$b$$, that is $$a\\triangle b=3a+2b$$, for example $$1\\triangle 4=3\\times 1+2\\times 4=11$$. (1) Calculate: $$5$$\u203b$$4=$$"}, {"key": "3168", "content": "Calculate: $$(1000-16)\\div 8=$$."}, {"key": "3169", "content": "$$275\\div 25-225\\div 25=$$."}, {"key": "3170", "content": "Eddie collects candy wrappers, on the first day he collects $$4$$ wrappers, on the second day he collects $$7$$ wrappers, on the third day he collects $$10$$ wrappers, on the fourth day he collects $$13$$ wrappers,... on the last day he collects $$61$$ wrappers in total."}, {"key": "3171", "content": "Given a sequence where each term is $6$ more than the previous term, the $10^{th}$ term is $62$, the $5^{th}$ term is."}, {"key": "3172", "content": "In the spectator seats of the World Cup, the seating arrangement in a certain area forms a trapezoid. Starting from the 2nd row, the number of seats in each row is the same amount more than the previous row. It is known that there are 22 seats in the 5th row and 31 seats in the 8th row. Question: (1) How many seats are there in the 1st row?"}, {"key": "3173", "content": "In an arithmetic sequence, the difference between two consecutive numbers is $$7$$, the $$12$$th item is $$107$$, the $$8$$th item is."}, {"key": "3174", "content": "Zhu Bajie eats watermelons, starting from the 2nd day, he eats 2 more than the previous day each day. On the 20th day, he ate 50 watermelons, and on the 1st day, he ate ."}, {"key": "3175", "content": "Given the third and seventh numbers of an arithmetic sequence are $$14$$ and $$38$$ respectively, the difference between adjacent numbers is."}, {"key": "3176", "content": "Sugar Monk went to the Western Paradise to acquire the technology of making Western sweets, and he had to eat sweets every day. Starting from the 2nd day, he ate 5 more sweets each day than the day before. On the 30th day, he ate 666 sweets, and on the 1st day, he ate sweets."}, {"key": "3177", "content": "The solid square formation of class 2 of the fifth grade has a total of $$56$$ people on its outermost layer. ($$2$$) The total number of people in this square formation is ."}, {"key": "3178", "content": "The solid square formation of Class 2, Grade 5, has a total of $$56$$ people on its outermost layer. ($$1$$) Each side of the square formation on the outermost layer has people."}, {"key": "3179", "content": "At the Max Elementary School Arts Festival, the third graders formed a solid square formation to perform magic, with 18 people on each side of the outermost layer, (3) counting from the outside in, the second layer has people on each side."}, {"key": "3180", "content": "There is a team of students arranged in a hollow square formation, with $$10$$ people on each side of the outer layer, totaling $$3$$ layers, these students have a total of people."}, {"key": "3181", "content": "During a group gymnastics performance, a solid square formation of $$12$$ rows by $$12$$ columns is changed into a two-layer hollow square formation. Calculate the number of people on each side of the most inner layer of the hollow square formation."}, {"key": "3182", "content": "A group of students formed a hollow square formation, with $$52$$ people on the outermost layer and $$28$$ people on the innermost layer, how many students are there in total?"}, {"key": "3183", "content": "In a Chinese chess competition, there are three possible outcomes: win, draw, and loss, scoring $$2$$, $$1$$, and $$0$$ points respectively. Now, five people participate in a round-robin tournament. After all the matches are completed, four of the participants scored $$6$$, $$5$$, $$4$$, and $$3$$ points respectively. Then, the score of the fifth person is."}, {"key": "3184", "content": "The fourth grade has $$10$$ classes participating in a tug-of-war competition. It is required that each pair of classes compete once, each class has to compete in games, and a total of games have to be conducted."}, {"key": "3185", "content": "Six students in the fourth grade participate in a round-robin chess tournament. If a scoring system of $$2-1-0$$ is used, the total points all students get after all matches have ended is."}, {"key": "3186", "content": "There are $$26$$ bricks, and $$2$$ brothers are competing to pick them up. The younger brother rushed in front, just set up the bricks when the older brother arrived. The older brother saw that the younger brother picked too many, so he took half from the younger brother for himself. The younger brother thought he could do it, so he took half from the older brother again. The older brother felt he took too less, so the younger brother had to give him $$5$$ more bricks, this way the older brother picked $$2$$ more bricks than the younger brother. Initially, the younger brother planned to pick bricks."}, {"key": "3187", "content": "A bag contains some glass beads. If half of them are taken out each time, and then one is added back, after repeating this process three times, there are $$4$$ glass beads left in the bag. How many glass beads were originally in the bag?"}, {"key": "3188", "content": "Eddy helps the doctor plant flowers, between every $$2$$ red flowers there should be $$5$$ yellow flowers, the first flower Eddy plants is a red flower, totaling $$59$$ flowers, among which there are yellow flowers."}, {"key": "3189", "content": "Given that August 5, 2016 is a Friday, what day of the week is September 5, 2016?"}, {"key": "3190", "content": "A little monk wrote a series of numbers on the ground: $$7$$, $$1$$, $$2$$, $$7$$, $$1$$, $$2$$, $$7$$, $$1$$, $$2$$, $$\\cdots \\cdots$$. So, the $$32$$nd number he wrote is."}, {"key": "3191", "content": "A store clerk went to the bank to exchange for change, using 100 one-hundred yuan RMB notes in exchange for a total of 260 twenty and fifty yuan RMB notes, including several twenties and fifties each."}, {"key": "3192", "content": "A worker transported 250 celadon vases, it was stipulated that for each vase successfully delivered to the destination, a freight charge of $20 would be given, while a compensation of $100 would be paid for each damaged vase. After delivering this batch of vases, the worker earned a total of $4400, then the number of vases damaged was."}, {"key": "3193", "content": "Eddie and Dengdeng participated in a math problem-solving competition, agreeing that for each correct answer they would earn $$10$$ points, and for each unanswered or incorrect answer they would lose $$5$$ points. Both of them answered $$10$$ questions each and scored a total of $$155$$ points. Knowing that Eddie scored $$15$$ points more than Dengdeng, how many questions did Dengdeng answer correctly."}, {"key": "3194", "content": "In a cage with both chickens and rabbits, the number of rabbits is 3 times less than that of chickens minus 6. Together, chickens and rabbits have 200 legs. There are chickens and rabbits."}, {"key": "3195", "content": "The zoo houses some sika deer and ostriches, with ostriches outnumbering sika deer by $$10$$, totaling $$140$$ legs. There are sika deer, and there are ostriches."}, {"key": "3196", "content": "Class 3($$2$$) has $$50$$ students, some can ride bicycles, some can swim, $$35$$ can ride bicycles, $$15$$ can do both, and $$4$$ students can't do either. Then, there are people who can swim."}, {"key": "3197", "content": "$$63$$ cats participated in the cat training camp. After a period of training, $$15$$ cats learned how to catch fish, $$12$$ cats learned how to catch mice, $$9$$ cats learned both how to catch fish and how to catch mice, $$6$$ cats learned both how to catch mice and how to climb trees, $$5$$ cats learned both how to climb trees and how to catch fish, $$2$$ cats learned all three skills, and it is known that these $$63$$ cats will necessarily learn at least one of these skills, so the number of cats that learned only how to climb trees is."}, {"key": "3198", "content": "[Warm-up 1 before class] In order to enrich their knowledge, the shrimp and the crab went to the library to read books. After one month, the shrimp read a total of $$48$$ books, and the crab read a total of $$32$$ books. There were $$12$$ books that they both read. Therefore, the total number of books they actually read was ."}, {"key": "3199", "content": "[Pre-class Warm-up 2] Among the $30$ consecutive integers from $$1$$ to $$30$$, there are some that are multiples of $$2$$ or multiples of $$3$$."}, {"key": "3200", "content": "[Warm-up 3 before class] On a hot summer day, several kids go to a cold drink shop, each person ordered at least one kind of cold drink. Among them, $$6$$ people ordered popsicles, $$6$$ people ordered soda, $$4$$ people ordered Sprite. $$3$$ people ordered both popsicles and soda, $$1$$ person ordered both popsicles and Sprite, $$1$$ person ordered both soda and Sprite; $$1$$ person ordered all three. So, in total, there were children who went to the cold drink shop."}, {"key": "3201", "content": "A book has a total of $$60$$ pages, the page numbers from $$1\\sim60$$ use a total of how many digits."}, {"key": "3202", "content": "A book has a total of $$150$$ pages, and the page numbers from $$1\\sim150$$ use a total of digits."}, {"key": "3203", "content": "To number a book, a total of $$333$$ digits were used. This book has a total of pages."}, {"key": "3204", "content": "The number of pages in a novel requires $$105$$ digits in total for printing. This book has a total of pages."}, {"key": "3205", "content": "A book has a total of 360 pages. In the page numbers from 1 to 360, the number \u201c2\u201d was used a total of times."}, {"key": "3206", "content": "A book has a total of $$500$$ pages. Across pages $$1\\sim 500$$, the number \u201c$$4$$\u201d is used a total of times."}, {"key": "3207", "content": "When numbering a book, a total of $$41$$ number \u201c$$6s$$\u201d were used, please calculate the minimum and maximum number of pages the book can have."}, {"key": "3208", "content": "There is a book, when summing up the page numbers of this book, one sheet's page numbers were mistakenly added twice, resulting in a sum of $$2047$$. Then, the inadvertently added page number is the sum. (Write from the smallest to the largest)"}, {"key": "3209", "content": "[Warm-up 1 before class] A book has $$35$$ pages, and the page numbers from 1 to 35 use a total of how many digits."}, {"key": "3210", "content": "[Warm-up 3 Before Class] A book has a total of $$500$$ pages. How many times does the number $$2$$ appear?"}, {"key": "3211", "content": "[Warm-up 2 before class] The page numbers of a novel used $$210$$ digits in printing. This novel has a total of pages."}, {"key": "3212", "content": "As shown in the figure, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$. It is known that the area of parallelogram $$ABCD$$ is $$32$$ square centimeters, $$CD=8$$ centimeters, the length of $$AE$$ is in centimeters. question_3212-image_0"}, {"key": "3213", "content": "As shown in the diagram, in the parallelogram $$ABCD$$, a line is drawn from point $$A$$ perpendicular to $$DC$$ at point $$F$$. It is known that $$AF=10$$ cm, $$CD=12$$ cm, the area of the parallelogram $$ABCD$$ is in square centimeters. question_3213-image_0"}, {"key": "3214", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$, given $$AB=5$$ cm, $$AE=3$$ cm, the area of parallelogram $$ABCD$$ is in square centimeters. question_3214-image_0"}, {"key": "3215", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AF$$ perpendicular to $$DC$$ at point $$F$$, it is known that the area of parallelogram $$ABCD$$ is $$48$$ square centimeters, $$AF=6$$ centimeters, the length of $$CD$$ is in centimeters. question_3215-image_0 \u200b"}, {"key": "3216", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, and $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$BC=30$$ cm, $$AE=20$$ cm, $$CD=24$$ cm. (1) The area of the parallelogram $$ABCD$$ is square centimeters. question_3216-image_0"}, {"key": "3217", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$BC=30$$ cm, $$AE=20$$ cm, $$CD=24$$ cm. (2) The length of line segment $$AF$$ is in centimeters. question_3217-image_0"}, {"key": "3218", "content": "As shown in the figure, the area of the parallelogram is $$180$$ square centimeters, $$AE=10$$ centimeters, $$AF=15$$ centimeters, $$AE$$ and $$AF$$ are the heights of the parallelogram, then the perimeter of the parallelogram is in centimeters. question_3218-image_0"}, {"key": "3219", "content": "As shown in the figure, in the rhombus $$ABDC$$, line segment $$AD$$ and line segment $$BC$$ intersect perpendicularly at point $$O$$, $$AO=60$$, $$CO=80$$, the height $$AE=96$$ on side $$BD$$. The area of rhombus $$ABDC$$ is, and the perimeter is. question_3219-image_0"}, {"key": "3220", "content": "The area of the trapezoid is $$84$$ square centimeters, the top base is $$9$$ centimeters, and the height is $$8$$ centimeters, then the bottom base is."}, {"key": "3221", "content": "The top base of the trapezoid is $$5$$ meters, the bottom base is $$13$$ meters, the height is $$20$$ meters, and the area of the trapezoid is square meters."}, {"key": "3222", "content": "The area of the trapezoid is $$60$$ meters, the upper base is $$8$$ meters, the lower base is $$12$$ meters, and the height of the trapezoid is meters."}, {"key": "3223", "content": "As shown in the diagram, the area of square $$ABCD$$ is $$16$$ square centimeters, $$ED=CH=4$$ centimeters, $$EF=2$$ centimeters, and quadrilateral $$EFGH$$ is a rectangle. (1) The upper base of trapezoid $$ABGF$$ is centimeters; the lower base is centimeters; the height is centimeters. question_3223-image_0"}, {"key": "3224", "content": "As shown in the figure, the area of square $$ABCD$$ is $$16$$ square centimeters, $$ED=CH=4$$ centimeters, $$EF=2$$ centimeters, quadrilateral $$EFGH$$ is a rectangle, (2) The area of trapezoid $$ABGF$$ is square centimeters. question_3224-image_0"}, {"key": "3225", "content": "As shown, the side length of the large square is $$8$$ cm, and the side length of the small square is $$6$$ cm. Please tell: what is the area of the shaded figure in square centimeters. question_3225-image_0"}, {"key": "3226", "content": "As shown in the parallelogram $$ABCD$$, $$AC$$ is perpendicular to $$CD$$ at point $$C$$, $$CF$$ is perpendicular to $$AD$$ at point $$F$$, $$BE=37$$ centimeters, $$CE=12$$ centimeters, $$AC=20$$ centimeters, $$CD=15$$ centimeters, the area of trapezoid $$ABED$$ is in square centimeters. question_3226-image_0"}, {"key": "3227", "content": "question_3227-image_0 [Warm-up before class 2] As shown in the figure, quadrilateral $$ABCD$$ is a rhombus, it is known that $$AC=20$$, $$BD=11$$, then the area of the rhombus is."}, {"key": "3228", "content": "[Warm-up 1 before class] As shown in the diagram, $$AB$$ is $$8$$ cm long, $$AD$$ is $$5$$ cm long, $$BE$$ is $$4$$ cm long, then the area of the parallelogram is square centimeters. question_3228-image_0"}, {"key": "3229", "content": "[Warm-up 3 before class] The upper base of a trapezoid is $$5$$ decimeters, the lower base is $$8$$ decimeters, and the height is $$4$$ decimeters, its area is square decimeters."}, {"key": "3230", "content": "Eddy and Vi drive towards each other from cities $$A$$ and $$B$$ respectively. Eddy's car travels at $$55$$ kilometers per hour, while Vi's car travels at $$45$$ kilometers per hour. They meet after $$3$$ hours. How many kilometers apart are the two cities?"}, {"key": "3231", "content": "[Warm-Up 3] The distance between two places is $$120$$ kilometers. When Eddie went there, his speed was $$20$$ kilometers/hour, and on the way back, his speed was $$30$$ kilometers/hour. The average speed of Eddie's round trip was kilometers/hour."}, {"key": "3232", "content": "[Warm-up before class 2] Da Bai and Xiao Ming set off from two places 1000 meters apart towards each other at the same time, Da Bai walks 47 meters per minute, and Xiao Ming walks 53 meters per minute, they are 100 meters apart for the second time after they set off."}, {"key": "3233", "content": "[Warm-up 1 before class] Locations A and B are $$140$$ kilometers apart, Eddie drove a car from A to B for $$5$$ hours. At this speed, it took $$6$$ hours to drive from B to C. The distance between B and C is kilometers."}, {"key": "3234", "content": "Eddy and Vi are racing, with Eddy running $$150$$ meters per minute and Vi running $$120$$ meters per minute. (1) If they start from the same place at the same time and move in the same direction, how many meters apart are they after $$5$$ minutes."}, {"key": "3235", "content": "Two cars set off simultaneously from two places, A and B, which are $$520$$ kilometers apart, heading in the same direction with car $$A$$ in front and car $$B$$ behind. Car $$B$$ travels at $$120$$ kilometers per hour and catches up with car $$A$$ after $$10$$ hours. The speed of car $$A$$ is kilometers/hour."}, {"key": "3236", "content": "Eddie and Vi are at places $$A$$ and $$B$$ respectively, which are $$100$$ meters apart. If they walk towards each other, then they meet after $$20$$ seconds; if they walk in the same direction with Vi in front, then Eddie catches up with Vi after $$100$$ seconds. So, Eddie's speed is meters/second, Vi's speed is meters/second."}, {"key": "3237", "content": "In a book, the number \u201c2\u201d appears $$167$$ times in total. Thus, this book has a total of pages."}, {"key": "3238", "content": "Person A and Person B are $$1500$$ meters apart, with A in front and B behind. A walks $$50$$ meters per minute, and B walks $$75$$ meters per minute. Both start moving forward at the same time, minutes later B catches up with A."}, {"key": "3239", "content": "In a math test with a total of $$20$$ questions, answering a question correctly earns $$5$$ points, answering incorrectly earns $$0$$ points, and not answering earns $$1$$ point. If Xiao Ming scored $$77$$ points, then the number of questions he answered correctly and incorrectly are respectively."}, {"key": "3240", "content": "On a straight road, Keke and Lele start running towards each other from a distance of $$100$$ meters at the same time, without changing their direction. Keke runs at $$6$$ meters per second, and Lele runs at $$4$$ meters per second. At the starting second, they are $$200$$ meters apart."}, {"key": "3241", "content": "Chen Chen and Yuan Yuan set off at the same time from two places $$500$$ meters apart, running towards each other. It is known that Chen Chen runs $$6$$ meters per second, and Yuan Yuan runs $$4$$ meters per second. Then, after setting off, the first time they were $$200$$ meters apart."}, {"key": "3242", "content": "The number of pages in a novel must use $$113$$ digits in printing. This book has a total of pages."}, {"key": "3243", "content": "Given a right-angled trapezium $$ABCD$$, where $$DC$$ is perpendicular to $$BC$$, $$AD=16$$, $$BC=24$$, $$CD=11$$. The area of the trapezium is.\n question_3243-image_0"}, {"key": "3244", "content": "The area of the parallelogram in the right picture is $$1800\\text{m}^2$$, then the perimeter of the parallelogram is $$\\text{m}$$\uff0e\n question_3244-image_0"}, {"key": "3245", "content": "Among all the natural numbers from $$1$$ to $$300$$, there are a total of ( ) numbers that are multiples of $$3$$ or $$5$$."}, {"key": "3246", "content": "Lao Jia buys water pens priced at $$3$$ yuan and $$5$$ yuan each, spending a total of $$80$$ yuan. It is known that the $$5$$ yuan pen has $$8$$ more than the $$3$$ yuan pen. How many $$3$$ yuan pens were bought?"}, {"key": "3247", "content": "There are a total of $$40$$ tortoises and cranes, with a total of $$112$$ legs between them. The number of tortoises is ( ) the number of cranes."}, {"key": "3248", "content": "Person A and person B set off from the East Village and the West Village respectively, both heading west at the same time. Person A rides a bicycle at $$13$$ kilometers per hour, while person B rides at $$10$$ kilometers per hour. After $$3$$ hours, person A catches up with person B. Thus, the distance between the two villages is kilometers."}, {"key": "3249", "content": "Third grade class four students participate in extracurricular interest groups, among them $$25$$ students participate in natural interest group, $$35$$ students participate in art interest group, $$27$$ students participate in Chinese interest group, $$12$$ students participate in both Chinese and art interest groups, $$8$$ students participate in both natural and art interest groups, $$9$$ students participate in both natural and Chinese interest groups, $$4$$ students participate in the natural, art, and Chinese interest groups, and $$1$$ student does not participate in any of the three interest groups. So, the number of students in this class is ."}, {"key": "3250", "content": "Find the value represented by the symbol below. $$2\\times \\blacksquare +3\\times \\blacksquare+5\\times \\blacksquare =20$$, $$\\blacksquare =$$."}, {"key": "3251", "content": "Find the value represented by the following symbol. $$37 -(3x +7)=(16 -5x\uff09+18$$, $$x =$$."}, {"key": "3252", "content": "Find the value represented by the symbols below. $$2+3\\times ($$ question_3252-image_0 $$-26)=52-($$ question_3252-image_1 $$-40)$$, question_3252-image_2 =."}, {"key": "3253", "content": "Find the value represented by the following expression. $$10-2 \\times (x-3)=3x-4 \\times (5-x)$$, $$x=$$."}, {"key": "3254", "content": "Tian Tian learns flower arranging. If each vase contains $$6$$ flowers, then the remaining flowers can just fill $$3$$ more vases; if each vase contains $$2$$ more flowers, then there will be $$3$$ empty vases, in total there are flowers."}, {"key": "3255", "content": "The standard track in the stadium is $$400$$ meters per lap. XiXi needs to run $$1$$ kilometer for the physical education test and has already run $$2$$ laps, how many meters are left?"}, {"key": "3256", "content": "As shown in the diagram, there are seven residential buildings $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, $$F$$, $$G$$ on the street, and every day there are $$80$$ people in each building who need to take the bus. Now, setting up a bus stop, to minimize the total distance residents need to travel to reach the stop, it should be located at . question_3256-image_0"}, {"key": "3257", "content": "There is a rectangular chicken coop, 15 meters long, and 4 meters longer than it is wide. Then, the area of this chicken coop is in square meters."}, {"key": "3258", "content": "25 times a number is 575, then 50 times this number is."}, {"key": "3259", "content": "The supermarket received $$25$$ boxes of apples in the morning and $$18$$ boxes in the afternoon. If each box of apples weighs $$20$$ kilograms, the total weight of the apples received that day was kilograms."}, {"key": "3260", "content": "Solve the equation $$4x+4=6+(8-x)$$$x=$"}, {"key": "3261", "content": "Solve the application problem by setting up an equation: Class 1 of Grade 3 has 27 boys. The number of boys is 3 less than twice the number of girls. How many students are there in total in Class 1 of Grade 3."}, {"key": "3262", "content": "$(1357+3571+5713+7135)\\div 8=$"}, {"key": "3263", "content": "It is known that the perimeter of a square is $$64$$ meters, its side length is meters."}, {"key": "3264", "content": "In Figure 1, the perimeter of the rectangle is meters; in Figure 2, the perimeter of the square is meters.\n question_3264-image_0 question_3264-image_1"}, {"key": "3265", "content": "(1) The perimeter of a square is $$36$$ cm, the side length = cm;\n(2) The perimeter of a rectangle is $$60$$ cm, the width is $$10$$ cm, the length = cm."}, {"key": "3266", "content": "The diagram represents a piece of land, surrounded by fences on all sides, with right angles at the turns. It is known that the fence on the west side is $$17$$ meters long and the fence on the south side is $$23$$ meters long, so the total length of the fence around is meters.\n question_3266-image_0"}, {"key": "3267", "content": "As shown in the figure below, stack three squares with a side length of $$8$$ cm each. The vertex of the subsequent square precisely falls in the center of the previous square, then the perimeter of the shape is cm.\n question_3267-image_0"}, {"key": "3268", "content": "Using the three cards $$2$$, $$3$$, and $$6$$, you can form different three-digit numbers."}, {"key": "3269", "content": "Using the digits $$3$$, $$7$$, $$5$$, different three-digit numbers without repeating digits can be formed."}, {"key": "3270", "content": "Calculate: $$63\\times 11=$$"}, {"key": "3271", "content": "$$437\\div 19$$="}, {"key": "3272", "content": "When solving the problem of 'evenly distributing $$58$$ books among $$2$$ classes', in light of the question, the '$$1$$' in the division on the right represents ( ) .\n question_3272-image_0"}, {"key": "3273", "content": "$$5$$ monkeys can eat $$60$$ peaches in $$3$$ days, now there are $$64$$ peaches enough for $$4$$ monkeys to eat for days."}, {"key": "3274", "content": "In a cookie factory, $$8$$ workers can pack $$360$$ boxes of cookies in $$3$$ hours. How many boxes can $$1$$ worker pack in $$1$$ hour?"}, {"key": "3275", "content": "The below image is a $$5\\times 5$$ area with $$5$$ trees planted. It is now required to set up tents on the empty land without trees, and the tents must be set up next to a tree. No two tents can share a common point in their grids, and the number of tents in each row is as shown on the far left, the number of tents in each column as shown at the top. Is there a tent in the 5th row and 3rd column? (  ) question_3275-image_0"}, {"key": "3276", "content": "In the minefield below, there might be mines in the spaces. Based on the numbers in the cells, find the positions of the mines. Is there a mine at the ( ) position?\n question_3276-image_0"}, {"key": "3277", "content": "Trees are planted along one side of a $$48$$ meters long road, planting at only one end and not the other, with a total of $$8$$ trees planted, each spaced at every meter. (The width of the trees is negligible)"}, {"key": "3278", "content": "The school has a path 60m long, and plans to plant trees along the road, planting one every 5m. If trees are not planted at both ends, a total of ( ) trees are needed."}, {"key": "3279", "content": "Xiaoming wrote a number on the blackboard. Xiaohong first multiplied this number by $$2$$, then added $$10$$, then divided by $$4$$, and the result was $$8$$. So, the number Xiaoming wrote on the blackboard was."}, {"key": "3280", "content": "As shown in the figure, two adjacent sides are perpendicular to each other, and the length of the line segments are as follows, the perimeter of the figure is centimeters. (Unit name: centimeters) question_3280-image_0"}, {"key": "3281", "content": "To form a rectangle using $$6$$ squares with a side length of $$1$$ cm each, the shortest possible perimeter of this rectangle is in centimeters."}, {"key": "3282", "content": "A square with a side length of $$10$$ cm is cut horizontally $$2$$ times and vertically $$3$$ times, resulting in $$12$$ small rectangles. The total perimeter of these $$12$$ small rectangles is equal to cm. question_3282-image_0"}, {"key": "3283", "content": "Calculate: $$39\\times 4+6\\times 39$$."}, {"key": "3284", "content": "Mother is $$35$$ years old this year, daughter is $$6$$ years old, how many years ago was the sum of the mother and daughter's age $$33$$ years?"}, {"key": "3285", "content": "The year before last, Mr. Wang was $$24$$ years older than Xiao Hua. This year, Mr. Wang's age is exactly $$3$$ times Xiao Hua's age. So, this year Xiao Hua is ____ years old."}, {"key": "3286", "content": "In the decimal number $$5.0893$$, $$5$$ is in the unit place, representing $$5$$ units of $$1$$; $$0$$ is in the tenths place, representing tenths; $$8$$ is in the hundredths place, representing hundredths; $$9$$ is in the thousandths place, representing thousandths; $$3$$ is in the ten-thousandths place, representing ten-thousandths."}, {"key": "3287", "content": "Break $13$ into three different non-zero integers, there are several different ways to do it."}, {"key": "3288", "content": "The older brother and the younger brother each have some reward points cards. The number of cards the older brother has is 5 times that of the younger brother's. If the older brother gives 12 cards to the younger brother, both will have the same number of reward points cards. How many reward points cards did the older brother originally have?"}, {"key": "3289", "content": "As shown in the figure, quadrilateral $$ABCD$$ is a rhombus, with $$AC=16$$, and the length of $$BD$$ is $$7$$ less than $$AC$$. Then, the area of the rhombus is.\n question_3289-image_0"}, {"key": "3290", "content": "Mingming, Junjun, and Pangpang went to the clinic to get vaccinated. There was only one school doctor in the clinic, so they had to be vaccinated one by one in order. Thus, there are different ways for the $$3$$ of them to line up for the vaccination."}, {"key": "3291", "content": "In a division equation, if the quotient is $$4$$ and the remainder is $$8$$, then the smallest possible divisor is."}, {"key": "3292", "content": "The figure that is not a quadrilateral is ( )."}, {"key": "3293", "content": "The figure in the following ( ) is a quadrilateral."}, {"key": "3294", "content": "To piece together a square, at least ( ) sticks are needed."}, {"key": "3295", "content": "Using a rope of length $$20$$ cm to form a rectangle, if the length of this rectangle is $$6$$ cm, then the width of this rectangle is cm."}, {"key": "3296", "content": "With a 20 cm long rope forming a square, the side length of this square is in cm."}, {"key": "3297", "content": "With your help, the doctor's precision instrument has finally been developed. The side view of the instrument is as shown below, where each of the shortest lines is $$5$$ cm long, and the part is $$30$$ cm high, the perimeter of the side of this instrument is centimeters.\n question_3297-image_0"}, {"key": "3298", "content": "Using $$4$$ squares with a side length of $$1$$ cm each to form either figure $$A$$ or figure $$B$$, the correct statement about the perimeter sizes of these two figures is ( ).\n question_3298-image_0"}, {"key": "3299", "content": "Using a rectangular cardboard of length $$8$$ dm and width $$4$$ dm, and two square cardboards with a side length of $$4$$ dm each to form a square. The perimeter of the resulting square is ( ) dm."}, {"key": "3300", "content": "\nJoining two squares with side lengths of $$5\\text{cm}$$ together into a new shape will change the perimeter of the original two squares by ( )."}, {"key": "3301", "content": "Eddy and Vi play a game, where among 10 identical small balls numbered from $$1$$ to $$10$$, Eddy randomly selects $$2$$ balls (order not considered), and Vi calculates the sum of the numbers on the two balls. If the sum is greater than $$10$$, then Vi wins. The total number of ways to select the balls that would result in Vi's victory is."}, {"key": "3302", "content": "A fruit store mixes $$2$$ kilograms of crispy sugar and $$3$$ kilograms of fruit sugar to make mixed sugar. It is known that crispy sugar sells for $$16$$ yuan per kilogram, and fruit sugar sells for $$6$$ yuan per kilogram. Question: How much should the mixed sugar be sold for per kilogram?"}, {"key": "3303", "content": "Class A and Class B have $$20$$ and $$30$$ students, respectively. It is known that the average score of Class A is $$93$$ points, and the total average score of both classes is $$90$$ points. Calculate the average score of Class B."}, {"key": "3304", "content": "The average of five numbers is $$60$$. If one of these numbers is changed to $$80$$, the average becomes $$70$$. The original value of the changed number is."}, {"key": "3305", "content": "Xiao Ke scored in four subjects: Math, Chinese, English, and PE during an exam. The average score for the four subjects is $$93$$ points. The scores for Chinese, English, and PE were $$93$$, $$92$$, and $$89$$ points, respectively. Can you calculate Xiao Ke's Math score? ( )"}, {"key": "3306", "content": "Eddie exercises by running every day, running an average of $$5000$$ meters from Monday to Friday and $$1500$$ meters on weekends. Thus, how many kilometers does Eddie run on average per day in a week?"}, {"key": "3307", "content": "A, B, C, and D four people went to the forest to pick mushrooms together. On the first day, they picked a total of $$108$$ mushrooms, on the second day, they picked a total of $$100$$ mushrooms, and on the third day, they picked a total of $$140$$ mushrooms. On average, each person picked ( ) mushrooms per day."}, {"key": "3308", "content": "A rope is cut into two pieces, the first piece is $$6$$ meters long, the second piece is $$\\frac{3}{5}$$ of the total length. Compare these two pieces ( )."}, {"key": "3309", "content": "Dakuan ate $$\\frac{1}{3}$$ of a box of chocolate, and Eddie also ate $$\\frac{1}{3}$$ of this box of chocolate. The amount of chocolate eaten by the two is ( )."}, {"key": "3310", "content": "Eddy took out $$\\frac{2}{5}$$ of his pocket money to donate to the disaster area, Vi took out $$\\frac{2}{5}$$ of her pocket money to donate to the disaster area. The amount of money donated by both ( )."}, {"key": "3311", "content": "Wei Er learns paper cutting, she first cuts off $$\\frac{1}{3}$$ of a sheet of paper, then cuts off $$\\frac{1}{2}$$ of the remainder, so the final remaining part of the paper is ( ) of the whole sheet."}, {"key": "3312", "content": "On Children's Day, 1/4 of the students in Grade 3 (Class $$1$$) went to the Youth Palace for a garden party, and 1/3 of the students in Grade 3 (Class $$2$$) went to the Youth Palace for the garden party. After counting, it was found that the number of students from both classes who attended the garden party was the same. Do you know which class has a greater total number of students? ( )."}, {"key": "3313", "content": "Two small sticks are covered by a wooden board, the first stick exposes $$ \\frac{1}{4} $$ of its length, and the second stick exposes $$ \\frac{2}{7} $$ of its length. The exposed parts of both sticks are the same length. Comparing the two sticks, ( ).\n question_3313-image_0"}, {"key": "3314", "content": "If the numerator of $$\\frac{7}{12}$$ is tripled, in order to keep the fraction the same, the denominator should be increased by ( )."}, {"key": "3315", "content": "Calculation without symbols: (Please reduce the calculation results to their simplest form)\n$$\\dfrac{2}{5}+\\dfrac{3}{10}$$\uff1b $$1\\dfrac{1}{2}+\\dfrac{1}{4}$$"}, {"key": "3316", "content": "The area of the shaded part as a fraction of the total area of the figure is ( )\uff0e\n question_3316-image_0"}, {"key": "3317", "content": "On one side of a highway that is $$2700$$ meters in length, a pine tree is planted every $$10$$ meters, and between every two adjacent pine trees, a willow tree is planted every $$2$$ meters. How many willow trees have been planted?"}, {"key": "3318", "content": "There is a rope $$61$$ centimeters long, first mark every $$3$$ centimeters from the left, then mark every $$4$$ centimeters from the right, and finally cut all the marks. The question is how many segments the rope will be cut into."}, {"key": "3319", "content": "Use the numbers $$1$$, $$2$$, and $$3$$ to form a four-digit number, requiring that there are no consecutive $$1$$s. How many possible arrangements are there?"}, {"key": "3320", "content": "As shown in the figure, an ant starts from the apex $$P$$ of a pyramid and traverses the edges of the pyramid, visiting every vertex exactly once until it has visited all $$5$$ vertices and stops (for example: $$P-A-B-C-D$$). How many different paths can the ant take in total? question_3320-image_0"}, {"key": "3321", "content": "Three-digit numbers made up of $$1$$, $$2$$, $$3$$ without consecutive $$1$$s are there."}, {"key": "3322", "content": "A person visits three cities $$A$$, $$B$$, and $$C$$. Today he is in this city, and tomorrow he must go to another city. He starts from city $$A$$ and returns to $$A$$ after $$5$$ days. Thus, there are several travel routes."}, {"key": "3323", "content": "On the playground, there are three kids $$A$$, $$B$$, and $$C$$ passing a basketball. Each pass is to one of the other two kids, and the kid who catches the ball then passes it to one of the other two kids. If starting with $$A$$, and after $$4$$ passes the ball arrives at $$B$$, there are a total of ways of passing the ball."}, {"key": "3324", "content": "Below are several transformations of some Chinese characters:\nWelcome students to take the test\nAfter the first transformation: Welcome students to participate in the test\nAfter the second transformation: Welcome students to take the participate test\nAfter the third transformation: Welcome students to participate in take test\nAfter the fourth transformation: Welcome students to participate in the test\n$$\\cdots\\cdots$$\nAccording to this pattern, at least several transformations are required before \"Welcome students to take the test\" appears again."}, {"key": "3325", "content": "Seven students with the surnames Zhao, Qian, Sun, Li, Zhou, Wu, and Wang stand in a row and count off in the following manner. Which student, with what surname, says \"$$2016$$\"? question_3325-image_0"}, {"key": "3326", "content": "The order of painting the small wooden balls on the assembly line is: first $$5$$ red, $$4$$ yellow, $$3$$ green, $$2$$ black, $$1$$ white, and then the order is repeated as $$5$$ red, $$4$$ yellow, $$3$$ green, $$2$$ black, $$1$$ white$$\\ldots \\ldots$$ continuing in this manner, what color should be painted on the $$154$$th small ball?"}, {"key": "3327", "content": "Is it possible to tear out any 20 pages from a book of 500 pages in such a way that the sum of all the page numbers on these 20 pages equals 1999?"}, {"key": "3328", "content": "There are enough apples, pears, and oranges mixed together, and they are divided into $$9$$ piles at random. Is it always possible that the number of all three kinds of fruits becomes even when any two piles are combined?"}, {"key": "3329", "content": "There are $$5$$ playing cards, face up. Xiao Ming flips $$4$$ of them each time. Can he, after a number of flips, make the faces of all $$5$$ cards face down?"}, {"key": "3330", "content": "(1) Is the product of the mathematical expression $$1\\times 3\\times 5\\times 7\\cdots \\times 1991\\times 1993$$ an even or odd number? Why? (2) Is the result of the calculation $$1+2\\times 3+4\\times 5+6\\times 7+\\cdots +98\\times 99$$ an even or odd number? Why?"}, {"key": "3331", "content": "Is the result of the calculation $$(101+102+\\cdot \\cdot \\cdot +170)-(41+42+\\cdot \\cdot \\cdot +100)$$ odd or even?"}, {"key": "3332", "content": "Is the sum of the series $$1+2+3+4+\\cdots +2015+2016$$ an odd or even number?"}, {"key": "3333", "content": "Calculate: $$55\\times 66+66\\times 77+77\\times 88+88\\times 99=$$."}, {"key": "3334", "content": "Calculate: $$62\\times 102+52\\times 101-48\\times 99-38\\times 98=$$."}, {"key": "3335", "content": "As shown in the figure, some numbers have already been filled in. The number in each of the remaining cells equals the product of the leftmost number of the same row and the topmost number of the same column (for example, $$a=8\\times 11=88$$). What is the sum of the numbers filled in all the blank cells? question_3335-image_0"}, {"key": "3336", "content": "As shown in the table, form pairs with the characters from the top and bottom of each column, for example, the first pair is (\u51cc\u5343), and the second pair is (\u5bd2\u6811). Then the $$42$$th pair is ().\n\n\n\nLing Han Du Zi Kai (Ling Han Alone Blooms) Ling Han Du Zi Kai Ling Han Du Zi Kai Ling Han Du Zi Kai $$\\cdots \\cdots$$\n\n\nQian Shu Wan Shu Li Hua Kai (Thousands of Trees, Pear Flowers Bloom) Qian Shu Wan Shu Li Hua Kai Qian Shu Wan Shu Li Hua Kai $$\\cdots \\cdots$$"}, {"key": "3337", "content": "Jiajia has $$7$$ hats, all brims facing down. Flipping $$2$$ hats at a time is considered one flip. Can she, through multiple flips, make all the $$7$$ hat brims face up?"}, {"key": "3338", "content": "The combined age of the brother and sister this year is $$17$$ years old. In a few years, when the brother's age is an even number, the sister's age will be ( ) number."}, {"key": "3339", "content": "\u2605\u2605\u2605\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u2026\u2026 In such a sequence of shapes, the $$30$$th one is ( ) shape."}, {"key": "3340", "content": "As shown in the diagram, from the starting point to the endpoint, it is required to take the flag on each station, and each station is allowed to be passed only once. How many different ways are there ( ).\n question_3340-image_0"}, {"key": "3341", "content": "A sequence of shapes arranged in a pattern: \u25a1, \u25b3, \u2606, \u25c7, \u25cb, \u25a1, \u25b3, \u2606, \u25c7, \u25cb$$\\cdots \\cdots$$, then in the first $$58$$ shapes there are ( ) \u25a1."}, {"key": "3342", "content": "Determining the parity of an expression: (odd number $$-$$ even number) $$\\times$$ odd number $$=$$ ( )."}, {"key": "3343", "content": "A frog jumps among three points $$ABC$$, if it starts from point $$A$$ and returns to point $$A$$ after jumping $$4$$ times, how many different ways of jumping are there in total? ( )"}, {"key": "3344", "content": "There are $$6$$ points and $$9$$ line segments in the diagram below. A beetle starts at point $$A$$ and has to crawl to point $$F$$ along certain line segments. During its journey, the beetle can only move right, down, or diagonally to the bottom right. How many different ways can the beetle reach point $$F$$? ( )\n question_3344-image_0"}, {"key": "3345", "content": "There are $$80$$ apples in the large basket and $$70$$ apples in the small basket. A certain number of apples need to be transferred from the large basket to the small basket, so that the number of apples in the small basket is exactly $$2$$ times that in the large basket."}, {"key": "3346", "content": "In the book corner of Class ($$1$$) of the third grade, there are a total of $$47$$ books, consisting of storybooks and comic books. If $$7$$ storybooks are taken away, then the number of storybooks will be $$4$$ times the number of comic books. How many comic books and storybooks are there originally?"}, {"key": "3347", "content": "Containers A and B have a total of $$1000$$ kilograms of oil. If $$15$$ kilograms of oil are transferred from container B to A, then the oil in container A is $$4$$ times the amount of oil in container B at that moment. How many more kilograms of oil did container A originally have compared to container B?"}, {"key": "3348", "content": "The sum of three numbers A, B, and C is $$183$$. B is $$4$$ less than twice C, A is $$7$$ more than three times C. Find the values of A, B, and C."}, {"key": "3349", "content": "Two ropes of the same length, the first one is cut by $$31$$ meters, the second one is cut by $$19$$ meters, the remaining length of the second rope is $$4$$ times the length of the first one, how long is each rope originally?"}, {"key": "3350", "content": "For two numbers, A and B, if 50 is added to number A, it becomes equal to number B. If 350 is added to number B, it becomes 3 times the number A. What are the values of A and B?"}, {"key": "3351", "content": "In the leap year of 2012, there were more Mondays than Tuesdays, so the New Year's Day of 2012 fell on a _____. (Monday to Sunday are represented by 1 to 7 respectively)"}, {"key": "3352", "content": "February 1, 2019 is a Friday, the third last day of the month is a week."}, {"key": "3353", "content": "The digits 1 to 9 are filled into the grid below $$3\\times 3$$, where each number is used exactly once. If the number written to the right and below of the grid represents the product of the numbers filled in that row or column, then the number filled in the \"*\" grid should be. question_3353-image_0"}, {"key": "3354", "content": "The so-called \"third-order multiplication magic square\" refers to filling a $$3\\times 3$$ grid with $$9$$ integers, none of which are equal to $$0$$, in such a way that the product of the three numbers in each row, each column, and each diagonal line is equal. Please complete the following \"multiplication magic square\". The number represented by \"$$x$$\" is. question_3354-image_0"}, {"key": "3355", "content": "An $$N$$th order magic cube is composed of $$N\\times N\\times N$$ different positive integers arranged in a matrix, satisfying that the sum of any row, column, or diagonal of $$N$$ numbers is the same. This sum is called the magic sum, and a magic cube made up of numbers from $$1$$ to $$N\\times N\\times N$$ is called a regular magic cube. An example of a 4th order regular magic cube is shown below, with four layers in total. Then, the magic sum of a 7th order regular magic cube is. question_3355-image_0 question_3355-image_1 question_3355-image_2 question_3355-image_3"}, {"key": "3356", "content": "As shown in the right figure, place the first $$9$$ odd positive numbers $$1$$, $$3$$, $$5$$, $$7$$, $$9$$, $$11$$, $$13$$, $$15$$, $$17$$ in the three-order magic square below, so that the sum of the numbers horizontally, vertically, and diagonally are equal, then $$A+E=$$ ( ).\n question_3356-image_0"}, {"key": "3357", "content": "Fill $$2$$, $$3$$, $$4$$, $$7$$, $$11$$, $$12$$, $$13$$, $$15$$ into the following $$8$$ blank spaces respectively, so that the average of each row is the same and the average of each column is also the same. $$1$$$$9$$$$5$$$$14$$"}, {"key": "3358", "content": "In the image below, the sum of every horizontal row and every vertical column of $$3$$ numbers is equal. Find the sum of $$A$$, $$B$$, $$C$$. question_3358-image_0"}, {"key": "3359", "content": "Please fill in the numbers $$1$$ to $$16$$ into the diagram below (some numbers are already filled in), so that the sum of the numbers in each row, each column, and the two diagonals are all equal. 31641271138"}, {"key": "3360", "content": "A certain city's transportation system consists of several intersections (the intersections of lines in the diagram below) and streets (the lines in the diagram below), with each street connecting two intersections. All streets are bidirectional, and each street has a length value (marked on the respective line in the diagram). A postman delivering newspapers and letters needs to start from the post office, pass through every street under his jurisdiction, and finally return to the post office (each street can be passed through more than once). He can arrange his route in such a way that the shortest total length he travels is. (Unit: kilometers) question_3360-image_0"}, {"key": "3361", "content": "A little bug crawls along the edge of a rectangular box that is $$6$$ meters long, $$4$$ meters wide, and $$5$$ meters high. If it can only move forward and not backward, and it cannot crawl along the same edge twice, then the maximum distance it can crawl is in meters. question_3361-image_0"}, {"key": "3362", "content": "The right image is the floor plan of an exhibition hall. Can a visitor pass through each door once without repeating? If not, please explain why. If yes, where should they start? question_3362-image_0"}, {"key": "3363", "content": "The figure is the floor plan of a certain restaurant, consisting of five small halls, with doors connecting adjacent halls, and there is an entrance. Can you enter from the entrance and pass through all the doors once without repeating? If possible, please indicate the route. If not, which door should be closed to make it possible? question_3363-image_0"}, {"key": "3364", "content": "As shown in the figure, the roads in a community garden consist of a rectangle that is $$480$$ meters long and $$200$$ meters wide; a rhombus with a side length of $$260$$ meters, and two roads that cross each other in a plus sign. One day, Mr. Wang enters the garden from point $$A$$, walks through all the roads in the garden, and leaves from point $$A$$. If he walks at a speed of $$60$$ meters per minute, then the minimum time he needs to enter and exit the garden is minutes.\n question_3364-image_0"}, {"key": "3365", "content": "Grandma Li walks on the path in the heart street garden (as shown below), can she walk all the paths once without repeating any, and return to the starting point? If not, what route should she choose to make the total journey the shortest? What is the shortest distance? question_3365-image_0"}, {"key": "3366", "content": "Each line in the diagram represents a street, and the numbers on the lines represent the kilometers of these streets. The postal van departs from the post office, must travel through each street, and finally return to the post office. Question: The minimum kilometers the postal van must travel is. question_3366-image_0"}, {"key": "3367", "content": "There are 15 chickens and rabbits in a cage, with a total of 44 legs. How many rabbits are there?"}, {"key": "3368", "content": "Dian Dian has raised some chickens and rabbits together in a cage. After counting, there are a total of $$35$$ heads and $$94$$ legs. How many chickens and how many rabbits does Dian Dian have?"}, {"key": "3369", "content": "Once upon a time, there was a mountain, and within the mountain was a temple, within the temple lived many young monks. Two young monks carried water with one pole and one bucket, while one young monk carried water with one pole and two buckets. In total, they used $$38$$ poles and $$58$$ buckets. So, there are young monks carrying water, and monks lifting water."}, {"key": "3370", "content": "A group of hunters and a group of dogs, two groups walking together. In total, there are 160 heads and 390 legs. How many hunters and dogs are there? (Note: Here 160 and 390 refer to the numbers 160 and 390.)"}, {"key": "3371", "content": "A car transports $$2000$$ pieces of glassware. It was agreed that the freight for each piece would be $$2$$ yuan, and if one piece was damaged, not only would the freight not be paid, but also an indemnity of $$10$$ yuan would have to be given. As a result, the actual freight received was $$3796$$ yuan. In this transport process, a total of pieces of glassware were damaged."}, {"key": "3372", "content": "In a cage where chickens and rabbits are kept together, there are a total of $$25$$ heads and $$80$$ legs. How many chickens and rabbits are there respectively?"}, {"key": "3373", "content": "A class has $$46$$ students, among which $$40$$ students can play table tennis, and $$38$$ students can swim. What is the maximum number of students who can do both activities?"}, {"key": "3374", "content": "A shepherd herded a flock of sheep across $$10$$ rivers, every time they crossed a river half of the sheep fell into the river, and each time he retrieved $$4$$ of them, finally, there were $$8$$ sheep left. The total number of sheep before crossing the rivers was ."}, {"key": "3375", "content": "Fill in the blanks with numbers $$1\\sim 6$$ so that each row, each column, and each bold-bordered palace contains unique numbers. In the Sudoku, each shape represents a number, and the same shape represents the same number, while different shapes represent different numbers (there are a total of $$6$$ shapes in the figure). Then $$\\bigcirc\\times\\square=$$."}, {"key": "3376", "content": "Fill in the blank with orange, peach, apple, or pear, so that each row and column of the table below does not have repeated fruits. What is the fruit in the second column of the fourth row?\n question_3376-image_0"}, {"key": "3377", "content": "In the right image, each row and column contains the numbers $$1-4$$, each number appears only once in each row and column, $$B$$ should be filled with ( ).\n question_3377-image_0"}, {"key": "3378", "content": "question_3378-image_0, question_3378-image_1 should be filled with ( )."}, {"key": "3379", "content": "A number is added to $$37$$, multiplied by $$37$$, subtracted by $$37$$, and then divided by $$37$$, the result is $$37$$. What is the number?"}, {"key": "3380", "content": "Class 6 ($$1$$) has $$48$$ people, of which $$26$$ people participate in the math competition, $$24$$ people participate in the essay competition, and $$12$$ people participated in both. There are ( ) people who did not participate in either."}, {"key": "3381", "content": "There are $$28$$ people with science books, $$26$$ people with story books, $$10$$ people have both, and $$2$$ people have neither. There are a total of students in the class."}, {"key": "3382", "content": "In a cage containing both chickens and rabbits, there are a total of $$206$$ feet, and there are $$52$$ more chickens than rabbits. The number of chickens is ( )."}, {"key": "3383", "content": "Class 3 ($$1$$) has $$14$$ people who participate in the art group, $$10$$ people who participate in the English group, and there are $$6$$ people who participate in both groups. The total number of people in both groups is ( ) people."}, {"key": "3384", "content": "A farm raises chickens and rabbits totaling $$210$$ animals. It is known that the number of chicken legs is $$2$$ times the number of rabbit legs. There are ( ) chickens."}, {"key": "3385", "content": "Today, there are chickens and rabbits living together in a cage. It is known that there are a total of $$35$$ heads and $$96$$ legs. How many rabbits are there?"}, {"key": "3386", "content": "The image below shows an unfinished fourth order magic square. So, the spaces $$A$$ and $$B$$ should be filled with ( ).\n question_3386-image_0"}, {"key": "3387", "content": "The figure below is a part of a third-order magic square, $$X= $$ ( ) .\n question_3387-image_0"}, {"key": "3388", "content": "Can the figure below be drawn in one stroke? ( )\n question_3388-image_0"}, {"key": "3389", "content": "The statistical chart that can reflect the increase or decrease in quantity is ( )."}, {"key": "3390", "content": "As shown in the diagram, fill in the appropriate numbers in the grid so that the sum of the three numbers in each row, each column, and each diagonal is equal. The number that should be filled in the cell marked with a \u201c\u2605\u201d is ().\n question_3390-image_0"}, {"key": "3391", "content": "The figure below is a statistical chart of Xiao Hua's scores for five math tests. The average score of Xiao Hua's five tests is ____.\n question_3391-image_0"}, {"key": "3392", "content": "Determine if the following figures can be drawn in one stroke. If so, please provide a method. If not, where should a line be added ( ) to make it drawable in one stroke.\n question_3392-image_0"}, {"key": "3393", "content": "The number equal in magnitude to $$4.02$$ is ( )."}, {"key": "3394", "content": "The highest digit of the decimal part is ( ) digits."}, {"key": "3395", "content": "Calculate: $$1998+199.8+19.98+1.998+2.222=$$"}, {"key": "3396", "content": "Expand $$0.00501$$ to $$5.01$$ times its original size; reduce $$67.15$$ to (fill in fraction) its original size, which is $$0.6715$$; reduce $$327.2$$ to (fill in fraction) its original size, which is $$3.272$$."}, {"key": "3397", "content": "Calculate: $$63.981-\\left( 19.52+1.3145 \\right)+41.7-0.09=$$"}, {"key": "3398", "content": "Calculate: (1) 139.05+8.74+47.26-32.1-75.05= (2) 321.19-5.552-121.448+67.81="}, {"key": "3399", "content": "As shown, the vertex $$O$$ of $$\\angle AOB$$ is on line $$l$$. It is known that the sum of all angles less than a straight angle in the figure is $$400$$ degrees. Then, $$\\angle AOB$$ is ___ degrees. question_3399-image_0"}, {"key": "3400", "content": "There is an acute angle and an obtuse angle in the picture. question_3400-image_0"}, {"key": "3401", "content": "A ray $$OA$$, if two more rays $$OB$$ and $$OC$$ are drawn from point $$O$$, making $$\\angle AOB=72{}^\\circ $$, and $$\\angle BOC$$ is three times $$\\angle AOC$$, find the degrees of $$\\angle BOC$$."}, {"key": "3402", "content": "As shown in the diagram, $$AB$$ is a straight line, $$OC$$ bisects $$\\angle AOD$$ into two equal angles, $$OE$$ is within $$\\angle BOD$$, and $$\\angle BOD=3\\angle DOE$$, $$\\angle COE=72{}^\\circ $$, then $$\\angle EOB$$= degrees. question_3402-image_0"}, {"key": "3403", "content": "As shown in the figure, it is known that $$\\angle ACE=4\\angle ECB$$. Find the degree of $$\\angle DCE$$. question_3403-image_0"}, {"key": "3404", "content": "As shown in the figure, $$\\angle AOD=7\\angle BOC$$, find the degree of $$\\angle DOC$$. question_3404-image_0"}, {"key": "3405", "content": "There are a total of squares in the picture.\n question_3405-image_0"}, {"key": "3406", "content": "In the figure below, there are a total number of rectangles.\n question_3406-image_0"}, {"key": "3407", "content": "Count the total number of triangles in the image on the right. question_3407-image_0"}, {"key": "3408", "content": "There are $$13$$ nails on a wooden board (as shown in the lower-left image). By using a rubber band around some of the nails, you can form shapes such as triangles, squares, trapezoids, etc. (as shown in the lower-right image). Please answer: How many squares can be formed. question_3408-image_0"}, {"key": "3409", "content": "The total number of squares in the diagram below is. question_3409-image_0"}, {"key": "3410", "content": "The image on the right is half of a square, and it is divided into small isosceles right-angled triangles. In the image, there are a number of squares and a number of triangles. question_3410-image_0"}, {"key": "3411", "content": "$$16$$ nails are arranged in a grid with both horizontal and vertical intervals of $$1$$ cm. Using a rubber band to loop around some of the nails, you can form shapes like triangles, squares, trapezoids, etc. Please answer: How many squares can be formed? question_3411-image_0"}, {"key": "3412", "content": "As shown in the diagram, it is composed of small triangles with a side length of $$1$$. Among them, the number of triangles with a side length of $$4$$ is.\n question_3412-image_0"}, {"key": "3413", "content": "Count the number of rectangles (including squares) in the picture. question_3413-image_0"}, {"key": "3414", "content": "3 years ago, the sum of Xiao Zhi's parents' ages was 8 times Xiao Zhi's age; 6 years later, the sum of his parents' ages will be 5 times Xiao Zhi's age minus 3 years. Therefore, Xiao Zhi\u2019s age this year is. If the father is 6 years older than the mother, the father's age was 10 times Xiao Zhi's age years ago."}, {"key": "3415", "content": "The two brothers both thought that only they themselves would age by one year each year and that others would not grow up. One day, the elder brother said to the younger brother, 'In $$3$$ more years, my age will be twice yours.' The younger brother said, 'That's wrong, in $$3$$ more years, I will be the same age as you.' At this time, the younger brother is years old, and the elder brother is years old."}, {"key": "3416", "content": "There are three people: A, B, and C. When A's age is twice that of B, C is $$22$$ years old; when B's age is twice that of C, A is $$31$$ years old; when A is $$60$$ years old, C is years old."}, {"key": "3417", "content": "When A is as old as B, A's age is $$3$$ times that of B; when B reaches A's current age, A will be $$2$$ times B's age minus $$15$$ years. Thus, A's current age is years and B's current age is years."}, {"key": "3418", "content": "Given $$A=a+b$$, $$B=a-b$$, $$C=2a$$, $$D={{b}^{2}}$$. When $$a=4$$, $$b=3$$, calculate $$A+B-C+D=$$"}, {"key": "3419", "content": "The perimeter of parts A and B in the right figure is ( )\uff0e\n question_3419-image_0"}, {"key": "3420", "content": "The perimeter of the shape below is ( ) centimeters. (Unit \"cm\")\n question_3420-image_0"}, {"key": "3421", "content": "Cutting a small square from a rectangular sheet of paper, the remainder's perimeter is equal to the original rectangle's perimeter is ( )."}, {"key": "3422", "content": "With the numbers $3,6$, a two-digit number can be formed."}, {"key": "3423", "content": "With three cards $$1,2,7$$, you can form a three-digit number."}, {"key": "3424", "content": "Using the numbers $$1$$, $$2$$, and $$4$$, how many unique two-digit numbers can be formed without repeating digits."}, {"key": "3425", "content": "$$72\\div$$$$=9$$\uff0e"}, {"key": "3426", "content": "Perform vertical calculation: $$69\\div 3=$$"}, {"key": "3427", "content": "$$1$$ frog has $$4$$ legs, $$20$$ legs belong to $$5$$ frogs."}, {"key": "3428", "content": "$$1$$ cat eats $$12$$ fish in $$3$$ days, $$1$$ cat can eat fish per day."}, {"key": "3429", "content": "Divide a mooncake evenly into $$4$$ pieces, take one of them, this piece accounts for the total, take $$3$$ pieces account for the total."}, {"key": "3430", "content": "Xiao Ming has some candies at home. If these candies are divided equally into $$3$$ parts, and Xiao Ming eats one of those parts, then Xiao Ming has eaten $$1$$ part out of the total candies. (Fill in the fraction)"}, {"key": "3431", "content": "A road is $$100$$ meters long, with a parasol tree planted every $$10$$ meters, and trees must be planted at both the beginning and the end, so how many trees are planted in total."}, {"key": "3432", "content": "Place colored flags along one side of a road that is $$20$$ meters long, inserting a flag every $$4$$ meters, without placing them at either end. How many flags in total can be placed along this road? (The width of the flags is negligible) ( )."}, {"key": "3433", "content": "In front of the 'Youth Palace', there is a road that is $$100$$ meters long leading straight to the entrance. On both sides of the road, there is a pine tree every $$10$$ meters. So, in total, there are trees."}, {"key": "3434", "content": "The figure below shows a $$4\\times 4$$ area with $$3$$ trees planted. It is now required to pitch tents on the empty ground where no trees are planted, with the condition that tents must be pitched beside the trees. Any two tents must not share a common point, and the number of tents in each row is as shown on the far right, while the number of tents in each column is as shown at the bottom. Please draw the position of the tents.\n question_3434-image_0"}, {"key": "3435", "content": "As shown in the diagram, the safety zones and minefield in the blank area have been marked with \"$$O$$\" and \"$$X$$\" respectively. For the remaining shaded areas, which squares can be definitely identified as safety zones, please mark them with \"$$O$$\". The square in the first row and first column is ( ).\n question_3435-image_0"}, {"key": "3436", "content": "Xiaoming decides to travel to these three places: Hong Kong, Macau, and Taiwan. To visit these three attractions (without repetition), he has a total of different visiting orders."}, {"key": "3437", "content": "$$A$$, $$B$$, and $$C$$, three kids, pass the ball to each other, starting with $$A$$ as the first pass. After 2 passes, there are a total of various ways of passing the ball."}, {"key": "3438", "content": "$$\\text{A}$$, $$\\text{B}$$, and $$\\text{C}$$ three people practice passing the ball. Initially, the ball is in $$\\text{A}$$'s hands. After $$3$$ passes, the number of ways the ball is not in $$\\text{A}$$'s hands is."}, {"key": "3439", "content": "The three-digit number $$157$$ is an ( ) number."}, {"key": "3440", "content": "The two even numbers adjacent to $$36$$ are (\u3000\u3000)"}, {"key": "3441", "content": "$$12345678$$ is odd or even? ( )"}, {"key": "3442", "content": "The product of $$25\\times 40$$ has () $$0$$ at the end."}, {"key": "3443", "content": "The result of $$698\\times 2$$ should be ( )."}, {"key": "3444", "content": "The result of $$41\\times 5\\times 2$$ is ( )."}, {"key": "3445", "content": "$$560\\div \\left( 7\\times 5 \\right)=$$\uff08 \uff09\uff0e"}, {"key": "3446", "content": "Which of the following problems has a quotient with a zero in the middle? ( )"}, {"key": "3447", "content": "Which of the following conversion is incorrect (    )."}, {"key": "3448", "content": "There are $$20$$ more white balls than red balls, the white balls are twice the number of red balls, there are red balls, there are white balls."}, {"key": "3449", "content": "There was some water in the bottle, and after adding $$20$$ grams, the weight became $$3$$ times the original. The original amount of water in the bottle was grams."}, {"key": "3450", "content": "Qingming Festival arrived, Eddie, and Vi went hiking. Eddie brought $$20$$ more snack packs than Vi. Eddie's snacks were twice as many as Vi's, and Vi brought snack packs."}, {"key": "3451", "content": "$$2016$$ year's $$11$$th month $$1$$st is Tuesday, then this year's $$11$$th month $$30$$th is Wednesday ( )."}, {"key": "3452", "content": "Please fill each cell of this unfinished $$3\\times 3$$ grid with a different number so that the sum of each row, each column, and each diagonal equals $$30$$.\n question_3452-image_0"}, {"key": "3453", "content": "Four students participated in the long jump competition, and the results are as follows. The first place is ( ).\n\n\n\n\nName\n\nXiao Lin\n\nXiao Qiang\n\nXiao Gang\n\nXiao Ming\n\n\n\nScores/meters\n\n$$3.4$$\n\n$$2.8$$\n\n$$2.9$$\n\n$$3.1$$"}, {"key": "3454", "content": "Here is the number of people who like sports in Class 32.\n\n\n\n\nSports\n\nJump Rope\n\nRacing\n\nTable Tennis\n\nShot Put\n\n\n\nNumber of People\n\n\u5341\u5341\n\n\u5341\u5341\u5341\n\n\u5341\u5341\u5341\n\n\u5341\u5341\n\n\n\nThe number of people who like racing is ( )."}, {"key": "3455", "content": "Below is a statistical table of the fruit preferences of students in a certain grade (Class 2), the fruit that the most people like is ( ).\n question_3455-image_0"}, {"key": "3456", "content": "A one-stroke drawing refers to a drawing that starts from a point on the graph, does not lift the pen off the paper, does not repeat, and can be completed in one stroke. Among the figures below, which one can be drawn in one stroke ( )."}, {"key": "3457", "content": "Among the following figures, the one that cannot be drawn with one stroke is ().\n question_3457-image_0 question_3457-image_1 question_3457-image_2"}, {"key": "3458", "content": "Determine if the following figures can be drawn with one stroke\n question_3458-image_0"}, {"key": "3459", "content": "There are $$3$$ chickens and rabbits in a cage, counting a total of $$8$$ legs, so there are ( ) chickens."}, {"key": "3460", "content": "There are $$4$$ chickens and rabbits in a cage, with a total of $$10$$ legs. The number of rabbits is ( )."}, {"key": "3461", "content": "There are $$6$$ chickens and rabbits in a cage with $$20$$ legs in total, the number of rabbits is ( )."}, {"key": "3462", "content": "Tie two $$10$$ meters long ropes together (with overlapping parts), the length is ( ) $$20$$ meters."}, {"key": "3463", "content": "The left circle represents students who like Chinese, the right circle represents students who like Math, so the shaded part represents ( ).\n question_3463-image_0"}, {"key": "3464", "content": "Two iron bars, one $$23$$ cm and the other $$37$$ cm in length, are welded together to form a single iron bar. Given that the welded joint is $$3$$ cm long, the total length of the iron bar after welding is cm."}, {"key": "3465", "content": "As shown in the diagram, it is a $$3\\times 3$$ magic square, where the sum of the three numbers in each row, each column, and each diagonal are equal. What number should fill in the \"?\". question_3465-image_0"}, {"key": "3466", "content": "The sum of $$1+2+3+4+5\\cdots \\cdots +2017+2018$$ is. (Odd or Even)"}, {"key": "3467", "content": "Chickens and rabbits in the same cage, there are $$30$$ heads in total, $$88$$ feet. How many chickens and rabbits are in the cage."}, {"key": "3468", "content": "The length of a rectangle is $$12$$ meters, and the width is $$5$$ meters. The width of the rectangle remains the same, and the length increases by $$8$$ meters. The area of the current rectangle has increased by square meters from the original rectangle."}, {"key": "3469", "content": "The cafeteria bought a batch of rice. For the first use, they used more than half of the total amount plus $$20$$ kilograms, and for the second use, they used $$39$$ kilograms, which exactly depleted the stock. This batch of rice had a total of kilograms."}, {"key": "3470", "content": "$$96\\times 57+96\\times 43=$$\uff0e"}, {"key": "3471", "content": "Two integers have a difference of $$20$$, one is $$5$$ times the other. Find the smaller and the larger numbers."}, {"key": "3472", "content": "Can the following figures be drawn in one stroke?\n question_3472-image_0 question_3472-image_1"}, {"key": "3473", "content": "Fill in the blank based on the diagram: The average monthly water usage of Apu's family in the third quarter is tons.\n question_3473-image_0"}, {"key": "3474", "content": "20.02 is read as (\u3000\u3000)."}, {"key": "3475", "content": "As shown in the diagram, there are ( ) squares in total.\n question_3475-image_0"}, {"key": "3476", "content": "The left image contains ( ) line segments."}, {"key": "3477", "content": "The side length of a square is $$m$$, the perimeter of this square is ( )."}, {"key": "3478", "content": "$$25\\times (80+4)=$$ ()\uff0e"}, {"key": "3479", "content": "A cookie box weighs $$a$$ grams, a cookie weighs $$5$$ grams, putting $$x$$ cookies into the cookie box, the total weight of the box and cookies is ( ) grams."}, {"key": "3480", "content": "Fill in the number according to the rule, only need to fill in ( ) on the line.\n$$2$$, $$6$$, $$10$$, $$14$$, , $$22$$."}, {"key": "3481", "content": "Which group's arrangement is different from the other three ()?"}, {"key": "3482", "content": "Insert brackets appropriately in the following expression to make the equation true. The correct way to insert them is ( ).\n$$17-7+5=5$$"}, {"key": "3483", "content": "Fill in the appropriate operator or parentheses in the equation below, the option that makes the equation valid is ( ).\n$$3$$ $$5$$ $$6=9$$"}, {"key": "3484", "content": "Eddie goes home from school, but he doesn't know how many ways there are to take the shortest route. Kids, please help out! ()\n question_3484-image_0"}, {"key": "3485", "content": "Eddie gives prizes to customers, giving out exactly $$6$$ per person results in no leftovers. So, did he make a profit, a loss, or neither? ( )"}, {"key": "3486", "content": "Wei'er distributes prizes to customers, giving each person 5 prizes, and then there are 10 remaining, so is it a profit or a loss? ( )"}, {"key": "3487", "content": "Xuexue has some apples, which are evenly distributed to $$5$$ kids. Each kid gets $$4$$ apples. After that, Xuexue has $$2$$ apples left. How many apples did Xuexue originally have?"}, {"key": "3488", "content": "A large rectangle-shaped cake on the right side, after taking a bite, turns into the shape on the left side. Compared to its original perimeter, what change has occurred?\n question_3488-image_0"}, {"key": "3489", "content": "Among the following shapes, the one with the longest perimeter is ( ). (Unit: $$\\text{cm}$$)"}, {"key": "3490", "content": "$$137-\\left( 350-263 \\right)=$$( )\uff0e"}, {"key": "3491", "content": "Calculate: $$432+261+68-161=$$."}, {"key": "3492", "content": "The correct result of using the distributive property of multiplication to remove the parenthesis in $$25\\times \\left( 40-2 \\right)$$ is ( )."}, {"key": "3493", "content": "A and B have $$360$$ yuan together, A's money is 3 times B's money, B's money is ( ) yuan."}, {"key": "3494", "content": "Eddie and Vi saved a lot of reward cards, after counting, they found: after Eddie gives Vi $$10$$ cards, both have equal numbers of reward cards, find how many more cards Eddie originally had than Vi ( )."}, {"key": "3495", "content": "Two bookshelves, where the number of books on bookshelf A is $$5$$ times the number on bookshelf B. If bookshelf A has $$120$$ more books than bookshelf B, then bookshelf B has ( ) books."}, {"key": "3496", "content": "\"Xiao Xiao has $$2$$ tops, $$4$$ pants, she has $$6$$ ways to match.\" This statement is"}, {"key": "3497", "content": "Lele has $$4$$ technology books and $$3$$ story books. He plans to donate one technology book and one story book. He has ( ) different methods of donation."}, {"key": "3498", "content": "The divisor () is smaller than the remainder."}, {"key": "3499", "content": "( )$$\\div 6=4\\cdots \\cdots 3$$, to make the expression valid, the number in ( ) is."}, {"key": "3500", "content": "A number divided by $$4$$, the quotient is $$9$$, the remainder could be ( )."}, {"key": "3501", "content": "The perimeter of a square is $$24$$ cm, the side length of this square is cm."}, {"key": "3502", "content": "With the numbers $$2$$, $$4$$, and $$6$$, how many different two-digit numbers can be formed. (Numbers can be reused)"}, {"key": "3503", "content": "The teacher brought three wooden boards, each marked with the numbers $$4$$, $$5$$, $$7$$. Xiaoyue can use these boards to form different numbers."}, {"key": "3504", "content": "Calculate: $$148\u00d75=$$\uff0e"}, {"key": "3505", "content": "The product of the largest two-digit number and the smallest two-digit number is ( )."}, {"key": "3506", "content": "$$5\\times 43=$$"}, {"key": "3507", "content": "Set up the calculation in columns:\n$$34\\times 12=$$\uff1b$$76\\times 11=$$\uff0e"}, {"key": "3508", "content": "In division, $$0$$ cannot be the ( )."}, {"key": "3509", "content": "If $$a\\div b=0$$ then ( )."}, {"key": "3510", "content": "If it takes $$8$$ minutes to cut a piece of wood into $$3$$ pieces, then to cut $$12$$ pieces of wood into $$6$$ pieces each, it requires minutes."}, {"key": "3511", "content": "When Sun Wukong fought with the monster, he mentioned his name 'Sun Xingzhe' in various ways several times. Sun Wukong could transform the three characters of 'Sun Xingzhe' into different names."}, {"key": "3512", "content": "$$89000\\div25\\div4=$$"}, {"key": "3513", "content": "Calculate:\n$$(4500+450+45)\\div 45=$$"}, {"key": "3514", "content": "As shown in the diagram, now one needs to walk from room $$1$$ to room $$4$$. If each room can only be passed through once at most, then there are a total number of different ways to do so.\n question_3514-image_0"}, {"key": "3515", "content": "There is a row of colored flags on the sports field, totaling $$34$$ flags, arranged in a sequence of $$3$$ red flags followed by $$1$$ yellow flag. Among these flags, there are $$26$$ red flags and $$8$$ yellow flags."}, {"key": "3516", "content": "Lulu has $$5$$ days to visit, she plans to visit $$A$$, $$B$$, and $$C$$ three scenic spots, changing to a different one each day. She has already planned to go to scenic spot $$A$$ on the first day, to $$B$$ on the second day, and back to $$A$$ on the fifth day. Given her current plans are not to be disrupted, she has a total of different visiting methods."}, {"key": "3517", "content": "Calculate: $$125\\times 29\\times 8=$$"}, {"key": "3518", "content": "Observe the following shapes:\n$$\\Phi \\ \\Phi \\ \\Phi \\ \\Delta \\ \\Delta \\ \\Phi \\ \\Phi \\ \\Phi \\ \\Delta \\ \\Delta \\cdots \\cdots $$\nThe $$100$$th shape is."}, {"key": "3519", "content": "Calculate: $$999\\div 3\\div 37\\div 3=$$\uff0e"}, {"key": "3520", "content": "$$900\\div25\\div4=$$"}, {"key": "3521", "content": "The Xiaolin family raised $$4$$ baby rabbits, and the number of adult rabbits they raised is $$3$$ times the number of baby rabbits. So, how many adult rabbits does the Xiaolin family have?"}, {"key": "3522", "content": "Simplified calculation: $$29\\times17+17\\times71=$$"}, {"key": "3523", "content": "Eddie and Dengdeng have a total of $$56$$ glass marbles, Eddie's number of glass marbles is $$6$$ times the number of Dengdeng's. Thus, Eddie has glass marbles, and Dengdeng has glass marbles."}, {"key": "3524", "content": "The area of a square with a side length of $$6\\text{cm}$$ is $${\\text{cm}}^{2}$$."}, {"key": "3525", "content": "The professor sold a total of 2.2 million copies of books last year and this year, with this year's sales volume being 200,000 copies more than three times last year's sales volume. How many copies were sold this year?"}, {"key": "3526", "content": "Complete the following clever calculation: $$870\\times 12\\div 87=$$\uff0e"}, {"key": "3527", "content": "Grandpa Li's family has $$18$$ more ducks than geese. It is known that the number of ducks is $$2$$ more than three times the number of geese."}, {"key": "3528", "content": "There are $$20$$ more white balls than red balls, the white balls are $$3$$ times the number of red balls, there are number of red balls, there are number of white balls."}, {"key": "3529", "content": "The perimeter of a rectangle and a square are equal, it is known that the perimeter of the square is $$60$$ cm. If the length of the rectangle is $$20$$ cm, then the area of this rectangle is square centimeters."}, {"key": "3530", "content": "Xiao Ai has $$20$$ rabbits at home, the number of baby rabbits is $$4$$ times the number of adult rabbits, there are adult rabbits, there are baby rabbits."}, {"key": "3531", "content": "Dengdeng has $$6$$ more apples than Adi, knowing that the number of Dengdeng's apples is $$3$$ times that of Adi's apples, then Adi has apples, Dengdeng has apples."}, {"key": "3532", "content": "$$2018$$ year $$10$$ month $$10$$ day is Wednesday, $$2028$$ year $$10$$ month $$10$$ day is Tuesday."}, {"key": "3533", "content": "The National Day of $$2000$$ was a Sunday, 20 days later it was ( )."}, {"key": "3534", "content": "If today is Monday, then the $$100$$th day from today is on a weekday."}, {"key": "3535", "content": "From $$2017$$ year $$10$$ month $$3$$ day to $$2017$$ year $$10$$ month $$30$$ day, a total of days."}, {"key": "3536", "content": "In the orchard, there are $$18$$ more peach trees than plum trees, and the number of peach trees is exactly $$4$$ times the number of plum trees. Now, the orchard has plum trees and peach trees."}, {"key": "3537", "content": "Xiao Nan, Xiao Bei, and Xiao Xi went to the bookstore to buy books together. The number of books Xiao Nan bought is twice as many as that of Xiao Xi, and the number of books Xiao Bei bought is three times as many as that of Xiao Xi. They bought a total of 60 books. Xiao Nan bought books, Xiao Bei bought books, Xiao Xi bought books."}, {"key": "3538", "content": "As shown in the diagram, there is a three-order magic square (i.e., the sums of the three numbers in each of the three rows, three columns, and two diagonals are all equal), then $$A$$ in the diagram is. question_3538-image_0"}, {"key": "3539", "content": "Among the following options, the area of ( ) is closest to $$1$$ square decimeter."}, {"key": "3540", "content": "The perimeter of a rectangle and a square are equal. The rectangle is $$20$$ meters long and $$10$$ meters wide. Thus, the area of the rectangle is square meters, and the area of the square is square meters."}, {"key": "3541", "content": "The number of white balls is $$60$$ more than the number of red balls, the white balls are $$2$$ times the number of red balls, there are ________ red balls, and ________ white balls."}, {"key": "3542", "content": "Today is Sunday, in another $$50$$ days it will be Monday."}, {"key": "3543", "content": "If today is Monday, then the $$86$$th day from today is ."}, {"key": "3544", "content": "As shown in the diagram, fill in appropriate numbers at $$A$$, $$B$$, $$C$$, $$D$$ to form a third-order magic square. Then $$C-B=$$. question_3544-image_0"}, {"key": "3545", "content": "Teacher Zhou and Teacher Xiao initially had a total of $$240$$ score cards, and Teacher Zhou had $$3$$ times more than Teacher Xiao plus $$40$$ cards. How many score cards did Teacher Xiao originally have?"}, {"key": "3546", "content": "If today is Monday, then the $$100$$th day from today is on a weekday."}, {"key": "3547", "content": "There are $$18$$ more white balls than red balls, and the number of white balls is $$4$$ times the number of red balls. There are _____ red balls and _____ white balls."}, {"key": "3548", "content": "In the orchard, there are $$38$$ more pear trees than apple trees, and the number of pear trees is exactly $$3$$ times the number of apple trees. There are now apple trees and pear trees in the orchard."}, {"key": "3549", "content": "$$2015$$ New Year's Day is Thursday, $$2016$$ New Year's Day is on a week."}, {"key": "3550", "content": "Fill in the remaining $$5$$ squares in the diagram below with natural numbers so that the sum of the numbers in each row, each column, and each diagonal is the same. What number should be filled in the rightmost space of the third row?\n question_3550-image_0"}, {"key": "3551", "content": "Given that the magic sum of a 3x3 magic square is $$90$$, then the center number of this 3x3 magic square is ."}, {"key": "3552", "content": "Observe the figure below, what is the minimum number of strokes needed to complete this figure.\n question_3552-image_0"}, {"key": "3553", "content": "There are a total of $$15$$ tricycles and cars in the parking lot, with $$52$$ wheels in total. How many tricycles and cars are there respectively?"}, {"key": "3554", "content": "A number plus $$5$$, then divided by $$5$$, the result is $$5$$, this number is."}, {"key": "3555", "content": "The ancient Chinese classic \"The Arithmetical Classic of Sun Zi\" records the problem of chickens and rabbits in the same cage, saying: There are a number of chickens and rabbits in a cage. Counting from above, there are $$8$$ heads, and from below, there are $$26$$ feet. Thus, there are chickens, and rabbits."}, {"key": "3556", "content": "The picture below has a singularity. \n question_3556-image_0"}, {"key": "3557", "content": "The third grade's Class 1 and Class 2 at Peihua Primary School have a total of $$54$$ students. If $$3$$ students are transferred from Class 1 to Class 2, then the number of students in the two classes become equal. Therefore, originally, Class 1 had people, and originally, Class 2 had people."}, {"key": "3558", "content": "Below is a statistical table for the number of skips in one minute by students of Class 3 (1).\n\n\n\n\nNumber of People\n\nBelow $$80$$\n\n$$80$$~$$90$$\n\n$$91$$~$$100$$\n\n$$101$$~$$110$$\n\nAbove $$110$$\n\n\n\nGender\n\nMale\n\n$$4$$\n\n$$6$$\n\n$$9$$\n\n$$4$$\n\n$$2$$\n\n\n\nFemale\n\n$$1$$\n\n$$4$$\n\n$$6$$\n\n$$6$$\n\n$$7$$\n\n\n\nIn class 3 (1) the total number of students who can skip more than $$100$$ times in one minute is\uff0e"}, {"key": "3559", "content": "Teacher Li gave two thinking problems to the students of class 3-1. After marking, it was found that every student in the class got at least one question correct. There were $$30$$ students who got the first question correct, $$25$$ students who got the second question correct, and $$13$$ students who got both questions correct. Class 3-1 has a total of students."}, {"key": "3560", "content": "In Class 4(2) during a self-study session, there are $$30$$ students who finished their Chinese homework, $$20$$ students who finished their Math homework, $$9$$ students who finished both Chinese and Math homework, and $$6$$ students who did not finish either. Hence, the total number of students in the class is ."}, {"key": "3561", "content": "The weasel pays a New Year visit to the chicken, knowing that there are $$25$$ weasels and chickens in total, with $$96$$ legs in total. Each weasel has $$4$$ legs, each chicken has $$2$$ legs. How many weasels and chickens are there?"}, {"key": "3562", "content": "A bundle of rope, cut in half for the first time, then half of the remainder the second time, and half of the remainder again the third time, finally left with $$5$$ meters. The original length of this bundle of rope was meters."}, {"key": "3563", "content": "Below is a bar chart and the water usage statistics table for Xiao Pang's family for the four quarters of 2017: Quarter First Quarter Second Quarter Third Quarter Fourth Quarter Total Water Usage/Tons $$11$$ $$14$$ $$16$$ $$56$$ (1) The water usage of Xiao Pang's family in the fourth quarter is tons. (2) Draw a bar chart for the water usage of Xiao Pang's family for the four quarters of 2017. question_3563-image_0"}, {"key": "3564", "content": "Groups A and B together have 120 books. If group B borrows 20 books from group A, then both groups have the same number of books. How many books did group A and group B originally have?"}, {"key": "3565", "content": "Can the figure below be drawn in one stroke ( ).\n question_3565-image_0"}, {"key": "3566", "content": "As shown in the figure $$\\angle 1=$$$${}^\\circ$$\uff0c$$\\angle 2=$$$${}^\\circ$$. question_3566-image_0"}, {"key": "3567", "content": "Fill in the appropriate places in the equation below with the operation symbols $$+$$, $$-$$, $$\\times $$, $$\\div $$ or ( ), to make the equation valid. $$1~~~2~~~3~~~4~~~5=10$$"}, {"key": "3568", "content": "Insert an operator between adjacent numbers in the expression below to make the equation correct. $$3\\ \\ \\ \\ 3\\ \\ \\ \\ 3\\ \\ \\ \\ 3=2$$"}, {"key": "3569", "content": "Fill in \"$$+$$\", \"$$-$$\", or \"$$\\left( {~~~~} \\right)$$\" to make the equation correct. $$2$$$$4$$$$6$$$$8=8$$."}, {"key": "3570", "content": "Fill in the blank between two numbers with \"$$+$$\" or \"$$-$$\" to make the equation valid. ( )\n$$6$$ $$6$$ $$6$$ $$6$$ $$6=6$$"}, {"key": "3571", "content": "Insert \"$$+$$\" at the appropriate places to make the equation correct. $$1$$$$2$$$$3$$$$4$$$$5=60$$"}, {"key": "3572", "content": "Fold a square with side length of $$10$$ cm in half, and then cut along the fold line to get two rectangles. How many centimeters is the total perimeter of these two rectangles greater than the perimeter of the original square? question_3572-image_0"}, {"key": "3573", "content": "The number of reward cards owned by A is 5 times that of B. Now, A gives 20 reward cards to B, and after giving them, both have the same number of reward cards. A originally had cards."}, {"key": "3574", "content": "Xiao Hei has $$3$$ different storybooks, $$4$$ different comic books, and $$5$$ different science books. He chooses one book from each category to read, resulting in a number of different selection methods."}, {"key": "3575", "content": "The area of the polygon in the shaded part of the figure is square centimeters. question_3575-image_0"}, {"key": "3576", "content": "There are two shelves of books, totaling $$173$$ books. After $$38$$ books are taken from the first shelf, the number of books on the second shelf is $$2$$ times the number of books on the first shelf. How many books are on the second shelf?"}, {"key": "3577", "content": "As shown in the diagram, a large rectangle is divided into $$3$$ small rectangles and one small square. The area of the small square is $$6$$ square centimeters, and the areas of the two rectangles are respectively $$9$$ and $$30$$ square centimeters. The area represented by rectangle $$A$$ is ( ) square centimeters. question_3577-image_0"}, {"key": "3578", "content": "Dakuan has $$3$$ ways from home to the breakfast shop, and $$4$$ ways from the breakfast shop to school. Therefore, Dakuan has different choices from home to the breakfast shop and then to school."}, {"key": "3579", "content": "Among the figures below, which one is a parallelogram ( )."}, {"key": "3580", "content": "The correct formula for calculating the area of the figure below is ( ).\n question_3580-image_0"}, {"key": "3581", "content": "Complete the following fill-in:\n$$\\square \\div 11=9\\cdots \\cdots 2$$\nThe number in the square is."}, {"key": "3582", "content": "\"A rocket flies 4500 meters per second, so, how many meters can it fly in half an hour?\" To solve this problem, one must rely on ()."}, {"key": "3583", "content": "$$100$$ meters race. Xiao Ming took $$20$$ seconds, Xiao Gang took $$18$$ seconds, ran faster."}, {"key": "3584", "content": "An ostrich can run $$64$$ kilometers per hour. At this speed, it can run kilometers in $$2$$ hours."}, {"key": "3585", "content": "The road ahead will go through a tunnel, where speed is monitored intermittently, with a speed limit of $$60$$ km per hour (equivalent to $$1000$$ meters per minute). The total distance for speed measurement is $$4500$$ meters, and it took the doctor $$5$$ minutes to drive through. Did the doctor's car exceed the speed limit? question_3585-image_0 question_3585-image_1"}, {"key": "3586", "content": "Locations A and B are 3000 meters apart. The doctor plans to cycle from location A to B in 20 minutes. Just as he was about to leave, the bicycle broke down, causing a 5-minute delay. The doctor hopes to arrive at location B at the originally planned time. (1) What is the cycling time for the doctor in minutes? (2) How many meters should the doctor cycle per minute?"}, {"key": "3587", "content": "Location A and B are $$240$$ kilometers apart. A car was originally planned to travel from location A to B in $$6$$ hours. (1) It takes hours to travel half the distance. (2) In reality, after traveling half the distance, the car broke down and was stopped for $$1$$ hour. If it is to arrive at location B according to the original schedule, how many kilometers per hour should the car travel in the second half of the journey?"}, {"key": "3588", "content": "Doctor and Da Kuan's homes are $$650$$ meters apart, Doctor walks $$60$$ meters per minute, and Da Kuan walks $$70$$ meters per minute. Both start from their homes at the same time and walk towards each other on the same road, how far apart are the two after $$3$$ minutes? question_3588-image_0"}, {"key": "3589", "content": "One day, Jojo and his classmate agreed to meet at some point between them. Jojo walks $$65$$ meters per minute, and his classmate walks $$45$$ meters per minute. They set off at the same time and after $$50$$ minutes, they are still $$43$$ meters apart. How far apart were Jojo and his classmate originally?"}, {"key": "3590", "content": "Xiao Ying started observing a hyacinth from last Friday. At that time, some flowers had already bloomed. Since then, the number of flowers that bloomed each day was exactly equal to the number of flowers that had bloomed the previous day, with no flowers withering during this process. If the day when all the flowers of the hyacinth had bloomed was Thursday, what day of the week was it when exactly half of the flowers had bloomed?"}, {"key": "3591", "content": "After using more than half a bag of sugar and $$50$$ grams, $$200$$ grams remain. Originally, the bag of sugar weighed grams."}, {"key": "3592", "content": "$$\\frac{3}{5}$$ represents the meaning of evenly dividing the unit \"$$1$$\" into parts, taking among them parts, its fractional unit is ;\n$$\\frac{20}{20}$$ represents the meaning of evenly dividing the unit \"$$1$$\" into parts, taking among them parts, its fractional unit is."}, {"key": "3593", "content": "Compare: $$\\frac{3}{4}$$ and $$\\frac{4}{5}$$."}, {"key": "3594", "content": "The number of boys and girls in the competition arena was the same initially. Later, the total number of girls decreased by $$10$$, while the total number of boys increased by $$30$$. At this time, the number of boys was exactly $$3$$ times the number of girls. How many boys and girls were there originally?"}, {"key": "3595", "content": "Mom bought a basket of oranges and distributed them among the family members. If two people get $$4$$ each and the rest $$2$$ each, then there are $$6$$ oranges left over; if one person gets $$6$$ each and the rest $$4$$ each, then there are $$12$$ oranges short. How many oranges did mom buy, and how many people are there in the family?"}, {"key": "3596", "content": "\"$$*$$\" represents a new operation symbol, for example: $$1*1=1$$, $$1*2=3$$, $$1*3=6$$, $$1*4=10$$, $$1*100=5050$$, $$100*2=201$$, $$\\cdots\\cdots$$ Based on the information above, infer: (2) $$2020*3$$."}, {"key": "3597", "content": "\u2605\u2605\u25cb\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u25cb\u2026\u2026 In such a sequence of symbols, the $$87$$th one is shaped ($$1$$ represents \u2605, $$2$$ represents \u25cb), and there are a total of $$36$$ stars among $$87$$ symbols."}, {"key": "3598", "content": "Car A and Car B initially are $$300$$ meters apart, both vehicles start moving in the same direction at the same time, with Car A in front and Car B behind. The speed of Car A is $$60$$ meters per minute. If Car B wants to catch up to Car A within $$30$$ minutes, then the minimum speed of Car B should be meters/minute."}, {"key": "3599", "content": "The diagram below shows the roads among five villages $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$. The number inside $$\\bigcirc$$ is the number of students in each village needing to go to school, and the numbers on the roads represent the distance between two villages (unit: kilometers). Now, a primary school is to be established in one of the five villages. To minimize the total distance travelled by all students, the primary school should be built in. question_3599-image_0"}, {"key": "3600", "content": "Xiao Hong and Xiao Hua have a total of $$44$$ comic books. If Xiao Hong gives Xiao Hua $$5$$ books, they will have an equal number of comic books. Then, the number of comic books Xiao Hong has is __."}, {"key": "3601", "content": "This year the sum of the ages of the grandfather and his grandson is $$74$$ years old, two years later the age of the grandfather will be $$5$$ times that of his grandson, the difference in age between the grandfather and his grandson this year is years."}, {"key": "3602", "content": "Xiaoming is $$7$$ years old this year, and his mother is $$35$$ years old. How old was Xiaoming when his mother was exactly $$3$$ times his age?"}, {"key": "3603", "content": "The teacher said to Xiao Ming, \"My age $$15$$ years ago was the same as your age $$6$$ years from now. $$7$$ years ago, my age was $$8$$ times your age,\" Xiao Ming is years old this year, and the teacher is years old this year."}, {"key": "3604", "content": "Answer the following question: Fill in the blank with the appropriate number to make the vertical equation in the diagram correct, then the sum of the numbers is. question_3604-image_0"}, {"key": "3605", "content": "Answer the following question: In the equation below, the same symbols represent the same number, and different symbols represent different numbers. According to this equation, it can be deduced that: $$\\square +\\bigcirc +\\triangle +$$\u2606$$=$$\uff0e question_3605-image_0"}, {"key": "3606", "content": "Count the number of rectangles (including squares) in the figure below. question_3606-image_0"}, {"key": "3607", "content": "Eddy and Vi are preparing to beautify the entire Maize Magic School. Vi plans to plant pine trees along one side of the straight road leading to the magic castle gate. This road is $$40$$ meters long, and there is a $$5$$ meter gap between each two trees. How many pine trees are going to be planted in total?"}, {"key": "3608", "content": "Eddy and Vi are preparing to beautify the entire Maxim Magic School Square with a circular flower bed, which has a perimeter of $$80$$ meters. Now, they plan to place a flower pot every $$8$$ meters around the flower bed. How many flower pots can be placed in total?"}, {"key": "3609", "content": "1) Planting trees along one side of a 10-meter-long road, with a tree every 2 meters, and planting at both ends, there will be a total number of trees on this road. (The width of the trees is considered negligible) 2) Planting trees along one side of a 24-meter-long road, with a tree every 4 meters, planting at one end and not the other, there will be a total number of trees on this road. (The width of the trees is considered negligible)"}, {"key": "3610", "content": "The figure is a patient's body temperature record chart.\n question_3610-image_0 \nThe highest temperature of the patient is $$^\\circ \\text{C}$$, and the lowest is $$^\\circ \\text{C}$$."}, {"key": "3611", "content": "The image is a patient's body temperature record chart. \n question_3611-image_0 \nAt $$4$$ PM on June $$2$$, the patient's temperature was $${}^\\circ \\text{C}$$."}, {"key": "3612", "content": "Below is the statistical chart of the number of heartbeats per minute before and after Tian Tian's physical education class rope skipping.\n question_3612-image_0 \nBased on the statistical chart, answer the question.\nAfter how many minutes of rope skipping, Tian Tian's number of heartbeats per minute returned to the level before rope skipping."}, {"key": "3613", "content": "Below is the statistical chart of Tian Tian's heartbeat per minute before and after jumping rope during PE class.\n question_3613-image_0 \u200b\nBased on the statistical chart, answer the question.\nIf our heart rate during physical education class is between $$120$$ and $$140$$ beats per minute, then the intensity of the exercise is appropriate. It can be seen from the chart that the exercise intensity of Tian Tian while jumping rope is ( )."}, {"key": "3614", "content": "There are a total of $$45$$ chickens and rabbits in the same cage, with a total of $$100$$ legs. Try to calculate the number of chickens and rabbits in the cage."}, {"key": "3615", "content": "In a parking lot, there are a total of $$24$$ vehicles, consisting of cars and motorcycles. Cars have $$4$$ wheels, and motorcycles have $$3$$ wheels. Together, these vehicles have a total of $$86$$ wheels. How many three-wheeled motorcycles are there."}, {"key": "3616", "content": "A worker transports 250 celadon vases, with a shipping fee of $$20$$ Yuan for each intact vase delivered, but compensates $$100$$ Yuan for each broken one. After delivering this batch of vases, the worker earned a total of $$4400$$ Yuan. How many were broken."}, {"key": "3617", "content": "There are $$50$$ chickens and rabbits together, locked in the same cage. Each chicken has two legs, and each rabbit has four legs. There are a total of $$120$$ legs in the cage. Try to calculate how many chickens and rabbits there are in the cage."}, {"key": "3618", "content": "In order to enrich students' extracurricular life, the school founded a table tennis club and a basketball club. Many students enthusiastically signed up. Among them, $$21$$ students signed up for the table tennis club, $$29$$ students signed up for the basketball club, but eventually, the school found that $$15$$ students had signed up for both the table tennis and basketball clubs, and there were $$13$$ students who didn't sign up for any club. The school has a total of students."}, {"key": "3619", "content": "On a sunny and breezy day, $$11$$ students arranged to go for a picnic, and each of them brought some food. Among them, $$6$$ people brought hamburgers, $$6$$ people brought chicken legs, $$4$$ people brought cheesecakes. There were $$3$$ people who brought both hamburgers and chicken legs, $$1$$ person who brought both chicken legs and cheesecake. $$2$$ people brought both hamburgers and cheesecake. Question: How many people brought all three types of food."}, {"key": "3620", "content": "A survey of the whole class found that there are $$20$$ people who can swim, $$25$$ people who can play basketball. There are $$10$$ people who can do both, and $$9$$ people who can do neither. The total number of people in this class is ."}, {"key": "3621", "content": "A read from page $$54$$ to page $$67$$ of a book, B read from page $$95$$ to page $$135$$, and C read from page $$180$$ to page $$237$$. They read a total of pages."}, {"key": "3622", "content": "A book has a total of $$40$$ pages, the page numbers from $$1\\sim 40$$ use a total number of digits."}, {"key": "3623", "content": "As shown in the figure, in trapezoid $$ABCD$$, $$AE$$ is perpendicular to $$DC$$ at $$E$$, $$AB=4$$ cm, $$AE=5$$ cm, $$CD=8$$ cm, therefore the area of trapezoid $$ABCD$$ is square centimeters.\n question_3623-image_0"}, {"key": "3624", "content": "As shown in the figure, in the right trapezoid $$ABCD$$, $$AB=5$$ cm, $$BC=6$$ cm, $$CD=15$$ cm, so the area of the right trapezoid $$ABCD$$ is square centimeters.\n question_3624-image_0"}, {"key": "3625", "content": "Xiao Ya and Xiao Qiao's homes are $$2000$$ meters apart. Xiao Ya rides his bike towards Xiao Qiao's home, while Xiao Qiao leaves his home at the same time walking towards Xiao Ya's home. Xiao Ya rides at $$70$$ meters per minute, and after $$12$$ minutes, they still haven't met, with a distance of $$800$$ meters between them at that time. Xiao Qiao walks meters per minute."}, {"key": "3626", "content": "Eddy and Gaga leave home at the same time, walking in opposite directions. (3) If they are 2 kilometers apart after 10 minutes, and Gaga's speed is 80 meters/min, Eddy's speed is meters/min. question_3626-image_0"}, {"key": "3627", "content": "As shown, places $$A$$ and $$B$$ are $$800$$ meters apart. Dawang is walking to the left from place $$A$$, and Kaios is walking to the right from place $$B$$. Both start at the same time. Dawang's speed is $$56$$ meters/minute, and Kaios's speed is $$74$$ meters/minute. 1) After $$8$$ minutes, the distance between the two people is meters. question_3627-image_0"}, {"key": "3628", "content": "As shown in the diagram, locations $$A$$ and $$B$$ are $$800$$ meters apart. Da Kuan is walking to the left from location $$A$$, and Kaios is walking to the right from location $$B$$. Both start at the same time. Da Kuan's speed is $$56$$ meters/minute, and Kaios's speed is $$74$$ meters/minute. 2) Starting from the beginning, minutes later, the distance between them is $$3400$$ meters. question_3628-image_0"}, {"key": "3629", "content": "A certain barber shop has only one barber, and three people arrived at the same time wanting a haircut. The time they need for a haircut is respectively $$20$$ minutes, $$50$$ minutes, and $$35$$ minutes. The barber can arrange their haircut order reasonably so that the total waiting time is the shortest. Therefore, the shortest total waiting time (including the haircut time) is minutes."}, {"key": "3630", "content": "When there are six people each holding a bucket going to the tap to fetch water at the same time, the time they need respectively is $$4$$, $$8$$, $$9$$, $$10$$, $$13$$, $$18$$ minutes. With two taps available, arranging these six people cleverly to fetch water so that their total waiting time is minimized, the shortest total waiting time (including fetching water time) is in minutes."}, {"key": "3631", "content": "If natural numbers are filled into the table below according to a certain rule, then $$25$$ is the number in the $$th row and $$th column.\n question_3631-image_0"}, {"key": "3632", "content": "There are some garbage recycling stations along the road, and now it is necessary to transport the garbage from each recycling station to a treatment facility (the treatment facility can also be set up at the station). It is hoped that the total distance from all stations to the treatment facility is the shortest. If there are a total of $$59$$ recycling stations, then the treatment facility should be located at the station number ."}, {"key": "3633", "content": "$11+101+1001+10001+100001=$"}, {"key": "3634", "content": "$21+201+2001+20001=$"}, {"key": "3635", "content": "Starting from $$1$$, natural numbers are filled into the table below following a certain pattern. Then, the number $$420$$ is in the row and column of the table.\n question_3635-image_0"}, {"key": "3636", "content": "Class 3-1 and Class 3-2 students form a square queue. Whether counting from the front to the back or from the back to the front, Xiao Ming is the 7th: 1) This square queue has a total number of students. 2) A few students from Class 3-3 came, just adding one row and one column to the square formation, bringing the number of students. 3) Some students got tired of standing and left to buy something to eat, leaving the rest to requeue. Compared to the situation in question 2, it now lacks the outermost layer, leaving people."}, {"key": "3637", "content": "There are $$100$$ people waiting in three lines at the entrance of the amusement park, the number of people in the first line is $$20$$ less than the total number of people in the other two lines, and the second line has $$10$$ more people than the third line. So, the first team has people."}, {"key": "3638", "content": "To welcome foreign children, Edie and Vivian decided to learn English together. Vivian memorized 9 more words than Edie each day. Over 30 days, Vivian had to stop studying for 15 days due to a new task, yet she still memorized twice as many words as Edie. Thus, over these 30 days, how many more words did Vivian memorize than Edie?"}, {"key": "3639", "content": "As shown in the figure, quadrilateral $$ABCD$$ is a rhombus (a parallelogram with adjacent sides being equal), $$AC$$ and $$BD$$ are perpendicular to each other, given $$AC=18$$, $$BD=6$$, the area of the rhombus is.\n question_3639-image_0"}, {"key": "3640", "content": "Solve application problems by setting up equations: In a outing, there were a total of $$320$$ students, among them the number of girls was $$2$$ more than twice the number of boys. The number of girls is."}, {"key": "3641", "content": "Solve application problems by setting up equations: In a field trip, there were a total of 320 students, where the number of girls was 2 more than twice the number of boys. How many boys were there?"}, {"key": "3642", "content": "Solve application problems by establishing equations: Niu Niu has $$100$$ more points cards than Ding Ding, given that the number of points cards Niu Niu has is $$8$$ less than $$3$$ times the number Ding Ding has. Niu Niu has points cards."}, {"key": "3643", "content": "Answer the question according to the requirement. As shown in figure $$2$$, $$\\angle 1+\\angle 2+\\angle 3+\\angle 4+\\angle 5=$$ degrees. question_3643-image_0"}, {"key": "3644", "content": "Answer the question according to the requirements. As shown in figure $$3$$, $$\\angle 1+\\angle 2+\\angle 3+\\angle 4+\\angle 5+\\angle 6=$$ degrees. question_3644-image_0"}, {"key": "3645", "content": "The sum of the interior angles of a polygon is $$1260{}^\\circ $$, it is a polygon with this number of sides."}, {"key": "3646", "content": "Car A and B initially had a total of $$43$$ passengers. After reaching a certain place, $$5$$ passengers got off car A, and $$2$$ people came on board car B. At this time, the number of passengers in car A was exactly three times the number of passengers in car B. How many passengers were originally in car A and car B respectively. question_3646-image_0"}, {"key": "3647", "content": "In the division equation $$\\square \\div \\square =13\\cdots \\cdots 27$$, the minimum value of the dividend is equal to $$13\\times 27+27=378$$"}, {"key": "3648", "content": "Please fill in the blanks with $$1\\sim 6$$ so that each number appears once in every row, every column, and each bold-bordered palace. The six numbers arranged from left to right in the first row form a six-digit number. question_3648-image_0"}, {"key": "3649", "content": "Observing the 50 meters running results of the four students below, (1) The shorter (longer/shorter) the time, the faster the run. (2) The first place is (Fill in the name) question_3649-image_0"}, {"key": "3650", "content": "Sixth-grade students form a solid square formation to perform group gymnastics, with $$15$$ people on each side of the outermost layer, the outermost layer has a total of students, and the entire square formation has a total of students."}, {"key": "3651", "content": "Calculate: $$1 + 2 + 3 + 4 + \\cdots + 18 + 19 = $$."}, {"key": "3652", "content": "This year, the father is $$32$$ years old, and the son is $$4$$ years old. When the combined age of the father and son is $$50$$ years old, the father's age will be , and the son's age will be ."}, {"key": "3653", "content": "The final result of simplifying the following expression is ( ).\n$$a\\times2+a=$$"}, {"key": "3654", "content": "A sequence of numbers $$8$$, $$11$$, $$14$$, $$17$$, $$\\cdots $$, in which $$41$$ is the ( ) term of this sequence."}, {"key": "3655", "content": "The outermost layer of a martial arts performance formation has $$20$$ people on each side, the total number of people on the outermost layer is ( )."}, {"key": "3656", "content": "As shown in the diagram, it is a variant spider web. It is known that spiders can only crawl upwards or to the right. If a spider crawls from point $$A$$ to point $$B$$, there are a total of possible routes.\n question_3656-image_0"}, {"key": "3657", "content": "The old monkey divides bananas among the young monkeys, giving each monkey $$5$$ bananas results in a shortage of $$30$$ bananas; giving each monkey $$3$$ bananas results in a shortage of $$2$$ bananas, in total there are little monkeys."}, {"key": "3658", "content": "Xinxin and Ranran went home after school. Ranran first sent Xinxin home and then went back home himself, so there are several shortest routes for Ranran.\n question_3658-image_0"}, {"key": "3659", "content": "Below is the menu of a fast-food restaurant. Lulu plans to order one main course, one snack, and one drink. She has a number of different combination plans question_3659-image_0"}, {"key": "3660", "content": "The hotel has a total of $$3$$ rooms to choose from, Eddie, Vi, and Da Kuan each choose one room, there are in total different selection schemes question_3660-image_0"}, {"key": "3661", "content": "Among the four people, A, B, C, and D, standing in a row for a photo, if A must stand as the second from the left, and B cannot stand as the first from the right, then (1) with A standing second from the left, B has several ways to stand. (2) In total, there are several ways to stand."}, {"key": "3662", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, $$AF$$ is perpendicular to $$CD$$ at point $$F$$. The area of the parallelogram is $$72$$ square centimeters, $$AE=6$$ centimeters, $$CD=9$$ centimeters, and the line segment $$BC$$ is in centimeters. question_3662-image_0"}, {"key": "3663", "content": "As shown in the figure, what should be in the place of the question mark ( )?\n question_3663-image_0"}, {"key": "3664", "content": "Following the pattern in the diagram below for the first $$3$$, there are ( ) black squares in the fourth figure.\n question_3664-image_0"}, {"key": "3665", "content": "Count, how many line segments are there in the figure ()\n question_3665-image_0"}, {"key": "3666", "content": "This year, Xiaoyu is $$15$$ years old, Xiaoliang is $$12$$ years old, $$($$ years ago, the sum of Xiaoyu and Xiaoliang's ages was $$15$$."}, {"key": "3667", "content": "The solid square formation of Class 2, Grade 5, has a total of $$56$$ people on the outermost layer. ($$1$$) Each side of the outermost layer of this square formation has people. ($$2$$) This square formation has a total of people."}, {"key": "3668", "content": "All students in a class can exactly be arranged into a triangular formation with each side having $$8$$ people. The question is: How many people are there in this class."}, {"key": "3669", "content": "Eddie arranged 48 chess pieces into a two-layer hollow square matrix. The outer layer used ( ) chess pieces."}, {"key": "3670", "content": "Xiao Bai and Xiao Hua encountered a magical insect that doubles in size every hour and can grow to 20 centimeters in 1 day. Clever children, how many hours does it take for the insect to grow to 5 centimeters?"}, {"key": "3671", "content": "The yard originally had a certain number of tons of coal.$$.$$ The first time, half of the original coal was shipped out, the second time $$150$$ tons were shipped in, the third time $$50$$ tons were shipped out, as a result, there were still $$300$$ tons left, the original number of tons of coal in the yard."}, {"key": "3672", "content": "A bookshelf is divided into three layers: top, middle, and bottom, holding a total of $$384$$ books. If the same number of books is taken from the top layer and placed into the middle layer, then the same number of books is taken from the middle layer and placed into the bottom layer, and finally, the same number of books as the current top layer is taken from the bottom layer and placed into the top layer, the number of books on each layer of the bookshelf becomes equal. Originally, the top layer held books, the middle layer held books, and the bottom layer held books."}, {"key": "3673", "content": "Three thirsty monks were each holding a water pot. Initially, the oldest monk had the most water, and one of the monks had no water to drink. Consequently, the old monk evenly distributed all his water to the other two monks, the elder and the younger; afterwards, the elder monk also evenly divided all his water between the old and the younger monk; then, the younger monk did the same with the remaining two monks. In this way, the three monks took turns in being considerate for a while. As a result, when the sun set, there were $$10$$ liters of water in the old monk's pot, the elder monk had none, and the younger monk's pot was filled with $$20$$ liters of water. The question is: How much water was there in the elder monk's pot initially."}, {"key": "3674", "content": "A, B, and C went fishing together. They put the fish they caught into a basket. Then, they lay down to rest on the spot and all fell asleep. A woke up first. He divided the fish in the basket into three equal parts and found one extra fish. He threw the extra fish back into the river and took one share of the fish home. B woke up next, divided the remaining fish in the basket into three equal parts, and also found one extra fish. He too threw the extra fish back into the river and took one share of the fish home. C woke up last; he also divided the fish in the basket into three equal parts, and there was also one extra fish. The three of them had caught at least several fish."}, {"key": "3675", "content": "Someone discovered a magical path, under which there is a small box for storing money. When he walked past the path, some money from the box would fly onto him, doubling the money he had, which made him very happy; when he walked back along the path, the money on him would fly into the box, doubling the money inside the box; after making three round trips, both the money in the box and on the person were $$64$$ one-dollar coins. So, originally, the person had dollars, and the box contained dollars."}, {"key": "3676", "content": "Li Bai took a flask to buy wine, doubling the amount at each tavern he encountered. He drank eight taels upon seeing flowers. After three encounters of taverns and flowers, he drank all the wine in the flask. Originally, there were two taels of wine in the flask."}, {"key": "3677", "content": "There is a peach tree on the top of the mountain, and a monkey steals some peaches. On the first day, it stole half of the total number plus $$2$$, and on the second day, it again stole half of the remaining plus $$2$$. At this point, there was $$1$$ peach left. The question is: How many peaches were there originally on the tree?"}, {"key": "3678", "content": "A group of little monsters were hurrying on their way, running away due to unbearable hunger. Half of them ran away in the morning; the remaining little monsters ran away again in the half of the afternoon; after escaping $$4$$ in the evening, only $$6$$ little monsters were left. So, there were originally a total number of little monsters\uff0e\n question_3678-image_0"}, {"key": "3679", "content": "While doing a subtraction problem, Xiao Dong mistook the minuend as $$90$$ instead of $$75$$, and the resulting difference was $$55$$. So, the correct result is ( )."}, {"key": "3680", "content": "When Xiao Xing was doing a subtraction equation, he mistook the subtrahend $$25$$ for $$52$$, then the result is ( )."}, {"key": "3681", "content": "The same letter represents the same number, different letters represent different numbers. In the following equation, $$A=$$\uff1b$$B=$$. \n question_3681-image_0"}, {"key": "3682", "content": "Fill in the blanks with appropriate numbers to make the column addition valid.\n\n\n\n\n\n3\n\n9\n\n\n+\n1\n\n7\n\n\n\n\n\n0\n6\n3"}, {"key": "3683", "content": "Among the following equations, $$\\bigstar=$$\uff0e\n question_3683-image_0"}, {"key": "3684", "content": "The average of the numbers: $$80$$, $$85$$, $$100$$, $$90$$, $$95$$ is."}, {"key": "3685", "content": "Xiao Huizi's scores in the first $$4$$ exams this term were $$85$$, $$95$$, $$80$$, and $$100$$, respectively. Therefore, the average score of these $$4$$ exams is points."}, {"key": "3686", "content": "Xiaohua weighs 40 kg, Xiaofang weighs 42 kg, Xiaohong weighs 38 kg, Xiaoli weighs 52 kg.$$Their average weight is kg."}, {"key": "3687", "content": "There are $$40$$ apple trees in the orchard, the number of apple trees is twice the number of pear trees, and the total number of apple trees and pear trees is six times the number of peach trees. There are ( ) peach trees in the orchard."}, {"key": "3688", "content": "Eddie has $$5$$ score cards, Vi's quantity is twice that of Eddie's, and Xiao Ming's quantity is three times that of Eddie's. The correct representation of the relationship between Eddie's and Xiao Ming's score card quantities is ( )."}, {"key": "3689", "content": " question_3689-image_0 \nThe price of the badminton racket is ( )."}, {"key": "3690", "content": "Mom bought some fish. Half of it was eaten on the first day, and half of the remainder was eaten on the second day, leaving $$3$$ fish. How many fish did mom buy?"}, {"key": "3691", "content": "Class 2 (Grade 1) students participated in a broadcast gymnastics competition, with the number of participants between 30 and 40. The number of people per row and the number of rows were the same. There were ( ) students who participated in the competition."}, {"key": "3692", "content": "The outermost layer of a performance square array has $$10$$ people on each side, this square array in total has ( ) people."}, {"key": "3693", "content": "The students of Class 1, Grade 4, participated in a calisthenics competition, forming a solid square formation with each row and each column having $$8$$ people. How many students are there in the square formation?"}, {"key": "3694", "content": "The younger sister is $$12$$ years old this year. When she is as old as her older sister is now, the older sister will be $$24$$ years old. The age of the older sister this year is ."}, {"key": "3695", "content": "How many intersection points can there be at most with $$20$$ lines on the same plane?"}, {"key": "3696", "content": "A unit of soldiers formed a solid square formation during a march. Another team of $$31$$ people joined their formation, which exactly increased the formation by one row both horizontally and vertically. Now there is a total of soldiers."}, {"key": "3697", "content": "$$64$$ people participate in a badminton contest, pairing up to compete in an elimination tournament. To determine the champion, a total of matches need to be conducted."}, {"key": "3698", "content": "The school is holding a table tennis selection competition, each contestant has to play a match against every other contestant, with a total of $$10$$ contestants, how many matches will be played in total?"}, {"key": "3699", "content": "5 players participate in a round-robin chess tournament, each pair of players play one game against each other. It is stipulated that winning a game scores 2 points, drawing scores 1 point for each, and losing scores 0 points. It is known that after the competition, 4 of the players have a total of 16 points, then the 5th player scored points."}, {"key": "3700", "content": "Big Dull and Little Dull move from point $$A$$ to point $$B$$ simultaneously. It is known that Big Dull walks $$70$$ meters per minute and Little Dull walks $$65$$ meters per minute. After $$10$$ minutes, Big Dull has walked more meters than Little Dull."}, {"key": "3701", "content": "As shown in the diagram, a large rectangle is divided into four parts: $$A$$, $$B$$, $$C$$, and $$D$$. It is known that the perimeter of part $$A$$ is $$4$$ cm, the perimeter of part $$B$$ is $$16$$ cm, the perimeter of part $$D$$ is $$20$$ cm, and the perimeter of the large rectangle is in cm. question_3701-image_0"}, {"key": "3702", "content": "In the addition column below, the same Chinese characters represent the same numbers, and different Chinese characters represent different numbers. Then the number represented by \"$$\\overline{\u597d\u591a\u5927\u7ef5\u7f8a}$$\" is.\n question_3702-image_0"}, {"key": "3703", "content": "Figure ($$1$$) has a triangle, Figure ($$2$$) has a triangle.\n question_3703-image_0"}, {"key": "3704", "content": "Starting from $$1$$, the sequence of consecutive odd numbers $$1$$, $$3$$, $$5$$, $$7$$, $$\\cdots$$, then $$21$$ is the nth number in this sequence."}, {"key": "3705", "content": "In a series of numbers, $$2$$, $$9$$, $$16$$, $$\\cdots$$, $$86$$, each number is $$7$$ more than the previous one, the total number of terms in this series is."}, {"key": "3706", "content": "During the physical education class, the teacher instructed everyone to line up, with Wei Er standing at the front of the line and Ai Di at the end of the line. From the front to the back of the line, each student calls out a number that is $$7$$ more than the previous one. If Wei Er calls out $$17$$ and Ai Di calls out $$150$$, then there are a total of people in the line.\n question_3706-image_0"}, {"key": "3707", "content": "Dian Dian reads a storybook, on the first day he read $$30$$ pages, starting from the second day, the number of pages he read each day was $$4$$ pages more than the day before, on the last day he read $$70$$ pages and just finished the book. So, the total number of pages in this book is.\n question_3707-image_0"}, {"key": "3708", "content": "Using $$12$$ matchsticks (exactly all used), the largest possible number that can be formed is. The smallest is. question_3708-image_0"}, {"key": "3709", "content": "Currently, there are $$16$$ matchsticks available to be arranged into numbers, using exactly all of them, the largest three-digit number that can be formed is. The smallest three-digit number that can be formed is. question_3709-image_0"}, {"key": "3710", "content": "Using $$10$$ matchsticks, place a number in each square within a frame, forming two numbers with all distinct digits, the largest possible result of the addition equation is, and the smallest is. question_3710-image_0"}, {"key": "3711", "content": "The distance between the two places is $$120$$ kilometers, Eddie's speed when going was $$20$$ kilometers/hour, and $$30$$ kilometers/hour when coming back, Eddie's average speed for the round trip was kilometers/hour."}, {"key": "3712", "content": "A rectangular lawn occupies an area of $$150$$ square meters, with a width of $$5$$ meters. Grandpa Zhang takes a walk around the lawn for $$3$$ laps every afternoon. He walks meters every day."}, {"key": "3713", "content": "The group then arrived at the elephant pavilion. There are a total of $$22$$ elephants here, divided into two categories: Asian elephants and African elephants. There are $$2$$ more African elephants than three times the number of Asian elephants. Hence, the number of African elephants is, and the number of Asian elephants is."}, {"key": "3714", "content": "There are two buckets of oil with equal weight. If $$12$$ kilograms are taken from bucket A and $$14$$ kilograms are added to bucket B, then the oil in bucket B is heavier than the oil in bucket A by kilograms."}, {"key": "3715", "content": "Xiaoming is $$8$$ years old this year, and his mother is $$44$$ years old. ($$1$$) The age difference between Xiaoming and his mother is. ($$2$$) When the mother's age is exactly $$4$$ times Xiaoming's age, Xiaoming is years old. question_3715-image_0"}, {"key": "3716", "content": "Xiaomei wants to go from point $$A$$ to point $$B$$ along the route shown in the diagram. Since point $$C$$ is being repaired and is temporarily impassable, the shortest route for Xiaomei to get to point $$B$$ is as follows. question_3716-image_0"}, {"key": "3717", "content": "In the evening, a heavy rain fell near the city center, and the area covered by the heavy rain (the shaded part) was impassable. (1) The area to the left of the city center $$A$$ (can or cannot) pass; the area to the right of the city center $$B$$ (can or cannot) pass; (2) There are a total of routes from the school to the nursing home. question_3717-image_0"}, {"key": "3718", "content": "Divide $$12$$ identical-sized watermelons into $$3$$ piles of different quantities, there are several different ways of division. question_3718-image_0"}, {"key": "3719", "content": "Divide $$8$$ watermelons of the same size into $$3$$ piles, there are different ways to do so. question_3719-image_0 \u200b\u200b\u200b"}, {"key": "3720", "content": "Splitting $$10$$ into the sum of $$3$$ natural numbers (1) Is $$10=0+5+5$$ acceptable? (2) There are a total of different methods."}, {"key": "3721", "content": "Distribute $$6$$ identical erasers to $$3$$ children, each child getting at least one piece, there are different ways. question_3721-image_0"}, {"key": "3722", "content": "A square with side length $$10$$ cm is cut horizontally once and vertically twice, turning into $$6$$ small rectangles. The total perimeter of these $$6$$ small rectangles is equal to centimeters. question_3722-image_0"}, {"key": "3723", "content": "Compute: $$40\\times 500=$$."}, {"key": "3724", "content": "Calculate: $$12\\times 400=$$."}, {"key": "3725", "content": "Calculate: $$20\\times 70=$$."}, {"key": "3726", "content": "One question_3726-image_0 needs $$3$$ wheels, $$48$$ wheels can fit at most ( ) question_3726-image_1."}, {"key": "3727", "content": "$$3$$ monks eat $$9$$ buns for $$3$$ meals, and each monk eats the same amount, $$6$$ monks eat $$6$$ meals and have a bun."}, {"key": "3728", "content": "$$3$$ monks eat $$144$$ buns for $$3$$ meals, and each monk eats the same amount, $$30$$ monks eat $$3$$ meals' worth of buns."}, {"key": "3729", "content": "A square with a side length of $$1$$ centimeter has a perimeter of ( ) centimeters."}, {"key": "3730", "content": "A rectangle that is $$10$$ cm long and $$2$$ cm wide has a perimeter of ( )\uff0e"}, {"key": "3731", "content": "Each piece of clothing is sewn with $$6$$ buttons, $$30$$ buttons can sew ( ) pieces of clothing."}, {"key": "3732", "content": "$$49\\times 34+49\\times 23+57\\times 51$$=."}, {"key": "3733", "content": "Calculate: $$264+451-216+136-184+149$$=."}, {"key": "3734", "content": "As shown in the figure, in a quadrilateral, the diagonals are perpendicular to each other. It is known that $$AC=10$$, $$BD=6$$, the area of the quadrilateral $$ABCD$$ is\uff0e question_3734-image_0"}, {"key": "3735", "content": "As shown in the figure, the large rectangle is divided into $$9$$ smaller rectangles, of which the areas of five rectangles are already marked on the diagram. Calculate the area of region $$A$$. question_3735-image_0"}, {"key": "3736", "content": "As shown in the diagram, two adjacent sides are perpendicular to each other, with the lengths of the segments as follows. The perimeter of the figure is in centimeters. question_3736-image_0"}, {"key": "3737", "content": "Vessel A and Vessel B initially had a total of $$114$$ passengers. After arriving at a certain place, $$20$$ people boarded Vessel A, and $$8$$ people disembarked from Vessel B. At this time, the number of people on Vessel A was exactly $$2$$ times the number of people on Vessel B. How many passengers were originally on Vessel A."}, {"key": "3738", "content": "When A, B, C, D $$4$$ students line up for a photo, if A must be at the far right and B cannot be at the far left, there are a total of different ways to line up."}, {"key": "3739", "content": "If a point emits an odd number of edges, it is called an odd point, and if the number of emitted edges is even, it is called an even point. Please identify the odd and even points in the figure below.\n question_3739-image_0"}, {"key": "3740", "content": "The following figure is a route map of a maze. If entering from point $$A$$ and passing through each point without repeating any paths and finally exiting from a point.\n question_3740-image_0"}, {"key": "3741", "content": "The teacher brought three wooden boards, which were respectively marked with the numbers $$1$$, $$2$$, and $$3$$. How many different natural numbers can be displayed using these boards?"}, {"key": "3742", "content": "The natural numbers $$12$$, $$135$$, $$1349$$ share a common feature: they have at least two digits, and for any two adjacent digits, the digit on the left is smaller than the digit on the right. We name them \"increasing numbers\". Using the digits $$5$$, $$6$$, $$7$$, $$8$$, you can form several two-digit \"increasing numbers\"."}, {"key": "3743", "content": "The natural numbers $$12$$, $$135$$, $$1349$$ share a common characteristic: they have at least two digits, and for any two adjacent digits, the left digit is smaller than the right digit. We call these numbers 'rising numbers.' With the digits $$5$$, $$6$$, $$7$$, $$8$$, you can form several 'rising numbers.'"}, {"key": "3744", "content": "The natural numbers $$21$$, $$654$$, $$7521$$ have one thing in common: for two adjacent digits, the digit on the right is less than the digit on the left, which we call a \u201cdescending number.\u201d Among the three-digit numbers composed of the digits $$1$$, $$4$$, $$6$$, $$7$$, $$9$$, there are several that are \u201cdescending numbers.\u201d"}, {"key": "3745", "content": "Dividing $$10$$ identical ballpoint pens into $$3$$ piles, there are different ways to do so."}, {"key": "3746", "content": "To divide $$14$$ identical exercise books into $$3$$ piles of different quantities, there are a total of different methods."}, {"key": "3747", "content": "Splitting $$18$$ into the sum of three different non-zero natural numbers, but the three natural numbers can only be chosen from $$1\\sim 9$$. How many different splitting methods are there? Please list them all."}, {"key": "3748", "content": "This is a famous snack street with a total length of $$500$$ meters. Now, trash cans are to be placed on one side of the street, one every $$100$$ meters. No trash can is placed at the entrance, but one is placed at the exit. Therefore, a total of trash cans are placed on this street. (The width of the trash cans is negligible)"}, {"key": "3749", "content": "There is a straight track with a length of $$40$$ meters. Flags are planted on one side of the track, with one flag every $$4$$ meters, and none at the ends, resulting in a total number of flags planted. (The width of the flags is considered negligible.)"}, {"key": "3750", "content": "Planting trees along one side of a road that is $$30$$ meters long, with one tree every $$5$$ meters and trees at both ends of the road, the total number of trees that can be planted is. (The width of the trees is negligible)"}, {"key": "3751", "content": "The following figure can be drawn in one stroke has ( )\uff0e question_3751-image_0"}, {"key": "3752", "content": "The figure below cannot be drawn in one stroke. By adding a line between the points ( ), it can become a figure that can be drawn in one stroke. question_3752-image_0"}, {"key": "3753", "content": "The figure below can't be drawn with one stroke. By removing line segment ( ) it can be turned into a one-stroke figure. question_3753-image_0"}, {"key": "3754", "content": "The figure below is the floor plan of the museum. The museum has 6 exhibition halls, and there is a door between every two exhibition halls. Pony wants to start from a certain room, pass through all the doors without repeating, and reach room F. Then, the room he starts from is room. question_3754-image_0"}, {"key": "3755", "content": "A cleaning vehicle sweeps the streets, each segment of the street is $$1$$ kilometer long. The cleaning vehicle starts from $$A$$, covers all the streets and then returns to $$A$$. What is the shortest path it can take, in kilometers for the entire journey. question_3755-image_0"}, {"key": "3756", "content": "Eddy and Viola have a total of $$30$$ candies. The number of candies Eddy has is twice the number Viola has. Then, Eddy has ____ candies."}, {"key": "3757", "content": "Xiao Yong's family raises a total of $$22$$ white and black rabbits. If they buy another $$4$$ white rabbits, the number of white rabbits will equal the number of black rabbits. The number of black rabbits Xiao Yong's family raises is ."}, {"key": "3758", "content": "Xueersi third grade, fourth grade, and fifth grade distribute textbooks, third grade has $$20$$ fewer textbooks than fourth grade, and fifth grade has $$30$$ more textbooks than fourth grade. The three grades have a total of $$280$$ textbooks. So, how many textbooks does the fourth grade have?"}, {"key": "3759", "content": "Wei'er wants to divide a bundle of cloth into three pieces. The bundle of cloth is $$190$$ meters in total. The second piece is $$20$$ meters longer than the first piece, and the third piece is $$30$$ meters longer than the second piece. The length of the first piece of cloth is meters, the length of the second piece of cloth is meters, and the length of the third piece of cloth is meters."}, {"key": "3760", "content": "There are a total of $$75$$ trees in the park, the number of poplar trees is $$5$$ times that of willow trees, and the number of pine trees is $$2$$ times that of willow trees plus $$3$$ trees. How many poplar trees and pine trees are there?"}, {"key": "3761", "content": "Warehouse A, B, and C together have $$109$$ tons of grain. The grain in warehouse A is $$1$$ ton more than three times the grain in warehouse B, and the grain in warehouse B is twice the grain in warehouse C. Then, warehouse A has how many more tons of grain than warehouse C."}, {"key": "3762", "content": "Answer the following question. There are a total of $$380$$ chickens, ducks, and geese on the farm. The number of ducks is $$10$$ more than twice the number of chickens, and the number of geese is $$10$$ more than three times the number of chickens. How many are there of each, chickens, ducks, and geese respectively?"}, {"key": "3763", "content": "Answer the following questions: Xiao Ming is $$8$$ years old this year, and Da Xiong is $$13$$ years old. When the sum of their ages is $$41$$ years old, how old is Da Xiong, and how old is Xiao Ming?"}, {"key": "3764", "content": "Answer the following questions: The current age sum of dad and mom is $$72$$ years; dad is $$6$$ years older than mom. This year, dad and mom's current ages are $$72$$ years in total; dad is $$6$$ years older than mom. This year, dad is ____ years old, mom is ____ years old."}, {"key": "3765", "content": "Da Mao's age $$5$$ years ago is equal to Er Mao's age $$7$$ years later. The sum of Da Mao's age $$4$$ years later and Er Mao's age $$3$$ years ago is $$35$$ years old. The sum of Da Mao and Er Mao's ages this year is years."}, {"key": "3766", "content": "Damao's age $$5$$ years ago is equal to Ermao's age $$7$$ years later, the sum of Damao's age $$4$$ years from now and Ermao's age $$3$$ years ago is $$35$$ years old, Damao's age this year is years old, Ermao's age this year is years old."}, {"key": "3767", "content": "Da Mao's age $$5$$ years ago is equal to Er Mao's age $$7$$ years later. The sum of Da Mao's age $$4$$ years later and Er Mao's age $$3$$ years ago is $$35$$ years old. Da Mao is older than Er Mao by years."}, {"key": "3768", "content": "Answer the following question. This year, the sum of Tongtong and her father's age is $$52$$ years old, and the father's age is $$4$$ times that of Tongtong's age plus $$2$$ years. Find the difference in age between Tongtong and her father."}, {"key": "3769", "content": "This year, the combined age of the mother and daughter is $$44$$ years old, and the mother's age is $$3$$ times that of the daughter's age this year. So, how old is the daughter this year."}, {"key": "3770", "content": "Dad is $$25$$ years older than Huanhuan, and together they are $$35$$ years old. Calculate Dad's age this year, and Huanhuan's age this year."}, {"key": "3771", "content": "Please answer the following questions: On the same plane, there can be at most intersections between $$4$$ straight lines, and there are intersections on each line."}, {"key": "3772", "content": "On the same plane, $$8$$ straight lines can have at most intersections."}, {"key": "3773", "content": "Please answer the following questions: On the same plane, $$101$$ straight lines can have at most intersections, and there are intersections on each line."}, {"key": "3774", "content": "Please answer the following questions: On the same plane, $$3$$ lines can have at most how many points of intersection, with each line having how many points of intersection."}, {"key": "3775", "content": "[Warm-up before class 2] The chart below is a bar graph statistical of the number of students in each class of the third grade at a school. According to the statistical graph, the following statement that is incorrect is (). question_3775-image_0"}, {"key": "3776", "content": "[Warm-up 3 before class] The figure below shows the statistical chart of the production situation of a mobile phone factory in the first quarter of this year. Please fill in the blanks based on the data in the chart. The month with the highest production is , and the month with the lowest production is . The average monthly production in the first quarter is ten thousand units."}, {"key": "3777", "content": "[Warm-up 1 before class] There are $$15$$ chickens and rabbits together, locked in the same cage. There are a total of $$34$$ legs in the cage. Try to calculate how many chickens and rabbits are in the cage."}, {"key": "3778", "content": "[Pre-class Warm-up 2] A cricket has $$6$$ legs, a spider has $$8$$ legs. There are $$9$$ crickets and spiders in total, with $$60$$ legs in total. There are crickets and spiders."}, {"key": "3779", "content": "[Warm-up before class 3] A forest park keeps some chickens and rabbits. It is known that the number of rabbits is equal to the number of chickens. They have a total of $$102$$ legs. Therefore, there are chickens, and rabbits."}, {"key": "3780", "content": "[Warm-up 3 before class] The top base of a trapezoid is $$5$$ decimeters, the bottom base is $$8$$ decimeters, and its height is $$4$$ decimeters. Its area is square decimeters."}, {"key": "3781", "content": "[Warm-up 1 before class] In parallelogram $$ABCD$$, the length of $$CD$$ is $$8$$ cm, then the length of $$AB$$ is cm. question_3781-image_0"}, {"key": "3782", "content": "[Warm-Up 2 before class] The figure below is a parallelogram, its area is $$\\text{c}{{\\text{m}}^{2}}$$. question_3782-image_0"}, {"key": "3783", "content": "Locations $$A$$ and $$B$$ are $$780$$ kilometers apart, a truck travels at $$56$$ kilometers per hour, and a passenger bus travels at $$74$$ kilometers per hour. Both the truck and the passenger bus start from the two locations at the same time and head towards each other. Question: (1) How many hours after they depart will they be $$130$$ kilometers apart for the first time."}, {"key": "3784", "content": "Locations $$A$$ and $$B$$ are $$780$$ kilometers apart, a truck travels at $$56$$ kilometers per hour, and a bus travels at $$74$$ kilometers per hour. The truck and bus start from the two locations at the same time and head towards each other. The question is: (2) How many hours after departure do they have a second instance of being $$130$$ kilometers apart?"}, {"key": "3785", "content": "Eddy and Gaga set off from home at the same time, walking in opposite directions. (1) If Eddy's speed is $$80$$ meters/min and Gaga's speed is $$60$$ meters/min, how far apart are they after $$9$$ minutes? question_3785-image_0"}, {"key": "3786", "content": "Eddie and Jiajia leave home at the same time, walking in opposite directions. (2) If Eddie's speed is $$80$$ meters per minute and Jiajia's speed is $$60$$ meters per minute, the number of minutes they need to be $$4200$$ meters apart is. question_3786-image_0"}, {"key": "3787", "content": "Eddie has $$a$$ candies, Vi's number of candies is twice his minus $$3$$, Vi has some candies."}, {"key": "3788", "content": "Fill in the blanks with appropriate numbers in the diagram to make the addition vertical method valid. The result of this vertical method is question_3788-image_0"}, {"key": "3789", "content": "Xiao Li bought $$10$$ baskets of apples, among which $$3$$ baskets of apples weigh $$15\\text{kg}$$ each, $$3$$ baskets of apples weigh $$25\\text{kg}$$ each, and $$4$$ baskets of apples weigh $$20\\text{kg}$$ each. These $$10$$ baskets of apples weigh an average of $$\\text{kg}$$ each."}, {"key": "3790", "content": "This year, the father's age is $$5$$ times the son\u2019s age. The sum of the ages of the father and son $$3$$ years from now will be $$54$$ years old. ($$1$$) The sum of the father and son's ages this year is ____ years old. ($$2$$) The father's age this year is ____ years old. question_3790-image_0"}, {"key": "3791", "content": "Count, the number of triangles below is .\n question_3791-image_0"}, {"key": "3792", "content": "Eddie exercises by running every day. From Monday to Friday, he averages 5000 meters per day, and on weekends, he averages 1500 meters per day. So, on average, Eddie runs ( ) meters every day in a week."}, {"key": "3793", "content": "Tingting's average monthly pocket money for the first four months of this year was $$100$$ yuan, and for the last two months of the first half of the year, it was $$130$$ yuan. Therefore, Tingting's average monthly pocket money for the first half of the year was yuan."}, {"key": "3794", "content": "$$\\frac{1}{4}>$$\uff08 \uff09\uff0e"}, {"key": "3795", "content": "The numerator of a fraction is $$8$$, which is $$2$$ less than the denominator, so the fraction is ( )."}, {"key": "3796", "content": "Among the figures below, the shaded part that can be represented by $$\\frac{1}{3}$$ is ( )."}, {"key": "3797", "content": "As shown in the diagram, the blank part occupies ( ) of the entire figure. question_3797-image_0"}, {"key": "3798", "content": "Among the following, the fraction with a denominator of $$3$$ is ( )."}, {"key": "3799", "content": "$$\\frac{3}{5}$$ This fraction is read as ( )."}, {"key": "3800", "content": "The fraction greater than $$\\frac{5}{7}$$ is ( )."}, {"key": "3801", "content": "The fractional unit of $$\\frac{3}{8}$$ is ( )."}, {"key": "3802", "content": "Among the following fractions, ( ) can represent the shaded part in question_3802-image_0."}, {"key": "3803", "content": "As shown in the diagram, there are $$100$$ trees in total. How many intervals are there?\n question_3803-image_0 \nList calculation: ."}, {"key": "3804", "content": "As shown in the figure, there are a total of $$100$$ trees, how many intervals are there?\n question_3804-image_0 \nList calculation: ."}, {"key": "3805", "content": "Write $$10$$ as the sum of $$3$$ natural numbers (1) Is $$10=0+5+5$$ feasible? (2) There are several different ways to do it."}, {"key": "3806", "content": "Placing $$10$$ identical radishes into three identical baskets, each basket must be used, and each basket can hold up to $$5$$ radishes. There are a total of different ways to do this."}, {"key": "3807", "content": "Lulu's family of $$3$$ people are preparing to stand in a row for a group photo in front of the Baotu Spring. How many different arrangements are possible?\n question_3807-image_0 \nWrite an equation: $$3\\times $$$$\\times $$$$=$$ (kinds).\nAnswer: There are a total of different ways of arrangement."}, {"key": "3808", "content": "It is known that the diagonals of the rhombus $$EFGH$$ paper piece are perpendicular to each other and bisected, and that $$EG=6$$ cm, $$FH=8$$ cm. (1) Cutting along the diagonals into four triangles and rearranging them, the area of the rhombus $$EFGH$$ is = square centimeters. question_3808-image_0 \u200b\u200b\u200b(2) Observing the figure below, how else can the area of the rhombus be calculated? question_3808-image_1"}, {"key": "3809", "content": "As shown in the figure, a large rectangle is divided into $$9$$ smaller rectangles, among which the area of $$3$$ small rectangles is shown in the figure (unit: square centimeters). Therefore, the area of the rectangle represented by \u201c\u2606\u201d is square centimeters. question_3809-image_0"}, {"key": "3810", "content": " question_3810-image_0 \nEddy made a mistake, what is the correct result?\n question_3810-image_1 \n\n\n\n\n$$169+99=268$$\uff08yuan\uff09\n\n$$199-169=30$$\uff08yuan\uff09\n$$298-30=$$\uff08yuan\uff09\n\n\n\nAnswer: These two toys cost a total of yuan\uff0e\n question_3810-image_2"}, {"key": "3811", "content": "Ming bought two sets of storybooks. When calculating the price, he mistook the price of one set of books as $$266$$ yuan instead of $$226$$ yuan, resulting in a calculation of $$400$$ yuan for both sets. What is the actual total price of these two sets of books? question_3811-image_0"}, {"key": "3812", "content": "Dakuan made a mistake when adding two three-digit numbers, misreading the tens digit $$4$$ of one addend, resulting in a result $$30$$ less than the correct answer. What did Dakuan mistakenly read $$4$$ as?"}, {"key": "3813", "content": "When Xin Xin was doing an addition problem, due to carelessness, she mistook a digit in the ones place of a number for $$7$$ instead of $$1$$, and mistook a digit in the tens place of another number for $$5$$ instead of $$3$$, resulting in a sum of $$94$$. What should the correct answer be?"}, {"key": "3814", "content": "When Xiao Shuai was doing a subtraction problem, due to carelessness, he mistook the subtrahend to be $$26$$ instead of $$38$$, and the result he got was $$47$$. Therefore, the correct answer is. question_3814-image_0"}, {"key": "3815", "content": "When Eddie was doing the subtraction, he mistakenly wrote the ten's digit of the minuend as $$9$$ instead of $$3$$, and the unit's digit as $$6$$ instead of $$8$$, thus the result was $$201$$. The correct difference should be"}, {"key": "3816", "content": "Given the difference between two numbers is $$90$$, Eddie mistakenly added an extra $$0$$ to the end of the minuend, resulting in a calculated difference of $$3240$$. What is the minuend?"}, {"key": "3817", "content": "It is known that the difference between two numbers is $$14$$. Eddie omitted the $$0$$ in the unit place of the minuend when calculating, and the result of the difference was $$122$$. (1) The correct minuend is multiple times the incorrect minuend (2) Then, what are the two numbers respectively?"}, {"key": "3818", "content": "In the Xueersi teachers' competition of eating steamed buns, Teacher Zhou and Teacher Dan can eat 20 buns in 2 minutes. If each teacher eats steamed buns at the same speed, then, 5 teachers can eat how many buns in 3 minutes"}, {"key": "3819", "content": "In the expression below, the same letters represent the same numbers. The sum of the numbers represented by letters $$A$$ and $$B$$ is.\n question_3819-image_0"}, {"key": "3820", "content": "Calculate.\n$$\\frac{5}{18}+\\frac{7}{18}=$$.\n$$\\frac{11}{25}-\\frac{6}{25}=$$.\n$$\\frac{6}{49}+\\frac{8}{49}=$$.\n$$\\frac{20}{39}-\\frac{7}{39}=$$."}, {"key": "3821", "content": "Student Zhang Ming ran from the first floor to the third floor in $$2$$ minutes, using the same speed, Zhang Ming ran from the first floor to the fifth floor, it will take minutes."}, {"key": "3822", "content": "A six-digit number is made up of $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, and the difference between any two adjacent digits is $$1$$. There are such six-digit numbers."}, {"key": "3823", "content": "Dahong has $$54$$ greeting cards, Xiaoqin has $$70$$ greeting cards. After Dahong gives some greeting cards to Xiaoqin, the number of greeting cards Xiaoqin has becomes $$3$$ times what Dahong has. How many greeting cards did Dahong give to Xiaoqin?"}, {"key": "3824", "content": "Two bookshelves, the number of books on shelf A is $$5$$ times plus $$20$$ books more than shelf B, and A has $$140$$ more books than B, then shelf A has ( ) books"}, {"key": "3825", "content": "$$2016$$ year $$9$$ month $$1$$ day is Thursday, please choose what day of the week $$2016$$ year $$10$$ month $$1$$ day is ( )."}, {"key": "3826", "content": "Xueersi School has a total of $$180$$ classes for grades three and four. The number of classes in grade three is twice that of grade four. How many classes are there in each grade?"}, {"key": "3827", "content": "There are two bags of rice, bag A has $$18$$ kilograms less than bag B. If another $$6$$ kilograms are poured from bag A into bag B, then the rice in bag A is half of bag B's. How many kilograms of rice did each bag originally have? ( )"}, {"key": "3828", "content": "Wei'er divides $$100$$ apples into two piles, one of which is exactly $$20$$ less than $$3$$ times the other. How many apples are in the smaller pile? ( )"}, {"key": "3829", "content": "The image below is a three-order magic square, then $$X=$$ ().\n question_3829-image_0"}, {"key": "3830", "content": "Please fill each cell of a $$3\\times 3$$ grid with the numbers $$1$$, $$3$$, $$5$$, $$7$$, $$9$$, $$11$$, $$13$$, $$15$$, $$17$$ without repetition, so that the sum of every row, every column, and each diagonal are equal. What is the number in the center? ( )\uff0e\n question_3830-image_0"}, {"key": "3831", "content": "The image below is a third-order magic square, $$Y=$$ ( )\uff0e\n question_3831-image_0"}, {"key": "3832", "content": "A cleaning vehicle sweeps the streets, each segment of the street is $$1$$ kilometer long, the cleaning vehicle starts from $$A$$, covers all the streets then returns to $$A$$. The shortest distance is kilometers.\n question_3832-image_0"}, {"key": "3833", "content": "Please fill in the following:\nPicture ($$1$$) can be drawn with at least strokes;\nPicture ($$2$$) can be drawn with at least strokes;\nPicture ($$3$$) can be drawn with at least strokes;\nPicture ($$4$$) can be drawn with at least strokes;\nPicture ($$5$$) can be drawn with at least strokes;\nPicture ($$6$$) can be drawn with at least strokes. (Fill in with Arabic numerals)\n question_3833-image_0 \n question_3833-image_1 question_3833-image_2 question_3833-image_3"}, {"key": "3834", "content": "In a certain painting room of the youth activity center, there are stools with $$3$$ legs and chairs with $$4$$ legs totaling $$40$$ pieces. Exactly $$40$$ kids are sitting on these $$40$$ stools and chairs. Haohao counted the legs of the stools, the legs of the chairs, and the legs of the kids, making a total of $$225$$ legs. Then, in the painting room, there are $$15$$ stools."}, {"key": "3835", "content": "There are two types of camels: the dromedary, which has only one hump, and the Bactrian camel, which has two humps. There is a group of camels with $$23$$ humps and $$60$$ legs. Then, the number of dromedary camels is, and the number of Bactrian camels is."}, {"key": "3836", "content": "There are 35 monkeys in total, both big and small, and they go together to pick peaches. When the Monkey King is not present, a big monkey can pick 15 kilograms in an hour, and a small monkey can pick 11 kilograms in an hour; when the Monkey King is supervising, each monkey, regardless of size, can pick an additional 12 kilograms per hour. One day, they picked for 8 hours, including the first and the last hour under the supervision of the Monkey King, resulting in a total of 4400 kilograms of peaches picked in 8 hours. There are in total small monkeys in this group of monkeys."}, {"key": "3837", "content": "In the morning, a food store sold three types of candies priced at $$20$$, $$25$$, and $$30$$ per kilogram respectively, totaling $$100$$ kilograms and earning $$2570$$ in total. It is known that the candies sold at $$25$$ per kilogram and $$30$$ per kilogram together earned $$1970$$. How many kilograms of the candy sold at $$25$$ per kilogram were sold?."}, {"key": "3838", "content": "A ballet troupe went to perform outside the province. Taking a day off, they have to pay $$600$$ yuan for theater rental; performing for a day, after deducting the theater rental and miscellaneous expenses, they can earn an average of $$2400$$ yuan. Now renting the theater for $$30$$ days, they earned a total income of $$42000$$ yuan from the performances. This ballet troupe performed for a total of days."}, {"key": "3839", "content": "A certain school has $$30$$ dormitories, each large dormitory houses $$6$$ people, and each small dormitory houses $$4$$ people. It is known that these dormitories together house a total of $$168$$ people, so how many large dormitories are there."}, {"key": "3840", "content": "There are 20 cards in total, consisting of three colors: red, yellow, and green. On the red cards, the two sides are marked with $$1$$ and $$2$$ respectively; on the yellow cards, the two sides are marked with $$1$$ and $$3$$ respectively; and on the green cards, the two sides are marked with $$2$$ and $$3$$ respectively. Now, these cards are placed on a table, displaying the side with the larger number facing up. After calculation, the sum of the numbers displayed by the cards is $$56$$. If all the cards are flipped over, the sum of the numbers displayed would then be $$31$$. How many yellow cards are there?"}, {"key": "3841", "content": "Class 3($$1$$) has a total of $$14$$ chess and flying chess sets, just enough for all $$40$$ students to participate in activities at the same time. Playing chess requires $$2$$ people per set, and playing flying chess requires $$4$$ people per set. Hence, there are sets of flying chess, and sets of chess."}, {"key": "3842", "content": "Sixth-grade students and first-grade students together have 120 people watering the trees, with each sixth-grade student carrying two buckets of water, and two first-grade students carrying one bucket of water together. Both grades together water 180 buckets in one time. Ask how many first-grade students there are."}, {"key": "3843", "content": "Grade 6 Class 2 of Guangming Primary School has $$35$$ students, among them $$20$$ participated in the math competition, $$11$$ participated in both the essay competition and the math competition, $$10$$ did not participate in either competition, some participated in the essay competition."}, {"key": "3844", "content": "In a picking event attended by $$46$$ people, there are $$18$$ people who only picked cherries, $$7$$ people who picked both cherries and apricots, $$6$$ people who neither picked cherries nor apricots, and a certain number of people who only picked apricots."}, {"key": "3845", "content": "Among these $$100$$ natural numbers from $$1$$ to $$100$$, there are some numbers that are not multiples of $$2$$, $$3$$, or $$7$$."}, {"key": "3846", "content": "Among the integers from $$1$$ to $$2000$$, there are several numbers that are multiples of $$3$$ but not multiples of $$5$$."}, {"key": "3847", "content": "Conducting a survey on $$100$$ people, the results are: $$28$$ people read $$A$$ magazine; $$30$$ people read $$B$$ magazine; $$42$$ people read $$C$$ magazine; $$8$$ people read both $$A$$ and $$B$$ magazines; $$10$$ people read both $$A$$ and $$C$$ magazines; $$5$$ people read both $$B$$ and $$C$$ magazines; $$3$$ people read all three magazines. Then, some people did not read any of the three magazines mentioned."}, {"key": "3848", "content": "There are $$2006$$ lamps lit, each controlled by a pull switch, and numbered in order as $$1$$, $$2$$, $$3$$, ..., $$2006$$. Pull the switches of lamps numbered with multiples of $$2$$ once; then pull the switches of lamps numbered with multiples of $$3$$ once, and finally pull the switches of lamps numbered with multiples of $$5$$ once. The number of lamps that remain lit afterwards is."}, {"key": "3849", "content": "The school's art troupe has a total of $$45$$ members. Among them, $$22$$ students can play the piano, $$27$$ students can play the violin, and the number of students who can do both is exactly $$3$$ times the number of students who can do neither. Therefore, the minimum number of students who can do at least one is ."}, {"key": "3850", "content": "There are 100 lamps numbered from 1 to 100, lined up while turned on. The first time, lamps with numbers that are multiples of 3 have their switches flipped once, and the second time, lamps with numbers that are multiples of 5 have their switches flipped once. How many lamps remain on?"}, {"key": "3851", "content": "Xiao Bai and Xiao Hua saw a magical insect that doubles in size every hour and can grow to 20cm in a day. How many hours does it take for the smart kids to see the insect grow to 5cm?"}, {"key": "3852", "content": "A and B each have a certain number of candies. The number of A's candies is less than B's. In each operation, the person with more candies gives some to the person with fewer candies, making the number of candies of the latter increase by 1 times; after 2017 such operations, A has 10 candies, and B has 8 candies. A originally had candies, and B originally had candies."}, {"key": "3853", "content": "Three brothers divided $$24$$ oranges among them, with each receiving a number of oranges equal to their respective ages three years ago. If the youngest brother first divides half of his oranges equally between the eldest and the second brother, then the second brother divides half of his current oranges equally between the youngest and the eldest, and finally the eldest divides half of his current oranges equally between the second and the youngest, then the number of oranges each person has becomes exactly the same. Therefore, the eldest brother is $$16$$ years old, the second brother is $$10$$ years old, and the youngest brother is $$7$$ years old."}, {"key": "3854", "content": "A construction team was repairing a road. On the first day, they completed more than half of the total length by $$6$$ meters, on the second day, they repaired half of what was left minus $$20$$ meters, and on the third day, they repaired $$30$$ meters, at this point, there were still $$14$$ meters left unrepaired, thus the length of this road in meters is\uff0e"}, {"key": "3855", "content": "Persons $$A$$, $$B$$, $$C$$, and $$D$$ have a total of $$64$$ bricks. $$A$$ gives some bricks to $$B$$ and $$C$$, doubling their number of bricks; then $$B$$ gives some bricks to $$C$$ and $$D$$, doubling their number of bricks; then $$C$$ gives some bricks to $$D$$ and $$A$$, doubling their number of bricks; finally, $$D$$ gives some bricks to $$A$$ and $$B$$, also doubling their number of bricks. At this point, all four individuals have an equal number of bricks. So, $$A$$ has bricks, $$B$$ has bricks, $$C$$ has bricks, and $$D$$ has bricks."}, {"key": "3856", "content": "A bookshelf is divided into three tiers: top, middle, and bottom, holding a total of $$384$$ books. If the same number of books as the middle tier is taken from the top tier and placed into the middle tier, then the same number of books as the bottom tier is taken from the middle tier and placed into the bottom tier, and finally, the same number of books as the current top tier is taken from the bottom tier and placed into the top tier, the number of books on each tier of the bookshelf becomes equal. Originally, the top tier had books, the middle tier had books, and the bottom tier had books."}, {"key": "3857", "content": "There are a total of $$26$$ peaches. The younger one grabbed some first, so the elder one had to take the rest. Seeing that the younger one took too many, the elder one grabbed half from the younger one; the younger one was unwilling, and grabbed half back from the elder one; the elder one was unhappy, so the younger one had to give the elder one $$5$$ more, at this point the elder one had $$2$$ more peaches than the younger one. How many peaches did the younger one originally take?"}, {"key": "3858", "content": "Someone discovered a magical path, beneath which was a small box for storing money. When they walked over the path, some money from the box would fly onto them, doubling the amount of money they had. They were very happy about this; however, when they walked back over the path, the money they had would fly into the box, doubling the amount of money in the box. After making 3 round trips, both the box and the person had 64 one-yuan coins each. Originally, the person had yuan, and the box had yuan."}, {"key": "3859", "content": "The coal yard originally had a certain number of tons of coal. The first time, half of the original coal was shipped out. The second time, $$450$$ tons were shipped in. The third time, half of the existing coal plus $$50$$ tons were shipped out, resulting in twice the remaining coal being $$1200$$ tons. The original number of tons of coal in the coal yard."}, {"key": "3860", "content": "48 kg of water is divided into three bottles. In the first round, some water from bottle $$A$$ is poured into bottles $$B$$ and $$C$$, causing the water in bottles $$B$$ and $$C$$ to double in volume compared to their original content. In the second round, some water from bottle $$B$$ is poured into bottles $$A$$ and $$C$$, also causing the water in bottles $$A$$ and $$C$$ to double in volume compared to their existing content. In the third round, some water from bottle $$C$$ is poured into bottles $$A$$ and $$B$$, causing the water in bottles $$A$$ and $$B$$ to double in volume compared to their existing content. After these three rounds of pouring, the three bottles contain the same amount of water. The original amount of water in bottle $$A$$ was ___ kilograms, in bottle $$B$$ was ___ kilograms, and in bottle $$C$$ was ___ kilograms,"}, {"key": "3861", "content": "Class A, Class B, and Class C have a total of 144 students. First, the same number of students from Class A is transferred to Class B to make their numbers equal. Then, the same number of students from Class B is transferred to Class C. After that, the same number of students from Class C is transferred back to Class A, making the number of students in Class A, Class B, and Class C equal. Originally, Class A had more students than Class B."}, {"key": "3862", "content": "Fill in the blanks: In the decimal number $$210.593$$, $$2$$ is in the hundred's place, representing $$2$$ hundreds; $$5$$ is in the _____ place, representing _____; $$9$$ is in the _____ place, representing _____; $$3$$ is in the _____ place, representing _____."}, {"key": "3863", "content": "To reduce $$35.148$$ to $$\\frac{1}{1000}$$ of its original size, you just need to move the decimal point by places, resulting in ."}, {"key": "3864", "content": "Arithmetic sequence calculation: $$357+352+347+\\cdots+22=$$."}, {"key": "3865", "content": "Arithmetic sequence calculation: $$1 + 3 + 5 + \\ldots + 73 = $$\uff0e"}, {"key": "3866", "content": "In ten boxes numbered $$1$$ to $$10$$, there are a total of $$180$$ grains of rice, knowing that each box contains more rice than the box before it by the same amount. If the $$6$$th box contains $$20$$ grains of rice, then the subsequent boxes contain more rice than the previous one by several grains."}, {"key": "3867", "content": "$(2005+2006+2007+2008+2009+2010+2011)\\div 2008$ = ."}, {"key": "3868", "content": "The correct description for the following sequences is ( ).\n(1) 2, 5, 8, 11, 14, 17, 20.\n(2) 1, 3, 9, 27, 81, 243.\n(3) 1, 1, 1, 1, 1, 1, 1, 1, 1.\n(4) 1, 2, 3, 5, 8, 13, 21.\n(5) 3, 7, 11, 15, 19, 23, 27."}, {"key": "3869", "content": "Given the arithmetic sequence $$13$$, $$18$$, $$23$$, $$28$$, $$\\cdots$$, $$1003$$. This arithmetic sequence has a total of ( ) terms."}, {"key": "3870", "content": "Students in the third grade of a certain school are arranged in a square formation. There are $$10$$ people on each side of the outermost layer. How many people are there in total on the outermost layer? "}, {"key": "3871", "content": "Students in the third grade of a school are arranged in a solid square formation. The outermost layer has $$10$$ people on each side. How many third-grade students are there in the square formation in total? ( )"}, {"key": "3872", "content": "As shown in the figure, there is a piece that needs to move from the lower left corner to the upper right corner. Each step can only move to the right, up, or diagonally up-right by one square. There are a total of different ways to do so.\n question_3872-image_0"}, {"key": "3873", "content": "As shown in the diagram, starting from \"\u513f\" to \"\u4e50\", the total number of different paths to form the five characters of \"\u513f\u7ae5\u8282\u5feb\u4e50\" is ____\uff0e(Each step can only move from one character to an adjacent character either horizontally or vertically)\n question_3873-image_0"}, {"key": "3874", "content": "As shown in the figure, $$27$$ unit cubes are assembled into a large cube. Following the grid lines on the surface, the total number of shortest paths from $$A$$ to $$B$$ is .\n question_3874-image_0"}, {"key": "3875", "content": "A certain school's ballroom dance team has a total of $$43$$ people, of which $$15$$ people can do Latin dance, $$13$$ people can do Tango, and $$5$$ people can do both. Thus, the number of people who can do neither is."}, {"key": "3876", "content": "Among the long division problems below, the meaning of \"80\" in the box is incorrectly represented as ( ).\n question_3876-image_0"}, {"key": "3877", "content": "If $$3$$ CNC (Computer Numerical Control) machines can process $$960$$ identical parts in $$4$$ hours, then $$1$$ CNC machine needs hours to process $$400$$ identical parts."}, {"key": "3878", "content": "The picture below shows a $6\\times 6$ area, with 8 trees planted. Now it is required to set up tents on the empty ground where no trees are planted, and the tents must be next to trees. Any two tents occupying squares do not share a common point, and the number of tents in each row is shown on the left, and the number of tents in each column is shown at the top. Is there a tent on the 4th row and 4th column ( )?\n question_3878-image_0"}, {"key": "3879", "content": "Kids, in the picture below, some of the squares definitely contain mines. Please try to find them. Is there a mine in row $$2$$, column $$1$$? ( )\n question_3879-image_0"}, {"key": "3880", "content": "Use the backward method to fill in the appropriate number in the first square on the left.\n question_3880-image_0"}, {"key": "3881", "content": "\u25cb\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u25cb\u2026\u2026 In such a sequence of patterns, observe the rule to answer the following question: In the first $$88$$ patterns, there are some five-pointed stars."}, {"key": "3882", "content": "Cut out the largest square from the rectangle on the right, the remaining area is ( ) $$\\text{cm}^2$$.\n question_3882-image_0"}, {"key": "3883", "content": "In the Asian Cup final, the number of Chinese journalists was $$3$$ times that of foreign journalists. After the match, $$180$$ Chinese journalists left the venue, leaving an equal number of Chinese and foreign journalists. Originally, there were Chinese journalists and foreign journalists."}, {"key": "3884", "content": "The year 2020 has days, February of $$2020$$ has days."}, {"key": "3885", "content": "As shown in the picture, fill in appropriate numbers in the diagram to make it a third-order magic square. Then, $$A+B+C+D+E=$$.\n question_3885-image_0"}, {"key": "3886", "content": "A class has $$45$$ students, many of whom joined extracurricular interest groups. $$22$$ students joined the music interest group, $$26$$ students joined the art interest group, and $$6$$ students did not join any interest group. How many students joined both the music and art interest groups?"}, {"key": "3887", "content": "A school held a sports meet, where class 1 of grade 4 had a total of $$50$$ people, among them $$18$$ participated in track and field competitions, $$26$$ participated in expansion type team activities, and $$7$$ people participated in both activities. How many did not participate in either activity?"}, {"key": "3888", "content": "Among the natural numbers from $$1$$ to $$60$$, there are several that are multiples of either $$3$$ or $$5$$."}, {"key": "3889", "content": "In the picture below, there are several acute angles, right angles, and obtuse angles.\n question_3889-image_0 question_3889-image_1 question_3889-image_2 question_3889-image_3 \n question_3889-image_4 question_3889-image_5 question_3889-image_6 question_3889-image_7"}, {"key": "3890", "content": "Move the decimal point of $$4.702$$ two places to the right, the decimal becomes ( )."}, {"key": "3891", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, and $$AF$$ is perpendicular to $$CD$$ at point $$F$$. It is known that the area of the parallelogram is $$72$$ square centimeters, $$CD=8$$ centimeters, and $$AE=6$$ centimeters. Then, the length of segment $$AF$$ is in centimeters. question_3891-image_0"}, {"key": "3892", "content": "Fill in the appropriate operators or parentheses in the question below to make the equation hold: ( ).\n$$1$$ $$2$$ $$3$$ $$4$$ $$5=20$$"}, {"key": "3893", "content": "How many different ways are there to divide $$12$$ apples into $$3$$ piles of unequal amounts?"}, {"key": "3894", "content": "Starting from $$2$$, the sequence of consecutive even numbers $$2$$, $$4$$, $$6$$, $$8$$, $$10\\cdots \\cdots $$, then $$36$$ is the ___th number in this sequence."}, {"key": "3895", "content": "Starting from $$1$$, the continuous odd numbers $$1$$, $$3$$, $$5$$, $$7$$, $$\u2026\u2026$$, then $$21$$ is the nth number in this sequence."}, {"key": "3896", "content": "Lili learns English words. On the first day, she learned $$10$$ words, and each day after, she learned $$3$$ more words than the previous day. On the $$7$$th day, she learned $$28$$ words. Lili learned a total of words in the $$7$$ days of this week. question_3896-image_0"}, {"key": "3897", "content": "As shown in the diagram, $$AB$$ is a straight line, $$OC$$ bisects $$\\angle AOD$$ into two equal angles, $$OE$$ is within $$\\angle BOD$$, and $$\\angle BOD=3\\angle DOE$$, $$\\angle COE=72{}^\\circ $$. Therefore, $$\\angle EOB$$ equals.\n question_3897-image_0"}, {"key": "3898", "content": "Insert either \"$$+$$\" or \"$$-$$\" between each pair of adjacent numbers below to make the equation true.\n$$5$$ \u3000$$5$$ \u3000$$5$$ \u3000$$5$$\u3000$$5$$ \u3000$$5=0$$"}, {"key": "3899", "content": "Fill in the blanks with \u201c$$+$$, $$-$$, $$\\times$$, $$\\div$$\u201d and parentheses at the appropriate places among the five $$2$$s to make the equation valid. The correct option among the following is ( ).\n$$2$$ $$2$$ $$2$$ $$2$$ $$2$$ = $$30$$"}, {"key": "3900", "content": "A little ant is at point $$\\text{A}$$ on a rectangular grid paper, it wants to go to point $$\\text{B}$$ to play, but it doesn't know which path is the shortest$.$ Children, can you find ( ) such shortest paths for it.\n question_3900-image_0"}, {"key": "3901", "content": "There are $$48$$ books to be distributed among two groups of children, and it is known that the second group has $$5$$ more children than the first group. If all the books are distributed to the first group, some of the children can get $$5$$ books each, and the remaining children can get $$4$$ books each; if all the books are distributed to the second group, some of the children can get $$4$$ books each, and the remaining children can get $$3$$ books each. The question is: how many people are there in total in the two groups."}, {"key": "3902", "content": "Select 7 different numbers from 1 to 9, requiring their sum to be 36, there are a total of different methods."}, {"key": "3903", "content": "There is a category of three-digit numbers, the sum of the digits on each place of the number is $$12$$, the product of the digits on each place of the number is $$30$$, the sum of all such three-digit numbers is."}, {"key": "3904", "content": "Divide $$50$$ into $$4$$ natural numbers so that the first number times $$2$$ equals the second number divided by $$2$$; the third number plus $$2$$ equals the fourth number minus $$2$$, there are at most types of methods for this division."}, {"key": "3905", "content": "The sum of three natural numbers A, B, and C is $$6$$. How many possible combinations of these three natural numbers are there?"}, {"key": "3906", "content": "How many different ways can $$10$$ identical glass balls be divided into $$2$$ piles?"}, {"key": "3907", "content": "Dividing $$7$$ identical apples into two piles, there are different ways of doing it."}, {"key": "3908", "content": "Calculate: $${{55}^{2}}-53\\times 57=$$."}, {"key": "3909", "content": "Calculate: $$(2012\\times 2013+2013\\times 2014-2)\\div(2011\\times 2015+3)=$$."}, {"key": "3910", "content": "If $$A=(1+2+3+\\cdots \\cdots +2009)\\times (2+3+4+\\cdots \\cdots +2010)$$, $$B=(2+3+4+\\cdots \\cdots +2009)\\times (1+2+3+\\cdots \\cdots +2010)$$, then the larger between $$A$$ and $$B$$ is."}, {"key": "3911", "content": "A hot drink shop sells milk tea and coffee. If the quantity of milk tea in the warehouse is 14 bottles less than 4 times the quantity of coffee, and on average, the shop sells 26 bottles of milk tea and 7 bottles of coffee each day. After calculating, the clerk found out that after some days, there were exactly 6 bottles of milk tea and 1 bottle of coffee left in the warehouse."}, {"key": "3912", "content": "Xiao Hong has $$30$$ pencils, Xiao Lan has $$45$$ pencils, after Xiao Lan gives Xiao Hong ( ) pencils, Xiao Hong has $$2$$ times more pencils than Xiao Lan."}, {"key": "3913", "content": "The apples in basket A are twice the amount of those in basket B. If $$10$$ kilograms of apples are taken from basket A and given to basket B, then the weight of the apples in both baskets becomes equal. How many kilograms of apples were originally in basket A?"}, {"key": "3914", "content": "After Eddie gave Viola $$10$$ dollars, Eddie had $$4$$ dollars less than Viola, originally Eddie had more dollars than Viola.\n question_3914-image_0"}, {"key": "3915", "content": "As shown in the figure below, there are four islands $$A$$, $$B$$, $$C$$, $$D$$, connected by a total of nine bridges. If a tourist wants to traverse these nine bridges once without repetition, it can be done. question_3915-image_0"}, {"key": "3916", "content": "As shown in the diagram, there are four islands $$A$$, $$B$$, $$C$$, $$D$$, with a total of nine bridges between them. If one more bridge is added, tourists would be able to visit each of the nine bridges exactly once. question_3916-image_0"}, {"key": "3917", "content": "As shown in the following figure, there are four islands: $$A$$, $$B$$, $$C$$, and $$D$$, connected by a total of nine bridges. question_3917-image_0 At least how many more bridges must be added to enable visitors to traverse all bridges without repeating any and return to the starting point."}, {"key": "3918", "content": "A water sprinkler truck needs to water the streets of a certain community. The street route is shown in the following diagram, which can be regarded as composed of three rectangles each 200 meters long and 100 meters wide. The sprinkler truck starts from point A and needs to cover all the streets before returning to A. Thus, the shortest total distance is ( ) meters. question_3918-image_0"}, {"key": "3919", "content": "Eddie is cleaning up the desk, dividing $$9$$ identical pencils into $$3$$ piles, there are a total of different methods."}, {"key": "3920", "content": "Eddie is tidying up the desk, dividing $$12$$ identical erasers into $$3$$ piles of different quantities, there are a total of different ways."}, {"key": "3921", "content": "The little rabbit's family planted three types of vegetables: carrots, cabbage, and spinach. They only eat one type of vegetable each day and do not eat the same vegetable on two consecutive days. If they eat carrots on day 1, then there can be several different arrangements for the continuous 4-day menu."}, {"key": "3922", "content": "The rabbit family grew three kinds of vegetables: carrots, cabbages, and spinach. They eat only one of these vegetables each day, without repeating the same vegetable on consecutive days. If they eat carrots on both the $$1^{st}$$ and the $$6^{th}$$ day, then there are different arrangements of the menu for these consecutive $$6$$ days."}, {"key": "3923", "content": "As shown in the diagram, a frog jumps between four lotus leaves, each time it jumps from one to an adjacent one. If the frog starts on lotus leaf $$B$$ and then jumps continuously $$4$$ times, then there are a total of different ways to jump. question_3923-image_0"}, {"key": "3924", "content": "Answer the following question. There are a total of $$350$$ chickens, ducks, and geese on the farm. There are $$10$$ more ducks than $$3$$ times the number of chickens, and there are $$20$$ more geese than $$2$$ times the number of ducks. There are, chickens, ducks, geese respectively."}, {"key": "3925", "content": "Please answer the following questions. There are $$2$$ layers on the bookshelf, the quantity of books on the upper layer is $$3$$ times plus $$8$$ books more than that on the lower layer, and it is known that the difference between the two layers is $$48$$ books, then the upper layer has $$68$$ books."}, {"key": "3926", "content": "Please answer the following questions: There are $$2$$ shelves in a bookcase. The number of books on the upper shelf is $$3$$ times less than the lower shelf minus $$4$$ books. It is known that the difference between the two shelves is $$66$$ books. How many books are there in total on the two shelves?"}, {"key": "3927", "content": "Calculate the following questions. A monkey and a rooster shared some milk candies, the rooster got $$3$$ times more candies than the monkey plus $$3$$ more, and the rooster got $$27$$ more candies than the monkey. How many milk candies did the monkey and the rooster get respectively?"}, {"key": "3928", "content": "Solve the following problems. Monkeys and roosters share some milk candies. The number of milk candies shared by the rooster is 3 less than 3 times the number shared by the monkey, and the rooster has 27 more milk candies than the monkey. Question: How many milk candies did the monkey and the rooster each get?"}, {"key": "3929", "content": "Answer the following question: $$6$$ years ago, the father's age was $$5$$ times that of his son. The sum of the father and son's ages this year is $$78$$ years old. Question: How old is the father this year?"}, {"key": "3930", "content": "This year, the sum of grandfather and grandson's ages is 74 years old. Two years later, the grandfather's age will be 5 times the grandson's age. The difference in age between grandfather and grandson this year is years."}, {"key": "3931", "content": "Eddie said: \"My mom is $$24$$ years older than me, and two years ago, my mom's age was $$4$$ times mine.\" Eddie is years old this year."}, {"key": "3932", "content": "The older brother is $$14$$ years old this year, and he says to his younger brother, 'When I was your current age, you were only $$6$$ years old.' How old is the younger brother this year?"}, {"key": "3933", "content": "Baby whale is $$21$$ years old this year. One day, his mother said to him: 'When you grow to my current size, I will be $$61$$ years old!', find the current age of the mother whale."}, {"key": "3934", "content": "Wei Er needs to choose one jacket out of $$7$$ different ones and one pair of trousers out of $$9$$ different pairs to get dressed to go out, and she has a number of different combination methods."}, {"key": "3935", "content": "As shown in the diagram, there are $$5$$ ways to go from place $$A$$ to place $$B$$, and $$3$$ ways to go from place $$B$$ to place $$C$$. Therefore, there are a total of different ways for Wei to go from place $$A$$ through place $$B$$ to place $$C$$. question_3935-image_0"}, {"key": "3936", "content": "Vi's wardrobe contains $$7$$ different tops, $$5$$ different pairs of pants, and $$2$$ different pairs of shoes. Before attending a dance party, she needs to choose the appropriate combinations from these tops, pants, and shoes. Thus, there are a total of different combinations."}, {"key": "3937", "content": "Vi's wardrobe has $$7$$ different tops, $$5$$ different pairs of trousers, and $$2$$ different pairs of shoes for attending a dance party. (2) If she also has $$3$$ hats, and needs to pick appropriate matches from these hats, tops, trousers, and shoes, then the total number of different combinations she can wear to the dance party is."}, {"key": "3938", "content": "Viola's wardrobe has $$7$$ different tops, $$5$$ different pairs of pants, and $$2$$ different pairs of shoes for going to a dance party. If she also has $$3$$ hats, where the hats can be chosen or not, then she has a total of different combinations for attending the dance party."}, {"key": "3939", "content": "The first class of third grade is going to participate in the sports meet! All the students are actively signing up, Qianqian, Yangyang, and Xixi all want to sign up. There are $$5$$ events: running, high jump, long jump, shot put, and rope skipping. Each person can only participate in one event. (1) If everyone can participate in the same event, there are a total of different options for participating."}, {"key": "3940", "content": "Class 1 of Grade 3 is going to participate in the sports meeting! All students are actively signing up, with Qianqian, Yangyang, and Xixi all wanting to register. There are 5 events: running, high jump, long jump, shot put, and jump rope. Each person can only participate in one event. (2) If everyone participates in a different event, there are a total of different options for participation."}, {"key": "3941", "content": "There are four running events in the sports meet, namely $$50$$ meters, $$100$$ meters, $$200$$ meters, and $$400$$ meters, with a rule that each participant can only participate in one of them. Four students, A, B, C, and D, registered to participate in these four events. Question: (1) If each student can register for any of these four events, how many total registration methods are there?"}, {"key": "3942", "content": "There are four running events in the sports meeting, which are $$50$$ meters, $$100$$ meters, $$200$$ meters, $$400$$ meters, respectively. It is stipulated that each participant can only take part in one of them. Students A, B, C, and D enroll to participate in these four events. Question: (2) If the four students enroll in different events, how many total enrollment methods are there."}, {"key": "3943", "content": "Using the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, (1) different two-digit numbers can be formed."}, {"key": "3944", "content": "Using the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$. (1) The number of different three-digit numbers that can be formed."}, {"key": "3945", "content": "Using the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, it is possible to form different three-digit numbers with no repeating digits."}, {"key": "3946", "content": "Using the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, (2) you can form different three-digit numbers without repeating digits."}, {"key": "3947", "content": "Using the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, it is possible to form different three-digit even numbers without repeating any digit."}, {"key": "3948", "content": "Using the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$. (3) You can form different four-digit numbers without repeated digits."}, {"key": "3949", "content": "As shown in the figure, there are areas $$A$$, $$B$$, $$C$$, $$D$$. Now using four different colors to color these four areas, to make the adjacent areas have different colors, there are different coloring methods. question_3949-image_0"}, {"key": "3950", "content": "As shown in the diagram, there are four countries $$A$$, $$B$$, $$C$$, $$D$$ on the map. Now using five different colors to color the map, so that adjacent countries have different colors, there are kinds of different coloring methods. question_3950-image_0"}, {"key": "3951", "content": "The perimeter of the figure below is in centimeters. question_3951-image_0"}, {"key": "3952", "content": "The perimeter of the figure below is in centimeters. question_3952-image_0"}, {"key": "3953", "content": "The perimeter of the figure below is in centimeters. question_3953-image_0"}, {"key": "3954", "content": "As shown in the figure below, a large rectangle is divided into four parts: $$A$$, $$B$$, $$C$$, $$D$$. It is known that the perimeter of block $$A$$ is $$4$$ cm, the perimeter of block $$B$$ is $$16$$ cm, the perimeter of block $$D$$ is $$20$$ cm. What is the perimeter of $$C$$ in centimeters? question_3954-image_0"}, {"key": "3955", "content": "A large rectangle is divided into $$9$$ small rectangles, among which the perimeter of $$3$$ pieces has been marked. Hence, the perimeter of the large rectangle is in centimeters. question_3955-image_0"}, {"key": "3956", "content": "In the diagram below, two adjacent sides are perpendicular to each other. The perimeter of this shape is in centimeters. question_3956-image_0"}, {"key": "3957", "content": "The perimeter of the figure below is. question_3957-image_0"}, {"key": "3958", "content": "In the diagram below, adjacent sides are perpendicular to each other, so the perimeter of this shape is ( ).\n\u200b\u200b\u200b\u200b\u200b\u200b question_3958-image_0"}, {"key": "3959", "content": "As shown in the diagram, a large rectangle is divided into 4 smaller rectangles A, B, C, D. It is known that the perimeters of A and D are 12 and 18, respectively. The perimeter of the large rectangle is.\n question_3959-image_0"}, {"key": "3960", "content": "As shown in the figure: (1) Figure \u2460 is a square with an area of $$25{{\\text{m}}^{2}}$$, and its side length is meters. question_3960-image_0"}, {"key": "3961", "content": "As shown in the diagram: (2) Diagram \u2461 is a rectangle with an area of $$72\\text{d}{{\\text{m}}^{2}}$$, and it is known that its width is $$8\\text{dm}$$, its length is in decimeters. question_3961-image_0"}, {"key": "3962", "content": "As shown in the figure, there are two small squares inside a large square, with areas of $$9$$ square centimeters and $$4$$ square centimeters, respectively. The area of the shaded part is in square centimeters. question_3962-image_0"}, {"key": "3963", "content": "As shown in the diagram, a large rectangle is divided into three smaller rectangles and one small square, where the area of the small square is $$4$$ square centimeters, the areas of the two small rectangles are respectively $$10$$ and $$18$$ square centimeters, the area represented by rectangle $$A$$ is square centimeters. question_3963-image_0"}, {"key": "3964", "content": "The area of the given shape is square centimeters. question_3964-image_0"}, {"key": "3965", "content": "The area of the given figure is square centimeters. question_3965-image_0"}, {"key": "3966", "content": "There is a rectangular flower bed with a perimeter of $$26$$ meters and a length of $$8$$ meters. A path $$1$$ meter wide is laid around the perimeter. The area of the path is in square meters. question_3966-image_0"}, {"key": "3967", "content": "There is a square pool with a side length of $$15$$ meters, and a $$2$$ meters wide path is laid around the pool. What is the area of the path?\n question_3967-image_0"}, {"key": "3968", "content": "As shown in the diagram, within a square garden with a side length of $$8$$ meters, there are $$2$$ shaded pathways each $$1$$ meter wide (shown in the shaded parts), the area of the garden (blank part) is in square meters. question_3968-image_0"}, {"key": "3969", "content": "As shown in the figure, a rectangular garden with a length of $$8$$ meters and a width of $$6$$ meters has a rectangular shaded path with a width of $$1$$ meter (the shaded part in the picture), and the area of the garden (the blank part) is square meters. question_3969-image_0"}, {"key": "3970", "content": "The area of a rectangular tablecloth is $$80$$ square decimeters, knowing the width is $$8$$ decimeters, then the length of the tablecloth is decimeters."}, {"key": "3971", "content": "As shown in the figure, a square piece of paper with a side length of $$10$$ cm is cut twice horizontally and once vertically, dividing it into $$6$$ rectangular pieces. The total perimeter of these $$6$$ small rectangles equals centimeters. question_3971-image_0"}, {"key": "3972", "content": "There is a rectangular piece of paper, the length is $$10$$ centimeters, and the width is $$8$$ centimeters. Cut it vertically with scissors (see below), the sum of the perimeters of these $$2$$ rectangles is centimeters. question_3972-image_0"}, {"key": "3973", "content": "There is a rectangle paper with a length of $$10$$ cm and a width of $$8$$ cm, cut horizontally with scissors (see below), the sum of the perimeters of these $$2$$ rectangles is cm. question_3973-image_0"}, {"key": "3974", "content": "There is a rectangular piece of paper, with a length of $$10$$ cm and a width of $$8$$ cm. Cutting once horizontally and once vertically with scissors (as shown in the diagram below), the sum of the perimeters of these $$4$$ rectangles is cm. question_3974-image_0"}, {"key": "3975", "content": "Using $$3$$ rectangles, each with a width of $$4$$ centimeters and of the same size, to create a larger rectangle (as shown below), the perimeter of this larger rectangle is in centimeters. question_3975-image_0"}, {"key": "3976", "content": "There is a rectangular piece of paper, the length is $$10$$ cm, and the width is $$8$$ cm. Cut once horizontally and vertically with scissors (see the figure below), the sum of the perimeters of these $$4$$ rectangles is cm. question_3976-image_0"}, {"key": "3977", "content": "As shown in the image, four identical small rectangles are combined into one large rectangle. It is known that the perimeter of this large rectangle is 42 cm. The perimeter of the small rectangle is ___ cm. question_3977-image_0"}, {"key": "3978", "content": "There is a square flowerbed (the shaded part in the picture) in the park, a path with a width of $$1$$ meter is constructed around its perimeter, the area of the path is $$12$$ square meters, then the area of the flowerbed in the middle is square meters. question_3978-image_0"}, {"key": "3979", "content": "In the diagram below, two squares overlap, and the area of the red shaded part is larger than the area of the green shaded part by square centimeters. question_3979-image_0"}, {"key": "3980", "content": "The right figure is made up of $$3$$ identical small rectangles, given that the length of the small rectangle is $$16$$ cm, then the perimeter of the formed large rectangle is cm. question_3980-image_0"}, {"key": "3981", "content": "As shown in the picture, the length of the rectangle is $$10$$ cm, and the width is $$7$$ cm. A teacher takes out a kitchen knife and makes $$3$$ horizontal cuts as shown in the picture. The total perimeter of the resulting small rectangles is in centimeters. question_3981-image_0"}, {"key": "3982", "content": "A rectangle overlaps with a square. The non-overlapping shaded areas have a difference in area. question_3982-image_0"}, {"key": "3983", "content": "After the science and technology exhibition, among the three kids $$A$$, $$B$$, and $$C$$, one of them won the grand prize. They gathered together to discuss who won the grand prize. $$A$$ said, 'It should be $$C$$.', $$B$$ said, '$$A$$ is wrong.', $$C$$ said, 'I didn't win the grand prize.' If only one of these statements is true, then the student who won the grand prize is."}, {"key": "3984", "content": "Four kids, Baby, Star, Strong, and Happy, were playing soccer in the yard. A loud noise disturbed Teacher Lu, who was reading. When Teacher Lu looked up, he found a windowpane had been broken. Teacher Lu came out and asked, 'Who broke the glass?' Baby said, 'Star did it unintentionally.' Star said, 'Happy broke it.' Happy said, 'Star is lying.' Strong said, 'I definitely didn't break it.' If only one child is telling the truth, who broke the glass? question_3984-image_0"}, {"key": "3985", "content": "Four children, Baby, Star, Qiangqiang, and Lele were playing football in the yard. Suddenly, a noise startled Mr. Lu, who was reading. Looking up, Mr. Lu found a window glass broken. Mr. Lu came out and asked, 'Who broke the glass?' Baby said, 'Star did it unintentionally.' Star said, 'Lele did it.' Lele said, 'Star is lying.' Qiangqiang said, 'Anyway, it wasn't me who broke it.' If only one child told the truth, then who is this child? question_3985-image_0"}, {"key": "3986", "content": "In a competition, five students $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ finished in the top five places (without tying for the same place). Everyone made the following guesses about the ranks: $$A$$ said: 'The second place is $$D$$, the third place is $$B$$.' $$B$$ said: 'The second place is $$C$$, the fourth place is $$E$$.' $$C$$ said: 'The first place is $$E$$, the fifth place is $$A$$.' $$D$$ said: 'The third place is $$C$$, the fourth place is $$A$$.' $$E$$ said: 'The second place is $$B$$, the fifth place is $$D$$.' As a result, everyone only guessed half correctly. So, who is the second place?"}, {"key": "3987", "content": "Zhao Ming, Qian Hong, and Sun Jie were admitted to Peking University, Tsinghua University, and Beijing Normal University respectively. Which universities did they get admitted to? The classmates made the following guesses: Classmate A guessed: Zhao Ming was admitted to Tsinghua University, Sun Jie was admitted to Beijing Normal University. Classmate B guessed: Zhao Ming was admitted to Beijing Normal University, Qian Hong was admitted to Tsinghua University. Classmate C guessed: Zhao Ming was admitted to Peking University, Sun Jie was admitted to Tsinghua University. As a result, each classmate's guess was half correct. So, which university was Zhao Ming admitted to?"}, {"key": "3988", "content": "Wang Wen, Zhang Bei, and Li Li are respectively parachuting, track and field, and swimming athletes. Now it is known that: (1) Zhang Bei has never been skydiving; (2) The parachuting athlete has won two gold medals; (3) Li Li has not yet won a first place, and she was born in the same year as the track and field athlete. Based on the above circumstances, what kind of athlete is Li Li?"}, {"key": "3989", "content": "Xueersi third grade's three classes held a mixed doubles table tennis exhibition match, with each class contributing one male and one female student. The male students were designated as A, B, and C, while the female students were labeled as $$A$$, $$B$$, and $$C$$. It was stipulated that students from the same class could not pair up. Known information includes: In the first game, A partnered with $$A$$ against C and $$B$$; in the second game, C and $$C$$ played against A and the female student from B's class. Question: Who is the female student from A's class? question_3989-image_0"}, {"key": "3990", "content": "Eddie, Vi, and Da Kuan went to participate in an event. The three of them wore hats and clothes of three different colors. It is known: \u2460 The colors of hats and clothes are only red, yellow, and blue; \u2461 Eddie did not wear a red hat, and Vi did not wear a yellow hat; \u2462 The person wearing the red hat did not wear blue clothes; \u2463 The person wearing the yellow hat was wearing red clothes; \u2464 Vi did not wear yellow clothes. Question: What color hat did Eddie wear?"}, {"key": "3991", "content": "Three people, A, B, and C, are from Liaoning, Guangxi, and Shandong, respectively, and their professions are teacher, worker, and actor, respectively. It is known that: (1) A is not from Liaoning, and B is not from Guangxi; (2) The person from Liaoning is not an actor, and the person from Guangxi is a teacher; (3) B is not a worker. (1) Where is B from?"}, {"key": "3992", "content": "There are three people, A, B, and C. Their hometowns are Liaoning, Guangxi, and Shandong respectively, and their occupations are teacher, worker, and actor respectively. It is known that: (1) A is not from Liaoning, B is not from Guangxi; (2) The person from Liaoning is not an actor, the person from Guangxi is a teacher; (3) B is not a worker. (1) What is B's occupation?"}, {"key": "3993", "content": "The tiger, the fox, and the rabbit had a race. After the race, the tiger said: 'I am first'. The fox said: 'I am second'. The rabbit said: 'I am not the first'. Only one of them lied. So, the second place is ______."}, {"key": "3994", "content": "After graduating, Li Zhiming, Zhang Bin, and Wang Dawei chose different professions. Among them, one became a journalist. Once, when asked about their professions, Li Zhiming said: 'I am a journalist.' Zhang Bin said: 'I am not a journalist.' Wang Dawei said: 'Li Zhiming is lying.' If only one of their statements is true, then ( ) is the journalist."}, {"key": "3995", "content": "Xiao Wang, Xiao Zhang, and Xiao Li, one is a worker, one is a farmer, and one is a teacher. Now, it is only known that: Xiao Li is older than the teacher; Xiao Wang and the farmer are of different ages; the farmer is younger than Xiao Zhang. Question: Who is the worker, who is the farmer, and who is the teacher? (Fill in the numbers on the line) $$1$$ Xiao Wang $$2$$ Xiao Zhang $$3$$ Xiao Li"}, {"key": "3996", "content": "Column subtraction calculation: (1) $$125\\times \\left( 80+8 \\right)=$$."}, {"key": "3997", "content": "Columnar subtraction method calculation: (2) $$45\\times \\left( 100-2 \\right)=$$."}, {"key": "3998", "content": "Simple calculation: (1)$$125\\times 103-125\\times 3=$$."}, {"key": "3999", "content": "Simplified calculation: (2)$$36\\times 62+38\\times 36=$$."}, {"key": "4000", "content": "Calculate: (1)$$48\\times 34+34\\times 52=$$."}, {"key": "4001", "content": "Calculate: (2)$$68\\times 144-44\\times 68=$$."}, {"key": "4002", "content": "Calculate: (1)$$13\\times 21+26\\times 13+13\\times 53=$$."}, {"key": "4003", "content": "Calculate: (2)$$21\\times 23+21\\times 95-21\\times 18=$$."}, {"key": "4004", "content": "Calculate: (3)$$63\\times 35-63\\times 38+63\\times 13=$$."}, {"key": "4005", "content": "Calculate: (4)$$25\\times 82-25\\times 34-25\\times 8=$$."}, {"key": "4006", "content": "Calculate: ($$1$$) $$57\\times 27+57\\times 72+57=$$."}, {"key": "4007", "content": "Calculate: ($$2$$) $$38\\times 65+38\\times 36-38=$$."}, {"key": "4008", "content": "Calculate: (1)$$57\\times 36+64\\times 32+64\\times 25=$$\uff0e"}, {"key": "4009", "content": "Calculate: (1)$$92\\times 46+96\\times 8+92\\times 50=$$\uff0e"}, {"key": "4010", "content": "Calculate: (2)$$29\\times 33+76\\times 53+29\\times 43+76\\times 18=$$."}, {"key": "4011", "content": "Calculate: (2)$$15\\times 39+82\\times 27+15\\times 43+82\\times 58=$$."}, {"key": "4012", "content": "Calculate: $$32\\times 28+64+32\\times 70=$$."}, {"key": "4013", "content": "$$12\u00d738+12\u00d734+24\u00d714=$$."}, {"key": "4014", "content": "Calculate: $$14000\\div 25=$$$$98400\\div 25\\div 4$$$$6300\\div \\left( 7\\times 25 \\right)$$="}, {"key": "4015", "content": "Calculate: $$1+2+3+4+\\cdots +19+20=$$."}, {"key": "4016", "content": "Calculate: $$3+5+7+9+11+13+15+17=$$."}, {"key": "4017", "content": "Fill in the blanks as required. (2) $$8+10+12+14+16= $$."}, {"key": "4018", "content": "In an arithmetic sequence with $$9$$ numbers, it is known that the 4th number is $$18$$ and the 5th number is $$21$$. Calculate the sum of this arithmetic sequence."}, {"key": "4019", "content": "If the sum of $$5$$ consecutive natural numbers is $$50$$, then the middle number is."}, {"key": "4020", "content": "Odd numbers starting from $$1$$, $$1$$, $$3$$, $$5$$, $$7$$, $$\u2026\u2026$$, what is the position of $$21$$ in this sequence."}, {"key": "4021", "content": "Compute: $$7+11+15+\\cdots \\cdots +43=$$."}, {"key": "4022", "content": "Eddy collects sugar paper wrappers, collecting $$4$$ on the first day, $$7$$ on the second day, $$10$$ on the third day, $$13$$ on the fourth day, ... and $$61$$ on the last day. How many wrappers did he collect in total?."}, {"key": "4023", "content": "There is a series of numbers, the first number is $$4$$, and the number following each pair of adjacent numbers is $$3$$ larger than the previous number. (1) The $$11$$th number is."}, {"key": "4024", "content": "There is a sequence of numbers, the first number is $$4$$, the number following each pair of adjacent numbers is $$3$$ larger than the previous one. (2) The sum of the first $$11$$ numbers is."}, {"key": "4025", "content": "Arithmetic sequence: $$7$$, $$11$$, $$15$$, $$\\ldots$$, the $$30$$th term is\uff0e"}, {"key": "4026", "content": "Sum: $$5+8+11+\\cdots +62=$$."}, {"key": "4027", "content": "Xiao Tie collects candies, on day $$1$$ he collected $$3$$ candies, and every day after that, he collected $$2$$ more candies than the previous day. Then, on day $$31$$, he collected how many candies."}, {"key": "4028", "content": "A certain theater has $$10$$ rows of seats, with each subsequent row having $$2$$ more seats than the previous one. The first row has $$12$$ seats, and the total number of seats in this theater is ."}, {"key": "4029", "content": "Given a sequence of numbers, starting from the second number, each number is 3 greater than the previous one. The 12th item is 49, what is the first item in the sequence."}, {"key": "4030", "content": "In an arithmetic sequence, the first term is $$11$$, the eleventh term is $$51$$, the difference between two consecutive terms is."}, {"key": "4031", "content": "Given that the 6th and 10th numbers of an arithmetic progression are $$60$$ and $$80$$ respectively, the difference between two consecutive numbers is."}, {"key": "4032", "content": "There are a total of $$200$$ apples in $$5$$ boxes numbered $$1\\sim 5$$, it is known that each box contains the same number of apples more than the previous one. If the $$5$$th box contains $$48$$ apples, then the later box contains more apples than its previous one by several apples."}, {"key": "4033", "content": "There are a total of $$351$$ candy pieces in $$9$$ boxes numbered from $$1\\sim 9$$, and it is known that each box contains the same number of candies more than the previous box. If box number $$1$$ contains $$11$$ pieces of candy, how many more pieces of candy does each subsequent box contain more than its predecessor."}, {"key": "4034", "content": "There is a line segment in the picture. question_4034-image_0"}, {"key": "4035", "content": "Picture $$1$$ has a triangle, picture $$2$$ has a triangle, picture $$3$$ has a triangle. question_4035-image_0"}, {"key": "4036", "content": "There is a triangle in the picture. question_4036-image_0"}, {"key": "4037", "content": "Count the number of triangles in the following picture. question_4037-image_0"}, {"key": "4038", "content": "The image contains a rectangle (including square)."}, {"key": "4039", "content": "There is a rectangle (including square) in the image. question_4039-image_0"}, {"key": "4040", "content": "The picture contains a rectangle (including a square). question_4040-image_0"}, {"key": "4041", "content": "Count the number of rectangles in the figure below. question_4041-image_0"}, {"key": "4042", "content": "There is a square in the picture. question_4042-image_0"}, {"key": "4043", "content": "Count the total number of squares in the picture. question_4043-image_0"}, {"key": "4044", "content": "There is a square in the image. question_4044-image_0"}, {"key": "4045", "content": "Eddy and Vera are preparing to beautify the entire Mace Magic School. First, they plant willow trees on one side of a 100-meter-long pedestrian street, planting one every 10 meters, including both ends, how many willow trees do they need to plant in total?"}, {"key": "4046", "content": "Eddie and Viola are preparing to beautify the entire Mace Magic School by planting poplar trees between the Sun and Moon academic buildings, which are $$50$$ meters apart. If a poplar tree is planted every $$5$$ meters, how many poplar trees in total need to be planted?"}, {"key": "4047", "content": "In order to restore the ecology of the magic forest, Eddie planted $$28$$ trees on one side of a road. It is known that the distance between two adjacent trees is $$3$$ meters. If Eddie planted trees from one end to the other, what is the length of this road in meters?"}, {"key": "4048", "content": "In order to restore the ecology of the magical forest, Eddie planted $$28$$ trees on one side of a path. Given that the distance between two adjacent trees is $$3$$ meters. If trees are not planted at one end, what is the length of this path in meters?"}, {"key": "4049", "content": "In order to restore the ecology of the magic forest, Eddie planted $$28$$ trees on one side of a road, knowing that the distance between two adjacent trees is $$3$$ meters. If trees are not planted at both ends of the road, what is the length of the road in meters?"}, {"key": "4050", "content": "A lake, where a willow tree is planted every $$12$$ meters around the lake, fits exactly $$150$$ trees. What is the perimeter of the lake in meters? (The width of the trees is negligible)"}, {"key": "4051", "content": "On one side of a road with a total length of 2700 meters, a pine tree is planted every 10 meters, including at both ends. Between every two adjacent pine trees, a willow tree is planted every 2 meters. How many willow trees have been planted?"}, {"key": "4052", "content": "On an oval track with a perimeter of $$400$$ meters at the magic school, a broom is placed every $$8$$ meters, and then an owl is arranged every $$2$$ meters between two brooms. How many brooms should be prepared? How many owls should be invited? ( )"}, {"key": "4053", "content": "During a parade, a convoy of parade floats consisting of $$30$$ vehicles, each vehicle being $$4$$ meters long, with a gap of $$5$$ meters between each. The total length of this convoy is meters."}, {"key": "4054", "content": "A train transporting wood has a total length of $$532$$ meters, which includes the engine measuring $$12$$ meters. Each of the remaining carriages has a length of $$25$$ meters, and it is known that the distance between every two carriages is $$1$$ meter. How many carriages does this train have in total? (Including the engine)"}, {"key": "4055", "content": "Cinderella was invited to attend the ball at Max's Magic School. The clock in the hall struck 3 times at 3 o'clock, completing in 6 seconds. It strikes 12 times at 12 o'clock. Cinderella must leave the ball before the 12th strike at 12 o'clock is completed. Starting from the first strike at 12 o'clock, how many seconds does Cinderella have left (ignoring the time it takes to strike)?"}, {"key": "4056", "content": "There is a circular flower bed. If a lilac is planted every $$5$$ meters around the flower bed, and a total of $$20$$ lilacs can be planted, then walking around the flower bed is $$100$$ meters."}, {"key": "4057", "content": "The marathon race is approximately $$\\text{42km}$$ long, with a drinking water service point set up on average every $$\\text{3km}$$ (none at the starting point, one at the finish), with a total of ( ) such service points throughout the course."}, {"key": "4058", "content": "$$10$$ children line up in a row to do exercises, with every two adjacent children standing $$2$$ meters apart, the length of the team doing the exercises in meters."}, {"key": "4059", "content": "There is a series of Chinese characters arranged as follows, \"Spring breeze flowers and grass fragrance spring breeze flowers and grass fragrance$$\\cdots\\cdots$$ \", according to this pattern, the $$52$$nd character is."}, {"key": "4060", "content": "There is a pile of Go pieces, and Wei'er arranges them according to a certain pattern (see below), with a total of $$72$$ pieces placed. What color is the last piece?"}, {"key": "4061", "content": "There is a series of numbers arranged in the order of $$385161713851617138516171 \\cdots \\cdots$$. What is the 50th number?"}, {"key": "4062", "content": "There is a series of numbers arranged in the order of $$385161713851617138516171\\cdots \\cdots$$. May I ask, in these $$50$$ numbers, how many times does \u201c$$1$$\u201d appear in total?"}, {"key": "4063", "content": "There is a sequence of numbers arranged in the order of $$11428571142857114\\ldots \\ldots$$, totaling $$100$$ numbers. How many number $$8$$ are there?"}, {"key": "4064", "content": "There is a series of numbers arranged in the order of $$11428571142857114\\ldots \\ldots$$, totaling $$100$$ numbers. How many number $$1$$s are there?"}, {"key": "4065", "content": "There is a series of numbers arranged in the order of $$11428571142857114\\ldots \\ldots$$, totaling $$100$$ numbers. What is the sum of these numbers?"}, {"key": "4066", "content": "The professor asked Dakuan to plant a row of trees on one side of the road. After Dakuan initially planted $$5$$ poplar trees in a row, the professor said, 'This is not the correct way to plant. You should follow the order of planting $$3$$ willow trees, $$2$$ pine trees, $$1$$ poplar tree, and then repeat the sequence of $$3$$ willow trees, $$2$$ pine trees, $$1$$ poplar tree $$\\cdots \\cdots$$' After that, Dakuan continued to plant according to this pattern. In the end, Dakuan planted a total of $$200$$ trees. The question is: How many willow, pine, and poplar trees did Dakuan plant? question_4066-image_0"}, {"key": "4067", "content": "$$12$$ individuals dressed in black form a circle and play a game of passing a box, as shown in the image. Starting from the individual number $$1$$ and passing clockwise $$100$$ times, the box should end up with individual number black. question_4067-image_0"}, {"key": "4068", "content": "$$12$$ people in black clothes form a circle to play a game of passing a box, as shown. Starting with the person in black labeled $$1$$, the box is passed counter-clockwise $$100$$ times, and the box should be in the hands of person number in black. question_4068-image_0"}, {"key": "4069", "content": "$$12$$ people dressed in black form a circle to play a game of passing a box, as shown in the picture. Starting from person number $$1$$ dressed in black, pass it clockwise $$160$$ times, then counter-clockwise $$80$$ times, the box should end up in the hands of person number black. question_4069-image_0"}, {"key": "4070", "content": "$$10$$ students form a circle to play the pass-the-handkerchief game, as shown in the figure. Starting from student number $$1$$, passing it clockwise $$80$$ times, the handkerchief should be in which student's hand? question_4070-image_0"}, {"key": "4071", "content": "$$10$$ students form a circle to play a game of passing the handkerchief, as shown in the figure. Starting with student $$1$$, it is passed counterclockwise $$99$$ times, whose hand does the handkerchief end up in? question_4071-image_0"}, {"key": "4072", "content": "$$10$$ students form a circle playing a game of passing a handkerchief, as shown in the diagram. Starting from student number $$1$$, it is passed clockwise $$150$$ times, and counterclockwise $$62$$ times, which student ends up with the handkerchief? question_4072-image_0"}, {"key": "4073", "content": "October 1, 2018, is a Monday. Starting from this day, what day of the week is the 25th day?"}, {"key": "4074", "content": "October 1, 2018 is a Monday. Starting from this day, after 27 more days it is a Sunday."}, {"key": "4075", "content": "October 1, 2018, is a Monday. Counting from this day, what day of the week is it after 21 more days?"}, {"key": "4076", "content": "$$2020$$ year $$6$$ month $$1$$ day is Monday. $$2020$$ year $$7$$ month $$5$$ day is Sunday."}, {"key": "4077", "content": "$$2020$$ year $$6$$ month $$1$$ day is Monday. $$2020$$ year $$8$$ month $$21$$ day is Friday."}, {"key": "4078", "content": "$$2018$$ year $$11$$ month $$1$$ day is Thursday, $$2019$$ year $$11$$ month $$1$$ day is Friday."}, {"key": "4079", "content": "Teacher Niu took $$37$$ students for a spring outing to the countryside. During a break, Eddie asked, 'How old are you this year, Teacher Niu?' Teacher Niu replied interestingly, 'If you multiply my age by $$2$$, subtract $$16$$, divide by $$2$$, and then add $$8$$, the result is exactly the total number of people participating in today's activity.' Kids, do you know how old Teacher Niu is this year?"}, {"key": "4080", "content": "There was a money-grubber who always wanted to make more money. One day, he met an old man on a bridge. The old man said to him: 'If you walk across this bridge and back, the money you carry will double. However, as a fee, you have to give me 32 copper coins for each round trip.' The money-grubber did the math, found it reasonable, and agreed. He walked across the bridge and back, and as promised, his money doubled. He happily gave the old man 32 copper coins. After the third round trip, he gave his last 32 copper coins to the old man, leaving him with not a single coin. Question: How many copper coins did the money-grubber originally have?"}, {"key": "4081", "content": "A PhD spends more than half of his monthly salary, $$300$$ more, on food and still has $$5500$$ left. The monthly salary of the PhD is."}, {"key": "4082", "content": "Dengdeng bought a basket of eggs, ate half minus $$2$$ eggs during one lunch, leaving $$12$$ eggs. How many eggs were in the basket originally?"}, {"key": "4083", "content": "On the way to the West to obtain the scriptures, three disciples ate peaches from a tree. Zhu Bajie ate more than half of all of them plus $$2$$, Sun Wukong ate half of what was left minus $$10$$, and Sha Seng ate $$15$$. At this point, there were exactly $$9$$ peaches left on the tree. So, how many peaches were there on the tree originally?"}, {"key": "4084", "content": "A bird pecked at the rice, the first time it ate more than half the quantity of millet by $$10$$ grains, the second time it ate less than half of the remaining by $$12$$ grains, the third time it ate $$14$$ grains, and finally $$15$$ grains of millet were left$$.$$ How many grains of millet were there originally?"}, {"key": "4085", "content": "There are a total of $$36$$ rabbits in $$3$$ cages. If $$8$$ rabbits are taken from cage $$1$$ and put into cage $$2$$, and then $$6$$ rabbits are taken from cage $$2$$ and put into cage $$3$$, such that each of the $$3$$ cages ends up with the same number of rabbits. How many rabbits were originally in the first cage?"}, {"key": "4086", "content": "Basket A and basket B have a different number of apples. Some apples were removed from basket A and placed in basket B, doubling the number of apples in basket B. Then, some apples were removed from basket B and placed back into basket A, doubling the number of apples in basket A. At this point, both baskets contained $$48$$ apples each. Initially, basket A contained ____ apples."}, {"key": "4087", "content": "There are two piles of chess pieces, A and B, with pile A having more chess pieces than pile B. Now, move the chess pieces in the following way: For the first move, take the same number of chess pieces from pile A as there are in pile B and place them into pile B; for the second move, take the same number of chess pieces from pile B as there are left in pile A and place them into pile A; for the third move, again take the same number of chess pieces from pile A as there are left in pile B and place them into pile B. Following this method, after three moves, both pile A and pile B exactly have $$16$$ chess pieces each. How many chess pieces were originally in pile B?"}, {"key": "4088", "content": "A number plus $$3$$, minus $$5$$, multiplied by $$4$$, divided by $$6$$ equals $$16$$, this number is."}, {"key": "4089", "content": "There are an equal number of chickens and rabbits, with a total of $$36$$ legs. Thus, there are chickens and rabbits."}, {"key": "4090", "content": "Three fund managers invested in a number of stocks. Manager Zhang bought 66 of them, Manager Wang bought 40 of them, and Manager Li bought 23 of them. There were 17 stocks that both Manager Zhang and Wang bought, 13 stocks that both Manager Wang and Li bought, 9 stocks that both Manager Li and Zhang bought, and all three managers bought 6 stocks. Question: How many stocks did the three managers buy in total."}, {"key": "4091", "content": "Find the area of the shape in the right picture in square centimeters. question_4091-image_0"}, {"key": "4092", "content": "Compute: $$240\\times 2\\div 6$$="}, {"key": "4093", "content": "Eddie and the doctor set off from point A. Eddie's speed is 20 kilometers per hour, and the doctor's speed is 30 kilometers per hour. Eddie set off 2 hours earlier, then the doctor started to chase Eddie. How many hours will it take for the doctor to catch up with Eddie."}, {"key": "4094", "content": "The sum of three even numbers is ()."}, {"key": "4095", "content": "Calculate the following: $$1234+2341+3412+4123=$$"}, {"key": "4096", "content": "Compute the following: $$23456+34562+45623+56234+62345=$$."}, {"key": "4097", "content": "Calculate: $$(2345+3452+4523+5234)\\div 7$$="}, {"key": "4098", "content": "Calculate: $$(34567+45673+56734+67345+73456)\\div 5=$$\uff0e"}, {"key": "4099", "content": "Calculate: $$8888\\times 9999=$$."}, {"key": "4100", "content": "Calculate: $$555555\\times 9999999=$$."}, {"key": "4101", "content": "Calculate: $$123\\times 1001=$$\uff1b$$23\\times 101=$$\uff0e"}, {"key": "4102", "content": "Calculate: $$9999\\times 1111$$=\uff0e"}, {"key": "4103", "content": "[Thinking Expansion] Calculate: $(135+351+513)\\div 3=$"}, {"key": "4104", "content": "[Thinking Expansion] Locations A and B are $$980$$ kilometers apart. A fire truck departs from location A towards location B at a speed of $$46$$ kilometers per hour, while another fire truck heads towards location A from location B at a speed of $$52$$ kilometers per hour. After how many hours will the two trucks meet on the way."}, {"key": "4105", "content": "[Thinking Expansion] Fill in the square with the appropriate number so that the three-digit number $$\\overline{76\\square}$$ is divisible by $$9$$. The three-digit number is."}, {"key": "4106", "content": "[Thinking Expansion] The upper base of the trapezoid is $$3$$ cm, the lower base is $$7$$ cm, and the height is $$5$$ cm, the area is square centimeters."}, {"key": "4107", "content": "As shown in the diagram, on the calendar of $$X$$ year $$X$$ month, $$A+B+C=45$$. Then, the first Sunday of that month is the . question_4107-image_0"}, {"key": "4108", "content": "As shown in the figure, natural numbers are filled into the grid in an orderly manner. Question: In which row and column is $$200$$? $$1$$$$2$$$$3$$$$4$$$$5$$$$6$$$$7$$$$8$$$$9$$$$10$$$$11$$$$12$$$$13$$$$14$$$$15$$$$16$$$$17$$$$18$$$$19$$$$20$$$$21$$$$22$$$$23$$$$24$$$$\\cdots$$"}, {"key": "4109", "content": "As shown in the diagram, natural numbers are filled into a grid in a regular pattern. Question: (2) What is the number in the 100th row and 2nd column? $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$ $$13$$ $$14$$ $$15$$ $$16$$ $$17$$ $$18$$ $$19$$ $$20$$ $$21$$ $$22$$ $$23$$ $$24$$ $$\\cdots$$"}, {"key": "4110", "content": "As shown in the figure, consecutive natural numbers starting from $$1$$ are filled into a table according to a pattern. The question is: What is the number in the third column of the tenth row? $$1$$$$2$$$$3$$$$4$$$$5$$$$6$$$$7$$$$8$$$$9$$$$10$$$$11$$$$12$$$$13$$$$14$$$$15$$$$16$$$$17$$$$18$$$$19$$$$20$$$$21$$$$22$$$$23$$$$24$$$$25$$$$26$$$$27$$$$28$$$$\\cdots$$$$\\cdots$$$$\\cdots$$$$\\cdots$$"}, {"key": "4111", "content": "As shown in the figure, consecutive natural numbers starting from $$1$$ are filled into a table according to a rule. The question is: In which row and column is $$100$$? $$1$$$$2$$$$3$$$$4$$$$5$$$$6$$$$7$$$$8$$$$9$$$$10$$$$11$$$$12$$$$13$$$$14$$$$15$$$$16$$$$17$$$$18$$$$19$$$$20$$$$21$$$$22$$$$23$$$$24$$$$25$$$$26$$$$27$$$$28$$$$\\cdots$$$$\\cdots$$$$\\cdots$$$$\\cdots$$"}, {"key": "4112", "content": "As shown in the figure, continuous natural numbers starting from $$1$$ are to be filled into the table according to a certain rule. The question is: (2) In which row and column should $$70$$ be placed? Column $$1$$ Column $$2$$ Column $$3$$ Column $$4$$\u2026 $$1$$$$5$$$$9$$$$13$$\u2026 $$2$$$$6$$$$10$$$$14$$\u2026 $$3$$$$7$$$$11$$$$15$$\u2026 $$4$$$$8$$$$12$$$$16$$\u2026"}, {"key": "4113", "content": "As shown in the figure, continuously natural numbers starting from $$1$$ are to be filled into the table according to a certain rule. Question: (1) What is the number in the $$2$$nd row and $$18$$th column? First column Second column Third column Fourth column\u2026$$1$$$$5$$$$9$$$$13$$\u2026$$2$$$$6$$$$10$$$$14$$\u2026$$3$$$$7$$$$11$$$$15$$\u2026$$4$$$$8$$$$12$$$$16$$\u2026"}, {"key": "4114", "content": "As shown in the diagram, consecutive natural numbers starting from $$1$$ are filled into a table according to a certain pattern. The question is: (2) In which column and position should $$568$$ be placed? First column, second column, third column, fourth column $$1$$$$7$$$$13$$$$19$$$$\\cdots$$$$2$$$$8$$$$14$$$$20$$$$\\cdots$$$$3$$$$9$$$$15$$$$21$$$$\\cdots$$$$4$$$$10$$$$16$$$$22$$$$\\cdots$$$$5$$$$11$$$$17$$$$23$$$$\\cdots$$$$6$$$$12$$$$18$$$$24$$$$\\cdots$$"}, {"key": "4115", "content": "As shown in the diagram, continuous natural numbers starting from $$1$$ are to be filled into a table according to a certain pattern. The questions are: (1) What is the number in the $$5$$th row and $$200$$th column? The numbers in the columns are as follows: First column Second column Third column Fourth column $$1$$$$7$$$$13$$$$19$$$$\\cdots$$$$2$$$$8$$$$14$$$$20$$$$\\cdots$$$$3$$$$9$$$$15$$$$21$$$$\\cdots$$$$4$$$$10$$$$16$$$$22$$$$\\cdots$$$$5$$$$11$$$$17$$$$23$$$$\\cdots$$$$6$$$$12$$$$18$$$$24$$$$\\cdots$$"}, {"key": "4116", "content": "Observe the following calendar for a month:\n question_4116-image_0 \n(1) Please circle three adjacent dates in a row so that the sum of the three numbers is $$42$$. The three circled numbers (written in ascending order) are, , ;\n(2) Please circle three adjacent dates in a column, so that the sum of the three numbers is $$42$$. The three circled numbers (written in ascending order) are, , ."}, {"key": "4117", "content": "There is only one barber in the barbershop, but five customers came at the same time. Based on the haircuts they desire, they require $$10$$, $$12$$, $$15$$, $$20$$, and $$24$$ minutes respectively. Arranging their haircut order rationally can minimize the total time spent on haircuts and waiting for these five people. Thus, the minimum total time in minutes is."}, {"key": "4118", "content": "Beijing and Luoyang each have $$11$$ and $$5$$ identical machines, respectively, prepared for Hangzhou $$7$$ units, Xi'an $$~9$$ units. The freight cost per machine is as shown in the table. The arrangement that minimizes the total freight cost, the minimum total freight cost is Yuan. question_4118-image_0"}, {"key": "4119", "content": "Beijing and Luoyang each have $$11$$ and $$5$$ identical machines, respectively, ready to send $$9$$ to Hangzhou and $$7$$ to Xi'an, with the shipping cost per machine as shown in the table, the total shipping cost is at least yuan. question_4119-image_0"}, {"key": "4120", "content": "Person A and Person B set off simultaneously from two places $$300$$ meters apart towards each other. It is known that Person A walks $$60$$ meters per minute, and Person B walks $$40$$ meters per minute. After a few minutes, the two meet."}, {"key": "4121", "content": "It is known that Eddie walks $$90$$ meters per minute, and Vi walks $$60$$ meters per minute. They set off from locations $$A$$ and $$B$$ respectively at the same time.$$ If they walk towards each other, they meet after $$10$$ minutes; if they walk in the same direction, with Vi in front, then the minutes Eddie needs to catch up with Vi are."}, {"key": "4122", "content": "Given that a Doctor walks $$80$$ meters per minute, and Da Kuan walks $$100$$ meters per minute. They both start at the same time from places $$A$$ and $$B$$ respectively. If they walk towards each other, they'll meet after $$5$$ minutes; if they walk in the same direction (with the Doctor ahead), then the time it takes for Da Kuan to catch up to the Doctor is minutes."}, {"key": "4123", "content": "The small animals in the forest go out for a picnic, forming a queue that is $$40$$ meters long and moving forward at a speed of $$3$$ meters per second. The little rabbit needs to rush from the end to the front of the queue and immediately return to the end. The speed of the rabbit is $$5$$ meters per second. Therefore, in total, it takes seconds for the little rabbit to return to the end."}, {"key": "4124", "content": "Person A and person B start from places $$A$$ and $$B$$ at the same time and walk towards each other. Person A walks at a speed of $$60$$ meters per minute, and person B walks at a speed of $$40$$ meters per minute. After a period of time, they meet at a place $$150$$ meters away from the midpoint. Then, the distance between places $$A$$ and $$B$$ is ____ meters."}, {"key": "4125", "content": "The sheep school organizes the little sheep to line up and walk for a picnic. The total length of the queue is $$630$$ meters, and the walking speed is $$60$$ meters per minute. The sheep at the end of the line catches up to the front at a speed of $$150$$ meters per minute, then immediately returns to the end of the line, taking a total of minutes."}, {"key": "4126", "content": "Solve the equation.$$6x+16=9x-2$$, $$x=$$."}, {"key": "4127", "content": "Dongdong needs to help his mother peel $$50$$ potatoes. Knowing that each box has $$18$$ potatoes, Dongdong has already peeled two boxes of potatoes, leaving some potatoes."}, {"key": "4128", "content": "The $$25$$ times of a number is $$375$$, then the $$50$$ times of the number is."}, {"key": "4129", "content": "The teacher distributed snacks to the students, giving out $$18$$ boxes of chips in the morning and $$17$$ boxes of chips in the afternoon. If each box contains $$20$$ packs of chips, then the total number of packs of chips distributed by the teacher that day was ."}, {"key": "4130", "content": "There is a rectangular tile, with a length of $$45$$ cm, and $$15$$ cm longer than its width, then the area of this tile is square centimeters."}, {"key": "4131", "content": "Solve the equation $$2x+3+4x=54-3$$ $x=$"}, {"key": "4132", "content": "Solve the applied problem by setting up an equation: Eddie has $$29$$ pieces of White Rabbit Creamy Candy. Eddie has $$3$$ more pieces than twice as many as Viola has, Viola has ____ pieces."}, {"key": "4133", "content": "The image below shows a $$4\\times 4$$ area with $$3$$ trees planted. It is required to set up tents on the empty ground not occupied by trees, and the tents must be located next to a tree. No two tents should occupy squares that have a common point, and the number of tents in each row and column should be as indicated to the right and bottom, respectively. Therefore, the tent in the first column is in the row. question_4133-image_0"}, {"key": "4134", "content": "The following image is a $$5\\times 5$$ area with $$7$$ trees planted. Now, the requirement is to set up tents on the empty ground where there are no trees, and the tents must be next to a tree. No two tents can share a border, and the number of tents in each row is shown on the far left, while the number of tents in each column is shown at the top. Thus, the tent on the $$2^{nd}$$ row is in which column. question_4134-image_0"}, {"key": "4135", "content": "As shown in the diagram, how many different shortest paths are there from point $$A$$ to point $$B$$ along the segment? question_4135-image_0"}, {"key": "4136", "content": "The path from Xiaojun's home to the school is shown in the figure. There are several different ways to get from Xiaojun's home to the school. (You can only move in the directions to the right or down as shown in the figure) question_4136-image_0"}, {"key": "4137", "content": "Eddie goes home after school, gets hungry on the way, and decides to go to the supermarket to buy bread before returning home. However, he doesn't know how many different shortest routes there are. Kids, please help! ( )\n question_4137-image_0"}, {"key": "4138", "content": "Eddie and Viola are planning to visit Grandma Li at the nursing home, but Viola wants to go shopping downtown first. They plan to go from the school through the downtown to the nursing home. How many shortest routes are there in total? question_4138-image_0"}, {"key": "4139", "content": "If Eddie does not want to pass by the supermarket on his way home, how many different shortest routes are there ( ). question_4139-image_0"}, {"key": "4140", "content": "One day, there was a strong wind, and a corner of the little spider's web was torn by the wind, turning it into the grid shown in the picture below. If the spider can only climb up or to the right, then there are several possible paths for it to get from $$A$$ to $$B$$.\n question_4140-image_0"}, {"key": "4141", "content": "If all sides of a triangle are integers, with two sides being $$3$$ and $$6$$, then the minimum and maximum lengths of the other side are."}, {"key": "4142", "content": "An equilateral triangle has three equal interior angles. The triangle in Figure $$2$$ is an equilateral triangle, so $$\\angle A=$$ degrees, $$\\angle B=$$ degrees, $$\\angle C=$$ degrees. question_4142-image_0"}, {"key": "4143", "content": "An isosceles triangle has a base angle of $$80\u00b0$$. What is the vertex angle in degrees?"}, {"key": "4144", "content": "In an isosceles triangle $$ABC$$, it is known that one of the base angles is $$30{}^\\circ $$. What is the apex angle of triangle $$ABC$$ in degrees?"}, {"key": "4145", "content": "An isosceles triangle with a top angle of $$80\u00b0$$, then what is the base angle in degrees?"}, {"key": "4146", "content": "The two base angles of an isosceles triangle are equal. The triangle in figure $$1$$ is an isosceles right triangle, therefore $$\\angle A=$$ degrees, $$\\angle B=$$ degrees, $$\\angle C=$$ degrees. question_4146-image_0"}, {"key": "4147", "content": "In triangle $$ABC$$, $$\\angle A=40\u00b0$$, $$\\angle B=50\u00b0$$, what is $$\\angle C$$ in degrees?"}, {"key": "4148", "content": "Grandpa is $$74$$ years old this year. When grandpa was as old as dad is, dad was only $$18$$ years old. So, how old is dad this year? question_4148-image_0"}, {"key": "4149", "content": "During the Spring Festival, Xue Xue and his parents went back to their hometown to visit his grandparents, first taking a $$3$$-hour high-speed train followed by a $$2$$-hour long-distance bus. Knowing that the high-speed train travels $$315$$ kilometers per hour, and the long-distance bus travels $$86$$ kilometers per hour. Thus, the total distance from Xue Xue's home to his grandparents' home is kilometers."}, {"key": "4150", "content": "The Hongguang Brigade plowed the fields with tractors, $$2$$ tractors for $$3$$ hours plowed $$75$$ mu of land, based on this calculation, $$4$$ tractors for $$5$$ hours plowed mu of land."}, {"key": "4151", "content": "After dividing each side of an equilateral triangle into four equal parts and then connecting the corresponding segments, the following figure is obtained, which contains several line segments.\n question_4151-image_0"}, {"key": "4152", "content": "There is a triangle in the figure ($$1$$). question_4152-image_0"}, {"key": "4153", "content": "There is a triangle in Figure ($$2$$). question_4153-image_0"}, {"key": "4154", "content": "There is a triangle in the picture ($$3$$). question_4154-image_0"}, {"key": "4155", "content": "There is a triangle in the figure ($$4$$). question_4155-image_0"}, {"key": "4156", "content": "The picture contains a total of triangles.\n question_4156-image_0"}, {"key": "4157", "content": "The picture contains a total of triangles. question_4157-image_0"}, {"key": "4158", "content": "Count the number of rectangles (including squares) in the picture. question_4158-image_0"}, {"key": "4159", "content": "Count the total number of rectangles (including squares) in the picture. question_4159-image_0"}, {"key": "4160", "content": "There are in total rectangular shapes (including squares) in the image.\n question_4160-image_0"}, {"key": "4161", "content": "There are a total of squares in the picture.\n question_4161-image_0"}, {"key": "4162", "content": "There are total squares in the picture. question_4162-image_0"}, {"key": "4163", "content": "There are $$8$$ nails nailed onto a plank, arranged in two rows and four columns in a dot matrix. Using rubber bands, a total of different isosceles right triangles can be formed (requirement: the vertices of the triangle must be on the nails).\n question_4163-image_0"}, {"key": "4164", "content": "The picture contains a rectangle (including squares).\n question_4164-image_0"}, {"key": "4165", "content": "The figure below is composed of small squares of the same side length. Therefore, there are a total of squares in this figure.\n question_4165-image_0"}, {"key": "4166", "content": "As shown in the figure, there is a square in the figure.\n question_4166-image_0"}, {"key": "4167", "content": "As shown in the figure, there are $$15$$ nails on a wooden board, arranged in a square dot matrix of three rows and five columns. How many different squares can be formed with rubber bands in total?\n question_4167-image_0"}, {"key": "4168", "content": "The picture below contains a total of triangles.\nquestion_4168-image_0"}, {"key": "4169", "content": "There is a triangle in the figure.\n question_4169-image_0"}, {"key": "4170", "content": "There is a rectangle in the picture.\n\n\n\n question_4170-image_0"}, {"key": "4171", "content": "The first term is $$\\frac{3}{5}$$, the second term is $$\\frac{5}{9}$$, the third term is $$\\frac{7}{13}$$, the fourth term is $$\\frac{9}{17}$$, the fifth term is $$\\frac{11}{21}$$, \u2026\u2026 then the $$n$$th term is."}, {"key": "4172", "content": "11 triangles can divide a plane into a maximum of parts."}, {"key": "4173", "content": "(1)The sequence $$3$$, $$7$$, $$11$$, $$\\cdots $$, the $$18$$th item is. (2)The sequence $$4$$, $$9$$, $$14$$, $$\\cdots $$, where $$254$$ is the term number of this sequence. (3)The sequence $$4$$, $$8$$, $$12$$, $$\\cdots $$, $$160$$, this sequence has a total number of terms."}, {"key": "4174", "content": "In a plane, $$6$$ circles can divide the plane into at most parts."}, {"key": "4175", "content": "There are now $$14$$ matchsticks, used for arranging numbers, exactly enough to be used up$$. The largest three-digit number that can be formed is, and the smallest three-digit number that can be formed is. question_4175-image_0"}, {"key": "4176", "content": "We can use matchsticks to form the numbers $$0\\sim 9$$. If you are given $$6$$ matchsticks (all $$6$$ must be used), then you can form a different number. question_4176-image_0"}, {"key": "4177", "content": "The following picture shows numbers arranged with matchsticks. With $$13$$ matchsticks, the largest number that can be made where each digit is different is; the smallest number that can be made where each digit is different is. question_4177-image_0"}, {"key": "4178", "content": "Using $$12$$ matchsticks, place a number inside each box, forming two numbers where all digits are different, the maximum result of the addition equation is, and the minimum is. question_4178-image_0"}, {"key": "4179", "content": "We can arrange numbers $$0\\sim 9$$ with matchsticks. Given $$11$$ matchsticks, using exactly all of them: (1)The largest three-digit number that can be formed is. (2)The smallest three-digit number that can be formed is."}, {"key": "4180", "content": "The route from Xiaojun's home to the school is shown in the figure. There are several different ways to get from Xiaojun's home to the school. (You can only move in the direction to the right or down as shown in the figure) question_4180-image_0"}, {"key": "4181", "content": "Eddie and Vi are preparing to visit Grandma Li at the nursing home, as shown below: (1) The shortest route from the school through the city center to the nursing home has ____ routes. question_4181-image_0"}, {"key": "4182", "content": "Eddie and Vee are planning to visit Grandma Li at the nursing home, as shown in the following figure: (2) If they do not want to go through the downtown area, then the shortest route to the nursing home has a total of. question_4182-image_0"}, {"key": "4183", "content": "As shown in the diagram, from point $$A$$ to point $$B$$, if it is required to pass through points $$C$$ and $$D$$, then there is a minimum number of routes. question_4183-image_0"}, {"key": "4184", "content": "As shown in the figure, from point $$A$$ to point $$B$$, if it is required to pass through point $$C$$ or $$D$$, then there are several shortest paths. question_4184-image_0"}, {"key": "4185", "content": "In the diagram, connect adjacent letters with horizontal or vertical line segments. When walking along these segments, the exact route that spells out \u201cAPPLE\u201d has a total of . question_4185-image_0"}, {"key": "4186", "content": "A bee starts from point $$A$$ and returns home to point $$B$$. It can only move from one hexagon to the next adjacent one on the right side and cannot go backwards. There are a total of methods to get home. question_4186-image_0"}, {"key": "4187", "content": "As shown in the figure, a bee leaves from point $$A$$ and returns home to point $$B$$. It can only crawl towards the right from one cell of the beehive to the adjacent cell on the right, and reversing direction is not allowed. There are a total of ways to get home.\n question_4187-image_0"}, {"key": "4188", "content": "Xuexue and Sisi wash $$5$$ distinct bowls together (in a fixed order), Sisi stacks the bowls one on top of the other as she finishes washing them, and Xuexue takes them from the top one by one and stacks them in the cabinet. As Sisi washes and Xuexue takes, the total number of different ways Xuexue can stack the bowls is."}, {"key": "4189", "content": "In the \"Math Grand Challenge\" finals, the Watermelon team was up against the Wintermelon team. The competition was based on a best-of-seven format, where winning a match awarded one point. Eventually, the Watermelon team won with a score of 4:2, and throughout the entire competition, the Watermelon team's score was never behind. Question: How many possible outcomes were there for the match results?"}, {"key": "4190", "content": "The shortest route from $$A$$ to $$B$$.\n question_4190-image_0"}, {"key": "4191", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$. It is known that $$AB=5$$ cm, $$AE=3$$ cm, the area of the parallelogram $$ABCD$$ is in square centimeters. question_4191-image_0"}, {"key": "4192", "content": "As shown in the figure, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$. It is known that the area of parallelogram $$ABCD$$ is $$32$$ square centimeters, $$CD=8$$ centimeters, and the length of $$AE$$ is in centimeters. question_4192-image_0"}, {"key": "4193", "content": "As shown in the figure, in the parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$BC=30$$ cm, $$AE=20$$ cm, $$CD=24$$ cm. The length of the line segment $$AF$$ is cm. question_4193-image_0"}, {"key": "4194", "content": "As shown in the figure, the area of the parallelogram is $$180$$ square centimeters, $$AE=10$$ centimeters, $$AF=15$$ centimeters, $$AE$$ and $$AF$$ are the heights of the parallelogram, then the perimeter of the parallelogram is centimeters. question_4194-image_0"}, {"key": "4195", "content": "As shown, the length of rectangle $$ABCD$$ is $$33$$ centimeters, and the width is $$15$$ centimeters. The shaded part inside is composed of a rectangle and a parallelogram. It is known that the area of the blank part is exactly twice the area of the shaded part. If the length of $$EF$$ is $$3$$ centimeters, the length of $$GH$$ is in centimeters. question_4195-image_0"}, {"key": "4196", "content": "As shown in the figure, the length of rectangle $$ABCD$$ is $$25$$ and the width is $$15$$. The lengths of the segments obtained by cutting the sides of the rectangle with four sets of parallel lines are marked on the figure, and the two sets of parallel lines in the horizontal direction are both parallel to $$BC$$. The area of the shaded part is. question_4196-image_0"}, {"key": "4197", "content": "As shown in the figure, the two diagonals of quadrilateral $$ABCD$$ are perpendicular to each other, $$AC=6$$, $$BD=10$$, the area of the quadrilateral $$ABCD$$ is. question_4197-image_0"}, {"key": "4198", "content": "As shown in the diagram, in rhombus $$ABDC$$, line segment $$AD$$ and line segment $$BC$$ intersect perpendicularly at point $$O$$, $$AO=60$$, $$CO=80$$, the altitude $$AE=96$$ on side $$BD$$. The area of the rhombus $$ABDC$$ and its perimeter are . question_4198-image_0"}, {"key": "4199", "content": "As shown in the diagram, it is known that the area of each small square is $$1$$ square centimeter. Calculate the area of the trapezoid in the diagram in square centimeters. question_4199-image_0"}, {"key": "4200", "content": "The upper base of the trapezoid is $$5$$ meters, the lower base is $$13$$ meters, and the height is $$20$$ meters. The area of the trapezoid is in square meters."}, {"key": "4201", "content": "The area of the trapezium is $$60$$ square meters, the upper base is $$8$$ meters, the lower base is $$12$$ meters, the height of the trapezium is meters."}, {"key": "4202", "content": "The area of the trapezoid is $$84$$ square centimeters, the upper base is $$9$$ centimeters, and the height is $$8$$ centimeters, then the lower base is centimeters."}, {"key": "4203", "content": "There are three line segments with lengths of $$6$$, $$8$$, and $$10$$. They can be used respectively as the top base, bottom base, and height of a trapezoid (without reuse). Among the trapezoids that can be formed, the maximum area is."}, {"key": "4204", "content": "As shown in the diagram, the small square $$ABCD$$ is placed on top of the large square $$EFGH$$. It is known that the side length of the small square is $$4$$ cm, and the area of trapezoid $$AEHD$$ is $$28$$ square cm. Then, the area of trapezoid $$AFGD$$ is square cm. question_4204-image_0"}, {"key": "4205", "content": "As shown in the diagram, the side length of parallelogram $$ABCD$$ is $$DC=15$$ cm, the height above this side $$AE=6$$ cm, a line segment $$AF$$ divides this parallelogram into two parts, their area differs by $$18$$ square centimeters. Question: What is the area of the trapezoid $$ABCF$$ in square centimeters. question_4205-image_0"}, {"key": "4206", "content": "As shown in the figure, in rectangle $$ABCD$$, $$AB=12$$ cm, $$BC=8$$ cm, one side $$BF$$ of the parallelogram $$BCEF$$ intersects $$CD$$ at point $$G$$. If the area of trapezoid $$CEFG$$ is $$64$$ square centimeters, then the length of $$DG$$ is in centimeters. question_4206-image_0"}, {"key": "4207", "content": "As shown in the figure, it is made of two squares. The side length of the smaller square is $$\\text{a}$$ centimeters, and the side length of the larger square is $$\\text{b}$$ centimeters. When $$\\text{a}=2$$ and $$\\text{b}=4$$, the area of the shaded part is square centimeters.\n question_4207-image_0"}, {"key": "4208", "content": "Eddy and Vi walk away from the same location in opposite directions. $$10$$ minutes later, Eddy reaches point $$A$$, and Vi reaches point $$B$$. The distance between points $$A$$ and $$B$$ is $$1000$$ meters. Vi walks $$40$$ meters per minute, Eddy's speed is meters per minute."}, {"key": "4209", "content": "Locations A and B are $$350$$ kilometers apart. A car departs from location A at $$8$$ AM, traveling towards B at a speed of $$40$$ kilometers per hour. $$2$$ hours later, another car starts from location B towards A at a speed of $$50$$ kilometers per hour. Question: At what time do the two cars meet each other on the way?"}, {"key": "4210", "content": "Car A and Car B set off simultaneously from two places, A and B, which are $$644$$ kilometers apart, heading towards each other. Car A travels at $$56$$ kilometers per hour, and Car B at $$44$$ kilometers per hour. Car A is delayed for $$1$$ hour due to some reason during the journey, and then continues to drive to meet Car B. How many hours did it take from departure to meeting?"}, {"key": "4211", "content": "Person A and person B set off from places $$A$$ and $$B$$ respectively at the same time, heading towards each other. It is known that person A walks at 50 meters per minute, and it takes person B 18 minutes to complete the entire journey. After setting off for 3 minutes, person A and B are still 450 meters apart. The question asks: how many more minutes will it take for person A and B to meet."}, {"key": "4212", "content": "Professor Su Buqing is a famous mathematician in our country. Once, he met a renowned German mathematician on a tram, who posed an interesting problem for him to solve. The problem was: 'Two places are $$50$$ kilometers apart, two persons A and B start from these two places at the same time and walk towards each other. Person A walks at a speed of $$3$$ kilometers per hour, and person B walks at a speed of $$2$$ kilometers per hour. Person A is accompanied by a dog that walks at a speed of $$5$$ kilometers per hour. The dog starts with person A and turns around heading towards person A whenever it encounters person B, and turns around heading towards person B whenever it encounters person A, until the two persons meet. How many kilometers does the dog walk in total?' After a brief thought, Professor Su Buqing gave the correct answer to the German mathematician before even getting off the tram. Students, you try it as well, how many kilometers does the dog walk in total."}, {"key": "4213", "content": "There are two Long March teams, Team A and Team B, moving towards each other. The leader of each team receives the task to count the number of people, which requires running from the front to the end of their respective teams. At this time, the distance between the leaders of the two teams is $$1500$$ meters. When the leaders of each team have run to the end of their line, the fronts of the two teams meet exactly. It is known that the marching speed of Team A is $$40$$ meters per minute, the marching speed of Team B is $$35$$ meters per minute, the running speed of Team A's leader is $$120$$ meters per minute, and the running speed of Team B's leader is $$150$$ meters per minute. When the two leaders each run to the end of their line, the distance between the two people is meters."}, {"key": "4214", "content": "Eddie and Vera are having a table tennis match, it is agreed that whoever wins three games first will be the victor. Thus, there are kinds of possibilities for the process of the match."}, {"key": "4215", "content": "A water sprinkler truck needs to water the streets of a certain community, and the street layout is shown in the following diagram, which can be seen as assembled by three rectangles, each 200 meters long and 100 meters wide. The sprinkler truck starts from point A, needs to cover all the streets and then return to A. Then the shortest total distance is meters. question_4215-image_0"}, {"key": "4216", "content": "Fill in the numbers $$1$$~$$4$$, so that the four numbers in each row, each column, and each bold-lined box are not repeated. The number that should be filled in the ? is. question_4216-image_0"}, {"key": "4217", "content": "The prizes prepared by the teacher for the fun sports day are lollipops. The teacher wants to divide $$8$$ identical lollipops into $$3$$ stacks, there are a total of different ways of splitting them."}, {"key": "4218", "content": "During the nature class, the teacher distributed some leaves to the students. If each person gets $$5$$ leaves, there would be $$3$$ leaves short; If each person gets $$7$$ leaves, there would be $$25$$ leaves short. How many students are there? How many total leaves are there?"}, {"key": "4219", "content": "A chess piece matrix of $$13$$ rows $$13$$ columns, removing a row and a column, results in removing a number of chess pieces."}, {"key": "4220", "content": "Look at the picture, the sum of the interior angles of this octagon is ( ).\n question_4220-image_0"}, {"key": "4221", "content": "A triangle has two angles covered, and the exposed angle is an acute angle. This triangle is ( ) triangle."}, {"key": "4222", "content": "One of the sides of a triangle measures $$5$$ cm and another measures $$7$$ cm, the third side cannot be ( )."}, {"key": "4223", "content": "Among the following groups of line segments, the one(s) that can form a triangle is (are) ( )."}, {"key": "4224", "content": "The natural numbers $$12$$, $$456$$, $$1256$$ share a common feature, they have at least two digits, and for any two consecutive digits, the digit on the left is smaller than the digit on the right. We call them \"Increasing Numbers\". Using the digits $$3$$, $$6$$, $$9$$, how many \"Increasing Numbers\" can be formed?"}, {"key": "4225", "content": "Moby has $$7$$ identical pieces of chocolate candy, ready to be divided into $$3$$ piles, there are different ways of splitting them."}, {"key": "4226", "content": "Calculate: $$124+158+76$$="}, {"key": "4227", "content": "Calculate: $$112+164+133+136+188$$="}, {"key": "4228", "content": "Calculate: $$(134+37+55)+(63+866+25)$$="}, {"key": "4229", "content": "Calculate: $$99+41-28-22$$=\uff0e"}, {"key": "4230", "content": "Calculate: $$2000-97+57-96-4-3$$=\uff0e"}, {"key": "4231", "content": "Calculate $$417+ (153+748)-(248+153)-(238+162)$$=\uff0e"}, {"key": "4232", "content": "Calculate $$4695+(1396+1365)-(433+596)-267$$=."}, {"key": "4233", "content": "Calculate: $$1358+(840-358)-840$$=."}, {"key": "4234", "content": "Calculate: $$356-(14+49)-(86-28)-(51+56)+72$$=\uff0e"}, {"key": "4235", "content": "Please calculate the following equation and write out the process $$9+99+999+9999$$="}, {"key": "4236", "content": "Please calculate the following equation and write the calculation process. $$74+85+83+75+77+80$$="}, {"key": "4237", "content": "Please calculate the following expression and write out the calculation process. $$35000-9-98-997-9996$$="}, {"key": "4238", "content": "Please calculate the following equation and write out the calculation process. $$92+93+95+97-98+100-101$$="}, {"key": "4239", "content": "Calculate the following: $$19+199+1999+19999$$=\uff0e"}, {"key": "4240", "content": "Calculate the following: $$201+302+403+504$$=."}, {"key": "4241", "content": "Calculate the following: $$81+82+85+76+77$$=\uff0e"}, {"key": "4242", "content": "Compute the following: $$302+295-398-98$$=\uff0e"}, {"key": "4243", "content": "Find the units digit of the following result: $$8+88+888+\\cdots +\\underbrace{888\\cdots 88}_{2019 8's}$$, the units digit is ."}, {"key": "4244", "content": "Calculate: $$974+362-(62-26)=$$."}, {"key": "4245", "content": "Calculate: $$68-53+132-47=$$."}, {"key": "4246", "content": "It is said that a long time ago, due to lack of effective measures to protect against insects, the calculations on books would often be partially eaten by bugs. Therefore, when people read books, they had to figure out the eaten numbers based on the remaining calculations. This type of problem was later referred to as 'Insect Bite Calculation'. Fill in the blanks with appropriate numbers to make the vertical addition equation in the picture correct, then the sum is."}, {"key": "4247", "content": "Fill in the blanks with appropriate numbers to make the vertical arithmetic in the figure valid, then the result of the addition is. question_4247-image_0 question_4247-image_1"}, {"key": "4248", "content": "Fill in the blanks with appropriate numbers to make the subtraction column in the figure valid. What is the result of the subtraction? question_4248-image_0"}, {"key": "4249", "content": "Fill in the blanks with appropriate numbers to make the subtraction column in the diagram valid. Then, the result of the subtraction is. question_4249-image_0"}, {"key": "4250", "content": "Answer the following questions: Fill in the appropriate numbers in the blanks to make the vertical arithmetic in the diagram correct. Then, the result of the addition is. question_4250-image_0"}, {"key": "4251", "content": "In the equation below, different Chinese characters represent different digits, and the same Chinese characters represent the same digit, making the equation valid. Thus, the four-digit number \u201c$$\\overline{{beautiful future}}$$\u201d is. $$\\begin{matrix}&& &&future \\\\& &&not & future \\\\&& good&not&future\\\\+&beautiful&good&not&future\\\\\\hline &8&1&0&2\\end{matrix}$$"}, {"key": "4252", "content": "In the following addition vertical problem, the same Chinese characters represent the same number, and different Chinese characters represent different numbers. What number does \u201c\u597d\u201d represent? ( ) question_4252-image_0"}, {"key": "4253", "content": "In the following subtraction equation, each shape represents a number, and different shapes represent different numbers. Then, \u25b3 =. question_4253-image_0"}, {"key": "4254", "content": "Fill in the appropriate numbers in the boxes of the following vertical operation so that the operation is valid. The final sum is.\n question_4254-image_0"}, {"key": "4255", "content": "Please set up in column form and calculate: $$136\\times 5=$$."}, {"key": "4256", "content": "Please arrange in column form for calculation: $$216\\times 3$$=."}, {"key": "4257", "content": "Please perform the calculation in vertical form: $$28\\times 51=$$\uff0e"}, {"key": "4258", "content": "Please arrange the following into a vertical calculation: $$36\\times 32$$=."}, {"key": "4259", "content": "Calculate: $$237\\times 2\\times 5 $$="}, {"key": "4260", "content": "Calculate: $$4\\times 139\\times 25$$="}, {"key": "4261", "content": "Calculate: $$125\\times (8\\times 23)$$="}, {"key": "4262", "content": "Calculate: $$25\\times 24$$="}, {"key": "4263", "content": "Calculate: $$84\\times 25$$="}, {"key": "4264", "content": "Compute: $$125\\times 72$$="}, {"key": "4265", "content": "Calculate: $$25\\times (100+4)$$="}, {"key": "4266", "content": "Calculate: $$125\\times (20+8)$$="}, {"key": "4267", "content": "Calculate: $$25\\times (100-4)$$="}, {"key": "4268", "content": "Calculate: $$36\\times (200-1)$$="}, {"key": "4269", "content": "Calculate: $$23\\times 99 =$$."}, {"key": "4270", "content": "Calculate: $$37\\times 101=$$."}, {"key": "4271", "content": "Compute: $$46\\times 99$$=."}, {"key": "4272", "content": "Calculate: $$25\\times 102$$=."}, {"key": "4273", "content": "Compute: $$125\\times \\left( 80+8 \\right)=$$"}, {"key": "4274", "content": "Calculate: $$125\\times 158\\times 8=$$."}, {"key": "4275", "content": "Perform vertical multiplication calculation: $$42\\times 47=$$"}, {"key": "4276", "content": "During the summer vacation from the second to the third grade, Eddie, Will, and Dakuan worked for the doctor to earn pocket money. If Eddie's pocket money is $$242$$, Eddie's money is $$75$$ less than Will's money, and Eddie's money is $$42$$ more than Dakuan's money, calculate the total amount of money earned by the three."}, {"key": "4277", "content": "Dakuan took his hard-earned pocket money of $$343$$ yuan to spend. When paying for pizza with everyone, he spent $$176$$ yuan, and his friends gave him $$111$$ yuan. How much did Dakuan's money decrease by?"}, {"key": "4278", "content": "Eddie spent $$50$$ yuan on watching a movie. The money he carried was $$5$$ times the amount spent on the movie plus $$3$$ yuan. The money spent on the movie was twice the amount spent on eating a hamburger. How much money does Eddie have left after watching the movie and eating the hamburger?"}, {"key": "4279", "content": "Please answer the following question: If $$32$$ pieces of chocolate are placed into two boxes, and if $$4$$ pieces are taken from the first box and put into the second box, the two boxes then contain an equal number of chocolate pieces. How many pieces of chocolate were originally in the first box."}, {"key": "4280", "content": "Please answer the following question: Eddie and Viola agreed to go to the amusement park together, they brought a total of $$170$$ yuan, and it is known that after Eddie gave Viola $$30$$ yuan, he still had $$10$$ yuan more than Viola. How much money did Eddie originally have, and how much money did Viola originally have?"}, {"key": "4281", "content": "Three aquariums have a total of $$100$$ goldfish. The total number of goldfish in the first aquarium is $$20$$ less than the combined total number of goldfish in the other two aquariums. The total number of goldfish in the second aquarium is $$10$$ more than in the third aquarium. So, the first aquarium has __ goldfish, the second aquarium has __ goldfish, and the third aquarium has __ goldfish."}, {"key": "4282", "content": "Please answer the following question: Class A and Class B have a total of 105 books. The number of books in Class A is 3 times the number of books in Class B plus 5 books. Class A has __ books, and Class B has __ books."}, {"key": "4283", "content": "Please answer the following question: Mom bought some lychees and grapes, spending a total of $$63$$ yuan. Knowing that the money spent on lychees is $$2$$ times plus $$3$$ yuan more than that on grapes, how much money was spent on lychees?"}, {"key": "4284", "content": "Please answer the following questions: Class A and Class B have a total of $$105$$ books. The number of books in Class A is $$3$$ times the number of books in Class B minus $$15$$ books. Class A has books, Class B has books."}, {"key": "4285", "content": "Please answer the following question: This year, the sum of the ages of Mom and McDull is $$45$$ years old, and it is known that Mom's age is $$5$$ times McDull's age minus $$3$$ years old. Find out how old Mom is this year."}, {"key": "4286", "content": "The oil in barrel A is $$410$$ kilograms, and in barrel B is $$190$$ kilograms, how many kilograms of oil need to be poured from barrel A to barrel B to make the oil in barrel A double that of barrel B?"}, {"key": "4287", "content": "Class A has $$130$$ books, Class B has $$30$$ books, Class A gives books to Class B, and the number of books in Class A is $$2$$ times plus $$10$$ more than that of Class B?"}, {"key": "4288", "content": "Two schools, A and B, have a total of $$295$$ students. School A transfers out $$10$$ students, and after School B receives $$15$$ students, the number of students in School A is twice that in School B. Originally, School A had  people, and School B had  people."}, {"key": "4289", "content": "There are a total of $$6$$ straight lines in the picture. Remove one line to make the number of intersections $$7$$. The line to remove is question_4289-image_0"}, {"key": "4290", "content": "(1) The perimeter of a square is $$36$$ cm, side length = cm; (2) The perimeter of a rectangle is $$60$$ cm, length is $$20$$ cm, width = cm"}, {"key": "4291", "content": "Fill in the blanks as required. (3) $$6+10+14+18+22+26+30=$$."}, {"key": "4292", "content": "From $$1$$st to $$4$$th floor, there are a total of $$48$$ steps. If the number of steps between every two floors is the same, then how many steps are there in total from the $$1$$st to the $$6$$th floor?"}, {"key": "4293", "content": "The doctor wants to make a wooden stool. He first saws a log into $$4$$ pieces, taking him $$12$$ minutes. If he wants to saw another log into $$8$$ pieces, how many minutes will it take? (Assuming it takes the doctor the same amount of time for each cut)."}, {"key": "4294", "content": "The distance between place $$A$$ and place $$B$$ is $$4800$$ meters. If person A walks at a speed of $$60$$ meters per minute, how many minutes does it take for person A to walk from place $$A$$ to place $$B$$?"}, {"key": "4295", "content": "$$A$$ and $$B$$ two cities are $$300$$ kilometers apart, a car originally planned to travel from city $$A$$ to city $$B$$ in $$6$$ hours, then how many kilometers should the car travel on average per hour?"}, {"key": "4296", "content": "A car travels $$150$$ kilometers in $$3$$ hours, at this rate, how many kilometers will it travel in $$10$$ hours?"}, {"key": "4297", "content": "Eddie and Vi set off from the base to go to Mason Forest Park for fun. On the way there, the car's speed was $$80$$ kilometers per hour, and it took $$3$$ hours to reach the destination. If the car's speed increases by $$40$$ kilometers per hour on the way back, then how many hours will it take to return to the base after departing from the forest park."}, {"key": "4298", "content": "Eddie and Vi set off from the base to play in Mason Forest Park together. When they went, the car's speed was 80 kilometers/hour, and it took 3 hours to reach the destination. When they actually came back, it started to drizzle, and the car took 3 hours longer to return to the base than when they went. On the return trip, the car's speed was kilometers/hour."}, {"key": "4299", "content": "Eddie goes shopping and finds the pricing of the products as follows. question_4299-image_0 Eddie wants to buy $$1$$ pencil, so Eddie needs to spend yuan."}, {"key": "4300", "content": "Eddy goes shopping and finds the pricing of goods as follows. Eddy noticed that a box contains $$5$$ ice pops, which is too many for him, so he plans to buy only $$2$$ of them and needs to pay in yuan."}, {"key": "4301", "content": "Daming and Xiaobai live in the same building. They climb the stairs at the same speed and take the same amount of time to climb each floor. It takes $$180$$ seconds to reach the $$6$$th floor. If they maintain the same speed, Xiaobai lives on the $$10$$th floor, and it will take him seconds to get from the $$1$$st floor to his home."}, {"key": "4302", "content": "Daming and Xiaobai live in the same building. They climb the stairs at the same speed and take the same amount of time to climb each floor. It takes $$180$$ seconds to reach the $$6$$th floor. If the speed is constant, and it takes Daming $$3$$ minutes to get home, which floor do they live on?"}, {"key": "4303", "content": "A doctor made $$3$$ robots to produce parts, which can produce $$60$$ parts in $$4$$ hours. Based on this rate, how many parts can $$5$$ robots produce in $$1$$ hour?"}, {"key": "4304", "content": "A doctor made $$3$$ robots to produce parts, $$4$$ hours can produce $$60$$ pieces, calculating at this speed. How many pieces can $$5$$ robots produce in $$3$$ hours?"}, {"key": "4305", "content": "Grandma Wang has $$5$$ cows, which produce $$630$$ kilograms of milk every $$7$$ days. Based on this calculation, how many kilograms of milk can $$8$$ cows produce in $$15$$ days?"}, {"key": "4306", "content": "Grandma Wang has $$5$$ dairy cows, which produce $$630$$ kilograms of milk in $$7$$ days. Based on this, how many kilograms of milk can $$10$$ dairy cows produce in $$14$$ days?"}, {"key": "4307", "content": "Little monkeys in the Flower Fruit Mountain are eating peaches. If $$6$$ little monkeys eat $$180$$ peaches in $$3$$ days, following this pattern\uff0chow many peaches can a single little monkey eat in $$5$$ days to reach $$400$$ peaches?"}, {"key": "4308", "content": "Little monkeys in Huaguoshan are eating peaches. If $$6$$ little monkeys eat $$180$$ peaches in $$3$$ days, how many days will it take for $$10$$ little monkeys to eat $$200$$ peaches, according to this calculation?"}, {"key": "4309", "content": "Below are the preliminary results of the recitation competition among students of the experimental primary school. (Unit: Points) Competitor Number Score Competitor Number Score Competitor Number Score Competitor Number Score Competitor Number Score $$1$$$$90$$$$6$$$$83$$$$11$$$$86$$$$16$$$$78$$$$21$$$$81$$$$2$$$$92$$$$7$$$$97$$$$12$$$$88$$$$17$$$$94$$$$22$$$$79$$$$3$$$$88$$$$8$$$$84$$$$13$$$$91$$$$18$$$$94$$$$23$$$$83$$$$4$$$$85$$$$9$$$$93$$$$14$$$$96$$$$19$$$$80$$$$24$$$$91$$$$5$$$$96$$$$10$$$$90$$$$15$$$$82$$$$20$$$$98$$$$25$$$$89$$ Answer the question. The student with the best score in the competition is number $$20$$ student, who scored $$98$$ points."}, {"key": "4310", "content": "The image shows a patient's body temperature record chart.\n question_4310-image_0 \nThe nurse takes the patient's temperature every few hours."}, {"key": "4311", "content": "According to the statistics, solve the following problems. question_4311-image_0 The average monthly output of Factory A in the first half of the year is units, and the average monthly output of Factory B in the first half of the year is units."}, {"key": "4312", "content": "In an exam, there were a total of $$20$$ questions. For each correct answer, a student would receive $$5$$ points, and for each question not attempted or answered incorrectly, $$2$$ points would be deducted. Edi scored $$79$$ points. How many questions did he answer correctly?"}, {"key": "4313", "content": "In a cage containing both chickens and rabbits, the number of rabbits is three times that of chickens. Together they have 140 legs. So, there are chickens and rabbits."}, {"key": "4314", "content": "If a book has a total of $$20$$ pages, the page numbers from $$1\\sim 20$$ use a total of several digits."}, {"key": "4315", "content": "If a book has a total of $$150$$ pages, the number of digits used for the page numbers from $$1\\sim 150$$ is."}, {"key": "4316", "content": "To assign a code to a book, a total of $$225$$ digits were used. This book has a total number of pages."}, {"key": "4317", "content": "A book has a total of $$400$$ pages. Among the page numbers $$1\\sim 400$$, the number \u201c$$3$$\u201d was used a total of times."}, {"key": "4318", "content": "A book has a total of 360 pages, among pages 1 to 360, the number '2' has been used a total of times."}, {"key": "4319", "content": "$$63$$ cats participated in a cat training camp, and after a period of training, $$15$$ learned to catch fish only, $$12$$ learned to catch mice only, $$9$$ learned both to catch mice and fish, $$6$$ learned both to catch mice and climb trees, $$5$$ learned both to climb trees and catch fish, $$2$$ learned all three skills, it is known that these $$63$$ cats will necessarily learn at least one of these skills, then the number of cats that only learned to climb trees is $$.$$"}, {"key": "4320", "content": "Every student in a certain class signed up for competitions. Among them, 12 students participated in the Hope Cup, 15 students participated in the Wisdom Cup, and 21 students participated in the Xueersi Cup. There were 7 students who participated in both the Hope Cup and the Wisdom Cup, 6 students who participated in both the Hope Cup and the Xueersi Cup, 9 students who participated in both the Xueersi Cup and the Wisdom Cup, and 2 students who participated in all three competitions. Therefore, this class has a total of people."}, {"key": "4321", "content": "A class has $$63$$ students, each holding flags of three colors: red, yellow, and blue. Each student holds at least one flag. It is known that there are a total of $$34$$ people holding red flags, $$26$$ people holding yellow flags, and $$18$$ people holding blue flags. Additionally, there are $$9$$ people holding both red and yellow flags, $$4$$ people holding both yellow and blue flags, and $$3$$ people holding both red and blue flags. How many students in this class are holding flags of all three colors?"}, {"key": "4322", "content": "Eddie and Vi went from their school to the Shanghai Natural History Museum. After Eddie ran 400 meters ahead, Vi started along the same route to catch up with Eddie. Vi ran at an average speed of 160 meters per minute and caught up with Eddie on the way after 4 minutes. Eddie's average speed per minute is meters."}, {"key": "4323", "content": "Wei and Eddie set off from two different places and walked towards each other. Wei walked at a speed of $$50$$ meters per minute, Eddie walked at a speed of $$60$$ meters per minute. They met at a point $$50$$ meters away from the midpoint between the two places. The distance between the two places in meters is ."}, {"key": "4324", "content": "Vi runs first for $$4$$ minutes at a speed of $$180$$ meters/min. Eddie, along with a dog, goes after her. Eddie's speed is $$200$$ meters/min, and the dog's speed is $$300$$ meters/min. The dog runs back and forth between the two. When Eddie catches up with Vi, the dog has run meters."}, {"key": "4325", "content": "Find the value represented by the symbol below. $$36-2\\times \\bullet =48-4\\times \\bullet $$.$$\\bullet =$$."}, {"key": "4326", "content": "Eddie and Viola return to school from the nursing home. Due to traffic congestion in the city center, they do not want to pass through the city center. So, how many shortest routes are there to the school in total? question_4326-image_0"}, {"key": "4327", "content": "As shown in the table below, please read out the nine characters of 'We learn fun math', requiring that the nine characters you choose are consecutive (i.e., adjacent characters in the table are also adjacent left or right, or above or below). How many complete ways are there to read 'We learn fun math'? question_4327-image_0"}, {"key": "4328", "content": "Solve the equation: $$2x+3x+2=30+6x-8x$$. Solution: $$x$$=."}, {"key": "4329", "content": "Solve the equation: $$13x+8=14x+2$$. Solution: $$x$$=."}, {"key": "4330", "content": "Given $$5x-3=17$$, then $$x=$$."}, {"key": "4331", "content": "Solve the equation: $$6x+9x-13=17$$. Find $$x=$$."}, {"key": "4332", "content": "Solve the equation: $$28=3x+12-x$$, $$x=$$"}, {"key": "4333", "content": "Every day, the child has to pass through the Young Pioneer Palace to get to the museum on his way to school, as shown in the following diagram, there are several ways for the child to go to school.\n question_4333-image_0"}, {"key": "4334", "content": "Using $$1$$, $$3$$, $$4$$, $$6$$, $$8$$ to form a three-digit number with no repeating digits."}, {"key": "4335", "content": "A postal worker delivers mail, there are $$3$$ roads from $$A$$ village to $$B$$ village, and $$5$$ roads from $$B$$ village to $$C$$ village. How many different ways are there for the postal worker to go from $$A$$ village to $$C$$ village via $$B$$ village?"}, {"key": "4336", "content": "Eddie distributed basketballs to his classmates. If each person gets 3 basketballs, there are 8 less than needed. If each person gets 2 basketballs, there is 1 less than needed. Eddie distributed the balls to some students, totaling a number of basketballs. question_4336-image_0"}, {"key": "4337", "content": "Third-grade students walk from school to the factory, covering $$75$$ meters per minute. After $$24$$ minutes, due to an important matter, Zhang Bing is sent to catch up with them by bicycle, starting from the school. If he covers $$225$$ meters per minute, then after how many minutes can he catch up with the classmates?"}, {"key": "4338", "content": "Two places are $$900$$ kilometers apart, it takes person A $$15$$ days and person B $$12$$ days to travel this distance. Now, A leaves $$2$$ days ahead of B, and B starts to chase A. When B catches up with A, B has traveled kilometers."}, {"key": "4339", "content": "Xiaoqiang walks $$70$$ meters per minute, Xiaoji walks $$60$$ meters per minute, both start at the same time in the same direction, after $$3$$ minutes Xiaoqiang catches up with Xiaoji, the initial distance between them was meters."}, {"key": "4340", "content": "Person A and person B set off from place $$A$$ to place $$B$$ at the same time. Person A walks at $$60$$ meters per minute, while person B walks at $$90$$ meters per minute. Upon reaching place $$B$$, person B immediately returns and meets with person A. At the time of their meeting, person A is $$180$$ meters away from place $$B$$. The total time taken from the start until their meeting is in minutes."}, {"key": "4341", "content": "Eddy and Vi are located at places $$A$$ and $$B$$ respectively, which are $$100$$ meters apart. If they head towards each other, they will meet after $$20$$ seconds; if they walk in the same direction with Vi in front, Eddy catches up with Vi after $$100$$ seconds. Therefore, the speeds of Eddy and Vi are meters per second, respectively."}, {"key": "4342", "content": "The brother and the younger brother leave home together for the library. The brother walks 60 meters per minute, while the younger brother walks 45 meters per minute. One day, the younger brother starts 8 minutes before the brother leaves home. When the brother catches up with the younger brother, he has exactly walked half of the journey. How many meters is it from home to the library?"}, {"key": "4343", "content": "$$\\frac{5}{9}=\\frac{45}{(\\ \\ \\ \\ )}=\\frac{(\\ \\ \\ \\ )}{99}$$, the numbers that should be filled in the blanks in order are:"}, {"key": "4344", "content": "The total age of father, mother, grandfather, and Qiangqiang this year is $$146$$ years old, and after the year, their total age is $$170$$ years old."}, {"key": "4345", "content": "This year, XinXin is $$6$$ years older than PengPeng. $$3$$ years ago, their combined ages were $$48$$ years old. This year, XinXin is years old, and PengPeng is  years old."}, {"key": "4346", "content": "Solve the equation: $$7x-17=39$$\n$$x=$$."}, {"key": "4347", "content": "Solving the equation $$6x-3=2x+13$$, we get $$x=$$ ( )."}, {"key": "4348", "content": "The third grade's second class formed a solid square formation, with 36 people on the outermost layer. (1) Circle around, dividing the outermost layer of the square formation into four equal parts. (2) There are people on each side of the outermost layer. question_4348-image_0"}, {"key": "4349", "content": "As shown in the figure, walking from point $$A$$ to point $$B$$ along the segment, there are a total of different shortest routes. question_4349-image_0"}, {"key": "4350", "content": "The area of the parallelogram in the picture is ( ) square centimeters. question_4350-image_0"}, {"key": "4351", "content": "$$3$$ people produce a total of $$150$$ parts in $$5$$ hours. The equation $$150\\div 5$$ represents ( )."}, {"key": "4352", "content": "Calculate each of the following: $$28+208+2008+\\cdots +2\\underbrace{00\\cdots 0}_{10 zeros}8$$."}, {"key": "4353", "content": "Aidy has $$5$$ reward cards, while Vi has $$10$$ reward cards. After Vi gives $$8$$ reward cards to Aidy, the total number of reward cards they have together is ( ) cards."}, {"key": "4354", "content": "As shown in the figure below, please fill in the respective number of strokes required for each shape at the lines below.\n\n\n\n question_4354-image_0 \n question_4354-image_1 \n question_4354-image_2 \n question_4354-image_3"}, {"key": "4355", "content": "A cleaning vehicle sweeps the streets, each segment of the street is $$1$$ kilometer long, the cleaning vehicle departs from $$A$$, covers all the streets and then returns to $$A$$. The shortest journey is kilometers.\n question_4355-image_0"}, {"key": "4356", "content": "As shown in the figure, at the vertices $$A$$ and $$B$$ of a hexahedron, there is an ant respectively, competing to see who can crawl all the edges and reach the end point $$C$$ first. If their crawling speeds are the same, which ant can win?"}, {"key": "4357", "content": "The diagram below is a plan view of the roads in a park. To enable visitors to walk through every road without repetition, where can the entrance and exit be set up respectively? ( ). question_4357-image_0"}, {"key": "4358", "content": "The streets through which the postal worker delivers the letters are shown in the figure, with each section of the street being 1 kilometer long. If the postal worker starts from the post office and must cover all streets, then the minimum distance the postal worker needs to travel is kilometers.\n question_4358-image_0"}, {"key": "4359", "content": "The diagram below is the floor plan of an exhibition hall. Can a visitor pass through each door without repeating? If yes, please provide a plan; if no, please explain why. (The starting point does not necessarily have to be outside the exhibition hall) question_4359-image_0"}, {"key": "4360", "content": "A city's transportation system is made up of several intersections (the intersections of lines in the diagram below) and streets (the segments in the diagram below), with each street connecting two intersections. All streets allow two-way traffic, and each street has a length value (marked on the corresponding segment in the diagram). A postal worker delivers newspapers and letters, starting from the post office and passing through every street under his jurisdiction before returning to the post office (each street can be passed more than once). He can plan his route in such a manner that the shortest total length he travels is (unit: meters).\n question_4360-image_0"}, {"key": "4361", "content": "The image below is a street map of a district in a city, where a postman needs to deliver letters. The numbers on the map indicate the kilometers of each street segment. He departs from the post office, has to traverse all the streets, and eventually return to the post office. Please design the most reasonable delivery route for him, so that he can pass through each street and minimize the distance traveled. The shortest route is in kilometers.\n question_4361-image_0"}, {"key": "4362", "content": "In Figure \u2460, each small square has a side length of $$8$$ meters. Then, from point $$A$$ to point $$B$$, without taking the same path twice (you can pass through the same point but cannot pass through the same line segment twice), the maximum distance you can walk is meters.\n question_4362-image_0"}, {"key": "4363", "content": "As shown in the diagram, there are two islands at the confluence of two rivers, connected by seven bridges to both the islands and the riverbanks.  The question is: Can a walker traverse all seven bridges once without retracing their steps? question_4363-image_0"}, {"key": "4364", "content": "In the pictures below, what is the minimum number of strokes needed for each shape? Picture one: ; Picture two: ; Picture three: ; Picture four: . question_4364-image_0"}, {"key": "4365", "content": "The image shows a schematic of a museum. Visitors enter the museum from the entrance. Can you find a tour route that passes through each door exactly once? question_4365-image_0"}, {"key": "4366", "content": "The diagram is the floor plan of a certain restaurant, consisting of five small halls. There are doors connecting adjacent halls, and there is an entrance. Can you enter from the entrance and pass through all the doors once without repeating? If yes, please specify the route. If not, which door should be closed to make it possible? question_4366-image_0"}, {"key": "4367", "content": "There are $$94$$ kilograms of flour and $$138$$ kilograms of rice in the canteen. Every day, $$9$$ kilograms of both flour and rice are used. After how many days will the remaining rice be $$3$$ times the amount of the remaining flour?"}, {"key": "4368", "content": "A certain school plans to plant poplar trees, willow trees, and scholar trees, totaling $$200$$ trees. After planting $$10$$ willow trees, $$5$$ more scholar trees were unexpectedly delivered. At this point, the remaining numbers of the three types of trees were exactly equal. How many of each type of tree were originally planned to be planted? ( )"}, {"key": "4369", "content": "A, B, and C together have $$109$$ dollars. The ratio of A's money to B's money, and B's money to C's money, is both $$2$$ to $$1$$, with a remainder of $$1$$. Then A has dollars, B has dollars, C has dollars."}, {"key": "4370", "content": "A certain school plans to plant a total of $$240$$ poplar trees, willow trees, and locust trees. It is known that the number of poplar trees is $$3$$ times the number of willow trees plus $$8$$, and the number of locust trees is twice the number of poplar trees minus $$14$$. The original plan was to plant a number of poplar trees, willow trees, and locust trees."}, {"key": "4371", "content": "The school fruit store transported apples and pears totaling $$40$$ kilograms, with apples being $$2$$ bags more than pears. Each bag of apples and pears weighs $$5$$ kilograms. Therefore, the fruit store transported bags of apples and bags of pears."}, {"key": "4372", "content": "Warehouses A and B store rice. If warehouse A gives warehouse B $$300$$ kilograms of rice, then they have the same amount of rice; if both of them sell $$200$$ kilograms of rice, then the rice left in warehouse A is $$3$$ times that in warehouse B. How much rice do they originally have in total?"}, {"key": "4373", "content": "Reservoir A has $$43$$ billion cubic meters of water, and Reservoir B has $$37$$ billion cubic meters of water. It is required to transfer billion cubic meters of water from Reservoir A to Reservoir B to make the water volume in Reservoir B twice as much as that in Reservoir A."}, {"key": "4374", "content": "There are two shelves with a total of $$216$$ books. After $$42$$ books are taken from the first shelf, the number of books on the second shelf is twice the number of books on the first shelf plus $$6$$ more. Thus, the second shelf has $$118$$ books."}, {"key": "4375", "content": "JiaJia and JianJian have a total of $$85$$ candies. After JiaJia gives JianJian $$3$$ candies, he still has $$1$$ more candy than JianJian. JiaJia has candies, JianJian has candies."}, {"key": "4376", "content": "Xiao Yue and Dong Dong play games. For each game, the loser has to give the winner $$1$$ chess piece. Initially, Xiao Yue has $$18$$ chess pieces, and Dong Dong has $$22$$ chess pieces. After a number of games, Dong Dong hasn't won any games, and Xiao Yue has $$10$$ more chess pieces than Dong Dong. How many games have they played?"}, {"key": "4377", "content": "$$5$$ boxes of apples and $$5$$ boxes of grapes together weigh $$75$$ kilograms, each box of apples weighs double that of each box of grapes. How much does each box of apples weigh in kilograms, and how much does each box of grapes weigh in kilograms?"}, {"key": "4378", "content": "A certain school's third grade has $$154$$ fewer students than the fourth grade. If $$46$$ more students transfer to the fourth grade, then the number of students in the fourth grade will be three times that of the third grade. How many students are in the third and fourth grades?"}, {"key": "4379", "content": "There are a total of $$140$$ black and white chess pieces, divided into $$5$$ piles, with the number of black chess pieces in each pile being $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ times the number of white chess pieces, respectively. Moreover, the number of white chess pieces in the second pile is $$2$$ times that in the first pile, in the third pile is $$3$$ times that in the first pile, in the fourth pile is $$4$$ times that in the first pile, and in the fifth pile is $$5$$ times that in the first pile. How many white chess pieces are there in total?"}, {"key": "4380", "content": "In the final of the Asia Cup, the number of Chinese journalists was $$3$$ times the number of foreign journalists. After the match, $$180$$ Chinese journalists and $$40$$ foreign journalists left the venue. The remaining number of Chinese and foreign journalists was equal. How many Chinese and foreign journalists were there originally?"}, {"key": "4381", "content": "Basket A and B have an equal weight of apples. Now, taking $$12$$ kilograms of apples from basket A and putting them into basket B results in the weight of the apples in basket B being $$2$$ kilograms less than triple the weight of basket A. The original weight of the apples in both baskets was in kilograms."}, {"key": "4382", "content": "A and B together have $$58$$ comic books. After A gives B $$5$$ books, B has $$4$$ books less than A. How many comic books did A originally have."}, {"key": "4383", "content": "Pool A contains $$260$$ cubic meters of water, Pool B contains $$120$$ cubic meters of water. If water flows from Pool A into Pool B at a rate of $$4$$ cubic meters per minute, after how many minutes will the water in Pool B be four times that of Pool A?"}, {"key": "4384", "content": "When the elder brother is celebrating his $$30$$th birthday, the younger brother says: 'When I grow to be the age my brother is this year, the sum of my brother's age at that time and my age this year will equal our father's age this year.' So, what is the father's age this year?"}, {"key": "4385", "content": "The elder brother said to the younger brother, \"When I was your age, you were only $$2$$ years old.\" The younger brother said to the elder brother, \"When I am your age, you will already be $$17$$ years old.\" So, the elder brother is $$12$$ years old this year, and the younger brother is $$7$$ years old."}, {"key": "4386", "content": "A family of three, the sum of their ages was $$66$$ years two years ago. The mother and father are the same age. This year the mother's age is $$4$$ times the child's age. This year the father is years old."}, {"key": "4387", "content": "Pea is $$10$$ years old this year, Potato is $$23$$ years old this year. When the sum of their ages is $$63$$ years, Pea is ____ years old, Potato is ____ years old."}, {"key": "4388", "content": "Xiao Ming is $$15$$ years old this year, his father is $$45$$ years old. When Xiao Ming was younger, his father was $$4$$ times as old as Xiao Ming."}, {"key": "4389", "content": "Old trees, large trees, and small trees are chatting. The old tree says: 'For as many days as the small tree has grown, the large tree has grown for that many weeks; and for as many months as the small tree has grown, I have grown for that many years. Together, we are a total of $$1000$$ years old.' The age of the old tree this year, the age of the large tree this year, the age of the small tree this year."}, {"key": "4390", "content": "The older brother said to the younger brother: 'When you reach my current age, I would have just obtained my doctoral degree; when I was your current age, you were just starting kindergarten.' It is known that the current combined age of the older brother and younger brother is 32 years old, and the age at which the older brother obtained his doctoral degree is 7 times the age of the younger brother when he started kindergarten. Calculate the age at which the older brother obtained his doctoral degree."}, {"key": "4391", "content": "The total age of the father and his two sons is $$84$$ years old. In $$12$$ years, the age of the father will exactly equal the combined age of the two sons. How old is the father now?"}, {"key": "4392", "content": "Xiaoming is $$8$$ years old this year, and his mom is $$44$$ years old. When Xiaoming was a certain age, his mom's age was exactly $$4$$ times that of Xiaoming's."}, {"key": "4393", "content": "The sum of the current ages of persons A, B, and C is 145 years. When C's age was half of B's age, A was 25 years old. So, how old is C now."}, {"key": "4394", "content": "A family of three, the father is $$3$$ years older than the mother, and now the total age of their family is $$80$$ years old. $$10$$ years ago, the total age of the family was $$51$$ years, the father's age this year is."}, {"key": "4395", "content": "12 years ago, the father's age was 11 times the daughter's age; this year, the father's age is 3 times the daughter's age. How many years from now will the father's age be twice the daughter's age?"}, {"key": "4396", "content": "This year, the brother's age is 3 times that of his younger brother. 24 years later, the brother's age will be 16 years less than double the age of his younger brother. So, how old is the brother and the younger brother this year?"}, {"key": "4397", "content": "This year is $$2020$$, the combined age of the parents is $$72$$ years, and the combined age of the siblings is $$18$$ years. By the year $$2022$$, the father's age will be $$4$$ times the brother's age, and the mother's age will be $$3$$ times the sister's age. So, in the year when the father's age is twice the sister's age, it will be the year $$.$$"}, {"key": "4398", "content": "When A is as old as B is now, A's age is $$3$$ times that of B; when B reaches A's current age, A is $$2$$ times that of B minus $$15$$ years. Therefore, currently, A is years old, and B is currently years old."}, {"key": "4399", "content": "In the polygon shown below, any two adjacent sides are perpendicular to each other. Find the perimeter of the polygon shown below (unit: cm).\n question_4399-image_0"}, {"key": "4400", "content": "There is a rectangular piece of paper, the length is $$12$$, and the width is $$8$$ cm. Cut with scissors three times (as shown in the figure), the sum of the perimeters of these $$6$$ rectangles is cm.\n question_4400-image_0"}, {"key": "4401", "content": "As shown in the diagram, a large rectangle is divided into $$9$$ small rectangles. The perimeter of some small rectangles is marked on the diagram. The perimeter of the shaded rectangle is.\n question_4401-image_0"}, {"key": "4402", "content": "Among the two pictures below, the one with the larger perimeter is . (Fill in the letter that represents the name of the figure on the line).\n question_4402-image_0"}, {"key": "4403", "content": "As shown in the figure, there is a rectangular piece of paper that is $$12$$ cm long and $$10$$ cm wide. If this piece of paper is cut into two parts along the dashed line, the sum of the perimeters of these two parts is in centimeters.\n question_4403-image_0"}, {"key": "4404", "content": "As shown in the figure, the shaded part is a square. Find the perimeter of the largest rectangle in the figure (unit: decimeters).\n question_4404-image_0"}, {"key": "4405", "content": "Four identical rectangles with a width of $$2$$ cm are combined to form a large rectangle. The perimeter of the large rectangle is in centimeters. question_4405-image_0"}, {"key": "4406", "content": "8 identical small rectangles each with a width of 2 cm are combined to form a large rectangle. The perimeter of the large rectangle is in cm.\n question_4406-image_0"}, {"key": "4407", "content": "Using a rectangular cardboard measuring $$8$$ dm in length and $$4$$ dm in width, and two square cardboards each with a side length of $$4$$ dm to assemble into a square. The perimeter of the assembled square is in dm."}, {"key": "4408", "content": "A square with a perimeter of $$20$$ cm has a square with a perimeter of $$8$$ cm cut from its edge. What is the perimeter of the remaining figure? List all possible results in ascending order: cm, cm."}, {"key": "4409", "content": "The picture below is a side profile of a machine part, with each of the shortest line segments in the diagram being $$5$$ cm long. The part is $$30$$ cm tall, and the perimeter of this side of the part is in centimeters. question_4409-image_0"}, {"key": "4410", "content": "As shown in the diagram, each of the adjacent sides of a square is increased by $$3$$ cm, and the area is increased by $$81$$ square centimeters. The original perimeter of the square is in centimeters.\n question_4410-image_0"}, {"key": "4411", "content": "As shown in the diagram, each of the adjacent sides of a square is reduced by $$2$$ cm, resulting in a decrease of the area by $$36$$ square cm. The area of the original square is square cm.\n question_4411-image_0"}, {"key": "4412", "content": "(1) The area of a rectangle is $$336$$ square meters, the width is $$14$$ meters, and the length is meters;\n(2) The area of a square is $$144$$ square meters, and its side length is meters."}, {"key": "4413", "content": "As shown in the figure, $$9$$ small rectangles make up one large rectangle, among which the rectangle numbered $$1$$ is also a square, and the areas of rectangles numbered $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ are respectively $$4$$ square centimeters, $$8$$ square centimeters, $$12$$ square centimeters, $$16$$ square centimeters, $$20$$ square centimeters. The area of the rectangle numbered $$6$$ is square centimeters.\n question_4413-image_0"}, {"key": "4414", "content": "There is a square pool, with a walkway 1 meter wide around its perimeter. The area of the walkway is 24 square meters, and the area of the pool (the blank part) is square meters.\n question_4414-image_0"}, {"key": "4415", "content": "There is a vegetable plot that is $$12$$ meters long and $$5$$ meters wide, with several $$1$$ meter wide paths left in the middle of the field. The area of the vegetable plot is in square meters.\n question_4415-image_0"}, {"key": "4416", "content": "The area of the shape in the picture is square meters.\n question_4416-image_0"}, {"key": "4417", "content": "The length and width of a rectangle each increased by $$2$$ cm, and the area increased by $$40$$ square cm. Calculate the perimeter of the original rectangle in centimeters. question_4417-image_0"}, {"key": "4418", "content": "A rectangular piece of paper, length $$7$$ cm, width $$5$$ cm. Fold its top right corner down, then fold the bottom left corner up, as shown in the figure, the area of the uncovered shaded part is square centimeters. question_4418-image_0"}, {"key": "4419", "content": "Place a small square inside a larger square so that the small square\u2019s vertices touch the larger square (as shown in the diagram). If the perimeters of the two squares differ by $$16$$ cm and their areas differ by $$96$$ square cm, find the area of the smaller square in square cm. question_4419-image_0"}, {"key": "4420", "content": "The numbers in the figure each represent the length of the corresponding line segments (unit: cm), and the area of the figure below is square centimeters.\n question_4420-image_0"}, {"key": "4421", "content": "Every edge in the figure is perpendicular to its adjacent edge, and the length of each edge is $$2$$ cm. Calculate the area of the figure in square centimeters. question_4421-image_0"}, {"key": "4422", "content": "As shown in the figure, there are four overlapping squares with side lengths of $$5$$, $$7$$, $$9$$, and $$11$$. The question is what is the difference in the area between the gray and black regions. question_4422-image_0"}, {"key": "4423", "content": "Four rectangles, each with a length of $$6$$ cm and a width of $$2$$ cm, form a larger rectangle. Draw all the possible arrangements and calculate the area of the larger rectangle in square centimeters."}, {"key": "4424", "content": "The figure below is made up of squares A and D, and rectangles B and C, where both A and D are squares with side lengths of whole centimeters, and both B and C are rectangles. The sum of the areas of A and D is $$100$$ square centimeters. Therefore, the sum of the areas of rectangles B and C is square centimeters. question_4424-image_0"}, {"key": "4425", "content": "As shown in the figure, several paths are set up on a square lawn with a side length of $$24$$ meters, and the width of the paths is marked on the diagram (unit: meters), the actual area of the lawn is in square meters. question_4425-image_0"}, {"key": "4426", "content": "Mom bought a basket of oranges and divided them among the whole family. If two people take $$4$$ oranges each, and the rest take $$2$$ each, there will be $$6$$ oranges left over; if one person takes $$6$$ oranges, and the rest take $$4$$ each, there will be $$12$$ oranges short. How many oranges did mom buy, and how many people are in the family?"}, {"key": "4427", "content": "From location A to location B, there are $$5$$ different routes. On the first day, Eddie went from location A to location B, and then returned from location B to location A; on the second day, he went from location A to location B again, and then returned to location A again. Each time Eddie returned from location B to location A, he did not take the same route he used to go from location A to location B. Therefore, in these two days, there are a total of different ways for Eddie to travel back and forth between locations A and B."}, {"key": "4428", "content": "A snack shop needs to make $$3$$ pancakes, each pancake must be fried for $$1$$ minute on each side. Now there are $$2$$ stoves, each stove can only fry one side of a pancake at a time. To fry all the pancakes, the minimum number of minutes needed is ____."}, {"key": "4429", "content": "Beijing and Luoyang each have $$9$$ and $$12$$ identical machines, respectively, prepared for Hangzhou $$13$$ and Xi'an $$8$$. The freight cost per machine is as shown in the table. The minimum total freight cost is in yuan.\n question_4429-image_0"}, {"key": "4430", "content": "On a highway, there is a warehouse every $$10$$ kilometers, for a total of $$8$$ warehouses. The numbers in the figure represent the weight of the goods stored in each warehouse (unit: tons), with $$C$$ and $$G$$ being empty warehouses. Now, it is desired to consolidate all the goods into one warehouse. If it costs $$1$$ yuan to transport one ton of goods one kilometer, then the minimum freight cost required is.\n question_4430-image_0"}, {"key": "4431", "content": "Beijing and Shanghai each have $$10$$ and $$6$$ identical machines, respectively, prepared to give $$5$$ to Wuhan and $$11$$ to Xi'an. The shipping cost per machine is shown in the table. How can the machines be transported to minimize the total shipping cost? The minimum total shipping cost is yuan. question_4431-image_0 \u200b"}, {"key": "4432", "content": "There are 3 milling machines, 3 lathes, and 1 automatic machine in a workshop, used to produce a product composed of two parts, A and B. Each milling machine can produce 10 part A or 20 part B per day; each lathe can produce 20 part A or 30 part B per day; each automatic machine can produce 30 part A or 80 part B per day. How should these machines be arranged to maximize the number of complete products produced? The maximum number of product sets that can be produced in a day."}, {"key": "4433", "content": "In a small grocery store, there was a clerk selling goods, and five customers, $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ came in. It takes $$2$$ minutes for $$A$$ to buy candy; $$6$$ minutes for $$B$$ to buy rice; $$4$$ minutes for $$C$$ to buy cigarettes and beer; $$3$$ minutes for $$D$$ to buy fruits; and $$5$$ minutes for $$E$$ to buy vegetables. The question is: How should the clerk arrange the order of the five people so that the total waiting time for the five people is minimized? The shortest time is in minutes. (Only the waiting time for each person is counted, not the time it takes to buy the items.)"}, {"key": "4434", "content": "Three mechanics, A, B, and C, plan to make 7 parts on 3 machines of the same efficiency. The time it takes to make each part is 4, 5, 6, 6, 8, 9, and 9 minutes, respectively. All three start working at the same time. The minimum number of minutes needed to make all 7 parts is $$7$$ parts."}, {"key": "4435", "content": "Warehouse A and Warehouse B need to deliver rice to Supermarket $$A$$ and Supermarket $$B$$. It is known that Warehouse A can dispatch $$100$$ tons of rice, and Warehouse B can dispatch $$80$$ tons. Supermarket $$A$$ needs $$70$$ tons of rice, and Supermarket $$B$$ needs $$110$$ tons of rice. The distance to the supermarkets and the freight cost are as follows: Distance (km) Freight (Yuan/ton\u00b7km) From Warehouse A to Warehouse A to Warehouse B to Supermarket $$A$$ $$20$$ $$15$$ $$12$$ $$12$$ and to Supermarket $$B$$ $$25$$ $$20$$ $$10$$ $$8$$. Question: How much rice should each of the warehouses deliver to Supermarkets $$A$$ and $$B$$ to minimize the total freight cost? What is the total freight cost in this case."}, {"key": "4436", "content": "A certain village has six wheat fields, each with the yield as shown in the following figure. Where is the best place to locate the wheat field. question_4436-image_0"}, {"key": "4437", "content": "There are $$89$$ children, and the teacher wants to give each a red pen and a blue pen. In the store, each type of pen comes in packs of either $$5$$ or $$3$$, and they cannot be sold individually. A pack of $$5$$ red pens is $$59$$ yuan, and blue pens are $$67$$ yuan; a pack of $$3$$ red pens is $$38$$ yuan, and blue pens are $$47$$ yuan. The teacher needs to spend at least yuan to buy the pens."}, {"key": "4438", "content": "There are some balls of the same size and shape in the pocket: there are $$8$$ red balls, $$12$$ yellow balls, $$15$$ white balls. At least how many balls need to be taken out to guarantee that there are at least $$3$$ balls of one color and $$7$$ balls of another color."}, {"key": "4439", "content": "The depot originally had several tons of coal. The first shipment was half of the original coal. The second shipment brought in $$450$$ tons, and the third shipment transported out half of the existing coal plus $$50$$ tons. As a result, twice the remaining coal is $$1200$$ tons. The original amount of coal in the depot was tons."}, {"key": "4440", "content": "Persons $$A$$, $$B$$, $$C$$, and $$D$$ together have $$64$$ bricks. $$A$$ gave some bricks to $$B$$ and $$C$$, doubling their number of bricks; then $$B$$ gave some bricks to $$C$$ and $$D$$, doubling their number of bricks; $$C$$ also gave some bricks to $$D$$ and $$A$$, doubling their number of bricks; finally, $$D$$ also gave some bricks to $$A$$ and $$B$$, doubling their number of bricks, making the number of bricks each person has equal. How many bricks did $$A$$, $$B$$, $$C$$, and $$D$$ originally have, respectively."}, {"key": "4441", "content": "Teacher Niu took $$37$$ students on a spring outing to the countryside. During the break, Aidi asked, 'How old are you this year, Teacher Niu?' Teacher Niu answered interestingly: 'If you multiply my age by $$2$$, then subtract $$16$$, divide the result by $$2$$, and add $$8$$, you'll get exactly the total number of people participating in today's activity.' Teacher Niu is $$38$$ years old this year."}, {"key": "4442", "content": "Person A, B, and C went fishing together. They put the fish they caught into a basket and lied down to rest on the spot, and as a result, they all fell asleep. Person A woke up first, divided the fish in the basket into 3 equal parts, and found one extra fish, which he threw back into the river, and took 1 part of the fish home. Person B then woke up and also divided the remaining fish in the basket into 3 equal parts, found one extra fish again, threw the extra fish back into the river, and took 1 part of the fish home. Finally, Person C woke up and also divided the remaining fish in the basket into 3 equal parts, and there was also one extra fish this time. The three people caught at least how many fish in total."}, {"key": "4443", "content": "Stringing alternately $$7$$ white beads and $$4$$ black beads on a rope in this order. If a total of $$120$$ beads are strung from the beginning, the white beads outnumber the black beads by ."}, {"key": "4444", "content": "Our country resumed sovereignty over Hong Kong on July 1, 1997, and this day was a Tuesday. Then, what day of the week was the 22nd anniversary celebration on July 1, 2019?"}, {"key": "4445", "content": "$$2018$$ year's $$11$$ month $$1$$ day is Thursday, so the $$12$$ month $$31$$ day of this year is a weekday."}, {"key": "4446", "content": "The units digit of $$\\underbrace{2\\times 2\\times \\cdots \\times 2}_{20 twos}-1$$ is."}, {"key": "4447", "content": "In a cage with chickens and rabbits, there are a total of $$3$$ heads and $$10$$ legs. How many chickens are there?"}, {"key": "4448", "content": "$$12$$ students form a circle to play a game of passing a handkerchief, as shown in the figure. Starting with student number $$1$$, it is passed counterclockwise $$200$$ times, and the handkerchief should end up with student number ____.\n question_4448-image_0"}, {"key": "4449", "content": "June 1, 2016, was a Wednesday, then June 1, 2013, was a Saturday ( )."}, {"key": "4450", "content": "The child's birthday is on June 27th, and June 1st of this year is a Saturday. What day of the week is the child's birthday?"}, {"key": "4451", "content": "Lele Department Store commissioned the carrying station to transport $$100$$ vases. It was agreed that the freight for each vase would be $$10$$ yuan, but if any were broken, not only would the freight not be paid, but also a compensation of $$10$$ yuan would have to be made for each broken one. As a result, the carrying station earned a total of $$920$$ yuan in freight. A total of vases were broken during the transportation"}, {"key": "4452", "content": "Originally, there were $$62$$ legs in total between chickens and rabbits. After swapping the chickens with rabbits, all the chickens became rabbits and all the rabbits became chickens, and now there are a total of $$88$$ legs. So, originally, there were how many chickens."}, {"key": "4453", "content": "A store clerk went to the bank to exchange change, using 80 one-hundred-yuan notes to exchange for a total of 220 notes of twenty and fifty yuan each, among which there were twenty yuan notes."}, {"key": "4454", "content": "In a math test with only $$10$$ questions, you earn $$10$$ points for each correct answer and lose $$3$$ points for each wrong answer or unanswered question. Wei Er did not pass this time, but she found that she could have scored $$61$$ points if she had made one fewer mistake. How many questions did she get right?"}, {"key": "4455", "content": "There is a square in the picture.\n question_4455-image_0"}, {"key": "4456", "content": "The first term of a sequence is $$\\frac{1}{2}$$, the second term is $$\\frac{1}{6}$$, the third term is $$\\frac{1}{12}$$, the fourth term is $$\\frac{1}{20}$$,..., then the $$n$$th term is ()."}, {"key": "4457", "content": "Draw $$6$$ straight lines on a piece of paper, at most how many parts can this piece of paper be divided into."}, {"key": "4458", "content": "Draw $$14$$ straight lines on a paper, there can be at most how many intersection points."}, {"key": "4459", "content": "The two diagonals of quadrilateral $$ABCD$$ are perpendicular to each other. It is known that $$AC=10$$ and $$BD=7$$. Find the area of the quadrilateral $$ABCD$$.\n question_4459-image_0"}, {"key": "4460", "content": "Given that the area of parallelogram $$ABCD$$ is $$60$$ square centimeters and $$CD=10$$ centimeters, then $$AE$$ equals centimeters.\n question_4460-image_0"}, {"key": "4461", "content": "As shown in the figure, the area of the trapezoid is.\n question_4461-image_0"}, {"key": "4462", "content": "There is a sequence of numbers: $$3$$, $$3$$, $$9$$, $$7$$, $$3$$, \u2026 starting from the third number, each number is the unit digit of the product of the previous two numbers. Then, the $$2014$$th number in this sequence is."}, {"key": "4463", "content": "Observe the sequence below (as shown in the pattern in the box), please calculate the total number of elements in this sequence.\n$$1$$, $$2$$, $$4$$, $$7$$, $$8$$, $$10$$, $$13$$, $$14$$, $$16$$, $$19$$, \u2026, $$100$$\n question_4463-image_0"}, {"key": "4464", "content": "There are $$7$$ cups with their openings facing up on the table, now it is allowed to turn over $$4$$ of them at the same time. Can all $$7$$ cups be flipped to have their openings facing down after several flips? ( )"}, {"key": "4465", "content": "As depicted, three cups of the same size, labeled A, B, and C, are arranged in sequence on a table, with cup A filled with water, and cups B and C empty. Now, all the water is poured into an adjacent (left or right) empty cup. Therefore, after pouring the water $$55$$ times, the cup with water is . question_4465-image_0"}, {"key": "4466", "content": "The little monkey went out and made sure the light was off. When the little monkey came back home in the evening, ready to turn on the light, he pressed the switch $$12$$ times, but the light was still not on because the power was out. Kids, guess what the state of the light would be when the power comes back on."}, {"key": "4467", "content": "As shown in the diagram, there are two islands at the confluence of two rivers, connected by seven bridges to each other and to the riverbanks. The question is: Can a walker cross all seven bridges once without doubling back?\n question_4467-image_0"}, {"key": "4468", "content": "Each line in the diagram represents a street, and the number on the line indicates the kilometers of that street. The mail truck leaves the post office, must travel through each street, and finally return to the post office. Question: What is the shortest path the mail truck can take in kilometers.\n question_4468-image_0"}, {"key": "4469", "content": "Grandma Li walks along the path in the street heart garden (as shown below). Can she walk all the paths once without repeating any and return to the starting point? If not, what kind of route should she choose to make the total distance the shortest? What is the shortest distance? question_4469-image_0"}, {"key": "4470", "content": "The diagram below contains $$6$$ points and $$8$$ lines. A beetle starts from point $$A$$ and wishes to crawl to point $$F$$, moving only right, down, or diagonally right down. There are a number of different methods for the beetle to do so.\n question_4470-image_0"}, {"key": "4471", "content": "Divide $$12$$ pieces of sugar into $$3$$ piles of different quantities, with at least one in each pile. There are a total of ________ different ways to divide them."}, {"key": "4472", "content": "There are five types of gifts priced at $$2$$, $$5$$, $$8$$, $$11$$, and $$14$$ respectively, and five types of gift boxes priced at $$3$$, $$5$$, $$7$$, $$9$$, and $$11$$ respectively. A gift paired with a gift box results in a total of different prices."}, {"key": "4473", "content": "The diagram below shows $$6$$ points and $$8$$ line segments. A beetle starts from point $$A$$ and wants to crawl to point $$F$$ along some of the line segments (it stops moving when it reaches point $$F$$). During its journey, it can pass through the same point or the same line segment at most $$1$$ time. There are a total of different ways for the beetle to do this.\n question_4473-image_0"}, {"key": "4474", "content": "Dividing $$12$$ identical balls into $$3$$ piles, there are a total of different ways to do it."}, {"key": "4475", "content": "As shown in the figure, an ant starts from the vertex $$A$$ of a regular tetrahedron and travels sequentially and without repeats across the $$4$$ vertices and back to vertex $$A$$. The question is: how many different paths can the ant take in total.\n question_4475-image_0"}, {"key": "4476", "content": "There are twelve natural numbers from $$1\\sim 12$$. Decomposing $$26$$ into three distinct natural numbers, there are a total of different situations."}, {"key": "4477", "content": "$$15$$ pieces of candy are divided into $$3$$ piles of different quantities, with a total of different ways of division."}, {"key": "4478", "content": "Divide $$25$$ into the sum of $$7$$ different natural numbers, how many ways can this division be done? List the different methods."}, {"key": "4479", "content": "Xinhua Primary School arranges $$4$$ extracurricular activities every week, which include sports, arts, and science. If it is required that each type of activity takes place at least once a week, and the same activity cannot be arranged consecutively, then, how many different arrangements are there in total?"}, {"key": "4480", "content": "Break $$7$$ into several (two or more) non-zero natural numbers, there are a total of kinds of situations."}, {"key": "4481", "content": "There are $$3$$ identical red balls, $$4$$ identical yellow balls, and $$5$$ identical white balls in the bag. Xiao Ming randomly takes out $$6$$ balls, how many possible outcomes are there for the balls he takes out?"}, {"key": "4482", "content": "Distribute $$8$$ identical rulers to $$3$$ kids, with each kid getting at least one, how many different ways can this be done?"}, {"key": "4483", "content": "A and B play table tennis, the person who wins the first two games in a row wins; if no one wins the first two games in a row, then the first person to win three games wins. From the start of the match to the determination of the winner, how many possible scenarios could there be?"}, {"key": "4484", "content": "A four-digit number, if separated by a comma between the hundreds and tens places, can be written as two two-digit numbers $$(3162\\to 31,62)$$. If the two two-digit numbers are in an integer multiple relationship, we call such a four-digit number a \"skillful number\". Please select 4 numbers from the five numbers $$1$$, $$2$$, $$4$$, $$6$$, $$8$$ to arrange into a four-digit number. Then, how many \"skillful numbers\" are there in total?"}, {"key": "4485", "content": "For a sequence of numbers, if there are three consecutive numbers $$abc$$ where either $$a>b$$ and $$c>b$$, or $$a < b$$ and $$c < b$$, we say that there is a turn. For example, $$4321$$ has no turns, $$1243$$ has one turn, $$1324$$ has two turns. If you arrange $$1$$, $$2$$, $$3$$, and $$4$$ in a row such that there are exactly two turns in the sequence, there are several ways to do so."}, {"key": "4486", "content": "There are seven plates, each containing $$1$$, $$2$$, $$3$$, $$5$$, $$6$$, $$7$$, and $$9$$ pears respectively. If you want to take out $$15$$ pears, and you must either take all the pears from a plate or none at all, how many different ways are there to do this?"}, {"key": "4487", "content": "Calculate: $$9999\\times 234=$$."}, {"key": "4488", "content": "Calculate: $$15\\times 37+45\\times 21=$$."}, {"key": "4489", "content": "Calculate: $$123\\times 999=$$."}, {"key": "4490", "content": "Calculate: $$52\\times 47+52\\times 52+52$$=\uff0e"}, {"key": "4491", "content": "Compute the following expressions: (1) $$36\\times 19+64\\times 19$$= (2) $$32\\times 25+68\\times 25$$= (3) $$268\\times 75-68\\times 75$$="}, {"key": "4492", "content": "Calculate: $$238\\times 397-237\\times 398=$$"}, {"key": "4493", "content": "Calculate: $$55\\times 66+66\\times 77+77\\times 88+88\\times 99$$=."}, {"key": "4494", "content": "As shown in the figure, some numbers are already filled in. The number in each of the remaining cells is equal to the product of the number at the far left of the same row and the number at the top of the same column (for example $$a=8\\times 11=88$$). Then, the sum of the numbers filled in all the empty cells is. question_4494-image_0"}, {"key": "4495", "content": "This year, the father's age is $$6$$ times the age of his son. In $$15$$ years, the father's age will be $$3$$ times the age of his son. The son's age this year is."}, {"key": "4496", "content": "Xiao Ying is $$2$$ years younger than Xiao Ming. This year, their combined age is half the age of their teacher. In $$16$$ years, their combined age will be equal to the teacher's age. Xiao Ying's age this year is."}, {"key": "4497", "content": "A square with a side length of $$10$$ cm is cut horizontally $$3$$ times and vertically $$3$$ times, turning into $$16$$ small rectangles. The total perimeter of these $$16$$ small rectangles equals centimeters.\n question_4497-image_0"}, {"key": "4498", "content": "Given a rectangle with a length of $$15$$ and a width of $$9$$, cutting the longer side by $$2$$ and the shorter side by $$1$$, the total perimeter of the $$6$$ smaller rectangles is. question_4498-image_0"}, {"key": "4499", "content": "A big rectangle is divided into $$16$$ smaller rectangles, and the perimeter of $$4$$ of them has already been marked. Then, the perimeter of the big rectangle is in centimeters. question_4499-image_0"}, {"key": "4500", "content": "Cutting twice horizontally and vertically with scissors on a rectangular piece of paper with a perimeter of $$36$$ centimeters results in the sum of the perimeters of the newly produced $$9$$ rectangles being centimeters."}, {"key": "4501", "content": "A piece of vegetable plot, shaped as shown in the figure, it is known that $$a=b=30$$ meters, $$c=12$$ meters, the perimeter of this plot is meters. question_4501-image_0"}, {"key": "4502", "content": "Arrange $$12$$ trees into $$6$$ rows, ensuring there are $$4$$ trees in each row, can it be done?"}, {"key": "4503", "content": "Adding a straight line in the diagram below, the number of intersection points in the diagram cannot become ( ) pieces. \n question_4503-image_0"}, {"key": "4504", "content": "The $$5$$ points in the diagram can form a total of $$6$$ straight lines. If another point is added to the diagram, the total number of newly formed straight lines is.\n question_4504-image_0"}, {"key": "4505", "content": "Given any $$9$$ points on the same plane, the maximum number of straight lines that can be determined is."}, {"key": "4506", "content": "In a plane, $$13$$ lines can divide the plane into the most parts."}, {"key": "4507", "content": "Given any 20 points on the same plane, the maximum number of straight lines that can be determined. On the same plane, 20 straight lines can have a maximum number of intersection points."}, {"key": "4508", "content": "If you draw $$4$$ straight lines on a plane, you can divide the plane into at most parts. If you draw $$20$$ straight lines, you can divide it into at most parts."}, {"key": "4509", "content": "A fleet bought back some new ships. Xiaoming counted and found that if all the front tires of each vehicle were changed, there would be $$20$$ tires left; if all $$4$$ tires of each vehicle were changed, there would only be $$6$$ tires left. Question: How many cars are there in the fleet?"}, {"key": "4510", "content": "Merchants need camels to carry goods through the desert. If among them $$2$$ camels each carry $$4$$ boxes, and the remaining camels each carry $$2$$ boxes, there will be $$4$$ boxes of goods left; if among them $$1$$ camel carries $$6$$ boxes of goods, and the remaining camels each carry $$4$$ boxes, there will be $$3$$ camels with no goods to carry. The question is how many camels there are in total."}, {"key": "4511", "content": "The National Day is coming soon, and the Young Pioneers from Xueersi School are going to set up flowers. If each person sets up $$6$$ pots of flowers, there are still $$3$$ pots left unset; if among them $$2$$ people each set up $$5$$ pots, and the rest set up $$7$$ pots each, then these flowers are just enough. There are a total of Young Pioneers participating in the flower setting activity, and a total of pots of flowers to be set."}, {"key": "4512", "content": "The teacher distributed reward cards to the new students, giving an equal amount to each. If each child were given 10 cards, there would be 30 cards short; if each child were given 8 cards, there would still be 8 cards short. Thus, the total number of children and reward cards are."}, {"key": "4513", "content": "Students from the Happy Primary School Young Pioneers went to the meeting room for a meeting. If 3 people sit on each bench, there are 7 people left standing, and if 7 people sit on each bench, there are 3 benches left over. The number of Young Pioneers attending the meeting is."}, {"key": "4514", "content": "Teacher Li bought a basket of tangerines. If they are all given to the children in the senior class, each child would get 3 tangerines and there would be 5 left over; if they are all given to the children in the junior class, each child would get 2 tangerines and there would be 8 left over. Knowing that the junior class has 1 more student than the senior class, how many tangerines are in the basket."}, {"key": "4515", "content": "There are several red and white balls in a box. If you take out 1 red ball and 1 white ball each time, until there are no red balls left, there will be 50 white balls remaining; if each time you take away 1 red ball and 3 white balls, until there are no white balls left, there will be 50 red balls remaining. Then, the total number of red balls in the box is."}, {"key": "4516", "content": "Elementary school students take a trip in the spring. If each vehicle seats $$60$$ people, then there will be $$15$$ people who cannot get on; if each vehicle seats an additional $$5$$ people, then there will be exactly one extra vehicle. Therefore, there are a total of students. There are a total of vehicles."}, {"key": "4517", "content": "Xiao Ming's mother took some money to buy meat. If she buys 10 kilograms of beef, she would be short of 6 yuan. If she buys 12 kilograms of pork, she would have 4 yuan left. Knowing that every kilogram of beef is 3 yuan more expensive than pork, the question is: how much money did Xiao Ming's mother bring?"}, {"key": "4518", "content": "A fruit shop has a batch of kiwis and cantaloupes to put together in fruit gift boxes. If each box contains $$5$$ kiwis and $$3$$ cantaloupes, in the end, there are $$4$$ extra kiwis and the cantaloupes exactly run out; if $$7$$ kiwis and $$3$$ cantaloupes are put in each box, in the end, there are $$12$$ extra cantaloupes, and the kiwis exactly run out. Then there are kiwis and cantaloupes."}, {"key": "4519", "content": "On March $$12$$th, the Tree Planting Day, the students of class 1, grade 3 went tree planting. If among them $$3$$ people each plant $$2$$ trees, and the rest each plants $$6$$ trees, then all the saplings will be exactly planted. If the number of people doubles, then each person plants $$2$$ trees and there will be $$8$$ trees left unattended. The total number of students participating in tree planting and the total number of trees to be planted are respectively."}, {"key": "4520", "content": "A school organized a group of teachers and students to go to another city to attend a conference and reserved some rooms in advance. If each room accommodates 3 people, then 20 people will have no place to stay; if each room accommodates 6 people, the last 2 people can each have their own room. If each room accommodates 10 people, then a room can be left empty."}, {"key": "4521", "content": "The Ministry of Health conducted a survey on whether $$120$$ kinds of food contain vitamins $$A$$, $$C$$, $$E$$, and the results are: $$62$$ kinds contain vitamin $$A$$, $$90$$ kinds contain vitamin $$C$$, $$68$$ kinds contain vitamin $$E$$, $$48$$ kinds contain both vitamin $$A$$ and $$C$$, $$36$$ kinds contain both vitamin $$A$$ and $$E$$, $$50$$ kinds contain both vitamin $$C$$ and $$E$$, and $$25$$ kinds contain all three vitamins $$A$$, $$C$$, and $$E$$. How many kinds of food contain only vitamin $$A$$?"}, {"key": "4522", "content": "There are 100 lamps numbered from $$1$$ to $$100$$, lined up while being on. For the first time, lamps with numbers that are multiples of $$3$$ are toggled once. For the second time, lamps with numbers that are multiples of $$5$$ are toggled once. Then, the number of lamps that remain on is."}, {"key": "4523", "content": "The third grade extracurricular activities include three groups: sports, music, and calligraphy, with participation numbers of $$54$$, $$46$$, and $$36$$ people respectively. There are $$4$$ people participating in both the sports and music groups, $$7$$ people in both the sports and calligraphy groups, and $$10$$ people in both the music and calligraphy groups. There are $$2$$ people participating in all three groups. The total number of third graders participating in extracurricular activities is $$117$$ people."}, {"key": "4524", "content": "Barrel A and Barrel B together weigh 240 kilograms. The first time, the same amount of oil is poured from Barrel A into Barrel B as what was in Barrel B. The second time, the same amount of oil is poured from Barrel B into Barrel A as what was in Barrel A at that time. At this time, both barrels have the same amount of oil. Originally, Barrel A had kilograms of oil, and Barrel B had kilograms of oil."}, {"key": "4525", "content": "A school held a chess competition, with a rule that every two players must play against each other once. There were a total of $$105$$ matches, so there were people participating in this chess competition."}, {"key": "4526", "content": "$$6$$ teams participate in a round-robin tournament, where each pair of teams competes in one match. If a match is a draw, each team receives $$1$$ point; otherwise, the winning team receives $$3$$ points and the losing team receives $$0$$ points. After the tournament concludes, it is found that there were $$2$$ draws, thus the total points scored by all six teams is points."}, {"key": "4527", "content": "In a certain knowledge competition, there are $$60$$ students participating. The average score of the top $$10$$ students is $$10$$ points higher than the average score of all the students participating in this competition. Therefore, the average score of the remaining $$50$$ students is lower than the average score of all the participating students by a certain number of points."}, {"key": "4528", "content": "Uncle Zhang went to the bank to withdraw money. The first time, he withdrew more than half of the deposit by $$5$$, and the second time, he withdrew more than half of the remaining amount by $$10$$, leaving $$125$$ in the end. How much did he originally have?"}, {"key": "4529", "content": "When solving a division problem, Xiaomaohu mistook the divisor $$26$$ for $$62$$, resulting in a quotient of $$15$$ and a remainder of $$32$$. The correct quotient is."}, {"key": "4530", "content": "The average of four numbers $$A$$, $$B$$, $$C$$, and $$D$$ is $$38$$; the average of $$A$$ and $$B$$ is $$42$$; the average of $$B$$, $$C$$, and $$D$$ is $$36$$, then $$B$$ is ( )."}, {"key": "4531", "content": "In a table tennis singles match, there were a total of $$16$$ players entering the final. If an elimination format is used (eliminating one player per match) to ultimately decide the champion, $$-$$ the total number of matches to be played is."}, {"key": "4532", "content": "The number of tons of rice in the granary is $$2$$ times that of flour. If each truck carries $$3$$ tons of flour, there will be $$5$$ tons of flour left; if each truck carries $$7$$ tons of rice, it will exactly transport all the rice. The granary has tons of rice and tons of flour."}, {"key": "4533", "content": "There are $$123$$ birds in total on three trees. If $$4$$ birds fly from the first tree to the second tree, and $$5$$ birds fly from the second tree to the third tree, then the number of birds on the three trees will be equal. Originally, how many birds were there on the first, second, and third trees respectively."}, {"key": "4534", "content": "Wei Er distributed mosquito repellent patches to Class 2 of Grade 4. If each person receives $$4$$ patches, then there are $$28$$ excess patches; if there are $$4$$ people receiving $$6$$ patches each, $$6$$ people receiving $$4$$ patches each, and the rest receive $$5$$ patches each, then the distribution is exactly right. There are people in Class 2 of Grade 4, with a total of mosquito repellent patches."}, {"key": "4535", "content": "In a round-robin football tournament attended by four teams: Team A, Team B, Team C, and Team D, where every two teams play against each other once. A win awards $$2$$ points, a loss awards $$0$$ points, and a tie awards $$1$$ point to each team. Currently, Team A and Team B have scored $$5$$ points and $$1$$ point respectively. It is known that Team C and Team D have tied in their match. Hence, Team D has scored a total of points in the end."}, {"key": "4536", "content": "Li Ming and Zhang Liang take turns to type a manuscript, Li Ming types 15 pages per day, Zhang Liang types 10 pages per day, they typed for 25 days in a row, averaging 12 pages per day, how many days did Li Ming type, and how many days did Zhang Liang type"}, {"key": "4537", "content": "Chickens and rabbits are in the same cage. There are $$4$$ more chickens than rabbits. The total number of legs of chickens and rabbits is $$32$$. There are chickens and rabbits."}, {"key": "4538", "content": "Chickens and rabbits are in the same cage, with rabbits outnumbering chickens by $$26$$, together they have $$254$$ feet, there are chickens and rabbits\uff0e"}, {"key": "4539", "content": "Monsters University has large dormitories and small dormitories, with the large dormitories accommodating $$6$$ people and the small dormitories accommodating $$4$$ people, for a total of $$172$$ residents. Now, if the large dormitories and small dormitories are swapped, with all the large dormitories becoming small dormitories and all the small dormitories becoming large dormitories, they can accommodate $$198$$ people. Calculate the original number of large and small dormitories."}, {"key": "4540", "content": "The bird with nine heads has nine heads and one tail, the bird with nine tails has nine tails and one head. Now there are $$580$$ heads and $$900$$ tails, the number of birds with nine heads and the number of birds with nine tails are."}, {"key": "4541", "content": "4 workers need to plant $$124$$ trees, and have already planted $$44$$ trees in the first $$3$$ days. It is known that during these $$3$$ days, one worker took a day off due to personal reasons. If each worker plants the same number of trees per day, and no one takes off in the coming days, how many more days are needed to finish the task."}, {"key": "4542", "content": "$$5$$ monkeys ate $$80$$ peaches in $$4$$ days, at this rate, $$280$$ peaches will last $$7$$ monkeys for days."}, {"key": "4543", "content": "$$3$$ people can plant $$150$$ trees in $$5$$ hours, based on this rate, $$6$$ people can plant trees in $$7$$ hours."}, {"key": "4544", "content": "Xiaoming was calculating a problem involving a three-digit number multiplied by a tens digit number, but accidentally left out the last $$0$$ from the tens digit number, resulting in an answer that was $$7452$$ less than the correct answer. What is the correct result?"}, {"key": "4545", "content": "Students practice group gymnastics, forming a two-layer hollow square formation, with 12 people on each side of the outer layer, requiring a total of people to form such a square formation."}, {"key": "4546", "content": "In a math competition, there were a total of $$15$$ questions. For each question answered correctly, one would score $$8$$ points, and for each question not attempted or answered incorrectly, $$5$$ points would be deducted. Xiao Hong scored $$81$$ points, indicating the number of questions Xiao Hong answered correctly."}, {"key": "4547", "content": "Six teams play in a single round-robin tournament, where each pair of teams play one match. If a match is drawn, each team scores $$1$$ point, otherwise, the winning team scores $$2$$ points and the losing team scores $$0$$ points. Thus, after all the matches are played, the total number of points scored by the six teams is ( ) points."}, {"key": "4548", "content": "Using the numbers $$0$$, $$2$$, $$3$$, $$7$$, you can form different four-digit numbers where all digits are distinct."}, {"key": "4549", "content": "Calculate: $$10+13+16+19+\\cdots +295+298$$=\uff0e"}, {"key": "4550", "content": "Xueersi organized chess competitions, divided into Go, Chinese chess, and international chess groups, with $$42$$ people participating in the Go competition, $$55$$ people participating in the Chinese chess competition, and $$33$$ people participating in the international chess competition. There were $$18$$ people who participated in both the Go and Chinese chess competitions, $$10$$ people who participated in both the Go and international chess competitions, and $$9$$ people who participated in both the Chinese chess and international chess competitions. There were $$5$$ people who participated in all three chess competitions. The question is how many people participated in the chess competitions in total."}, {"key": "4551", "content": "A story book has a total of $$91$$ pages, and these page numbers used a total of digits."}, {"key": "4552", "content": "There are $$7$$ numbers, and their average is $$154$$. If these $$7$$ numbers are arranged in order from smallest to largest, then the average of the first $$2$$ numbers is $$136$$, and the average of the last $$4$$ numbers is $$164$$. Find what the $$3$$rd number is."}, {"key": "4553", "content": "The National Day in $$2018$$ was on Wednesday. The National Day in $$2019$$ was on ( )."}, {"key": "4554", "content": "There are $$25$$ students in the interest group who were born in the same year, among these students, there is at least one who was born in the same month."}, {"key": "4555", "content": "$$5$$ workers can process $$320$$ parts in $$1$$ day. Based on this calculation, if another $$3$$ workers are added, the total number of parts processed in $$2$$ days would be."}, {"key": "4556", "content": "Calculate: $$3333\\times 2222\\div 6666$$=."}, {"key": "4557", "content": "On the way to the snack warehouse, Eddie and Will found a group of residents discussing about the location for a new bus station. Will decided to help them figure out the most reasonable place to build it. As shown in the diagram, there are five residential buildings labeled $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ on the street, with each building having the same number of residents. Now, to establish a bus stop that minimizes the total distance for the residents of all five buildings to the bus stop, the bus stop should be located at (fill in the capital letter). question_4557-image_0"}, {"key": "4558", "content": "Locations A and B are $$240$$ kilometers apart. A car was originally planned to travel from location A to location B in $$6$$ hours, so the car should travel kilometers per hour. In reality, after the car traveled half the distance, it broke down and stopped for $$1$$ hour. To reach location B as originally planned, the car should travel kilometers per hour for the second half of the journey."}, {"key": "4559", "content": "Jiajia Elementary School is preparing to hold a cultural and art performance, and currently, $$8$$ students need to make $$792$$ flowers. In the first $$3$$ days, $$360$$ flowers have been made. It is known that during these $$3$$ days, $$4$$ students were reassigned for $$1$$ day each. Assuming each student makes the same number of flowers each day, and no one is reassigned in the following days, how many more days are needed to complete the task."}, {"key": "4560", "content": "$$8$$ workers can produce $$360$$ machine parts in $$3$$ hours. At this rate, if the number of workers is reduced to half and the time is increased by $$5$$ hours, the number of machine parts that can be produced is ."}, {"key": "4561", "content": "$$3$$ people plant $$150$$ trees in $$5$$ hours, at this rate, how many trees can $$10$$ people plant in $$6$$ hours."}, {"key": "4562", "content": "A rectangular tank can hold 480 tons of water. The tank is equipped with an inlet pipe and an outlet pipe. If only the inlet pipe is open, it takes 8 hours to fill the empty tank; if only the outlet pipe is open, it takes 6 hours to empty the full tank. When both pipes are open at the same time, it requires hours to empty the full tank."}, {"key": "4563", "content": "$$2$$ large trucks and $$6$$ small trucks can transport $$1500$$ tons of goods in $$5$$ hours. Now, there is a batch of goods that requires $$5$$ large trucks and $$15$$ small trucks to transport in $$4$$ hours. After $$3$$ hours of transport, $$4$$ large trucks and $$12$$ small trucks are called away. How many hours are needed to complete the transport of the remaining goods?"}, {"key": "4564", "content": "To fill a reservoir with water, a total of 144 liters can be stored. It takes 18 hours to fill it using 8 pipes. Now, if using 12 pipes to fill it, the required time in hours to fill the reservoir is."}, {"key": "4565", "content": "Four soccer teams participate in a round-robin tournament, where each pair of teams plays one match. If a match is a draw, each team gets $$1$$ point, otherwise, the winning team gets $$3$$ points, and the losing team gets $$0$$ points. (3) It is known that the scores of teams $$A$$, $$B$$, $$C$$, and $$D$$ are: $$1$$, $$2$$, $$4$$, $$9$$, respectively. Determine the total number of draws in the matches."}, {"key": "4566", "content": "Xiao Mei has a box of black and white beads, she arranges the beads in the following manner: (1) The 18th bead should be of color; (2) There are a total of white beads in the first 20 beads. question_4566-image_0"}, {"key": "4567", "content": "Calculate: (1) $$25\\times 28$$ = (2) $$125\\times 64$$ = (3) $$125\\times 16\\times 5$$ ="}, {"key": "4568", "content": "Which slice of bread has a larger area? ( )"}, {"key": "4569", "content": "A square picture frame with a side length of $$5$$ decimeters has a perimeter of decimeters."}, {"key": "4570", "content": "The length of a rectangular pond is $$8$$ meters, and the width is $$5$$ meters. The perimeter of this pond is meters."}, {"key": "4571", "content": "The east area of the Beautiful Scenery Community has $$30$$ households, the west area has $$3$$ times fewer residents than the east area minus $$10$$ households, the west area of the Beautiful Scenery Community has a certain number of households."}, {"key": "4572", "content": "A class has $$18$$ female students. The number of male students is $$4$$ more than twice the number of female students. There are male students."}, {"key": "4573", "content": "Fill in the blanks.\n\n\n\n$$7$$ square decimeters $$=$$ square centimeters\n$$12$$ square meters $$=$$ square decimeters\n\n\n$$300$$ square centimeters $$=$$ square decimeters\n$$500$$ square decimeters $$=$$ square meters"}, {"key": "4574", "content": "The group then arrived at the elephant pavilion. There are a total of $$22$$ elephants here, divided into two main categories: Asian elephants and African elephants, where the number of African elephants is $$3$$ times more than the Asian elephants plus $$2$$ more. So, the number of Asian elephants and the number of African elephants are."}, {"key": "4575", "content": "Everyone arrived at the deer park again. Eddie counted and found there were a total of $$24$$ sika deer and giraffes, and the number of sika deer was $$4$$ less than $$3$$ times the number of giraffes. So, Eddie saw sika deer and giraffes."}, {"key": "4576", "content": "There are three types of monkeys on the monkey mountain, which are golden monkeys, macaques, and black leaf monkeys. There are a total of $$56$$ monkeys, and the number of golden monkeys is $$2$$ times the number of macaques, and the number of black leaf monkeys is $$4$$ times the number of macaques. So, the number of macaques, golden monkeys, and black leaf monkeys are, respectively."}, {"key": "4577", "content": "There are so many visitors to Monkey Mountain today. Wei'er counted a total of $$50$$ people, including the elderly, young people, and children. The number of young people is $$2$$ times that of the elderly, and the number of children is $$3$$ times that of the elderly plus $$2$$ more people. So, the number of elderly, young people, and children are."}, {"key": "4578", "content": "The doctor arrived at the tropical fish exhibit with Eddie and Vi. In one of the fish tanks, there were a total of $$37$$ fish, comprising three colors. Eddie noticed that the number of red fish was double the number of blue fish, and the number of green fish was three times the number of red fish plus $$1$$ more. Hence, the number of fish that are blue, red, and green respectively are."}, {"key": "4579", "content": "Complete the following questions: (Fill in the order $$1.2.3.4.5.6.7$$) (1) Today is Thursday. Counting from today, the $$25$$th day is a week. (2) Today is Tuesday, and $$22$$ days later is a week."}, {"key": "4580", "content": "March 5, 2008, was a Wednesday. Calculate what day of the week March 28, 2008, was ( )."}, {"key": "4581", "content": "March 3, 2008 was a Monday, what day of the week was the opening ceremony of the Olympics on August 8, 2008?"}, {"key": "4582", "content": "$$2018$$ year $$10$$ month $$10$$ day is Wednesday, $$2028$$ year $$10$$ month $$10$$ day is a weekday\uff0e"}, {"key": "4583", "content": "Of the following $$4$$ letters, one can be drawn with a single stroke. question_4583-image_0"}, {"key": "4584", "content": "The following $$4$$ characters, the first one that can be drawn in one stroke. question_4584-image_0"}, {"key": "4585", "content": "Based on the table below, answer the questions. Statistics table of jelly sales from January to March in a supermarket. Unit: kilograms. Month Sales Situation Category January February March Xizhilang $$257$$$$263$$$$260$$ KissKiss $$265$$$$252$$$$248$$ (1) In January, the sales of Xizhilang jelly were less than KissKiss jelly by kilograms. (2) The average sales volume of Xizhilang jelly over these three months was more than that of KissKiss jelly by kilograms."}, {"key": "4586", "content": "In a bar chart, a 2 cm long bar represents 10 kilograms, and a bar in centimeters represents 30 kilograms."}, {"key": "4587", "content": "The figure below can ( ) (fill in \"can\" or \"cannot\") be drawn in one stroke. If not, draw a direct line between the ( ) two points to make it possible to draw in one stroke. question_4587-image_0"}, {"key": "4588", "content": "The image below is of a river in the countryside with six bridges built over it. Is it possible for you to start from one of the villages and cross all the bridges once without repeating any? Please state your reason. (Each bridge can only be crossed once, but you may walk back and forth on land as needed) question_4588-image_0"}, {"key": "4589", "content": "The school held a science and knowledge quiz with a total of $$10$$ questions. Each correct answer was awarded $$3$$ points, and each wrong answer deducted $$1$$ point. Xiao Jun completed all the questions and scored $$18$$ points. He answered correctly questions."}, {"key": "4590", "content": "In the cage, there are total $$12$$ chickens and rabbits, with a total of $$30$$ feet. So, how many chickens are there in total?"}, {"key": "4591", "content": "A certain English test consisted of two parts, and as a result, 12 students in Class 3, Grade 3 scored full marks, 25 students got the first part right, 19 students made errors in the second part, and there were people in Class 3, Grade 3 who made errors in both parts."}, {"key": "4592", "content": "Students numbered from $$1\\sim 60$$ stand in a line on the playground. Students whose numbers are multiples of $$2$$ call out their numbers, and students whose numbers are multiples of $$3$$ also call out their numbers. question_4592-image_0 (1) The number of students who called out their numbers is . (2) The number of students who did not call out their numbers is ."}, {"key": "4593", "content": "40 students stand in a line facing the teacher. The teacher first asks everyone to count from left to right as 1, 2, 3, ..., 39, 40; then asks students whose number is a multiple of 4 to turn around, and then asks students whose number is a multiple of 5 to turn around. Now, the number of students facing the teacher is ."}, {"key": "4594", "content": "A number divided by $$3$$, subtract $$5$$, multiply by $$4$$, and add $$6$$ equals $$26$$, so this number is."}, {"key": "4595", "content": "The following picture requires at least how many pens to draw.\n question_4595-image_0"}, {"key": "4596", "content": "Stick two strips of paper, each 15 cm long, together to form a longer strip of paper, with an overlap of 3 cm. Then, the length of the longer strip of paper is in centimeters."}, {"key": "4597", "content": "Chickens and rabbits in the same cage, there are a total of $20$ chickens and rabbits, and a total of $72$ legs, then there are chickens and rabbits."}, {"key": "4598", "content": "Mao Mao and his friends would have fruit after lunch at the kindergarten, and each child would choose only one type of fruit every time (different letters represent different fruits, for example, $$\\text{A}$$ represents banana). The following figure shows the choices of fruit by all the children after a meal: Based on these statistical results, please answer the following questions: question_4598-image_0 (1) Which fruit is favored by the most people? (Just write the letter) (2) How many people are in the class in total? (3) The number of children who like bananas is more than the number of children who like pears by how many people?"}, {"key": "4599", "content": "A certain class in Hope Primary School has $28$ students who joined the science group, and $$32$$ students who joined the art group, among them $10$ people participated in both groups, and there are also $5$ people who did not join any group, so there are people in this class."}, {"key": "4600", "content": "There are $$24$$ birds on three trees. $$3$$ birds flew from the first tree to the second tree, and $$5$$ birds flew from the second tree to the third tree. Eventually, the number of birds on the three trees became the same. Originally, there were ____ birds on each of the three trees, respectively. (Fill in the order)"}, {"key": "4601", "content": "There are two piles of chess pieces, A and B, with pile A having more pieces than pile B. Now, the pieces are moved in the following manner: for the first move, take the same number of chess pieces from pile A as there are in pile B and put them into pile B; for the second move, take out the same number of chess pieces from pile B as the remaining in pile A and put them into pile A; for the third move, again take out the same number of chess pieces from pile A as the remaining in pile B and put them into pile B. Following this method, after three moves, both piles A and B exactly have $$32$$ pieces each. The original number of chess pieces in pile A and pile B were"}, {"key": "4602", "content": "A and B each had a number of candies, with each operation involving the person with more candies giving some to the person with fewer candies, doubling the amount for the person with fewer candies. After three such operations, A had $$5$$ candies and B had $$12$$ candies. The original number of candies A had is $$7$$, and B had $$10$$."}, {"key": "4603", "content": "Fill in the blanks with $$1\\sim 4$$, so that each row, each column, and each bold-lined box contains the numbers $$1\\sim 4$$ exactly once. What is the number in the third row, third column? question_4603-image_0"}, {"key": "4604", "content": "A rope, first cut off more than half its total length by $$1$$ meter, the second time cut off half of what was left minus $$2$$ meters, the third time cut off $$8$$ meters, and finally $$5$$ meters remained. Question: How many meters was the rope originally?"}, {"key": "4605", "content": "Two oil barrels have a total of $$70$$ kilograms of oil. If $$15$$ kilograms of oil are transferred from the larger barrel to the smaller one, then the amount of oil in both barrels becomes equal. Calculate the initial amount of oil in the larger barrel."}, {"key": "4606", "content": "Complete the flow chart below, the number in the first box is.\n question_4606-image_0"}, {"key": "4607", "content": "The number represented by the abacus is. question_4607-image_0"}, {"key": "4608", "content": "In $$5246$$, the numbers represented by $$2$$ and $$4$$ differ by ."}, {"key": "4609", "content": "Calculate vertically. (1) $$8.4+2.8=$$ (2) $$7.2-4.5=$$"}, {"key": "4610", "content": "Calculate the following problems in columnar form. (1) $$3.64+0.48=$$\uff0e question_4610-image_0 (2) $$8.24-3.56=$$\uff0e question_4610-image_1"}, {"key": "4611", "content": "According to the size of the angles, arrange the sequence numbers of the following angles.\n question_4611-image_0 question_4611-image_1 question_4611-image_2 question_4611-image_3 \n$$<{}$$$$<{}$$$$<{}$$."}, {"key": "4612", "content": "Among the following statements, the incorrect one is ( )."}, {"key": "4613", "content": "Draw two rays from the vertex of a straight angle to divide the angle into three basic angles. Given that $$\\angle 2$$ is three times $$\\angle 1$$, and $$\\angle 3$$ is five times $$\\angle 1$$, calculate the degree of $$\\angle 1$$. question_4613-image_0"}, {"key": "4614", "content": "$$(8-1)\\times5$$="}, {"key": "4615", "content": "During the military training, the students formed a three-layer hollow square formation, with 60 people in the innermost layer, then each side of the outermost layer has people."}, {"key": "4616", "content": "Volunteers formed a hollow square formation for a group photo, with $$52$$ people on the outermost layer, totaling $$4$$ layers, and a total number of volunteers."}, {"key": "4617", "content": "If $$100$$ people stand in a solid square formation, then the outermost layer of this square formation contains people."}, {"key": "4618", "content": "A group of 4th grade students from a certain school formed a square formation. The total number of people on the outermost layer is 40. How many people are there on each side of the outermost layer, and how many people are there in total in this square formation?"}, {"key": "4619", "content": "As the festival approaches, students arranged a hollow flower bed on the playground using potted plants, with each side of the outermost layer having $$15$$ pots, totaling $$3$$ layers, using a total of potted plants."}, {"key": "4620", "content": "At the sports meet, the teachers formed a solid square formation. Knowing that the outermost layer of this square formation has $$116$$ people, then the third layer counting inward has people, and the number of teachers participating in the square formation is people."}, {"key": "4621", "content": "Insert $$+$$ or $$-$$ between each pair of the following nine digits to achieve a result of $$33$$. There is a method. $$1\\ \\ \\ \\ 2\\ \\ \\ \\ 3\\ \\ \\ \\ 4\\ \\ \\ \\ 5\\ \\ \\ \\ 6\\ \\ \\ \\ 7\\ \\ \\ \\ 8\\ \\ \\ \\ 9=33$$ question_4621-image_0"}, {"key": "4622", "content": "Fill in \"$$+$$\", \"$$-$$\", or \"$$\\left( {~~~~} \\right)$$\" to make the equation correct. $$2$$$$~~~~4$$$$~~~~6$$$$~~~~8=8$$."}, {"key": "4623", "content": "Fill in the appropriate places in the equation below with the operation symbols $$+$$, $$-$$, $$\\times $$, $$\\div $$, or ( ), to make the equation valid. $$1$$$$2$$$$3$$$$4$$$$5$$$$=10$$"}, {"key": "4624", "content": "Place an operator between each pair of adjacent numbers in the equation below to make the equation valid. $$3\\ \\ \\ \\ 3\\ \\ \\ \\ 3\\ \\ \\ \\ 3=2$$"}, {"key": "4625", "content": "Xiao Lu needs to travel from point $$A$$ to $$B$$, passing through point $$C$$ as shown in the diagram. What is the shortest route for Xiao Lu to reach point $$B$$? question_4625-image_0"}, {"key": "4626", "content": "The teacher is distributing lollipops to the children on the boat, giving $$3$$ each person, then there are $$2$$ lollipops short; giving $$4$$ each person, then there are $$10$$ lollipops short. How many children and lollipops are there? question_4626-image_0"}, {"key": "4627", "content": "On Arbor Day, several kids went to the forest park to plant trees. If each person plants $$3$$ saplings, then there are $$3$$ saplings left over; if each person plants $$4$$ saplings, then there are $$3$$ saplings short. The question is: how many kids are there in total."}, {"key": "4628", "content": "As shown in the following figure, Eddie walks from point $$A$$ along the road shown in the figure to point $$B$$ taking the shortest route, there are a total of routes. \n question_4628-image_0"}, {"key": "4629", "content": "In the figure below, taking the shortest path from point $$P$$ to point $$Q$$, how many different ways are there to do so?.\n question_4629-image_0"}, {"key": "4630", "content": "A fleet bought some new tires, Xiao Ming counted and found that if the $$2$$ front tires of each vehicle were replaced, there would still be $$20$$ new tires left; if all $$4$$ tires of each vehicle were replaced, only $$6$$ new tires would remain. (1) The fleet has a total of vehicles. (2) The fleet bought back tires. question_4630-image_0"}, {"key": "4631", "content": "Eddie is responsible for distributing mineral water to Class 3-3. He has prepared less mineral water than needed. If he distributes $$4$$ boxes per group, he will be short of $$2$$ boxes; if he distributes $$6$$ boxes per group, he will be short of $$14$$ boxes. Then, how many groups are there in Class 3-3, and how many boxes of mineral water did Eddie prepare? question_4631-image_0"}, {"key": "4632", "content": "The school allocates dormitories for new students. If each room accommodates $$3$$ people, there will be $$22$$ people left over; if each room accommodates $$8$$ people, there will be $$1$$ room left over. (1) Having $$1$$ room left over means having fewer people. (2) There are rooms in the dormitory, and there are people among the new students. question_4632-image_0"}, {"key": "4633", "content": "The expansion task for the Young Pioneers is tree planting. If each Young Pioneer digs $$5$$ tree pits, there are still $$3$$ tree pits left undug; if two of them each dig $$4$$ tree pits and the rest dig $$6$$ tree pits each, then all the tree pits can be exactly filled. There are a total of Young Pioneers, and a total of tree pits to be dug. question_4633-image_0"}, {"key": "4634", "content": "Divide $$10$$ candies into $$2$$ groups of unequal quantities, there are a total of different ways to divide them."}, {"key": "4635", "content": "$$5$$ apples are distributed between Dakuan and Lel, each person gets at least one, there are different ways of distribution."}, {"key": "4636", "content": "Split the number $$10$$ into the sum of two different integers. There are several ways to do this."}, {"key": "4637", "content": "Calculate: $$9\\times 8\\times 125=$$."}, {"key": "4638", "content": "Compute the following questions.\n$$26+54+14=$$\uff0c$$35+19+31=$$\uff0e"}, {"key": "4639", "content": "Tian Tian goes from point $$A$$, where her home is located, to point $$B$$, where her school is located, but she cannot pass through the store at point $$C$$ along the way. How many different shortest routes are there in total? question_4639-image_0"}, {"key": "4640", "content": "Distribute all $$6$$ pieces of sugar to Eddie and Vi, how many ways of distribution are there?"}, {"key": "4641", "content": "In the fourth grade, students are dividing apples. If each student gets $$8$$ apples, there are $$20$$ left over. If each student gets $$11$$ apples, there are $$4$$ apples short. How many students are there and how many apples are there in total?"}, {"key": "4642", "content": "Fill in the appropriate operation symbols and brackets in the following equation to make the equation correct.\n$$5$$ $$5$$ $$5$$ $$5=3$$"}, {"key": "4643", "content": "As shown, a piece of irregular polygon cheese $$ABCDEFGH$$ each adjacent side is perpendicular to each other, (1) if an ant crawls in a counterclockwise direction, then the upward segments are:, the downward segments are:, the leftward segments are:, the rightward segments are:. (2) To calculate its perimeter, at least the length of segments must be known. question_4643-image_0"}, {"key": "4644", "content": "Three small rectangles, each with a length of $$5$$ centimeters and a width of $$2$$ centimeters, are combined to form one large rectangle. (1) When the small rectangles are combined, they can be joined either by their centimeter sides or by their centimeter sides. (2) The perimeter of this large rectangle is either centimeters or centimeters. (Fill in the blanks in ascending order)"}, {"key": "4645", "content": "Xiaoming's window is made of $$6$$ small rectangles of the same size combined into a large rectangle, with each small rectangle being $$60$$ cm in length. Recently, he wanted to attach a windproof sealing strip around the outer perimeter of the window. (1) The width of the small rectangle is cm. (2) The total length of the sealing strip needed is cm. question_4645-image_0"}, {"key": "4646", "content": "There is a rectangular piece of paper, the length is $$10$$ cm, and the width is $$5$$ cm. ($$1$$) Cut horizontally with scissors once (as shown in the figure), increase centimeters; cut vertically once, increase centimeters. question_4646-image_0 ($$2$$) Cut horizontally and vertically with scissors $$5$$ times each, then the sum of the perimeters of all the small rectangles formed is centimeters."}, {"key": "4647", "content": "Xiao Hong and Xiao Lan have a total of $$80$$ stamps. If Xiao Hong gets $$10$$ more stamps and Xiao Lan uses $$6$$ stamps, then Xiao Hong will have $$3$$ times the number of stamps Xiao Lan has. How many stamps did Xiao Hong originally have?"}, {"key": "4648", "content": "As shown in the diagram, how many different ways are there for Eddie to return home from school?\n question_4648-image_0"}, {"key": "4649", "content": "Below is a fast food restaurant's menu. Lulu plans to order one main dish, one snack, and one drink. How many different combinations can she choose from? question_4649-image_0"}, {"key": "4650", "content": "Vera has $$3$$ different dresses, $$4$$ different tops, $$3$$ different pairs of pants, and $$2$$ different pairs of shoes in her wardrobe. How many different outfit combinations does she have? question_4650-image_0"}, {"key": "4651", "content": "Max Hotel has a total of $$4$$ rooms to choose from, Eddie, Viola, Da Kuan, and Doctor each choose one room, how many different selection plans are there in total? question_4651-image_0"}, {"key": "4652", "content": "As shown in the diagram, there is a square garden with a straight path running diagonally across it. The path is $$8$$ meters long. Therefore, the area of the square garden is square meters (the area of the path is negligible).\n question_4652-image_0"}, {"key": "4653", "content": "It is known that the diagonals of quadrilateral $$ABCD$$ are perpendicular to each other, and the area of the quadrilateral is $$80$$ square centimeters. Given that $$AC=10$$ centimeters, find the length of $$BD$$. question_4653-image_0"}, {"key": "4654", "content": "Below, a large rectangle is divided into $$9$$ smaller rectangles, among which the area of $$5$$ rectangles is shown in the diagram (unit: square centimeters), then the area of \u201c*\u201d is in square centimeters. question_4654-image_0"}, {"key": "4655", "content": "As shown in the figure, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$BC$$ at point $$E$$. Given that the area of parallelogram $$ABCD$$ is $$48$$ square centimeters, and $$AE=8$$ centimeters, what is the length of $$AD$$ in centimeters? question_4655-image_0"}, {"key": "4656", "content": "As shown in the figure, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$ from point $$A$$. Given $$AB=5$$ cm, $$AE=3$$ cm, find the area of parallelogram $$ABCD$$. question_4656-image_0"}, {"key": "4657", "content": "As shown in the figure, the side length of the large square $$DEFG$$ is $$12$$ cm, and the side length of the small square $$ABCD$$ is $$6$$ cm. Please answer: What is the area of the parallelogram $$ABFH$$ in square centimeters? question_4657-image_0"}, {"key": "4658", "content": "As shown in the figure, two squares with a side length of $$10$$ centimeters are staggered by $$3$$ centimeters. The shaded part is a parallelogram. What is the area of this parallelogram in square centimeters? question_4658-image_0"}, {"key": "4659", "content": "Given \u2606$$\\div 7=8\\cdots \\cdots \\triangle $$, what is the largest possible value for $$\\triangle $$."}, {"key": "4660", "content": "Compared to the area of the parallelogram, the area of the rectangle in the figure is ( ). question_4660-image_0"}, {"key": "4661", "content": "Da Mao, Er Mao, and San Mao pass the ball to each other, starting with Da Mao, passing it 3 times, there are different ways of passing."}, {"key": "4662", "content": "Using $$8$$ matchsticks, place a number in each square frame. You can place a single-digit number or a multiple-digit number. The numbers placed can be the same or different. The final addition equation formed should have the maximum and minimum possible results, respectively. question_4662-image_0"}, {"key": "4663", "content": "There are a total of $$5$$ lines and $$5$$ points of intersection in the diagram. Removing the line with number allows the intersections to remain unchanged.\n question_4663-image_0"}, {"key": "4664", "content": "On the same plane, $$20$$ straight lines can have at most how many intersection points."}, {"key": "4665", "content": "A teacher distributes candies to the students. If each student receives 2 candies, there will be 20 candies left over; if each student receives 5 candies, there will be 2 candies left over. Thus, there are in total students, and the teacher has prepared candies. question_4665-image_0"}, {"key": "4666", "content": "The teacher distributes candies to the students. If each student is given $$9$$ candies, there is a shortage of $$2$$ candies; if each student is given $$11$$ candies, there is a shortage of $$14$$ candies. Therefore, there are a total of students, and the teacher prepared candies."}, {"key": "4667", "content": "The Monkey King distributes peaches to the little monkeys. If he gives each little monkey 4 peaches, there will be 5 peaches left; if he gives each little monkey 5 peaches, he will be short of 4 peaches. So, how many little monkeys are there in total, and how many peaches has the Monkey King prepared?"}, {"key": "4668", "content": "The school allocates dormitories for new students. If each room accommodates $$3$$ people, there are $$22$$ people more; if each room accommodates $$8$$ people, there is $$1$$ room left. How many rooms are there and how many new students are there? question_4668-image_0"}, {"key": "4669", "content": "Young pioneers go to plant trees. If each person plants $$5$$ trees, there will be $$3$$ trees left un-planted; if among them two people each plant $$4$$ trees, and the rest each plant $$6$$ trees, then all the trees will be just completely planted. There are a total of young pioneers and a total of trees planted."}, {"key": "4670", "content": "Wei'er divides $$100$$ apples into two piles, where one pile is exactly $$10$$ more than $$4$$ times the other pile. How many apples does the smaller pile have? ( )"}, {"key": "4671", "content": "As shown in the figure, there are four islands $$A$$, $$B$$, $$C$$, $$D$$, connected by a total of nine bridges. If tourists want to cross all nine bridges once without repeating, it is possible. question_4671-image_0"}, {"key": "4672", "content": "As shown in the diagram, there are four islands $$A$$, $$B$$, $$C$$, $$D$$, connected by a total of nine bridges. If one more bridge is added, it is possible for visitors to walk over all nine bridges without repeating any of them. question_4672-image_0"}, {"key": "4673", "content": "As shown in the figure below, there are four islands $$A$$, $$B$$, $$C$$, and $$D$$, connected by a total of nine bridges. To allow a visitor to traverse all bridges without repeating any and return to the starting point, at least how many more bridges need to be added? question_4673-image_0"}, {"key": "4674", "content": "In the middle of a river there are two small islands, with six bridges connecting the islands to both banks. Please find a route that starts from one bank, crosses all the bridges without repeating, and then reaches the opposite bank. question_4674-image_0"}, {"key": "4675", "content": "The figure below shows the floor plan of a museum, with a door connecting adjacent exhibition halls, and each exhibition hall has a door leading outside. The question is, can a visitor pass through each door once without repeating? question_4675-image_0"}, {"key": "4676", "content": "The image below is a floor plan of a museum, with $$6$$ rooms, each adjacent room is connected by a door. Eddie wants to start from a certain room and pass through all the doors once without repeating to another room, can he do it? question_4676-image_0"}, {"key": "4677", "content": "The diagram below is a street layout of a community, the length of the streets are as shown in the diagram (unit: kilometers), and each letter in the diagram represents a different building code. A courier starts from the dispatch center (located at point $$P$$ between buildings $$C$$ and $$D$$) and must walk through all the streets and return to the dispatch center. What is the shortest route he can take? The shortest route is in kilometers. question_4677-image_0"}, {"key": "4678", "content": "A city's street map is composed of some rectangles, as shown below. A policeman starts from point $$A$$ to patrol, passing through each road segment at least once before returning to $$\\text{A}$$ point. How many meters does he need to walk at least? question_4678-image_0"}, {"key": "4679", "content": "Each small line segment in the figure is $$10$$ meters long, question: If going from point $$A$$ to point $$B$$ without repeating any path, what is the maximum distance that can be traveled in meters. question_4679-image_0"}, {"key": "4680", "content": "In the diagram below, each small square has a side length of $$100$$ meters. Xiao Ming walks from point $$A$$ to point $$B$$ along the line segments without repeating any path. The maximum distance he can cover is meters. question_4680-image_0"}, {"key": "4681", "content": "Which of the following two points need to be connected or disconnected to make the figure drawable in one stroke?\n question_4681-image_0"}, {"key": "4682", "content": "The streets through which the postman delivers letters are shown in the right image, each segment of the street is $$1$$ kilometer long. If the postman departs from the post office and must cover all streets, the minimum distance the postman needs to walk in kilometers is.\n question_4682-image_0"}, {"key": "4683", "content": "Natural numbers $$12$$, $$135$$, $$1349$$ have one thing in common, they have at least two digits, and for any two adjacent digits, the left digit is smaller than the right digit, these numbers are named \"rising numbers\". Using the digits $$5$$, $$6$$, $$7$$, $$8$$, these four numbers can form \"rising numbers\"."}, {"key": "4684", "content": "Dividing $$10$$ identical ballpoint pens into $$3$$ piles, there are a total of different ways to do so."}, {"key": "4685", "content": "The sum of the digits of a three-digit number is $$8$$. There are such three-digit numbers."}, {"key": "4686", "content": "As shown in the diagram, an ant starts from the apex $$P$$ of a pyramid and travels along the edges of this pyramid, visiting each of the $$5$$ vertices exactly once before stopping. How many different routes can this ant take? question_4686-image_0"}, {"key": "4687", "content": "Three warehouses store a total of $$9800$$ items, the first warehouse has $$1400$$ fewer items than the other two warehouses combined, the second warehouse has $$200$$ more items than the third warehouse. Find the number of items in the first, second, and third warehouses."}, {"key": "4688", "content": "In the doctor's orchard, there are a total of $$358$$ apple trees, pear trees, and peach trees. Among them, the number of pear trees is $$2$$ times the number of apple trees, and the number of peach trees is $$2$$ less than $$3$$ times the number of pear trees. So, there are apple trees, pear trees, and peach trees."}, {"key": "4689", "content": "When dividing two numbers, the quotient is $$3$$ with a remainder of $$10$$. The sum of the dividend, divisor, quotient, and remainder is $$143$$. What is the dividend?"}, {"key": "4690", "content": "Dividing $$523$$ by a number results in a quotient of $$10$$, and the difference between the divisor and the remainder is $$5$$. Find the divisor and the remainder."}, {"key": "4691", "content": "There are two barrels of oil, the first barrel is $$55$$ kilograms, and the second barrel is $$35$$ kilograms. After pouring the same amount of oil from both barrels, what remains in the first barrel is $$3$$ times what remains in the second barrel. How many kilograms of oil are left in the first barrel?"}, {"key": "4692", "content": "There are two bags of rice, bag A has $$18$$ kilograms less than bag B. If $$6$$ kilograms are transferred from bag A to bag B, at that moment, the rice in bag A is half of that in bag B. How many kilograms were originally in each bag? ( )"}, {"key": "4693", "content": "Both person A and person B have some candies. If A gives B $$10$$ candies, then they would have the same amount of candies; if both A and B eat $$8$$ candies, then the remaining candies of A would be $$3$$ times the remaining candies of B. How many candies did they have together originally?"}, {"key": "4694", "content": "Master Li produced a batch of parts one day, and he divided them into two piles, A and B. If 15 parts are taken from pile A and placed into pile B, then the two piles have an equal number of parts; if 15 parts are taken from pile B and placed into pile A, then the number of parts in pile A is 3 times that of pile B. Question: How many original parts were there in pile A, and how many parts did Master Li produce in total that day."}, {"key": "4695", "content": "Eddy's pocket money is $$2$$ times more than that of Da Kuan plus $$1$$ yuan, Veer's pocket money is $$5$$ times that of Da Kuan minus $$11$$ yuan, and Veer has $$24$$ yuan more pocket money than Eddy. How much pocket money do Da Kuan, Eddy, and Veer have respectively?"}, {"key": "4696", "content": "$$12$$ years ago, the father's age was $$11$$ times the age of his daughter; this year, the father's age is $$3$$ times the age of his daughter, how many years from now will the father's age be $$2$$ times the age of his daughter?"}, {"key": "4697", "content": "$$2$$ years ago, mom's age was $$6$$ times that of Binbin; $$3$$ years later, the sum of the ages of mom and Binbin is $$45$$ years. So, Binbin's age this year is years."}, {"key": "4698", "content": "The perimeter of the figure below is (cm) question_4698-image_0 \u200b"}, {"key": "4699", "content": "Calculate the perimeter of the following figure (in centimeters) question_4699-image_0"}, {"key": "4700", "content": "A large rectangle is divided into $$9$$ small rectangles, among which the perimeter of $$4$$ pieces has already been marked. Then, the perimeter of the large rectangle is in centimeters. question_4700-image_0"}, {"key": "4701", "content": "A large rectangle is composed of $$9$$ smaller rectangles, among which the perimeters of $$5$$ rectangles are shown in the diagram. What is the perimeter (in centimeters) of the rectangle marked with a \u201c?\u201d question_4701-image_0"}, {"key": "4702", "content": "Please calculate the perimeter of the figure below. question_4702-image_0"}, {"key": "4703", "content": "As shown in the figure, line segment $$a=12$$ cm, $$b=9$$ cm, $$c=4$$ cm, $$d=6$$ cm, the perimeter of the figure is cm. question_4703-image_0"}, {"key": "4704", "content": "As shown in the diagram, to find the perimeter of the shape, you need to know the length of at least one of the edges. question_4704-image_0"}, {"key": "4705", "content": "There is a rectangular piece of paper, the length is $$2$$ cm more than the width, and the perimeter is $$36$$ cm. Cut it with scissors $$3$$ times (as shown in the figure), the sum of the perimeters of these $$6$$ rectangles is cm. question_4705-image_0"}, {"key": "4706", "content": "Make three cuts along a straight line to divide a rectangle of length $$60$$ cm and width $$30$$ cm into several smaller rectangles. The minimum total perimeter of these smaller rectangles is in centimeters."}, {"key": "4707", "content": "Using four identical rectangles and one small square to form a large square with a side length of $$25$$ cm, the perimeter of each rectangle is cm. question_4707-image_0"}, {"key": "4708", "content": "As shown in the figure, a large rectangle is pieced together with $$5$$ identical small rectangles. If the perimeter of a small rectangle is $$40$$ centimeters, then, the perimeter of the large rectangle is centimeters. question_4708-image_0"}, {"key": "4709", "content": "In the picture, $$9$$ identical rectangles form a large rectangle, whose perimeter is $$90$$. The perimeter of each small rectangle is ( ). question_4709-image_0"}, {"key": "4710", "content": "$$A$$ and $$B$$ are two rectangles of the exact same size. It is known that the length of the rectangle is $$8$$ cm longer than its width, and the letters in the diagram represent the corresponding part lengths. Then, the difference in the perimeter of the shaded parts in $$A$$ and $$B$$ is in centimeters. question_4710-image_0"}, {"key": "4711", "content": "The diagram shows a homestead's floor plan, where each pair of adjacent lines is perpendicular. Find the area of this homestead in square meters $$\\text{m}^{2}$$ question_4711-image_0"}, {"key": "4712", "content": "There is a square flower bed (the shaded area in the diagram) in the park. A pathway 1 meter wide is built around it. The area of the path is 12 square meters. Then, the area of the flower bed in the middle is square meters. question_4712-image_0"}, {"key": "4713", "content": "The two squares in the figure below overlap partially. The difference in area of the two non-overlapping shaded parts is (in square centimeters) question_4713-image_0"}, {"key": "4714", "content": "As shown in the image, the areas of two rectangles are $$24$$ and $$15$$ respectively. If the area of triangle $$A$$ is $$9$$, then the area of triangle $$B$$ is. question_4714-image_0"}, {"key": "4715", "content": "In the figure, there are three squares of different sizes: large, medium, and small. The area of the large square is larger than that of the medium square by $$32$$, and the perimeter of the large square is $$16$$ more than that of the small square. Then the area of the large square is. question_4715-image_0"}, {"key": "4716", "content": "Use rectangles of the same size to form the figure below. Knowing that the perimeter of the large rectangle is 220 cm, find the area of the shaded part in cm\u00b2. question_4716-image_0"}, {"key": "4717", "content": "As shown in the diagram, there is a square flowerbed in the middle. Around the square flowerbed, there is a path with a width of $$2$$ meters. It is known that the area of the path is $$112$$ square meters. Then, the area of the central square flowerbed is square meters.\n question_4717-image_0"}, {"key": "4718", "content": "As shown in the diagram, several paths are set on a square lawn with a side length of $$28$$ meters, and the width of each path is $$4$$ meters. Thus, the actual area of the lawn is square meters.\n question_4718-image_0"}, {"key": "4719", "content": "As shown in the diagram, the side length of square $$ABCD$$ is $$12$$ $$\\text{cm}$$, and the length and width of rectangle $$EFGH$$ are $$10$$ $$\\text{cm}$$ and $$6$$ $$\\text{cm}$$ respectively. The difference in area between shadowed part A and shadowed part B is in square centimeters.\n question_4719-image_0"}, {"key": "4720", "content": "In the figure below, there are a total of $$8$$ straight lines, positioned as shown in the figure, among which $${{l}_{1}}$$, $${{l}_{2}}$$, $${{l}_{3}}$$ are parallel to each other, and $${{l}_{4}}$$, $${{l}_{5}}$$ are parallel to each other, thus: these lines altogether have how many intersection points question_4720-image_0"}, {"key": "4721", "content": "The image below contains a total of $$8$$ lines, positioned as shown in the diagram, among which $${{l}_{1}}$$, $${{l}_{2}}$$, $${{l}_{3}}$$ are parallel to each other, and $${{l}_{4}}$$, $${{l}_{5}}$$ are parallel to each other. If a new line is added to the diagram, the maximum number of intersection points that can be added is . question_4721-image_0"}, {"key": "4722", "content": "In the figure, there are a total of $$8$$ straight lines, positioned as shown, among them $${{l}_{1}}$$, $${{l}_{2}}$$, $${{l}_{3}}$$ are parallel to each other, and $${{l}_{4}}$$, $${{l}_{5}}$$ are parallel to each other, then: removing one line can reduce the number of intersections by at most question_4722-image_0"}, {"key": "4723", "content": "Please answer the following questions: The maximum number of intersection points that can exist among $$3$$ lines on the same plane is , and each line has intersection points."}, {"key": "4724", "content": "Please answer the following questions: On the same plane, there can be at most intersections among $$4$$ straight lines, with each line having intersections."}, {"key": "4725", "content": "Please answer the following questions: On the same plane, there are $$101$$ straight lines that can have at most how many intersection points, with each line having how many intersection points."}, {"key": "4726", "content": "Answer: Given any $$4$$ points on the same plane, the maximum number of straight lines that can be determined is."}, {"key": "4727", "content": "Solution: On the same plane, given any $$10$$ points, the maximum number of straight lines that can be determined is."}, {"key": "4728", "content": "A single line can divide a plane into at most two parts, so $$10$$ lines can divide a plane into as many parts."}, {"key": "4729", "content": "\"$$XES$$\" is an abbreviation for Xueersi. There are currently $$5$$ different colors of pens. (1) If the same color is allowed for the $$3$$ letters, there are various different ways of writing."}, {"key": "4730", "content": "\"$$XES$$\" is an abbreviation for Xueersi, now available in $$5$$ different colors of pens. (2) Write these $$3$$ letters in three different colors, there are kinds of different methods."}, {"key": "4731", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, (2) to form different three-digit numbers without repeating digits."}, {"key": "4732", "content": "Using the numbers $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$. (1) How many different two-digit numbers can be formed."}, {"key": "4733", "content": "Using digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, (4) different non-repeating digit odd numbers can be formed."}, {"key": "4734", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, how many different four-digit even numbers can be formed without repeating any digit."}, {"key": "4735", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$ (4) to form different four-digit even numbers without repeating any digit."}, {"key": "4736", "content": "A signal soldier has one flag each of red, yellow, blue, and green colors. He can hang one, two, or three flags at a time on the flagpole, with different colors and different orders representing different signals. So, this signal soldier can represent a total of different signals."}, {"key": "4737", "content": "On a certain railway line, including the starting and ending stations, there were originally $$7$$ stations. Now, $$3$$ new stations have been added. The tickets for the round trip between any two stations on the railway are different. Therefore, the number of different tickets needs to be increased."}, {"key": "4738", "content": "Students A, B, C, and D from Grade 3, Class ($$1$$), stand in a row wanting to take a group photo with Santa Claus in the school plaza. If A cannot stand on the far left, and B cannot stand on the far right, there are a total of different ways to stand."}, {"key": "4739", "content": "Calculate. $$123000000\\div 64\\div 125\\div 5\\div 25=$$."}, {"key": "4740", "content": "Calculate: $$2002\\times 81\\div (7\\times 9\\times 11\\times 13)=$$."}, {"key": "4741", "content": "Calculate: $$3\\times 5\\times 7\\times 11\\times 13\\times 17\\div (51\\times 65\\times 77)=$$."}, {"key": "4742", "content": "Calculate: $$\\left(11\\times 10\\times 9\\times\\cdots \\times 3\\times 2\\times 1\\right)\\div \\left(22\\times 24\\times 25\\times 27\\right)=$$"}, {"key": "4743", "content": "Calculate: $$156\\div 7+194\\div 7+329\\div 7+371\\div 7=$$."}, {"key": "4744", "content": "Calculate: $$1\\div 2+2\\div 4+3\\div 6+\\cdots +2017\\div 4034+2018\\div 4036=$$."}, {"key": "4745", "content": "Let $$a\u203bb=(a+b)\\times b$$, find $$(2\u203b3)\u203b5=$$."}, {"key": "4746", "content": "The sum of $$7$$ consecutive natural numbers is $$70$$. The middle number is:"}, {"key": "4747", "content": "Among the following numbers: $$1$$, $$3$$, $$5$$, $$7$$, $$9$$, $$\\cdots$$, the sum of the first $$100$$ numbers is."}, {"key": "4748", "content": "A movie theater auditorium has a total of $$11$$ rows of seats, with each succeeding row having $$2$$ more seats than the previous one. The last row has $$30$$ seats. The auditorium has a total number of seats of ."}, {"key": "4749", "content": "Given that the 6th and the 10th numbers of an arithmetic sequence are 38 and 62 respectively, the difference between two consecutive numbers is."}, {"key": "4750", "content": "In the nine boxes numbered $$1\\sim 9$$, there are $$351$$ small glass beads. Except for the box numbered $$1$$, every box contains a number of beads more than the previous box by the same amount. (1) If box number $$1$$ contains $$11$$ small glass beads, then how many more beads does each subsequent box contain compared to its preceder."}, {"key": "4751", "content": "Mr. Wang has $$117$$ candies, and he decides to eat some every day. Since the candies are very delicious, starting from the second day, the amount of candies he eats each day increases by $$3$$ compared to the previous day. After $$9$$ days, he finishes all the candies. Then, how many candies did Mr. Wang eat on the second day?"}, {"key": "4752", "content": "The figure shows the character '\u5de8' formed with chess pieces. Continue to lay out according to the following pattern, a total of $$16$$ '\u5de8' characters are laid out. Then, how many chess pieces are needed in total. question_4752-image_0 question_4752-image_1"}, {"key": "4753", "content": "The sum of three consecutive natural numbers is $$78$$, the largest of these three numbers is."}, {"key": "4754", "content": "The 10th term of an arithmetic sequence is 62, and the 25th term is 152, so, \n(1) The common difference of this arithmetic sequence is; \n(2) The first term of this arithmetic sequence is; \n(3) The 67th term of this arithmetic sequence is;"}, {"key": "4755", "content": "To celebrate the 16th anniversary of the school, Xueersi School organized a sports meet. During the opening ceremony, representative teams from each grade entered and performed in turn. The first-grade students formed a solid square formation to perform gymnastics, with 18 people on each side of the outermost layer, (2) there are people in the outermost layer."}, {"key": "4756", "content": "To celebrate the $$16$$th anniversary of the founding of the school, Xueersi School organized a sports meet. At the opening ceremony, representative teams from each grade entered the field in sequence. The first-grade students formed a solid square formation to perform gymnastics, with the outermost layer having $$18$$ people on each side, (3) counting from the outside inwards, the second layer has people on each side, and the second layer has a total of people."}, {"key": "4757", "content": "To celebrate the school's 16th anniversary, Xueersi School organized a sports meet. At the opening ceremony, representative teams from each grade entered the field in succession. The first-grade students formed a solid square formation to perform gymnastics, with 18 people on each side of the outermost layer, (4) the outermost three layers have a total of people."}, {"key": "4758", "content": "To celebrate the $$16$$th anniversary of the school's establishment, Xueersi School organized a sports meeting. During the opening ceremony, representative teams from each grade entered and performed in sequence. The first graders formed a solid square formation to perform gymnastics, with $$18$$ people on each outer side. (5) This square formation has layers."}, {"key": "4759", "content": "A solid square formation, with a total of $$48$$ people on the outermost layer. How many people are there in total in the square formation; how many layers are there."}, {"key": "4760", "content": "Second-grade students are preparing to perform a chorus. All the boys participating in the chorus just form a solid square. $$17$$ girls line up outside the square, adding one more row and one more column outside the square, forming a slightly larger solid square. There are a total of male students participating in the chorus in the second grade."}, {"key": "4761", "content": "Third-grade students form a solid square formation, holding colored flags for a performance. If one row and one column are removed, exactly $$19$$ people are removed. Then, how many third-grade students are left for the performance."}, {"key": "4762", "content": "Using $$336$$ pieces to form a six-layer hollow square matrix, then the outermost layer has pieces, and the innermost layer has pieces."}, {"key": "4763", "content": "Transform a solid square matrix with $$16$$ pieces per side into a four-layer hollow square matrix, with each side of the outermost layer of this hollow square matrix having pieces."}, {"key": "4764", "content": "Please answer the following question: (1) It is known that there are $$12$$ chess pieces on each side of the outer layer of a solid equilateral triangle formation, totaling chess pieces."}, {"key": "4765", "content": "Please answer the following question: (2) It is known that the outermost layer of a solid equilateral triangle formation has $$72$$ chess pieces in total, how many chess pieces are there in total."}, {"key": "4766", "content": "This is a set of chess pieces arranged in an equilateral triangular lattice. Similar to the 'hollow square formation', there can also be a 'hollow triangular formation'. (1) If there is a 5-layer hollow triangular formation, with each side of the outermost layer having 20 chess pieces, then there are a total of chess pieces. question_4766-image_0"}, {"key": "4767", "content": "At the sports meeting, the teachers performed a program together, forming a hollow regular hexagon similar to the formation in the diagram below. There are a total of $$8$$ layers from the outside in, consisting of two layers of sixth grade teachers, two layers of fifth grade teachers, two layers of fourth grade teachers, and two layers of third grade teachers. Knowing that there are $$126$$ participating sixth grade teachers, please answer: (1) How many people are in the outermost layer? question_4767-image_0"}, {"key": "4768", "content": "Several students form a $$15\\times 15$$ square matrix. How many people are there in the seventh layer from the inside out?"}, {"key": "4769", "content": "There are six sugarcane fields in a certain place, and the yield of each field is as shown in the figure below. Now a sugar factory is planned to be built. Where should the sugar factory be built to minimize the total transportation cost? question_4769-image_0"}, {"key": "4770", "content": "$$5$$ people each take a bucket and wait in line at the tap to fetch water, the time they take to fetch water is $$1$$ minute, $$2$$ minutes, $$3$$ minutes, $$4$$ minutes, and $$5$$ minutes respectively. If there is only one tap, the shortest total time for them to queue up and fetch water is minutes."}, {"key": "4771", "content": "\nTen people each with a bucket arrive simultaneously at the tap to fill their buckets. It takes $$2$$ minutes to fill the first person's bucket, $$4$$ minutes to fill the second person's bucket, $$\\cdots \\cdots $$. Accordingly, it takes $$20$$ minutes to fill the tenth person's bucket. When there are only two taps, the shortest combined time for these ten people to fill their buckets and wait is minutes."}, {"key": "4772", "content": "If there are $$5$$ pigeonholes and the pigeon keeper keeps $$6$$ pigeons, then when the pigeons fly back into the pigeonholes, there must be at least one pigeonhole that contains at least $$2$$ pigeons."}, {"key": "4773", "content": "Now place $$143$$ balls in $$5$$ boxes, please ask what is the minimum number of balls in the box with the most balls."}, {"key": "4774", "content": "Complete the following problem: (2) Among any $$25$$ persons, there is at least a number of people of the same gender."}, {"key": "4775", "content": "Complete the following question: (3) Among any $$100$$ people, the maximum number of people sharing the same Chinese zodiac sign is at least."}, {"key": "4776", "content": "In a pocket, there are $$50$$ beads, consisting of five colors: black, white, red, blue, and green, with each color having $$10$$ beads. If you close your eyes to draw beads: ($$1$$) at least how many beads must be drawn at one time to ensure there are $$5$$ beads of the same color."}, {"key": "4777", "content": "A pocket contains $$50$$ beads of five different colors: black, white, red, blue, and green, with each color having $$10$$ beads. If you close your eyes to pick the beads: ($$2$$) How many beads must you take out at once to ensure that you have at least $$5$$ beads of each color."}, {"key": "4778", "content": "A pocket contains $$50$$ beads of five different colors: black, white, red, blue, and green, with $$10$$ beads of each color. If you close your eyes and draw beads: ($$3$$) At least how many beads must be drawn at once to ensure that there are $$5$$ beads of three different colors."}, {"key": "4779", "content": "A standard deck of playing cards has $$54$$ cards in total, including $$2$$ jokers, and $$13$$ cards each of the four suits: spades, hearts, clubs, and diamonds. (1) At least how many cards must be drawn to guarantee that two different suits are drawn."}, {"key": "4780", "content": "A deck of poker cards has $$52$$ cards after the two jokers are removed. There are four suits: spades, hearts, clubs, and diamonds, each with $$13$$ cards numbered $$1$$ to $$13$$. What is the minimum number of cards that need to be drawn to ensure that two cards of different suits are drawn? ( )"}, {"key": "4781", "content": "There are $$9$$ yellow socks, $$7$$ green socks, $$4$$ white socks, $$2$$ red socks, $$1$$ black sock, and Eddie is picking socks with his eyes closed: (1) At least how many socks need to be picked to ensure $$1$$ pair of socks can be made."}, {"key": "4782", "content": "There are $$9$$ yellow socks, $$7$$ green socks, $$4$$ white socks, $$2$$ red socks, and $$1$$ black sock. Eddie picks socks with his eyes closed: (2) At least how many socks need to be picked to ensure $$2$$ pairs of socks can be formed."}, {"key": "4783", "content": "There are three colors of chopsticks in the pocket, each with $$10$$ sticks. Question: (1) At least how many sticks need to be taken out to ensure that all three colors are obtained."}, {"key": "4784", "content": "There are three colors of chopsticks in the pocket, 10 of each color. Question: (2) At least how many chopsticks must be taken out to guarantee there are 2 pairs of chopsticks of the same color?"}, {"key": "4785", "content": "A pigeon farm has $$70$$ pigeons. If when the pigeons return to the cages, there is at least one cage with $$8$$ pigeons, then the maximum number of pigeon cages the farm can have is."}, {"key": "4786", "content": "There are red, yellow, black balls in a pocket, $$4$$, $$7$$, $$8$$ respectively. To ensure that there are $$6$$ balls of the same color, a minimum number of balls needed to be taken out is."}, {"key": "4787", "content": "Among any $$99$$ people, there is at least one person of the same gender."}, {"key": "4788", "content": "Answer the following questions: (1) A certain restaurant has $$40$$ signature dishes, Eddie has tried $$15$$ of them, Vi has tried $$9$$ of them, and there are $$4$$ dishes both have tried, and there is a signature dish neither of them has tried."}, {"key": "4789", "content": "Answer the following question: (2) In the third grade, $$50$$ students go to the cafeteria for lunch, where a lot of dishes are prepared. $$26$$ students chose tomato scrambled eggs, $$21$$ students chose braised pork, $$17$$ students did not choose either of these two dishes, and there were some who chose both dishes."}, {"key": "4790", "content": "Complete the following questions: (1) Class 3 ($$1$$) had $$55$$ students participate in the sports meet, each participating in at least one of the running or rope skipping competitions. It is known that $$36$$ people participated in running and $$38$$ people participated in rope skipping. The number of people who participated only in rope skipping."}, {"key": "4791", "content": "Complete the following questions: (2) Class 3 ($$2$$) has 50 students. Some can ride bicycles, some can swim. There are 35 people who can ride bicycles, 15 people who can do both, and no students who can't do either. Therefore, there are people who can swim."}, {"key": "4792", "content": "Among the natural numbers from $$1$$ to $$100$$, there are $$33$$ numbers that cannot be divided by $$2$$ or $$3$$."}, {"key": "4793", "content": "The school has $$90$$ teachers, among which $$66$$ teachers like drinking tea, and $$42$$ teachers like drinking coffee. The number of people who like both drinks is exactly $$3$$ times the number of people who do not like either. Therefore, the minimum number of teachers in the school who like at least one of the two drinks is."}, {"key": "4794", "content": "Conducting a questionnaire survey among $$100$$ people, the results show that $$28$$ people read $$A$$ magazine; $$30$$ people read $$B$$ magazine; $$42$$ people read $$C$$ magazine; $$8$$ people read both $$A$$ and $$B$$ magazines simultaneously; $$10$$ people read both $$A$$ and $$C$$ magazines simultaneously; $$5$$ people read both $$B$$ and $$C$$ magazines simultaneously; $$3$$ people read all three magazines. Thus, there are people who did not read any of the aforementioned three magazines."}, {"key": "4795", "content": "On a bright and sunny day, $$11$$ classmates decided to go for a picnic, each bringing some food. Among them, $$6$$ people brought burgers, $$6$$ people brought chicken legs, $$4$$ people brought cheesecakes, $$3$$ people brought both burgers and chicken legs, $$1$$ person brought both chicken legs and cheesecake. $$2$$ people brought both burgers and cheesecake, and there were people who brought all three."}, {"key": "4796", "content": "The Youth Palace's spring calligraphy class, art class, and instrumental music class are enrolling. The calligraphy class has enrolled $$29$$ students, the art class has enrolled $$28$$ students, and the instrumental music class has enrolled $$27$$ students. Among these students, $$13$$ are enrolled in both calligraphy and art, $$12$$ are enrolled in both calligraphy and instrumental music, $$11$$ are enrolled in both art and instrumental music, and $$5$$ are enrolled in all three subjects. Therefore, the number of students enrolled in only one subject is."}, {"key": "4797", "content": "During the physical education class, $$60$$ students stand in a row facing the teacher and count from left to right as per the teacher\u2019s command: $$1$$, $$2$$, $$3$$, \u2026, $$60$$. Then, the teacher asks students whose numbers are multiples of $$4$$ to turn around, followed by those whose numbers are multiples of $$5$$ to turn around, and finally, those whose numbers are multiples of $$6$$ to turn around. Now, there are some students facing the teacher."}, {"key": "4798", "content": "On a long wooden stick, there are three types of scale marks. The first type divides the stick into ten equal parts; the second type divides the stick into twelve equal parts; the third type divides the stick into fifteen equal parts. If the stick is sawed along each scale line, the total number of segments the stick is cut into is."}, {"key": "4799", "content": "In a self-service orchard, the number of people who only picked raspberries was twice the number of people who only picked plums; the number of people who picked strawberries, raspberries, and plums was $$3$$ more than the number of people who only picked plums; the number of people who only picked strawberries was $$4$$ more than those who picked raspberries and strawberries but did not pick plums; $$50$$ people did not pick strawberries; $$11$$ people picked raspberries and plums but did not pick strawberries; a total of $$60$$ people picked plums. If the total number of people participating in fruit picking was $$100$$, then the number of people who picked all three kinds of fruit is."}, {"key": "4800", "content": "Grade 4 class 1 has $$46$$ students participating in three extracurricular groups: mathematics, Chinese language, and arts. Among them, $$24$$ students joined the math group, $$20$$ students joined the Chinese language group. There are $$10$$ students who joined both the math and Chinese language groups, $$6$$ students who joined both the math and arts groups, and $$6$$ students who joined both the arts and Chinese language groups. There are $$3$$ students who participated in all three groups. Therefore, the number of students in the arts group is."}, {"key": "4801", "content": "Fangcao Primary School has 58 students learning piano, 43 students learning painting, and 37 students learning both piano and painting. How many students are learning only piano, and how many are learning only painting?"}, {"key": "4802", "content": "Among all the natural numbers from $$1\\tilde{\\ }120$$, the number of those that are neither multiples of $$3$$ nor multiples of $$5$$ is ."}, {"key": "4803", "content": "(1) A book has a total of $$60$$ pages, the page numbers from $$1\\sim60$$ use a total of number digits."}, {"key": "4804", "content": "(2) A book has a total of $$150$$ pages, and the page numbers from $$1\\sim150$$ use a total of digits."}, {"key": "4805", "content": "(1) The number of digits required to print the page numbers of a novel is $$105$$. The total number of pages in this book is ."}, {"key": "4806", "content": "(2) Assigning a code to a book used a total of $$225$$ numbers, this book has a total of pages."}, {"key": "4807", "content": "(1) If a book has a total of $$120$$ pages, the page numbers from $$1\\sim 120$$ use a total of several digits."}, {"key": "4808", "content": "(2) Numbering a book with page numbers, a total of $$333$$ numbers are used, this book has a total of pages."}, {"key": "4809", "content": "Arrange the natural numbers in ascending order without any gaps to form a large number: $$123456789101112\\cdots $$ What is the digit in the $$500$$th position from the left."}, {"key": "4810", "content": "A book has a total of $$520$$ pages, among the page numbers from $$1$$ to $$520$$, a total of $$0$$ digits were used."}, {"key": "4811", "content": "(2) When paginating a book, a total of $$41$$ \"$$6$$\" digits were used. This book has at least pages, and at most pages."}, {"key": "4812", "content": "A book has a total of $$500$$ pages, among which a number of pages contain the digit \u201c$$4$$\u201d."}, {"key": "4813", "content": "The original page numbers of a storybook used $$195$$ digits, and then $$15$$ pages were added, so the number of digits needed to be increased by."}, {"key": "4814", "content": "When printing a book, page numbers need to be assigned. A total of $$1992$$ digits are used in this book, and the book has pages that contain the digit \u201c$$2$$\u201d a total of times."}, {"key": "4815", "content": "(1) Sixteen basketball teams compete according to the following single-elimination tournament rules: divided into eight groups for head-to-head matches, determining eight teams to advance, then four teams... until the champion is determined. A total of matches were played."}, {"key": "4816", "content": "In a class, four students participate in a checkers competition, where each pair of students plays a match. The winner of each match earns $$2$$ points, a draw awards $$1$$ point to each, and the loser receives $$0$$ points. (3) It is known that students A, B, and C have scored $$3$$, $$4$$, and $$4$$ points respectively, with C having no draws, A having at least one win, and B having a draw. What is the score of student D?"}, {"key": "4817", "content": "In a Chinese chess competition, there are three possible outcomes: winning scores $$2$$ points, drawing scores $$1$$ point, and losing scores $$0$$ points. Now six people are participating in a round-robin tournament, and it is known that the scores of five people are respectively $$7$$, $$6$$, $$5$$, $$4$$, and $$3$$. Then, the score of the last person is points."}, {"key": "4818", "content": "Four football teams play a round-robin tournament, where every two teams will play against each other once. If a match is drawn, each team gets $$1$$ point, otherwise, the winning team gets $$3$$ points and the losing team gets $$0$$ points. (1) The total points of the four teams can be at least points, and at most points."}, {"key": "4819", "content": "Four students participate in a district Go competition, where each pair of players play a match. According to the rules, winning a match awards $$2$$ points, drawing awards $$1$$ point, and losing awards $$0$$ points. If each person ends up with a different total score, and the first-place winner does not win all their matches, then the maximum number of draws is."}, {"key": "4820", "content": "A school holds a volleyball competition with $$8$$ teams participating. If a single-elimination tournament system is used, a total of __ matches will be played. If a round-robin tournament system is used, a total of __ matches will be played."}, {"key": "4821", "content": "A, B, C, D, E five people participate in a table tennis competition, each pair competes in one match, with the rule that the winner gets 2 points, and the loser gets no points, no ties. It is known that the competition results are as follows: A and E are tied for first place; B is in third place; C and D are tied for fourth place. Calculate the score of B."}, {"key": "4822", "content": "Soccer teams $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ participate in a round-robin tournament (each pair of teams plays one match), where the winning team gets $$3$$ points, the losing team gets $$0$$ points, and in the event of a tie, both teams get $$1$$ point. If the total points for teams $$A$$, $$B$$, $$C$$, and $$D$$ are respectively $$1$$, $$4$$, $$7$$, and $$8$$, what is the maximum and minimum number of points team $$E$$ could have scored?"}, {"key": "4823", "content": "Fourteen basketball teams compete according to the rules of a single-elimination tournament, ultimately determining the champion. Please ask how many games were played in total. If the competition is conducted according to the rules of a round-robin tournament, please ask how many games were played in total."}, {"key": "4824", "content": "The sixth grade's six classes held a competition where each class competes against every other class once, with a win earning $$2$$ points, a draw earning $$1$$ point, and a loss earning $$0$$ points. After the competition, it was known that the champion, class 6-1, earned $$7$$ points and lost once, thus class 6-1 won $$3$$ matches."}, {"key": "4825", "content": "Four football teams play in a round-robin tournament, where each pair of teams plays one match. If a match is drawn, each team earns $$1$$ point; otherwise, the winning team earns $$3$$ points, and the losing team earns $$0$$ points. It is known that Teams A, B, and C have scored $$7$$ points, $$4$$ points, and $$4$$ points respectively. How many points does Team D have? How many draws are there in all the matches? ( )"}, {"key": "4826", "content": "Some oranges are distributed among several people, each person gets $$5$$ and there are $$10$$ left over; if the number of people triples, then each person gets $$2$$ and there are $$8$$ short. So there are $$100$$ oranges."}, {"key": "4827", "content": "Use a long rope to measure the depth of a well. If the rope is doubled, it is $$5$$ meters longer; if the rope is tripled, it is $$4$$ meters shorter. Find the length of the rope in meters and the depth of the well in meters. (Ignoring the length at the bending point, each fold length is considered equal)"}, {"key": "4828", "content": "There is a well without water, and its depth is measured using a rope. After folding the rope in half and letting it dangle to the bottom of the well, one end of the rope extends $$9$$ meters above the mouth of the well; after tri-folding the rope and letting it dangle to the bottom, one end of the rope extends $$2$$ meters above the mouth of the well. Thus, the length of the rope is meters, and the depth of the well is meters."}, {"key": "4829", "content": "Eddie goes from home to school, and he calculates: if he walks at $$80$$ meters per minute, he will arrive $$6$$ minutes before class starts; if he walks at $$50$$ meters per minute, he will be $$3$$ minutes late for class. Then, the distance from Eddie's home to the school is meters."}, {"key": "4830", "content": "Master Wang processed a batch of parts, processing 20 parts per day, and was able to finish 1 day ahead of schedule. After working for 4 days, due to technological improvements, he was able to process an additional 5 parts per day, and as a result, finished 3 days ahead of schedule. Question: How many parts were in this batch."}, {"key": "4831", "content": "Box A contains only 50-cent coins, Box B contains only 20-cent coins, the amount of money in Box A is \\$1.50 more than that in Box B, and Box B has 24 more coins than Box A. The total number of coins in boxes A and B together is."}, {"key": "4832", "content": "Master A and Master B need to process a batch of parts. If they process 40 parts per hour, they will finish 2 hours later than planned; if they process 35 parts per hour, then they will finish 3 hours later than planned. This batch of parts has a total of ."}, {"key": "4833", "content": "In a basketball team of five people, the average height of the four players is 182 cm. The fifth player is 8 cm shorter than the average height of the entire team. What is the height of this player in cm?"}, {"key": "4834", "content": "There are $$4$$ numbers, their average is $$32$$. The average of the first $$3$$ numbers is $$29$$, and the average of the last $$2$$ numbers is $$35$$. What is the third number ( )?"}, {"key": "4835", "content": "First input a number into the computer, it will perform the following operations according to the given instructions: if the input number is an even number, it will be divided by $$2$$; if the input number is an odd number, it will be increased by $$3$$. Such operation is carried out $$3$$ times, and the result is $$27$$. There are several original numbers that could lead to this outcome."}, {"key": "4836", "content": "There were $$15$$ kilograms of oil in each of the two barrels, A and B. After selling $$14$$ kilograms of oil, the salesperson redistributed the oil between the two barrels. First, he poured part of the oil from barrel A into barrel B, increasing the oil in barrel B by $$5$$ kilograms. Then, he poured part of the oil from barrel B back into barrel A, doubling the amount of oil in barrel A. At this point, the oil in barrel A was exactly $$7$$ times the amount of oil in barrel B. The question is how many kilograms of oil were sold from barrel A and barrel B originally."}, {"key": "4837", "content": "There are $$26$$ bricks, two brothers are competing to pick them up. The younger brother rushed ahead and had just arranged the bricks when the older brother arrived. Seeing that the younger brother had picked up too many, the older brother took half from the younger brother for himself. The younger brother thought he could manage, so again he took half from the older brother. The older brother felt he had taken too little, so the younger brother had to give the older brother $$5$$ more bricks, making the older brother pick up $$2$$ more bricks than the younger brother. How many bricks did the younger brother initially plan to pick up?"}, {"key": "4838", "content": "There are three piles of apples labeled A, B, and C, totaling $$96$$ apples. In the first move, the same number of apples as in pile B is taken from pile A and placed into pile B. In the second move, the same number of apples as in pile C is taken from pile B and placed into pile C. In the third move, the same number of apples as the remaining in pile A is taken from pile C and placed into pile A. At this point, the number of apples in the three piles is equal. Originally, pile A had apples, pile B had apples, and pile C had apples."}, {"key": "4839", "content": "$$A$$, $$B$$, and $$C$$ each had a different number of bricks. $$A$$ gave away part of his bricks to $$B$$ and $$C$$, doubling the number of bricks each of them had; then $$B$$ also gave away part of his bricks to $$A$$ and $$C$$, doubling the number of bricks each of them had; following that, $$C$$ also gave away part of his bricks to $$A$$ and $$B$$, doubling the number of bricks each of them had. At this point, all three people had $$48$$ bricks each. Calculate the original number of bricks $$A$$, $$B$$, and $$C$$ each had."}, {"key": "4840", "content": "While solving a subtraction problem, Eddie mistakenly wrote the units digit of the minuend as $$3$$ instead of $$5$$, the tens digit as $$6$$ instead of $$0$$, and the hundreds digit of the subtrahend as $$7$$ instead of $$2$$. As a result, the difference obtained was $$1994$$. What should the correct difference be?"}, {"key": "4841", "content": "At the beginning of the school term, students collected textbooks. Xiao Tang collected $$20$$ books, Xiao Li collected $$6$$ books, and Xiao Gang also collected some books, but the number was unknown. At this time, the teacher asked Xiao Tang to give $$4$$ books to Xiao Li, and gave some books to Xiao Gang as well, and then they each had the same number of books. So, how many books did Xiao Gang originally have?"}, {"key": "4842", "content": "Xiaomaohu mistakenly calculated \"$$\\square \\times (100+1)$$\" as \"$$\\square \\times 100+1$$\", resulting in a result that is $$6$$ less than the correct number. The correct number is ( )."}, {"key": "4843", "content": "First, write a two-digit number $$11$$, then write the sum of these two numbers $$2$$ at the right end of $$11$$, obtaining $$112$$. Next, write the sum of the last two digits $$1$$ and $$2$$, which is $$3$$, to get $$1123$$. Using the aforementioned method, we get a number with $$2018$$ digits $$112358134711\\ldots $$, then the $$2018$$th digit is."}, {"key": "4844", "content": "First write a two-digit number $$11$$, then write the sum of these two digits $$2$$ at the right end of $$11$$, getting $$112$$. Next, write the sum of the last two digits $$1$$ and $$2$$, which is $$3$$, to get $$1123$$. Using the method described above, we get a number with $$2018$$ digits $$112358134711\\ldots $$. The sum of the digits of this number is."}, {"key": "4845", "content": "Observe the following equations, answer the question: $${{2}^{1}}=2$$$${{2}^{2}}=2\\times 2$$$${{2}^{3}}=2\\times 2\\times 2$$$${{2}^{4}}=2\\times 2\\times 2\\times 2$$$${{2}^{5}}=2\\times 2\\times 2\\times 2\\times 2$$......$${{2}^{10}}$$ is."}, {"key": "4846", "content": "Observe the following equations and answer the question: $${{2}^{1}}=2$$$${{2}^{2}}=2\\times 2$$$${{2}^{3}}=2\\times 2\\times 2$$$${{2}^{4}}=2\\times 2\\times 2\\times 2$$$${{2}^{5}}=2\\times 2\\times 2\\times 2\\times 2$$......$${{2}^{100}}$$'s units digit is."}, {"key": "4847", "content": "Observe the following equations and answer the question: $${{2}^{1}}=2$$$${{2}^{2}}=2\\times 2$$$${{2}^{3}}=2\\times 2\\times 2$$$${{2}^{4}}=2\\times 2\\times 2\\times 2$$$${{2}^{5}}=2\\times 2\\times 2\\times 2\\times 2$$\u2026\u2026$${{2}^{2018}}$$'s units digit is ."}, {"key": "4848", "content": "Find the unit digit of $${{1}^{100}}+{{2}^{100}}+{{3}^{100}}+{{4}^{100}}+{{5}^{100}}+{{6}^{100}}+{{7}^{100}}+{{8}^{100}}+{{9}^{100}}$$."}, {"key": "4849", "content": "$$2020$$ year $$10$$ month $$7$$ day is Wednesday. $$2021$$ year $$1$$ month $$1$$ day is a weekday."}, {"key": "4850", "content": "$$2020$$ year $$10$$ month $$7$$ day is Wednesday. $$2021$$ year $$5$$ month $$1$$ day is Saturday"}, {"key": "4851", "content": "$$2020$$ year $$10$$ month $$7$$ day is Wednesday. $$2024$$ year $$5$$ month $$1$$ day is a weekday."}, {"key": "4852", "content": "$$2012$$ year $$1$$ month $$1$$ day is Sunday, then $$2020$$ year $$5$$ month $$1$$ day is a week"}, {"key": "4853", "content": "October 1, 2019, is the 70th National Day, which happens to be a Tuesday. So, what day of the week was October 1, 1949?"}, {"key": "4854", "content": "Complete the following questions: A month has $$31$$ days, with $$4$$ Tuesdays and $$4$$ Fridays. What day of the week is the $$20$$th of this month?"}, {"key": "4855", "content": "Xiaoxin goes to exercise. After the first exercise, he goes again after $$1$$ day. After the second exercise, he waits for $$2$$ days before going again. After the third exercise, he waits for $$3$$ days before going again. If Xiaoxin's first exercise session was on a Monday, according to the pattern above, the $$10$$th time Xiaoxin goes to exercise would be on a ____."}, {"key": "4856", "content": "In 2018, students lined up one after another from front to back and counted off according to the following rules: If the number said by a student is a single-digit, then the next student will report the sum of this number and $$9$$; if the number said by a student is a two-digit number, then the next student will report the sum of the units place of this number and $$6$$. Let the first student report $$1$$, then the number reported by the last student is."}, {"key": "4857", "content": "As shown in the chart, the text in each row repeats in a cycle: the first row repeats the four characters of \"Riemann hypothesis\", the second row repeats the five characters of \"Poincar\u00e9 conjecture\", and the third row repeats the six characters of \"Goldbach's conjecture\". Which three characters are in column $$200$$ from top to bottom, respectively?\n question_4857-image_0"}, {"key": "4858", "content": "$$2020$$ year $$4$$ month $$1$$ day is Wednesday, $$2019$$ year $$8$$ month $$20$$ day is week."}, {"key": "4859", "content": "$$100$$ students line up from left to right and then count off in a pattern from left to right: have the first student say $$1$$, then starting from the second student, each student multiplies the number reported by the previous student by $$7$$, and reports the last digit of the product. So, what number does the $$100$$th student report."}, {"key": "4860", "content": "In the zoo, there are $$55$$ ostriches and zebras living together on the same grassland, the number of legs of ostriches is $$14$$ more than that of zebras, then there are zebras, and there are ostriches."}, {"key": "4861", "content": "Answer the following question: The distance between places $$A$$ and $$B$$ is $$4800$$ meters. If person A walks $$60$$ meters per minute, how many minutes does it take for A to walk from $$A$$ to $$B$$?"}, {"key": "4862", "content": "Answer the following question: Two cities $$A$$ and $$B$$ are $$300$$ kilometers apart, a car initially planned to travel from city $$A$$ to city $$B$$ in $$6$$ hours, then the car should travel an average of kilometers per hour."}, {"key": "4863", "content": "Solve the following questions: A car travels $$150$$ kilometers in $$3$$ hours, according to this speed, how many hours are needed to travel $$500$$ kilometers."}, {"key": "4864", "content": "Da Kuan walks 20 meters per minute. According to this speed, it takes him minutes to walk 100 meters."}, {"key": "4865", "content": "Dakuan walks 20 meters per minute. If Dakuan rushes 300 meters in 3 minutes, then the average speed of rushing this distance is meters per minute."}, {"key": "4866", "content": "Walking at a wide pace covers $$20$$ meters per minute. $$3$$ minutes can cover meters."}, {"key": "4867", "content": "Eddie and Vi set off from the base to have fun at Mason Forest Park. When they went, the speed of the car was $$80$$ kilometers per hour, and it took $$3$$ hours to reach the destination. If the speed of the car on the way back is $$120$$ kilometers per hour, then how many hours will it take to return to the base after departing from the forest park."}, {"key": "4868", "content": "Eddie and Viola set out from the base to go to Mason Forest Park for a trip. On the way there, the speed of the car was $$80$$ km/h, and it took $$3$$ hours to reach the destination. On the way back, it started to drizzle, and it took $$6$$ hours for the car to return to the base. The speed of the car on the way back was km/h."}, {"key": "4869", "content": "Location A is $$3000$$ meters away from location B. The doctor plans to cycle from location A to B in $$20$$ minutes, but just before leaving, the bicycle broke down, causing a $$5$$ minute delay. To arrive at location B at the originally planned time, the doctor should cycle at a speed of meters per minute."}, {"key": "4870", "content": "Locations A and B are $$200$$ kilometers apart. Wei Er first walked $$120$$ kilometers in $$15$$ hours, rested for a while, and then continued at the same pace towards location B. How many more hours are needed to reach location B?"}, {"key": "4871", "content": "Complete the following questions as required. If 5 workers make 80 parts in 2 hours, then 15 people can make parts in 6 hours."}, {"key": "4872", "content": "Complete the following questions as required. If $$5$$ workers can manufacture $$80$$ parts in $$2$$ hours, then $$4$$ people can manufacture $$7$$ hours of parts."}, {"key": "4873", "content": "Complete the following questions as required. $$3$$ monkeys eat $$40$$ peaches in $$2$$ days, so $$8$$ monkeys eat $$9$$ days."}, {"key": "4874", "content": "The engineering team originally planned to repair a 4800 meters long road with 60 people in 5 days. However, at the start of work, an additional 40 people were added, and each person repaired 8 meters more than originally planned per day. Therefore, the road can actually be repaired in days."}, {"key": "4875", "content": "The aquarium prepared $$230$$ kilograms of fish for the $$8$$ walruses in the aquarium. In the first two days, the $$8$$ walruses ate a total of $$80$$ kilograms of fish. Two days later, $$2$$ of the walruses were transported away. If each walrus eats the same amount of fish every day, then the remaining fish can still feed the walruses left for days."}, {"key": "4876", "content": "$$5$$ workers need to process $$735$$ parts, and $$135$$ parts have been processed in the first $$2$$ days. It is known that $$1$$ worker took a day off for personal reasons during these $$2$$ days. If each worker processes the same number of parts per day, and no more days off will be taken, how many more days are needed to complete the task."}, {"key": "4877", "content": "A factory has to finish assembling a batch of recorders, having already completed $$635$$ units. If they increase the assembly by $$2$$ units per day, they would need $$40$$ more days to finish, with the final day seeing a reduction of $$5$$ units in assembly. If they continue at the original pace, it would require an additional $$3$$ days of work. The workshop needs to assemble a total of recorders."}, {"key": "4878", "content": "It is known that $$3$$ model workers and $$6$$ regular workers can produce $$360$$ parts in $$4$$ hours. Now, there is a batch of production tasks that requires $$6$$ model workers and $$12$$ regular workers to work for $$10$$ hours to complete. If after working for $$3$$ hours, $$1$$ more model worker and $$2$$ more regular workers join, the task can be finished ahead of schedule by hours."}, {"key": "4879", "content": "A long-distance ship has a total of $$30$$ sailors on board, and the fresh water on the ship can last all the crew for $$40$$ days. $$10$$ days after leaving the port, the ship rescued $$15$$ foreign sailors who were in distress on the high seas. Assuming each person uses the same amount of fresh water each day, the remaining fresh water can last for more days for everyone on the ship."}, {"key": "4880", "content": "There are a total of rectangles (including squares) in the picture. \n question_4880-image_0"}, {"key": "4881", "content": "$$20$$ nails form a $$4\\times 5$$ dot matrix. Using $$4$$ nails as vertices to form a square with a rubber band, you can form different squares. question_4881-image_0"}, {"key": "4882", "content": "Please identify the pattern of each term in the following sequence and fill in the blank: (2) The first term is $$2$$, the second term is $$4$$, the third term is $$8$$, the fourth term is $$16$$, $$ \\cdots $$, then the $$n$$th term is."}, {"key": "4883", "content": "As shown in the diagram, quadrilateral $$ABCD$$ is a right-angled trapezoid, which is divided into two identical small right-angled trapezoids and a parallelogram. It is known that the length of $$CD$$ is $$5$$, the length of $$AB$$ is $$15$$, and the area of the trapezoid $$ABCD$$ is four times the area of the parallelogram $$DCFM$$. question_4883-image_0"}, {"key": "4884", "content": "An ant is at point $$A$$ on a square grid paper, and it wants to go to point $$B$$ along the grid lines, but it doesn't know which route is the shortest. Kids, can you find a different shortest route for it.\n question_4884-image_0"}, {"key": "4885", "content": "A little bee goes through the beehive rooms, it is stipulated that entry is only allowed from a room with a smaller number to a room with a larger number. Therefore, there are methods for the little bee to go from room $$1$$ to room $$7$$.\n question_4885-image_0"}, {"key": "4886", "content": "The phrase \"I love Xueersi\" in the below image can be read in a different way.\n question_4886-image_0"}, {"key": "4887", "content": "As shown in the diagram, starting from point $$A$$ to point $$B$$, how many different shortest routes are there in total?\n question_4887-image_0"}, {"key": "4888", "content": "As shown in the diagram, there is a chess piece that needs to move from the bottom-left corner to the top-right corner, taking steps only to the right, upwards, or diagonally to the upper right, with a total of different methods of doing so. question_4888-image_0"}, {"key": "4889", "content": "A bee leaves from point $$A$$ and returns to point $$B$$. It can only move to the adjacent hive on its right side at any time and is not allowed to move backward. There are a total of methods to return home. question_4889-image_0"}, {"key": "4890", "content": "$$A$$ and $$B$$ participate in a chess match, with no draws allowed. The first to win three more games than the other wins the match. If after $$11$$ games $$A$$ wins with a score of $$7$$ wins to $$4$$ losses, then there are a total of kinds for the win-loss arrangements of these $$11$$ games. (For example, 'win-lose-win-lose-win-lose-win-lose-win-win-win' is one kind of win-loss arrangement)"}, {"key": "4891", "content": "A seven-digit number $$\\overline{274a815}$$ can be divisible by $$11$$, $$a$$ could be."}, {"key": "4892", "content": "With the four numbers $$2$$, $$3$$, $$5$$, $$7$$, many four-digit numbers without repeated digits can be formed. Among these numbers, there are two numbers that are multiples of $$25$$, and the difference between these two numbers is $$450$$. The sum of these two four-digit numbers is."}, {"key": "4893", "content": "A six-digit number $$\\overline{4067\\square \\square }$$ has all different digits and is divisible by $$25$$. Then this six-digit number is."}, {"key": "4894", "content": "For a natural number $$N$$, it is called a 'disruptive number' if it has the following property: adding it to the right end of any natural number, the new number formed cannot be divided by $$N+1$$. The question is: there are a total of how many disruptive numbers not greater than $$10$$."}, {"key": "4895", "content": "For $$\\overline{26abcd2}$$ to be divisible by $$36$$, and for the quotient to be the smallest, the sum of $$a$$, $$b$$, $$c$$, and $$d$$ is."}, {"key": "4896", "content": "From the nine digits $$1$$ to $$9$$, choose $$5$$ digits to form a five-digit number, such that it is a multiple of $$9$$. What is the largest possible five-digit number?"}, {"key": "4897", "content": "Using the nine digits $$1\uff5e9$$ to form three three-digit numbers (each digit must be used), and each number is a multiple of $$4$$. The smallest of these three three-digit numbers is at most."}, {"key": "4898", "content": "A four-digit number $$\\overline{2\\square 9\\square}$$ can be divided by both $$3$$ and $$5$$ at the same time, there are a total of such four-digit numbers that meet the requirements."}, {"key": "4899", "content": "There is a series of numbers arranged in the order $$11428571142857114\\cdots \\cdots $$, totaling $$100$$ numbers. (1) The number of times $$1$$ appears is . (2) The sum of these numbers is ."}, {"key": "4900", "content": "Third-grade students line up for a physical examination, they are arranged in the order of $$3$$ males followed by $$3$$ females successively, this arrangement presents a cyclical phenomenon, then the cycle is."}, {"key": "4901", "content": "As shown in the figure, among such a sequence of figures, the 24th figure is ( ).\n question_4901-image_0"}, {"key": "4902", "content": "The result of $$23857+2359$$ is odd or even ( )."}, {"key": "4903", "content": "The product of an odd number and an even number is ()."}, {"key": "4904", "content": "Find the pattern and fill in the blanks. $$37\\times 3=111$$$$37\\times 6=222$$$$37\\times 9=$$$$37\\times 27=$$"}, {"key": "4905", "content": "Fill in the blanks. (1) The perimeter of a square is $$36$$ meters, the side length of this square is meters, and the area of this square is square meters; (2) The perimeter of a rectangle is $$40$$ meters, the length is $$12$$ meters, the area of this rectangle is square meters."}, {"key": "4906", "content": "Farm A harvested 80 million tons more sorghum than Farm B, and the harvest of Farm A was 5 times that of Farm B. Thus, Farm A harvested __ million tons of sorghum, and Farm B harvested __ million tons of sorghum. question_4906-image_0"}, {"key": "4907", "content": "Farm A harvested 50 million tons of corn more than Farm B, and the corn harvested by Farm A is 20 million tons more than 3 times that of Farm B. Thus, Farm A harvested million tons of corn, and Farm B harvested million tons of corn. question_4907-image_0 \u200b"}, {"key": "4908", "content": "Farm A harvested 50 million tons more wheat than Farm B, and the wheat harvested by Farm A was 10 million tons less than 4 times that of Farm B. Therefore, Farm A harvested million tons of wheat, and Farm B harvested million tons of wheat. question_4908-image_0"}, {"key": "4909", "content": "In the competition arena, the number of boys and girls was the same. Later, the total number of girls decreased by $$10$$ people, while the total number of boys increased by $$30$$ people. At this point, the number of boys was exactly $$3$$ times the number of girls. So, how many boys and girls were there originally?"}, {"key": "4910", "content": "Among three people, A, B, and C, A is 12 years older than B, C is 15 years older than A, and C's age is 4 times B's age. The ages of A, B, and C are as follows: A years old, B years old, C years old."}, {"key": "4911", "content": "Eddie and Elgin $$PK$$, Elgin's energy value is $$62$$, Eddie's energy value is $$38$$. After the first round, both consumed the same energy value, Elgin's remaining energy value is 3 times Eddie's remaining energy value, then Elgin's remaining energy value, Eddie's remaining energy value. question_4911-image_0"}, {"key": "4912", "content": "In the orchard, there are $$200$$ more pear trees than apple trees, and the number of pear trees is exactly $$6$$ times the number of apple trees. Question: How many pear trees are there in the orchard now?"}, {"key": "4913", "content": "Eddy has $$30$$ more apples than Vivian, and the number of Eddy's apples is $$6$$ times that of Vivian's. How many apples does Vivian have?"}, {"key": "4914", "content": "There are two pieces of iron wire, one is $$20$$ cm long and the other is $$40$$ cm long. These two pieces are welded together into a long iron wire of $$50$$ cm. Thus, the length of the overlapping welded part in the middle is in cm."}, {"key": "4915", "content": "The school organized a picking activity, with a total of $$46$$ people participating. $$18$$ people only picked cherries, $$7$$ people picked both cherries and apricots, $$6$$ people picked neither cherries nor apricots, and there were people who only picked apricots."}, {"key": "4916", "content": "There are a total of $$12$$ birds on three trees. $$3$$ birds from the first tree flew to the second tree, and $$2$$ birds from the second tree flew to the third tree, by then the number of birds on each of the three trees was the same. Can you calculate how many birds were originally on each tree?\n question_4916-image_0 \nThe first tree originally had birds.\nThe second tree originally had birds.\nThe third tree originally had birds."}, {"key": "4917", "content": "In the decimal $$5.0893$$, $$5$$ is in the ones place, indicating $$5$$ units of $$1$$; $$8$$ is in the tens place, indicating; $$9$$ is in the place, indicating; $$3$$ is in the place, indicating."}, {"key": "4918", "content": "$$4.25$$ is composed of $$1$$, $$0.1$$, and $$0.01$$."}, {"key": "4919", "content": "$$x+x=$$ represents ( )."}, {"key": "4920", "content": "Can be represented by the letter $$n$$ ( )\uff0e"}, {"key": "4921", "content": "The quality of the nutritional solution retained in the second phase experiment is as follows (unit: grams): $$5$$, $$11$$, $$17$$, $$23$$, $$29$$, $$\\cdots $$, then the quality retained on the $$40$$th day is grams."}, {"key": "4922", "content": "As shown in the diagram, there are several different shortest paths from point $$A$$ to point $$B$$ along the line segment. question_4922-image_0"}, {"key": "4923", "content": "Wei wants to get from home to Xueersi, please count the total number of different shortest paths for Wei. question_4923-image_0"}, {"key": "4924", "content": "Answer the following question: As shown in the figure, there is a shortest route from $$A$$ to $$B$$ along the line segment, without passing through $$C$$. question_4924-image_0"}, {"key": "4925", "content": "Answer the following question: As shown in the diagram, there is a shortest path from $$A$$ passing through $$C$$ to $$B$$ along the line segment. question_4925-image_0"}, {"key": "4926", "content": "It's raining, and the little ant needs to quickly return home from point $$B$$ to point $$C$$. If it can only follow the paths along the grid lines, there are several different shortest routes to choose from. question_4926-image_0"}, {"key": "4927", "content": "The Monkey King distributes peaches to the little monkeys. If each little monkey gets $$4$$ peaches, there will be $$5$$ peaches left; if each little monkey gets $$5$$ peaches, then the peaches are just fully distributed. So, in total, there are how many little monkeys. question_4927-image_0"}, {"key": "4928", "content": "Splitting $$12$$ identical watermelons into $$3$$ piles with different amounts, there are several different ways to do this\uff0e question_4928-image_0"}, {"key": "4929", "content": "The prizes prepared by the teacher for the fun sports meet are lollipops. The teacher wants to divide $$8$$ identical lollipops into $$3$$ piles, there are a total of different ways."}, {"key": "4930", "content": "Divide all $$9$$ identical candies among Eddie, Vi, and Kuan, with each person getting at least two candies, then there are a total of ways to distribute them. question_4930-image_0"}, {"key": "4931", "content": "Car A and car B originally had a total of $$43$$ passengers. After arriving at a certain place, $$5$$ people got off car A and $$2$$ people got on car B. At this point, the number of people in car A was exactly $$3$$ times larger than the number in car B. The original number of passengers in car B; the original number of passengers in car A. question_4931-image_0"}, {"key": "4932", "content": "There are two stations in a certain town, east and west. The east station has $$84$$ buses, and the west station has $$56$$ buses. To make the number of buses at the east station four times the number at the west station, the west station needs to transfer buses to the east station. question_4932-image_0"}, {"key": "4933", "content": "Initially, Class C had 6 times more books than Class D. Now, after giving 20 books to Class D, Class C has 5 books less than Class D. Originally, Class C had books, and Class D had books."}, {"key": "4934", "content": "As shown in the figure, in the parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$BC=12$$ cm, $$AE=6$$ cm, $$CD=9$$ cm. Then segment $$AF$$ is __ cm. question_4934-image_0"}, {"key": "4935", "content": "As shown in the picture, this is a parallelogram vegetable garden, and its area is in square meters. question_4935-image_0"}, {"key": "4936", "content": "Dividing two numbers, the quotient is $$20$$, and the remainder is $$8$$. Therefore, the smallest possible divisor is, and the smallest possible dividend is."}, {"key": "4937", "content": "Wei'er is $$7$$ years old this year, and her mother is $$35$$ years old. When Wei'er was certain age, her mother's age was exactly $$3$$ times that of Wei'er."}, {"key": "4938", "content": "The figure below has a straight line and several intersection points. question_4938-image_0"}, {"key": "4939", "content": "If a straight line is added in the figure, additional intersections can be created. question_4939-image_0"}, {"key": "4940", "content": "The figure below has a straight line with several intersections question_4940-image_0"}, {"key": "4941", "content": "After the New Year, school started again, and some students had to buy new uniforms. Wei Er collected the uniform fees from $$9$$ students (each person paid the same amount) and gave it to the teacher. The teacher gave Wei Er a note, which read \"Paid $$\\overline{2\\square 38}$$ yuan for the uniform fees\", where a drop of ink smeared the number in the square to the point it was unreadable. Edi quickly figured out the number in the square. Smart kids, what is the number."}, {"key": "4942", "content": "$72\\div\\left( 6\\times5\\right)\\times5$ simplification is ( )."}, {"key": "4943", "content": "The simplified calculation for $700\\div4\\div25$ is ( )."}, {"key": "4944", "content": "The side length of a square is $$3$$ cm, the area of this square is square centimeters; the length of a rectangle is $$6$$ cm, and the width is $$4$$ cm, the area of this rectangle is square centimeters."}, {"key": "4945", "content": "A class has a total of $$42$$ people, $$21$$ people participated in the school-organized music activity, and $$16$$ people participated in the sports activity. There are $$6$$ people who did not participate in either activity. Therefore, the number of people who participated in both activities is ."}, {"key": "4946", "content": "What number is represented by the abacus? ( )\uff0e question_4946-image_0"}, {"key": "4947", "content": "In the decimal $$5.0893$$, $$5$$ is in the ones place, indicating $$5$$ ones; $$8$$ is in the tenths place, indicating tenths; $$9$$ is in the hundredths place, indicating hundredths; $$3$$ is in the thousandths place, indicating thousandths."}, {"key": "4948", "content": "Three years later, the young elephant will turn $$18$$ years old. The adult elephant says to the young elephant: 'When you are as old as I am, I will be $$61$$ years old.' How old is the adult elephant this year?"}, {"key": "4949", "content": "Volunteers lined up to form a hollow square for a group photo, with a total of $$52$$ people on the outermost layer, consisting of $$4$$ layers, totaling a number of volunteers."}, {"key": "4950", "content": "A group of fourth-grade students at a certain school are arranged in a square formation, with the number of people on the outermost layer being $$40$$. How many people are there on each side of the outermost layer, and how many people are in the entire square formation?"}, {"key": "4951", "content": "Fill in \"$$+$$\", \"$$-$$\", or \"$$\\left( {~~~~} \\right)$$\" to make the equation valid. $$2$$$$~~~~4$$$$~~~~6$$$$~~~~8=8$$."}, {"key": "4952", "content": "Wei Er wants to go from home to Xueersi, please help Wei Er count, there are a total of different shortest routes. question_4952-image_0"}, {"key": "4953", "content": "Please use the four numbers $$2$$, $$3$$, $$4$$, $$6$$, fill in $$+$$, $$-$$, $$\\times$$, $$\\div$$, and () between them arbitrarily, and each number can only be used once, to make their result equal to $$24$$. 4623=24"}, {"key": "4954", "content": "Choose the appropriate \"$$+$$, $$-$$, $$\\times$$, $$\\div$$\" to fill in between each pair of numbers, so that the following equation holds. $$3$$$$3$$$$3$$$$3=2$$"}, {"key": "4955", "content": "Fill in the appropriate operators and parentheses on the left side of the equation below. 815=35"}, {"key": "4956", "content": "Autumn has arrived, and the little white rabbit has harvested a basket of radishes. Based on its plan of consumption, it calculated that if it eats 4 radishes per day, there will be 48 radishes left over; if it eats 6 per day, then there are 8 left over. So, how many radishes did the little white rabbit buy?"}, {"key": "4957", "content": "Distribute $$15$$ identical balls into three piles, with each pile having at least $$3$$ balls. There are a number of ways to do this."}, {"key": "4958", "content": "Xiaobai wants to place $$18$$ identical car models on a $$3$$-tier shelf, with at least $$5$$ on each tier, there are various different ways to do this."}, {"key": "4959", "content": "Distribute $$8$$ tanks to three kids: Xiao Xiao, Zhong Zhong, and Da Da, with each receiving at least one tank. There is a certain method."}, {"key": "4960", "content": "The prize prepared by the teacher for the fun sports day is lollipops, with $$8$$ identical lollipops to be divided into $$3$$ piles, there are a total of different ways to divide them."}, {"key": "4961", "content": "Using $$12$$ squares with a side length of $$2$$ centimeters to form a rectangle, the perimeter of this rectangle could be centimeters, centimeters, or centimeters."}, {"key": "4962", "content": "Xiao Hong and Xiao Lan have a total of $$80$$ stamps. If Xiao Hong adds another $$10$$ stamps and Xiao Lan takes out $$6$$ stamps, then the number of Xiao Hong's stamps will be $$3$$ times that of Xiao Lan's. How many stamps does Xiao Hong have now?"}, {"key": "4963", "content": "As shown in the picture, a $$5 \\times 5$$ grid is divided into five sections; you are to fill in each cell with one of the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, so that each row, each column, and each diagonal line has five distinct numbers, and the sum of numbers in each section is equal.$$ Now, two cells have been filled with $$1$$ and $$2$$ respectively, please fill in the other cells with appropriate numbers, then $$\\overline{ABCDE}$$ is.\n question_4963-image_0"}, {"key": "4964", "content": "In the given $$5\\times5$$ grid, fill in the letters $$ABCD$$ with the requirement that each of the four letters appears exactly once in every row and column: If a letter is marked on the left side of a row, it represents the first letter to appear in that row; if a letter is marked on the right side of a row, it represents the last letter to appear in that row; similarly, if a letter is marked at the top (or bottom) of a column, it represents the first (or last) letter to appear in that column. Then, in the second row from left to right, $$B$$ is the ____th to appear. question_4964-image_0"}, {"key": "4965", "content": "Fill in the blanks with numbers $$1-6$$, so that each snowflake and the six cells in three directions do not have repeated numbers. The following left image is a complete example. Please fill in the numbers in the blanks of the right image, then the four-digit number $$\\overline{ABCD}$$ represented by the four English letters in the image is.\n question_4965-image_0"}, {"key": "4966", "content": "Fill in each square with a number from $$1$$ to $$6$$ such that the numbers in each row and column are all different. The number on the right represents the sum of the three numbers formed by the first three digits separated by a thick line, the middle two digits, and the last single digit. What is the five-digit number $$\\overline{ABCDE}=$$.\n question_4966-image_0"}, {"key": "4967", "content": "Please fill in each cell of the $$5\\times 5$$ table below with one of $$1$$, $$2$$, $$3$$, $$4$$, or $$5$$, ensuring that the five numbers filled in each row, each column, and each diagonal are all different, and the number in cell $${A}$$ is greater than the number in cell $${B}$$, the number in $${B}$$ is greater than the number in $${C}$$, the number in $${C}$$ is greater than the number in $${D}$$, the number in $${E}$$ is greater than the number in $${F}$$, and the number in $${G}$$ is greater than the number in $${H}$$. Thus, what are the five numbers from left to right in the second row.\n question_4967-image_0"}, {"key": "4968", "content": "There is a quadrangle courtyard that happens to be a square with a side length of $$10$$ meters, as shown in the figure below. There is a path in the courtyard with a width of $$2$$ meters, as shown in the shaded part of the figure below. Calculate the area of the unshaded part in square meters. question_4968-image_0"}, {"key": "4969", "content": "As shown in the figure, there is a square vegetable garden with two paths each of width $$1$$ meter. It is known that the area of the shaded part is $$35$$ square meters, what is the area of the vegetable garden (blank part) in square meters? question_4969-image_0"}, {"key": "4970", "content": "As shown in the figure, a rectangle is divided into $$6$$ smaller rectangles (the length and width of each rectangle are integers), among which the areas of $$4$$ small rectangles are shown in the figure (unit: square centimeters), then the area represented by $$B$$ is square centimeters. question_4970-image_0"}, {"key": "4971", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, one can form different three-digit numbers with no repeating digits."}, {"key": "4972", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, (1) a different three-digit number can be formed."}, {"key": "4973", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$ (3), you can form different four-digit numbers with non-repeating digits."}, {"key": "4974", "content": "The figure below shows a deformed mushroom, which is divided into six areas. Now you need to color it with four different colors, requiring that two adjacent areas (two areas with a common side are considered adjacent) are colored differently. If colors can be reused, then there are a total of different coloring methods. question_4974-image_0"}, {"key": "4975", "content": "The children want to use four colors (red, green, yellow, and blue) to color the seven regions (head, body, and wings) on the little bee in the picture. Each region should be colored with one color, and adjacent regions sharing a common edge should be colored differently. Thus, there are several different ways to color it. question_4975-image_0"}, {"key": "4976", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$ to form a three-digit even number without repeating digits."}, {"key": "4977", "content": "Calculate: $$ (26\\div 25)\\times (27\\div 17)\\times (25\\div 9)\\times (17\\div 39)=$$."}, {"key": "4978", "content": "Calculate. $$\\left( 18000-72 \\right)\\div 9=$$."}, {"key": "4979", "content": "Calculate: $$25\\div 4+25\\div 6+35\\div 4+35\\div 6=$$."}, {"key": "4980", "content": "Calculate the following problems. $$1\\div 3+2\\div 6+3\\div 9+4\\div 12+5\\div 15+6\\div 18=$$."}, {"key": "4981", "content": "For any two numbers $$P$$, $$Q$$, it is defined that $$P\\Delta Q=\\left( P\\times Q \\right)\\div 4$$. For example: $$2\\Delta 8=\\left( 2\\times 8 \\right)\\div 4=4$$. (1) If $$x\\Delta \\left( 8\\Delta 5 \\right)=10$$, the value of $$x$$ is ."}, {"key": "4982", "content": "For any two numbers $$P$$, $$Q$$, it is defined that $$P\\Delta Q=\\left( P\\times Q \\right)\\div 4$$. For example: $$2\\Delta 8=\\left( 2\\times 8 \\right)\\div 4=4$$. (2) If $$14\\Delta (10\\Delta y)=105$$, the value of $$y$$ is."}, {"key": "4983", "content": "Calculate: $$7+11+15+\\cdots +91+95=$$."}, {"key": "4984", "content": "With $$3$$ matches of equal length, arrange one equilateral triangle, and using such equilateral triangles, pave a larger equilateral triangle as shown in the figure. If the base of this larger equilateral triangle requires $$10$$ matches, then in total, how many matches are needed. question_4984-image_0"}, {"key": "4985", "content": "Please answer the following question: Using $$210$$ pieces to form a solid regular triangular formation, how many layers does this triangle have?"}, {"key": "4986", "content": "At the sports meet, the teachers performed a program together, forming a hollow regular hexagonal array, similar to the array shown in the diagram below. There are a total of $$8$$ layers from the outside to the inside, with two layers of sixth grade teachers, two layers of fifth grade teachers, two layers of fourth grade teachers, and two layers of third grade teachers. It is known that $$126$$ sixth grade teachers participated in the performance, please answer: (2) How many people are there in the array now. question_4986-image_0"}, {"key": "4987", "content": "The diagram below shows the schematic of the roads between five villages: A, B, C, D, and E. The numbers in $$\\bigcirc$$ represent the number of students in each village who need to go to school, and the numbers on the roads represent the distances between two villages (unit: kilometers). Now, one of the five villages needs to be chosen for the construction of an elementary school. In order to minimize the total distance all students have to travel to school, the elementary school should be built in the village of.\n question_4987-image_0"}, {"key": "4988", "content": "On a highway, there is a warehouse every $$10$$ kilometers (as shown in the figure), with a total of five warehouses. The numbers in the figure indicate the weight of the goods stored in each warehouse. Now, if all the goods need to be gathered and stored in one warehouse, and transporting every ton of goods for $$1$$ kilometer costs $$1$$ yuan, then the minimum transportation cost to gather the goods in one warehouse, the least cost is in yuan. question_4988-image_0"}, {"key": "4989", "content": "At the New Year's party, a total of $$90$$ people participated in the performances of three programs: dancing, choir, and playing instruments. If the number of people who only participated in dancing was $$3$$ times the number of people who only participated in the choir; the number of people who only participated in playing instruments was $$4$$ more than those who participated in both playing instruments and dancing but not in choir; $$50$$ people did not participate in the choir; $$10$$ people participated in both dancing and choir but not in playing instruments; $$40$$ people participated in playing instruments; then, the number of people who participated in both playing instruments and dancing but not in choir is."}, {"key": "4990", "content": "Eddie and Dengdeng had a math problem-solving competition. They agreed that for each correct answer, they would earn $$20$$ points and for each unanswered or wrong answer, they would lose $$12$$ points. Each solved $$10$$ questions and together they scored a total of $$208$$ points. It is also known that Eddie scored $$64$$ points more than Dengdeng. In this case, how many questions did Dengdeng answer correctly?"}, {"key": "4991", "content": "The cage contains $$21$$ crickets and $$30$$ grasshoppers. Every time the red-haired magician performs a magic trick, he turns $$2$$ grasshoppers into $$1$$ cricket; every time the green-haired magician performs a magic trick, he turns $$5$$ crickets into $$2$$ grasshoppers. After both magicians have performed a total of $$15$$ magic tricks, there are only grasshoppers left in the cage, with no crickets. At this time, there are $$24$$ grasshoppers."}, {"key": "4992", "content": "In a cage with both chickens and rabbits, the number of rabbits is three times that of chickens, with a total of 140 legs. Then, there are chickens and rabbits."}, {"key": "4993", "content": "Buying some ice creams at $$4$$ dollars and $$8$$ dollars each, spending a total of $$680$$ dollars. It is known that there are $$40$$ more $$8$$ dollar ice creams than $$4$$ dollar ice creams, then for the two types of ice creams, there are pieces of $$4$$ dollars and pieces of $$8$$ dollars."}, {"key": "4994", "content": "Chickens and rabbits are in the same cage, there are $$40$$ in total. It is known that the number of chicken legs is twice the number of rabbit legs. Therefore, there are chickens, and rabbits."}, {"key": "4995", "content": "Chickens and rabbits are kept in the same cage, with a total of $$107$$ chickens and rabbits combined. The number of rabbit legs is $$56$$ more than the number of chicken legs. How many chickens and rabbits are there respectively?"}, {"key": "4996", "content": "A certain school used $$16$$ buses for a spring outing (all fully seated), with each large bus seating $$60$$ people, and each small bus seating $$20$$ people. There were $$560$$ more people in large buses than in small buses. Calculate the number of small buses."}, {"key": "4997", "content": "Initially, there were $$84$$ legs in total with both chickens and rabbits. After swapping all chickens with rabbits and all rabbits with chickens, there are now $$126$$ legs in total. How many chickens and rabbits were there originally?"}, {"key": "4998", "content": "An octopus-like yaksha with eight arms and one head, Nezha with three heads and six arms, both competing fiercely, without a clear winner, engaging in conflict. Thirty-six heads in total are mobilized, with one hundred and eight hands chaotically clashing. Onlookers nearby ask earnestly, how many are there of the yaksha and Nezha. (Note: In ancient Chinese, one hundred and eight specifically refers to the current one hundred and eight)"}, {"key": "4999", "content": "There are currently $$12$$ matchsticks, used for laying out numbers, and exactly all are used.$$.$$ The largest three-digit number that can be formed is, and the smallest three-digit number that can be formed is. question_4999-image_0"}, {"key": "5000", "content": "We can arrange the numbers $$0\\sim 9$$ with matches. (2) Given $$19$$ matches (all used up), the largest number you can form is, and the smallest number you can form is. question_5000-image_0"}, {"key": "5001", "content": "Using $$16$$ matchsticks (all must be used), the largest number that can be formed with each digit being different is. question_5001-image_0"}, {"key": "5002", "content": "Using $$9$$ matchsticks, place a number inside each square frame. The placed number can be a single digit or multiple digits, and the placed numbers can be the same or different. The final addition expression formed has a maximum and a minimum result. question_5002-image_0"}, {"key": "5003", "content": "Using $$9$$ matchsticks, place a number inside each box so that all digits are different between the two numbers, making an addition equation. The maximum result is, and the minimum is. question_5003-image_0"}, {"key": "5004", "content": "Please identify the pattern of each term in the following expressions and complete them: (1) The 1st term is 2, the 2nd term is 5, the 3rd term is 10, the 4th term is 17, $$ \\cdots $$ then the 10th term is."}, {"key": "5005", "content": "Person A and Person B are coloring a $$3$$ meter long stick. First, Person A starts from the end of the stick, painting $$5$$ centimeters in black, leaving $$5$$ centimeters unpainted, then painting another $$5$$ centimeters in black, and so on alternately to the end. Then, Person B starts from the same end of the stick, leaving $$6$$ centimeters unpainted, then painting $$6$$ centimeters in black, again leaving $$6$$ centimeters unpainted, and so on alternately to the end. In the end, the total length of the parts of the stick that were not painted black is in centimeters."}, {"key": "5006", "content": "Rectangles of the same size are arranged to form the pattern shown in the illustration. It is known that the width of each small piece of paper is $$12$$ cm. Calculate the total area of the shaded parts. question_5006-image_0"}, {"key": "5007", "content": "Student Eddie got a cactus on April 1, 2017, but the careless Eddie always forgot to water it, only remembering to do so every Sunday and Monday. If the cactus is watered for less than 9 days in a month, it will degenerate into a ball cactus. Knowing that April 1, 2017, was a Saturday, then in which month will the cactus degenerate into a ball cactus due to insufficient watering days."}, {"key": "5008", "content": "Xiaoming will participate in a math competition in March $$2017$$. This month has $$5$$ Wednesdays, $$5$$ Thursdays, and $$5$$ Fridays. Therefore, the $$23$$rd of this month is a Thursday."}, {"key": "5009", "content": "The following image is a street map of a neighborhood in a city. A postman needs to deliver letters$$.$$ The numbers on the map represent the kilometers of each street section$$.$$ Starting from the post office, he needs to cover all streets and finally return to the post office$$.$$ To pass through each street with the shortest distance covered, he has to walk a total of kilometers.\n question_5009-image_0"}, {"key": "5010", "content": "As shown, the area of the rectangle card is $$40$$, the area of the square card is $$25$$, the area of the triangle card is $$12$$, and the area of the overlap between the rectangle card and the square card is $$6$$, the area of the overlap between the rectangle card and the triangle card is $$4$$, the area of the overlap between the triangle card and the square card is $$3$$, and the area of the overlap among all three cards is $$2$$. Therefore, the total area covered by the three cards is\uff0e\n question_5010-image_0"}, {"key": "5011", "content": "A class has $$42$$ students, among them $$26$$ love playing basketball, $$17$$ love playing volleyball, $$19$$ love playing soccer, $$9$$ love both basketball and soccer, $$4$$ love both volleyball and soccer, no one loves all three sports, and no one dislikes all three sports. There are people who love both basketball and volleyball."}, {"key": "5012", "content": "A class has $$60$$ students, wearing either white or black tops, and black or blue pants. Among them, $$12$$ students wear white tops with blue pants, $$34$$ students wear black pants, and $$29$$ students wear black tops. Then, there are people wearing black tops and black pants."}, {"key": "5013", "content": "During the spring outing study trip, classmates discovered some cute little white rabbits. Hence, the math teacher posed the following question: There are $$100$$ white rabbits living in the forest. All rabbits that do not like carrots love cabbage. Among them, the number of rabbits that love carrots is twice the number of rabbits that love cabbage, and the number of rabbits that do not love cabbage is three times the number of rabbits that do not love carrots. There is a rabbit among them that loves both carrots and cabbage."}, {"key": "5014", "content": "There is a wonderful number now. We subtract $$13$$ from this number, multiply by $$2$$, divide by $$4$$, add $$1013$$, and then get the number $$2013$$. We call the above process one operation. If the robot Xiaogang performs $$2013$$ operations on this number, then, the final result is."}, {"key": "5015", "content": "3 explorers set out to explore a primeval forest together. Feeling quite bored on the way, they gathered to play cards. In the first game, A lost to B and C, doubling their money. In the second game, A and B won together, doubling the money in their wallets. In the third game, A and C won together, again doubling the money in their wallets. As a result, each of the 3 explorers won two games and lost one, ending up with the same amount of money. Carefully counting the money in his wallet, A found that he had lost 100 yuan. So, how much money did A, B, and C each start with?"}, {"key": "5016", "content": "Old trees, big trees, and small trees are chatting. The old tree said: 'For as many days as the small tree grows, the big tree grows for that many weeks; for as many months as the small tree grows, I grow for that many years. Together, we are a total of $$1000$$ years old.' How old are the small tree, the big tree, and the old tree this year?"}, {"key": "5017", "content": "Try in sequence, among the following figures, those that can be drawn in one stroke (without lifting the pen from the paper and without repeating lines, allowing intersections between lines) include.\n question_5017-image_0"}, {"key": "5018", "content": "$$\\times6=54$$"}, {"key": "5019", "content": "Set up the multiplication in column form: $$12\\times 4=$$."}, {"key": "5020", "content": "Set up vertically for calculation: $$14\\times 6=$$"}, {"key": "5021", "content": "True or false: A rectangle is a special type of parallelogram. ( )"}, {"key": "5022", "content": "What are the perimeters of these two figures? (Unit: centimeters) question_5022-image_0 (1) centimeters (2) centimeters"}, {"key": "5023", "content": "List the long division calculation, and check the answers for question (2) and (3). (1)$$48\\div 4=$$\uff0e(2)$$69\\div 3=$$\uff0e(3)$$845\\div 4=$$$$\u2026\u2026$$\uff0e"}, {"key": "5024", "content": "Perform vertical calculations and verify the second one: (1)\\$72\\div 4=\\$\uff0e(2)\\$112\\div 9=\\$\\$\u2026\u2026\\$\\$\uff0e"}, {"key": "5025", "content": "Eddie and Viola are preparing to beautify the entire Mace Magic School (1) First, they plant willow trees alongside a $$100$$ meter long pedestrian street, planting a tree every $$10$$ meters, including at both ends, how many willow trees do they need to plant in total? (2) The distance between the Sun and the Moon teaching buildings is $$50$$ meters, Eddie now wants to plant poplar trees between these two buildings, planting one every $$5$$ meters, how many poplar trees are needed in total? (3) Viola wants to plant pine trees on one side of the straight road leading to the magic castle gate, this road is $$40$$ meters long, with each tree spaced $$5$$ meters apart, how many pine trees need to be planted in total?"}, {"key": "5026", "content": "There is a circular flower bed in the square, the circumference of the flower bed is $$80$$ meters. Now, if a flower pot is placed every $$8$$ meters along the edge of the flower bed, how many flower pots can be placed in total?"}, {"key": "5027", "content": "To saw a piece of wood into $$5$$ pieces, try to draw it out, how many times does it need to be sawed? question_5027-image_0"}, {"key": "5028", "content": "To restore the ecology of the magic forest, Eddie planted $$28$$ trees on one side of a road, knowing that the distance between two adjacent trees is $$3$$ meters. (1) If Eddie planted the trees from one end to the other, what is the length of this road in meters? (2) If trees are not planted at one end, what is the length of this road in meters? (3) If trees are not planted at both ends, what is the length of this road in meters?"}, {"key": "5029", "content": "The wood brought back from the magic forest, Eddie is planning to make it into a gift for Vivi. (1) It takes him $$6$$ minutes to saw a piece of wood into $$3$$ pieces, so it would take minutes to saw this piece of wood into $$6$$ pieces. (2) Vivi lives on the sixth floor, and it takes Eddie a total of $$48$$ steps to walk from the first floor to the fourth floor. If the number of steps per floor is the same, then the total number of steps Eddie has to walk from the first floor to Vivi's home is ."}, {"key": "5030", "content": "Xiao Tie, Xiao Ye, and Xiao Zin pass the ball to each other, starting with Xiao Tie. After $$3$$ passes, there are a total of different ways to pass the ball."}, {"key": "5031", "content": "With cards $$5$$, $$7$$, and $$8$$, how many different two-digit numbers can be formed?"}, {"key": "5032", "content": "The area of a square is $$81$$ square meters, and the side length is meters. question_5032-image_0"}, {"key": "5033", "content": "Farm A harvested 50 million tons more wheat than Farm B, and the wheat harvested by Farm A was 10 million tons less than 4 times that of Farm B. Thus, Farm A harvested million tons of wheat, and Farm B harvested million tons of wheat. question_5033-image_0"}, {"key": "5034", "content": "A certain year's June 5th is a Friday. (1) What day of the week is June 30th of that year? (Fill in the number) (2) What day of the week is August 10th of that year? (Fill in the number)"}, {"key": "5035", "content": "(1) There is a line segment in the diagram below. question_5035-image_0 (2) There are a total of line segments in the diagram below. question_5035-image_1"}, {"key": "5036", "content": "The prizes prepared by the teacher for the fun sports meet are lollipops. How many different ways can the teacher divide $$8$$ identical lollipops into $$3$$ piles?"}, {"key": "5037", "content": "How many different ways can you divide $$12$$ watermelons of the same size into $$3$$ piles of different quantities? question_5037-image_0"}, {"key": "5038", "content": "Put $$7$$ identical lollipops into two different boxes, with no box being empty. How many different arrangements are there in total? question_5038-image_0"}, {"key": "5039", "content": "Divide $$6$$ identical erasers among $$3$$ kids, with each kid getting at least one eraser. How many different ways are there to divide them? question_5039-image_0"}, {"key": "5040", "content": "Distribute all $$9$$ identical pieces of candy among Eddie, Vi, and Dakuang, with each person getting at least two pieces. How many different ways can the candy be distributed? question_5040-image_0"}, {"key": "5041", "content": "Originally, Class A had $$6$$ times as many books as Class B. Now, Class A gave Class B $$30$$ books, and at this time Class A has $$5$$ more books than Class B. How many books did Class A and Class B originally have? (1) Complete the arrow diagram to show how many more books Class A had than Class B originally. question_5041-image_0 (2) How many books did Class A and Class B originally have, respectively?"}, {"key": "5042", "content": "Below is a menu from a fast-food restaurant. Lulu plans to order one main course, one snack, and one drink. How many different combination options does she have? question_5042-image_0"}, {"key": "5043", "content": "The Max Hotel has a total of $$4$$ rooms to choose from. Eddie, Vira, Dakuang, and Doctor each pick one room. How many different selection plans are there in total? question_5043-image_0"}, {"key": "5044", "content": "It is known that the diagonals of the quadrilateral $$ABCD$$ are perpendicular to each other and the area of the quadrilateral is $$80$$ square centimeters. Given $$AC=10$$ centimeters, the length of $$BD$$ is in centimeters. question_5044-image_0"}, {"key": "5045", "content": "The numbers in the figure respectively represent the areas of two rectangles and a right-angled triangle, the area of another triangle is. question_5045-image_0"}, {"key": "5046", "content": "Below, a large rectangle is divided into $$9$$ smaller rectangles, among which the area of $$5$$ rectangles is shown in the diagram (unit: square centimeters), then the area of \u201c*\u201d is in square centimeters. question_5046-image_0"}, {"key": "5047", "content": "As shown in the figure, in parallelogram $$ABCD$$, a line through point $$A$$ is drawn perpendicular to $$BC$$ at point $$E$$. It is known that the area of the parallelogram $$ABCD$$ is $$48$$ square centimeters, and $$AE=8$$ centimeters. What is the length of $$AD$$ in centimeters? question_5047-image_0"}, {"key": "5048", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$ from point $$A$$. It is known that $$AB=5$$ cm, $$AE=3$$ cm, the area of parallelogram $$ABCD$$ is square centimeters. question_5048-image_0"}, {"key": "5049", "content": "As shown in the figure, two squares with a side length of $$10$$ centimeters are staggered by $$3$$ centimeters. The shaded part is a parallelogram. What is the area of this parallelogram in square centimeters? question_5049-image_0"}, {"key": "5050", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$AB=12$$ cm, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$AF=15$$ cm, $$AE=10$$ cm. question_5050-image_0 \u200b(1) The area of parallelogram $$ABCD$$ is square centimeters. (2) The length of line segment $$BC$$ is cm."}, {"key": "5051", "content": "As shown in the figure, the side length of the large square $$DEFG$$ is $$12$$ centimeters, the side length of the small square $$ABCD$$ is $$6$$ centimeters, please answer: What is the area of the parallelogram $$ABFH$$ in square centimeters? question_5051-image_0"}, {"key": "5052", "content": "Eddie took out 35 pieces of his prized chocolate to share with everyone, but he did not eat any himself. He shared them evenly among the third-grade students who participated in a competition, fewer than 10 people, and was left with 5 pieces that could not be distributed. How many third-grade students participated in the competition?"}, {"key": "5053", "content": "We can arrange numbers $$0\\sim 9$$ with matchsticks. If given $$20$$ matchsticks (all to be used), the largest possible number that can be formed, and the smallest possible number that can be formed. question_5053-image_0"}, {"key": "5054", "content": "Using $$16$$ matchsticks (all used up), the largest number that can be formed with each digit being different is\uff0e question_5054-image_0"}, {"key": "5055", "content": "Perform the following operation on a natural number: if it is an even number, then divide by $$2$$; if it is an odd number, then subtract $$1$$. Continue this process until the number becomes $$1$$ and the operation stops. Ask how many numbers become $$1$$ after $$6$$ operations."}, {"key": "5056", "content": "There are flights from Beijing to Tokyo, Moscow, Paris, New York, and Sydney, with other city routes shown in the diagram (dashed lines indicate routes on the opposite side of the Earth). The number of distinct routes that depart from Beijing and visit each of the other cities once is. question_5056-image_0"}, {"key": "5057", "content": "Person A and person B play table tennis, the first to win two consecutive games wins. If no one wins the first two consecutive games, then the first to win three games wins. Continue until the winner is determined. Question: In total, how many possible outcomes are there."}, {"key": "5058", "content": "A little bee passes through the hive rooms, with the rule: it can only enter from a smaller numbered room to a larger numbered room. There is a way for the little bee to get from room No.1 to room No.6. question_5058-image_0"}, {"key": "5059", "content": "The National Day is approaching, and the Young Pioneers of the Xueersi School are going to arrange flowers. If each person arranges $$6$$ pots of flowers, there are $$3$$ pots left unarranged; if $$2$$ of them arrange $$5$$ pots each, and the rest arrange $$7$$ pots each, then the flowers will be exactly enough. There are members of the Young Pioneers participating in the flower arranging activity, arranging a total of pots of flowers."}, {"key": "5060", "content": "Calculate: $$888\\times 888-887\\times 889=$$."}, {"key": "5061", "content": "Calculate: $${{256}^{3}}-255\\times 256\\times 257=$$."}, {"key": "5062", "content": "Xiao Wang used $$5$$ identical rectangular paper pieces to form a larger rectangle, with the length of this large rectangle being $$3$$ cm longer than its width (as shown in Figure $$1$$). If he arranges these $$5$$ rectangular paper pieces into the shape shown in Figure $$2$$, then the perimeter of the shape in Figure $$2$$ is in centimeters.\n question_5062-image_0"}, {"key": "5063", "content": "There is a rectangular piece of paper, its length is $$4$$ cm more than its width, and its perimeter is $$36$$ cm. After cutting it $$8$$ times with scissors, it is divided into $$24$$ small rectangles as shown in the following figure. The sum of the perimeters of these $$24$$ rectangles is (\u3000\u3000) cm.\n question_5063-image_0"}, {"key": "5064", "content": "As shown in the figure, a square is divided into $$4$$ identical rectangles. The area of the square is $$64$$ square centimeters. Then, the perimeter of a small rectangle is centimeters.\n question_5064-image_0"}, {"key": "5065", "content": "Using $$4$$ identical rectangles and one small square to form a large square with a side length of $$25$$ cm (as shown in the picture), each rectangle has a perimeter in cm.\n question_5065-image_0"}, {"key": "5066", "content": "The figure below is composed of $$9$$ identical rectangular pieces of paper, with the shadowed rectangle having a length and width of $$11$$cm and $$8$$cm, respectively. What is the length and width of the rectangular paper pieces in centimeters? ( )\n question_5066-image_0"}, {"key": "5067", "content": "In the table shown in the figure, each column combines the characters above and below into a pair of words, for example, the first pair of words is (Spring\u6295), the second pair of words is (Wind\u6211), then the $$48$$th pair of words is. Spring wind flowers and grass fragrance Spring wind flowers and grass fragrance Spring wind flowers and grass fragrance$$......$$Peach\u6295 me to repay with plum\u62a5\u4e4b\u4ee5\u674ePeach\u6295 me to repay with plum\u62a5\u4e4b\u4ee5\u674e$$......$$"}, {"key": "5068", "content": "The image below is the floor plan of Wei'er's new home. The new home has $$6$$ rooms, with doors connecting adjacent rooms. She wants to start from a room and pass through all the doors without repeating any. The room is the starting point, and the room is the endpoint. question_5068-image_0"}, {"key": "5069", "content": "Eddie reads a book, reading $$2k$$ pages per day. After reading for $$7$$ days, there are $$52$$ pages left unread. Express the total number of pages of the book using an expression that includes letters; when $$k=5$$, the book has pages."}, {"key": "5070", "content": "Answer the following questions: (1) Eddie used a 28 cm long ribbon to exactly frame a photo of a big-eyed monster with a colored border. The side length of this square frame is in centimeters. question_5070-image_0 (2) Vi used a 40 cm long ribbon to exactly frame a photo of a big-eyed monster with a colored border, the width of this rectangular frame is 5 cm, and the length of this frame is in centimeters. question_5070-image_1 \u200b"}, {"key": "5071", "content": "There are $$3$$ rows of chess pieces, with each row having $$14$$ pieces, so there are a total of pieces. question_5071-image_0"}, {"key": "5072", "content": "Perform vertical calculation: (1) $$408\\div 4$$ = (2) $$1216\\div 4$$ ="}, {"key": "5073", "content": "Perform vertical multiplication: (1) $$232\\times 23=$$; (2) $$435\\times 321=$$."}, {"key": "5074", "content": "Tree Planting Day has arrived, and the Xueersi School organized a tree planting event. If $$5$$ people can plant $$100$$ trees in $$2$$ hours, assuming each person plants the same number of trees per hour: (1) then $$5$$ people plant trees in $$1$$ hour. (2) then $$1$$ person plants trees in $$2$$ hours. (3) then $$1$$ person plants trees in $$1$$ hour."}, {"key": "5075", "content": "To welcome new students, the Xueersi restaurant has launched a new roasted chicken leg machine. It is known that $$3$$ machines can roast $$600$$ chicken legs in $$4$$ days. Based on this rate, calculate: (1) How many chicken legs can $$1$$ machine roast in $$1$$ day\uff0e(2) How many chicken legs can $$5$$ machines roast in $$1$$ day\uff0e(3) How many chicken legs can $$5$$ machines roast in $$3$$ days\uff0e"}, {"key": "5076", "content": "There is a series of numbers arranged in the following order $$385161713851617138516171\\cdots \\cdots $$. (1) The $$50$$th number is. (2) Among these $$50$$ numbers, the number \u201c$$1$$\u201d appears a total of times. (3) The sum of these $$50$$ numbers is."}, {"key": "5077", "content": "Given $$7\\times 11\\times 13=1001$$, calculate the value of the following expressions: (1) $$7\\times 9\\times 11\\times 13$$=\uff0e(2) $$14\\times 22\\times 26$$=\uff0e"}, {"key": "5078", "content": "Column subtraction calculation: (1) $$140\\times18\\div14$$= (2) $$1600\\times15\\div8$$="}, {"key": "5079", "content": "Serial division calculation: (1) $$600\\div25\\div4$$ = (2) $$1500\\div \\left(15\\times25\\right)$$ = (3) $$400\\div \\left(40\\div25\\right)$$ ="}, {"key": "5080", "content": "Calculate the following expressions: (1) $$(140+77)\\div 7$$= (2) $$(2400-666)\\div 6$$="}, {"key": "5081", "content": "Column Detachment Calculation: (1) $$91\\div 5+9\\div 5$$=. (2) $$294\\div 7+56\\div 7$$=. (3) $$24\\div 3+24\\div 2+24\\div 1$$=."}, {"key": "5082", "content": "Calculate using a simple method: (1) $$25\\times \\left( 40+2 \\right)$$=; (2) $$\\left( 100+8 \\right)\\times 125$$=."}, {"key": "5083", "content": "Calculate: (1) $$12\\times 79\\div 12$$=\uff0e(2) $$35000\\times 45\\div 7000\\div 45$$=\uff0e"}, {"key": "5084", "content": "The area of a square is $$81$$ square meters, and the side length is meters. question_5084-image_0"}, {"key": "5085", "content": "Originally in the grain store, there were $$20$$ more bags of rice than flour. After selling $$30$$ bags of rice and $$16$$ bags of flour, is there now more rice or more flour? ( )"}, {"key": "5086", "content": "Complete the following questions: (Fill in according to $$1.2.3.4.5.6.7$$) October $$1$$, 2020 is a Thursday. Counting from this day, the $$25$$th day is a week day."}, {"key": "5087", "content": "Given that the magic sum of a 3x3 magic square is 30, then the center number of this 3x3 magic square is."}, {"key": "5088", "content": "In a parking lot, there are sedans (four wheels) and motorcycles (two wheels) totaling $$32$$ vehicles, with a total of $$108$$ wheels. Motorcycles number; sedans number."}, {"key": "5089", "content": "There are a total of 100 RMB bills, consisting of 5 RMB and 10 RMB denominations, with a total value of 800 RMB. There are some 10 RMB and some 5 RMB bills."}, {"key": "5090", "content": "Eddie put chickens and rabbits in the same cage, counted them, and there were a total of $$6$$ heads and $$16$$ legs, how many chickens were there in the cage?"}, {"key": "5091", "content": "There are $$108$$ third graders going on a spring outing, $$65$$ of them brought mineral water, and $$63$$ brought fruits, with each person bringing at least one kind. Among them, the number of people who brought both mineral water and fruits is ."}, {"key": "5092", "content": "Below is a table of statistics on the favorite sports activities of students in two third-grade classes. Activity Number of People Class Jump Rope ($$1$$) Playing Shuttlecock ($$2$$) Playing Table Tennis ($$3$$) Playing Badminton ($$4$$) Class 3($$1$$) $$20$$$$16$$$$15$$$$12$$ Class 3($$2$$) $$15$$$$14$$$$10$$$$18$$ (1) The number of students in Class 3($$1$$) who favor an activity the most, and the number of students in Class 3($$2$$) who favor an activity the most. (Answer with numbers only) (2) The number of students from these two classes who prefer jump rope over playing table tennis."}, {"key": "5093", "content": "Among the methods below, the one that can make the following figure drawable in one stroke is ( )\n question_5093-image_0"}, {"key": "5094", "content": "Complete the flowchart below, the number in the first box is.\n question_5094-image_0"}, {"key": "5095", "content": "The kindergarten gives candy to the award-winning children. If each child receives $$6$$ pieces, there are $$12$$ pieces short. If each child receives $$9$$ pieces, there are $$24$$ pieces short. How many children have won awards."}, {"key": "5096", "content": "Eddie put some small balls into boxes. If each box contains 15 small balls, he is short of 10 balls at the end; if each box contains 12 small balls, he has an excess of 5 balls at the end. There are a total of boxes."}, {"key": "5097", "content": "A teacher is distributing candies to students. If each student gets 4 candies, there are 19 candies left. If each student gets 5 candies, there is 1 candy left. There are a total number of students."}, {"key": "5098", "content": "The older brother has $$95$$ books, and the younger brother has $$155$$ books. After the older brother gave some books to the younger brother, the total number of books the younger brother has becomes exactly $$4$$ times that of the older brother's. (1) After the older brother gave some books to the younger brother, the total number of books both brothers have is. (2) The number of books the older brother gave to the younger brother is."}, {"key": "5099", "content": "Originally, Class A had $$6$$ times the number of books as Class B. Now, Class A gives Class B $$30$$ books, and at this point, Class A has $$5$$ more books than Class B. How many books did Class A and Class B originally have? (1) Complete the arrow diagram to show how many more books Class A had originally than Class B. question_5099-image_0 (2) Originally, Class A had ____ books, and Class B had ____ books."}, {"key": "5100", "content": "The hotel has a total of $$3$$ rooms to choose from, Eddie, Vera, and Dakuang each choose one room, how many different selection schemes are there in total? question_5100-image_0"}, {"key": "5101", "content": "As shown in the figure, a rectangle is divided into four rectangles of different sizes by two line segments. The areas of three of the rectangles are respectively $$6$$ square meters, $$8$$ square meters, and $$4$$ square meters. The area of the other rectangle is square meters.\n question_5101-image_0"}, {"key": "5102", "content": "The track of the school playground is shown in the diagram below (unit: meters). Eddie ran around the track for one lap, running a total of meters. \n question_5102-image_0"}, {"key": "5103", "content": "Given that the area of parallelogram $$ABCD$$ is $$72$$ square centimeters, $$DE=6\\text{cm}$$, $$DF=8\\text{cm}$$, then the perimeter of the parallelogram is in centimeters.\n question_5103-image_0"}, {"key": "5104", "content": "Da Mao, Er Mao, San Mao, Si Mao$$4$$ people line up from left to right to play a game, San Mao can only stand on the far left, so how many different ways are there for them to line up."}, {"key": "5105", "content": "Eddie took out his treasured collection of $$35$$ pieces of chocolate to share with everyone, but he didn't eat any. The chocolate was shared among the third-grade students who participated in a competition, less than $$10$$ people, and there were $$5$$ pieces left, which could not be divided further. How many third-grade students participated in the competition?"}, {"key": "5106", "content": "When performing addition with two three-digit numbers, Da Kuan mistakenly saw the digit $$4$$ in the tens place of one of the addends, resulting in a sum that was $$30$$ less than the correct answer. What did Da Kuan mistakenly see $$4$$ as?"}, {"key": "5107", "content": "Eddie made a mistake when doing a subtraction problem, accidentally writing the tens digit of the minuend as $$9$$ instead of $$3$$, and the units digit as $$6$$ instead of $$8$$, resulting in an answer of $$201$$. What should the correct difference be?"}, {"key": "5108", "content": "Given the difference between two numbers is $$90$$, Eddie mistakenly added an extra $$0$$ to the end of the minuend, resulting in a calculated difference of $$3240$$. What is the minuend?"}, {"key": "5109", "content": "Given the difference between two natural numbers is $$120$$, Eddie accidentally omitted the $$0$$ at the end of the subtracted number during calculation, resulting in a difference of $$912$$. (1) What multiple is the correct subtracted number of the mistaken one? (2) What could the minuend possibly be?"}, {"key": "5110", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, it is possible to form different three-digit numbers."}, {"key": "5111", "content": "Eddie and the doctor set off from two places 32 kilometers apart towards each other at the same time, the doctor walks 4 kilometers per hour, Eddie uses his superpower to fly 12 kilometers per hour. After they meet, Eddie realizes he forgot to bring something and immediately returns to the starting point, then turns around and proceeds towards the doctor. Please ask: The distance in kilometers from the second meeting point to Eddie's starting point."}, {"key": "5112", "content": "In the street schematic below, passage at $$C$$ is blocked due to construction, how many shortest paths are there from $$A$$ to $$B$$? question_5112-image_0"}, {"key": "5113", "content": "Besides passive defense measures, the doctor also developed a bionic robot - Anteater model $$A$$. During a test, the Anteater model $$A$$ after moving up, down, left, and right several times, returned to the starting point, forming a mountain shape with a missing corner. How many meters did it travel in total? question_5113-image_0"}, {"key": "5114", "content": "A square piece of paper has a side length of $$12$$ cm. Now, this square piece of paper is folded twice along the direction parallel to the side length. After unfolding, the perimeter of each figure could be centimeters, or it could be centimeters."}, {"key": "5115", "content": "After a square is cut into $$2$$ rectangles, the sum of the perimeters of the two rectangles is ( ) than the perimeter of the original square."}, {"key": "5116", "content": "The figure below is a rectangle formed by assembling $$5$$ small squares with a side length of $$2$$. The perimeter of the rectangle is\uff0e\n question_5116-image_0"}, {"key": "5117", "content": "In a certain place, there are four types of coins with different denominations, as shown in the figures. Assuming you have exactly one coin of each type. How many different amounts of money can you form? question_5117-image_0 question_5117-image_1 question_5117-image_2 question_5117-image_3"}, {"key": "5118", "content": "There are four number cards: $$1$$, $$2$$, $$3$$, $$4$$. It is required that number $$1$$ cannot be in the thousand's place, number $$2$$ cannot be in the hundred's place, number $$3$$ cannot be in the ten's place, and number $$4$$ cannot be in the unit place. How many four-digit numbers that meet these requirements can be formed with these four cards?"}, {"key": "5119", "content": "There are a total of $$17$$ sticks, divided evenly into $$3$$ portions, each portion $$5$$ sticks, with $$2$$ sticks remaining. The number pointed by the arrow in the vertical calculation below, the correct meaning of that number is ( ).\n question_5119-image_0"}, {"key": "5120", "content": "With $$30$$ flowers to make bouquets, making one bouquet with every $$4$$ flowers, how many bouquets can be made? Xiao Jun calculated the result using vertical calculation method. The number in the box in the vertical calculation below represents (\u3000\u3000).\n question_5120-image_0"}, {"key": "5121", "content": "Mom bought $$45$$ oranges, and every $$8$$ of them should be packed in a box, at least ( ) boxes are needed."}, {"key": "5122", "content": "$3$ monks eat $$12$$ buns for $$4$$ meals, if each monk eats the same amount for each meal, then $$1$$ monk eats ( ) buns per meal."}, {"key": "5123", "content": "$$3$$ mice in $$5$$ days stealthily ate $$30$$ corns. According to this rate, $$4$$ mice in $$7$$ days can stealthily eat ( ) corns."}, {"key": "5124", "content": "After a test ended, Wei and her friends discussed their scores. Including Wei, their average score was $$87$$. Later, Wei found out that her total score was miscalculated by the teacher, and after checking with the teacher, she got an additional $$10$$ points. At this time, including Wei, the average score of the friends changed to $$89$$. How many friends did Wei discuss the scores with."}, {"key": "5125", "content": "Xiaohong has $$10$$ pieces of candy, Xiaolan has $$6$$ pieces of candy, Xiaohong gives Xiaolan ( ) pieces of candy, then they both have the same number of candies."}, {"key": "5126", "content": "The total score for Xiao Chengyu in Chinese and Mathematics is $$182$$ points, English $$85$$ points, the average score for these three subjects is ( )."}, {"key": "5127", "content": "In the figure below, the colored part can be represented by $$\\frac{1}{3}$$ is ( )."}, {"key": "5128", "content": "Convert the following mixed numbers into improper fractions: $$1\\frac{2}{3}=$$; $$2\\frac{3}{5}=$$; $$1\\frac{4}{7}=$$."}, {"key": "5129", "content": "Convert the following fractions to mixed numbers: $$\\frac{4}{3}=$$; $$\\frac{7}{5}=$$; $$\\frac{15}{7}=$$."}, {"key": "5130", "content": "To saw a piece of wood into $$5$$ pieces, how many times do you need to saw?"}, {"key": "5131", "content": "Divide a $$5$$ meter long rope into $$8$$ equal parts, each part is ( ) meters long."}, {"key": "5132", "content": "The unit building where Xiao Hua's family lives has $$32$$ floors above ground for residential housing, and $$2$$ underground levels for parking. When Xiao Hua takes the elevator from the second basement level to the $$26$$th floor, the elevator ascends ( ) floors."}, {"key": "5133", "content": "Jingjing walked up $$36$$ steps from the first floor to the third floor. She lives on the fifth floor, and in total, she needs to climb (\u3000\u3000) steps to get home."}, {"key": "5134", "content": "There are three squares $$A$$, $$B$$, and $$C$$. It is known that the area of $$B$$ is four times that of $$A$$, and the perimeter of $$C$$ is twice that of $$B$$. Thus, the area of $$C$$ is how many times that of $$A$$?"}, {"key": "5135", "content": "Xiaopi's number of credit cards increased by $$6$$, then decreased by $$5$$, multiplied by $$2$$, and then divided by $$10$$, happens to be $$1$$ card. How many credit cards does Xiaopi originally have?"}, {"key": "5136", "content": "In the equation $$2+8+3=2\\bigcirc 8\\square 3$$, what operators should be filled in for $$\\bigcirc $$ and $$\\square $$ respectively to make the equation correct?"}, {"key": "5137", "content": "The school rented several large limousines for the students participating in the summer camp. If each limousine carries $$28$$ people, then $$13$$ students will not have a ride. If each car carries $$32$$ people, there will be $$3$$ empty seats. The total number of students is ( )."}, {"key": "5138", "content": "The diagram shows a street map, starting from $$A$$ through the intersection $$B$$, but not passing through $$C$$ to reach $$D$$. There are different shortest routes. question_5138-image_0"}, {"key": "5139", "content": "In the diagram below, there are ( ) different ways to go from $$A$$ to $$B$$\uff0e(Only upwards, to the right)\n question_5139-image_0"}, {"key": "5140", "content": "A bee sets off from point $$A$$, heading back home to point $$B$$. It can only crawl from one cell to the adjacent cell on the right and is not allowed to move backwards. How many ways are there for it to return home?\n question_5140-image_0"}, {"key": "5141", "content": "The school allocates dormitories for new students. If each room houses 3 people, there are 23 people left over; if each room houses 5 people, there are 3 rooms left over. How many rooms are there in the dormitory? How many new students are there?"}, {"key": "5142", "content": "As shown in the diagram, starting from point $$A$$ to reach point $$B$$, it is mandatory to pass through segment $$CD$$ and forbidden to go through segment $$EF$$. How many different shortest routes are there? question_5142-image_0"}, {"key": "5143", "content": "Please fill in $$+$$, $$-$$, $$\\times$$, $$\\div$$, or () among the four numbers $$7$$, $$3$$, $$8$$, $$6$$ in any order, making sure each number is used exactly once, so that their result equals $$24$$. Among the following options, the one that makes the equation true is ().\n$$7\\;\\;\\;\\;\\;\\;\\;\\;3\\;\\;\\;\\;\\;\\;\\;\\;8\\;\\;\\;\\;\\;\\;\\;\\;6=24$$"}, {"key": "5144", "content": "Members of the Young Pioneers in Class 1 of Grade 3 participate in school brick-moving labor. If each person moves $$4$$ bricks, there are $$7$$ bricks left; if each person moves $$5$$ bricks, there are $$2$$ bricks short. The total number of bricks this class needs to move is ( ) bricks."}, {"key": "5145", "content": "$$8-7-6+5+4-3-2+1=$$ ( )\uff0e"}, {"key": "5146", "content": "Da Kuan has $$7$$ eggs and plans to eat them all in three days, eating at least $$1$$ egg per day. How many ways are there to do this?"}, {"key": "5147", "content": "Divide $$10$$ identical balls into $$3$$ piles, each with a different number of balls. How many ways can this be done?"}, {"key": "5148", "content": "Calculate: $$2009\\times 2009-2008\\times 2008$$=."}, {"key": "5149", "content": "Among the two images below, the one with the larger perimeter is ( )\uff0e\n question_5149-image_0"}, {"key": "5150", "content": "Calculate: $$2004^2-2003\\times 2005$$\uff0e( )"}, {"key": "5151", "content": "A square with a side length of $$8$$ cm from which two small squares, each with a side length of $$2$$ cm, are cut out as shown in the following diagram. The perimeter of the remaining figure is ( ) cm.\n question_5151-image_0"}, {"key": "5152", "content": "How many ways can 9 balls be split into three piles?"}, {"key": "5153", "content": "A piece of chocolate was bitten once by both Bear Da and Bear Er, turning into what's shown in the picture below. What is the perimeter of the chocolate now?\n question_5153-image_0"}, {"key": "5154", "content": "The perimeter of the figure below equals ( ) cm.\n question_5154-image_0"}, {"key": "5155", "content": "Weier has to choose from $$3$$ different hats, $$7$$ different dresses, and $$2$$ pairs of different shoes before attending the dance party. It is optional to choose a hat. So, how many different combinations can she have? ( )"}, {"key": "5156", "content": "Tingting plans to travel from Beijing to Shanghai on October 1. The travel options include high-speed train and plane, with known $$5$$ direct flights to Shanghai that day; there are $$15$$ high-speed train rides directly to Shanghai; there is also the option to transfer in Hangzhou: there are $$10$$ high-speed trains from Beijing to Hangzhou, and upon any time of arrival in Hangzhou, there are $$5$$ high-speed trains available to Shanghai. How many different travel options does Tingting have from Beijing to Shanghai in total?"}, {"key": "5157", "content": "The New Year has arrived, and Mom bought $$7$$ different gifts to give to the $$5$$ children of relatives and friends, one for each. Among them, Big Sister's son, Xiaoqiang, wants to choose between a puzzle and a remote-controlled car, and a friend's daughter, Xiaoyu, wants to choose between a learning machine and a remote-controlled car. Thus, there are a total of $$5$$ ways for Mom to distribute these gifts."}, {"key": "5158", "content": "Red, yellow, blue, white, and black, five different colors of small flags, there are $$3$$, $$3$$, $$3$$, $$1$$, $$3$$ flags of each color respectively. If one takes out three flags at random and arranges them in a row in a certain order to represent a signal, the question is: How many different signals can be represented in total?"}, {"key": "5159", "content": "Red, yellow, blue, and white, four different colored flags, each have $$1, 2, 3, 4$$ pieces respectively. Taking out three pieces randomly and arranging them in a row in sequence represents a signal. How many different signals can be represented in total?"}, {"key": "5160", "content": "When Lingling was doing division, she wrote the divisor as $$47$$ instead of $$74$$, and got a quotient of $$5$$ with a remainder of $$6$$. What should the correct quotient be?"}, {"key": "5161", "content": "Two numbers are divided, and the quotient is $$12$$, the sum of the dividend, divisor, and quotient is $$129$$. What is the divisor?"}, {"key": "5162", "content": "The remainder of $$2461\\times 135\\times 6047$$ divided by $$11$$ is."}, {"key": "5163", "content": "Regarding the statements about parallelograms and trapezoids, the correct statement is ( )."}, {"key": "5164", "content": "In a division equation with a remainder, the sum of the dividend, divisor, quotient, and remainder is $$519$$. It is known that the quotient is $$15$$ and the remainder is $$12$$. Then, the divisor is, and the dividend is."}, {"key": "5165", "content": "\u25c7$$\\div 8=5\\cdots \\cdots $$\u2605, there is a remainder, \u2605what is the maximum? \u25c7What is the minimum? ( )"}, {"key": "5166", "content": "Mr. Wang travels on a business trip from Chongqing to Nanjing, he can directly take a plane or car, or he can go to Wuhan first and then from Wuhan to Nanjing. From Chongqing to Wuhan, he can take a boat or train; from Wuhan to Nanjing he can take a boat, train or plane, as shown in the diagram. So, how many different ways can Mr. Wang travel from Chongqing to Nanjing? ( )\n question_5166-image_0"}, {"key": "5167", "content": "Mo Mo went out for lunch and found that there were $$9$$ Chinese restaurants nearby, $$3$$ Western restaurants, and $$2$$ Japanese restaurants. He plans to choose a restaurant to eat at, totaling ( ) different choices."}, {"key": "5168", "content": "The password for the $$\\text{ofo}$$ yellow bike is a four-digit number, made up of the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$. Therefore, the number of possible $$\\text{ofo}$$ yellow bike passwords is ( )."}, {"key": "5169", "content": "The school selects programs for the art festival, and needs to pick $$2$$ out of $$4$$ choir programs, and $$1$$ out of $$3$$ dance programs, making a total of ( ) selection schemes."}, {"key": "5170", "content": "Eddie has $$20$$ pieces of candy, Vi's number of candies is $$3$$ times that of Eddie's plus $$5$$ more. Together, they have ( ) pieces of candy."}, {"key": "5171", "content": "Panda Huanhuan ate a total of $$80$$ bamboo shoots in one day, in the morning, at noon, and in the evening. The number he ate at noon was $$2$$ times what he ate in the morning, and the number he ate in the evening was $$2$$ times plus $$5$$ more than what he ate in the morning. So, how many bamboo shoots did Huanhuan eat at noon on this day?"}, {"key": "5172", "content": "Two bookshelves, the number of books on shelf A is $$5$$ times the number of books on shelf B. Shelf A has $$120$$ more books than shelf B. How many books are on shelf B? ( )"}, {"key": "5173", "content": "The remainder of $$a\\div17$$ is $$13$$, the remainder of $$b\\div17$$ is $$5$$, the remainder of $$(a+b)\\div17$$ is ( )."}, {"key": "5174", "content": "Given $$48\\div 5=9\\cdots \\cdots 3$$, ask: Subtract a natural number from $$48$$ so that the dividend is divisible by $$5$$, what is the minimum of this number?"}, {"key": "5175", "content": "When two numbers are divided, the quotient is $$11$$ with a remainder of $$5$$. The smallest possible value of the dividend is ( )."}, {"key": "5176", "content": "When two numbers are divided, the quotient is $$5$$ with a remainder of $$2$$. If both the dividend and divisor are increased to three times their original size, then the sum of the dividend, divisor, quotient, and remainder equals $$287$$. What were the original dividend and divisor? ( )"}, {"key": "5177", "content": "After cutting and splicing a parallelogram into a rectangle (as shown), the correct option is (\u3000\u3000)\n question_5177-image_0"}, {"key": "5178", "content": "Find the area of the trapezoid below, the correct formula is ( ).\n question_5178-image_0"}, {"key": "5179", "content": "As shown in the figure, the area of the triangular cardboard, the square cardboard, and the circular cardboard are equal, each being $$60$$ square centimeters. The total area of the shaded part is $$40$$ square centimeters. The total area covered by the $$3$$ pieces of cardboard is $$100$$ square centimeters. The area of the overlapping part of the $$3$$ pieces of cardboard is square centimeters. question_5179-image_0"}, {"key": "5180", "content": "Fill each square in the figure with one of the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, in such a way that the seven numbers in each row and column are all different; and the number in the circle equals the product of the four numbers adjacent to it. Hence, the number to fill in at the $$\\bigstar$$ is.\n question_5180-image_0"}, {"key": "5181", "content": "Fill in the letters $$ABCD$$ into the $$5\\times5$$ grid as shown, with the requirement that each of the four letters appears exactly once in every row and column: If a letter is marked on the left side of a row, it represents the first letter to appear in that row; if a letter is marked on the right side of a row, it represents the last letter to appear in that row; similarly, if a letter is marked on the top ($$or bottom$$) of a column, it represents the first ($$or last$$) letter to appear in that column. Then, the sequence in which $$A$$, $$B$$, $$C$$, $$D$$ appear from left to right in the second row is.\n question_5181-image_0"}, {"key": "5182", "content": "The two sides of an angle are two ( )."}, {"key": "5183", "content": "Among the following groups of shapes, the one where the two lines can meet is ( )."}, {"key": "5184", "content": "Grandfather is $$60$$ years old this year, and Naughty is $$8$$ years old this year. $$3$$ years later, Naughty is ( ) years younger than Grandfather."}, {"key": "5185", "content": "Xiao Ning and Xiao Chun have a total of $$72$$ stamps, Xiao Chun has $$12$$ more stamps than Xiao Ning. Xiao Ning has ( ) stamps."}, {"key": "5186", "content": "In the division equation $$\\square \\div \\square =20\\cdots \\cdots 8$$, the minimum value of the dividend is ( )."}, {"key": "5187", "content": "A bundle of wires, the first time it was used more than half of its total length $$3$$ meters, the second time it used less than half of the remaining $$10$$ meters, the third time it used $$15$$ meters, and finally $$7$$ meters remained. The original length of this bundle of wires in meters."}, {"key": "5188", "content": "Xiao Ming wrote a number on the blackboard, Xiao Hong first multiplies this number by $$2$$, then adds $$4$$ to it, resulting in $$8$$. Thus, the number Xiao Ming wrote on the blackboard is."}, {"key": "5189", "content": "To entertain guests visiting Happy Country, the doctor prepared a lot of delicious cakes. Eddie asked the doctor how many children were visiting. The doctor said: 'I prepared 2 cakes for each child, and there were 7 left over.' Eddie counted a total of 57 cakes. Do you know how many children came to visit?\n question_5189-image_0"}, {"key": "5190", "content": "A doctor made $$3$$ robots to produce parts, capable of producing $$60$$ parts in $$4$$ hours. Calculating at this rate, how many parts does $$1$$ robot produce in $$1$$ hour?"}, {"key": "5191", "content": "As shown in the picture, please fill in the blanks with the appropriate numbers to make the multiplication vertical problem correct. In this case, the first factor is.\n question_5191-image_0"}, {"key": "5192", "content": "Figure ($$1$$) has one square, figure ($$2$$) has one square.\n question_5192-image_0 question_5192-image_1"}, {"key": "5193", "content": "Fill in the blank. (1) As shown in the figure, a square is dug from the side of a large rectangle to form a polygon. The length of the large rectangle is $$6$$ centimeters, and the width is $$4$$ centimeters. The side length of the square is $$2$$ centimeters. The perimeter of this shape is centimeters. question_5193-image_0 (2) As shown in the bottom right figure, four rectangles form a polygon (unit: centimeters), then the perimeter of this polygon is centimeters. question_5193-image_1"}, {"key": "5194", "content": "Calculate the following problems: (1) A doctor wants to buy a set of books to donate to children. There are $$20$$ books in the set, each costing $$15$$ dollars. The doctor needs to prepare dollars to buy the books. (2) The doctor also wants to buy some milk for the children, each box of milk costs $$40$$ dollars, for a total of $$150$$ boxes. The doctor needs to prepare dollars to buy the milk."}, {"key": "5195", "content": "The area of a square is $$36$$ square centimeters, so its side length is in centimeters, and its perimeter is in centimeters."}, {"key": "5196", "content": "Divide $$100$$ apples into two piles, where one pile has exactly $$10$$ more than $$5$$ times the other pile. Then, the smaller pile has apples, and the larger pile has apples."}, {"key": "5197", "content": "Two bookshelves, the number of books in bookshelf A is $$5$$ times plus $$20$$ more than that in bookshelf B. Bookshelf A has $$140$$ more books than bookshelf B, thus bookshelf A has books."}, {"key": "5198", "content": "The figure below is part of a three-order magic square, $$X=$$\uff0e question_5198-image_0"}, {"key": "5199", "content": "The bookshelf has two shelves, the number of books on the upper shelf is 2 times plus 3 more than the lower shelf, knowing that the difference between the two shelves is 30 books, then the upper shelf has books."}, {"key": "5200", "content": "There are two wooden boards of the same length, each one is $$30$$ cm. If after overlapping the two boards and nailing them together into one board (as shown in the diagram), the overlapping part is $$10$$ cm, find the length of the resultant board in cm.\n question_5200-image_0"}, {"key": "5201", "content": "A class has a total of $$42$$ people, $$21$$ people participated in the school-organized music activity, $$16$$ people participated in the sports activity, and $$1$$ person participated in both activities, so there are people who did not participate in either activity."}, {"key": "5202", "content": "In the appropriate places between the eight $$8$$s, fill in the operation symbols $$+$$, $$-$$, $$\\times$$, $$\\div$$, (), to make the equation correct.\n$$8~~~~8~~~~8~~~~8~~~~8~~~~8~~~~8~~~~8=1000$$\nThe correct option is:"}, {"key": "5203", "content": "Xiao Jin needs to complete a certain number of math application questions within a specified number of days. If she does 9 questions per day, she will have 5 questions left by the end of the specified days. However, if she does 12 questions per day for the first three days and 7 questions per day for the remaining days, she will be able to just finish all the questions within the specified days. Thus, calculate the total number of math application questions Xiao Jin needs to complete within the specified days."}, {"key": "5204", "content": "Autumn has arrived, and the little white rabbit has harvested a basket of radishes. Calculating the number of days it planned to eat, if it eats 4 radishes per day, there would be 48 radishes left over; if it eats 6 per day, then 8 radishes would be left over. How many radishes did the little white rabbit buy?"}, {"key": "5205", "content": "Insert \"$$+$$, $$-$$, $$\\times $$, $$\\div $$\" into the appropriate dashes to make the equations below true.\n$$2$$$$3$$$$4=24$$\n$$54$$$$9$$$$2=4$$\n$$3$$$$ 8$$$$ 5=43$$\n$$7$$$$12$$$$6=13$$"}, {"key": "5206", "content": "Calculate: $$80\\times 75-150\\times3+75\\times 26=$$."}, {"key": "5207", "content": "Using $$12$$ squares with a side length of $$2$$ cm to form a rectangle, the perimeter of this rectangle could be cm, cm, or cm."}, {"key": "5208", "content": "As shown in the figure, there are $$9$$ small rectangles, among which the areas of $$5$$ small rectangles are $$4$$, $$8$$, $$12$$, $$16$$, $$20$$ square meters, respectively. The areas of the remaining $$4$$ rectangles are , , , square meters. question_5208-image_0"}, {"key": "5209", "content": "The perimeter of a parallelogram is $$30$$ cm, one side is $$8$$ cm, its other side is cm."}, {"key": "5210", "content": "Xiaoming and Xiaohong have a total of $$103$$ candies. Xiaoming ate $$3$$ candies, and Xiaohong bought $$5$$ more candies. At this point, the number of Xiaoming's candies is 4 times that of Xiaohong's. Then, how many candies did Xiaoming originally have?"}, {"key": "5211", "content": "At the ball, there is a segment for the children's model showcase, with four kids: A, B, C, D participating. If A cannot go first, there are a total of different sequences for them to appear."}, {"key": "5212", "content": "When Mingming was doing an addition problem, he mistook one of the addends $$45$$ for $$54$$, and the result of the sum was $$87$$. The correct sum should be."}, {"key": "5213", "content": "When Xiao Yu was doing a subtraction problem, he mistakenly wrote the subtrahend as $$38$$ instead of $$83$$, resulting in an answer of $$513$$. What should the correct difference be?"}, {"key": "5214", "content": "When Xiao Shuai was checking out at the supermarket, the cashier carelessly mistook the 'amount due' of $$69$$ yuan for $$96$$ yuan, as a result, gave Xiao Shuai $$4$$ yuan in change, the cashier should have given Xiao Shuai yuan."}, {"key": "5215", "content": "The doctor asked Dakuan to plant a row of trees on one side of the road. Initially, Dakuan planted $$5$$ poplar trees in a row, after which the doctor said: 'This is not the right way to plant. You should follow the sequence of planting $$3$$ willow trees, $$1$$ pine tree, and then again $$3$$ willow trees, $$1$$ pine tree $$\\cdots \\cdots $$' After that, Dakuan continued to plant according to this pattern. In the end, Dakuan planted a total of $$187$$ trees. question_5215-image_0 \u200b\u200b (1) Trees repeat once. (2) The total number of trees planted in this pattern is $$182$$. These patterned trees can be divided into the same groups, with $$2$$ remaining. (3) There are $$45$$ pine trees, and $$137$$ willow trees."}, {"key": "5216", "content": "$$2021$$ year $$3$$ month $$27$$ day is Saturday, then $$2021$$ year $$3$$ month $$10$$ day is a weekday."}, {"key": "5217", "content": "After filling in appropriate numbers in each cell of the 3$$\\times$$4 grid as shown in the figure, the sum of the numbers filled in each row can be equal, and the sum of the numbers filled in each column can also be equal. Now some numbers have already been filled in, so what is the sum of the numbers filled in each row?\n question_5217-image_0"}, {"key": "5218", "content": "The following picture requires at least how many strokes to complete. question_5218-image_0"}, {"key": "5219", "content": "The diagram below has an odd number of dots. question_5219-image_0"}, {"key": "5220", "content": "The number of books in Class A is $$80$$ more than that in Class B, and the number of books in Class A is $$3$$ times that of Class B."}, {"key": "5221", "content": "Wenjiang Jiaxiang Foreign Languages Primary School held a sports meeting, the number of participants in the running race was 4 times the number of participants in the long jump, and there were 66 more people participating in the running race than in the long jump, there were people participating in the running race."}, {"key": "5222", "content": "Eddie and Viola attended a tree-planting event, where Eddie planted $$20$$ more trees than Viola, and the number of trees planted by Eddie was exactly $$5$$ times that of Viola. How many trees did Viola plant?"}, {"key": "5223", "content": "Fill in the remaining $$5$$ squares with integers in the diagram below, so that the sum of the numbers in each row, each column, and each diagonal is the same. The second number in the third row is.\n question_5223-image_0"}, {"key": "5224", "content": "In a magic square, the sums of the numbers in each row, each column, and each main diagonal are the same. Then, in the shown incomplete magic square, $$A$$ should be.\n question_5224-image_0"}, {"key": "5225", "content": "The following image is a third-order magic square, please fill in the \u203b. question_5225-image_0"}, {"key": "5226", "content": "The diagram below is part of a third-order magic square, $$X=$$\uff0e question_5226-image_0"}, {"key": "5227", "content": "Fill in the appropriate numbers in the squares below so that the sum of the three numbers on each row, column, and diagonal is equal to $$24$$ (three numbers have already been filled in). What number should be filled in the space with a red circle in the middle? question_5227-image_0"}, {"key": "5228", "content": "Which figure has an odd point? (Indicate whether it can be drawn in one stroke) question_5228-image_0"}, {"key": "5229", "content": "Below is a plan of a certain street, Xiao Ming wants to run through all the streets once without repeating, please help Xiao Ming to see if it can be achieved. (write out your reasoning) question_5229-image_0"}, {"key": "5230", "content": "A class has a total of $$35$$ people, each person participates in at least one activity. There are $$21$$ people participating in the school-organized music event, and $$16$$ people participating in the sports activity. So, there are people who participated in both activities."}, {"key": "5231", "content": "Xiaoming's family raises some chickens and rabbits, and they are kept together in the same cage. Xiaoming counted them and found there were a total of $$35$$ heads and $$110$$ feet. How many rabbits are there in Xiaoming's family?"}, {"key": "5232", "content": "Find the pattern and fill in the blank. $$2$$, $$6$$, $$10$$, $$14$$, , $$22$$, $$26$$."}, {"key": "5233", "content": "Eddie goes home after school, gets hungry on the way, decides to go to the supermarket to buy some bread before going home, but he doesn't know how many different shortest routes there are. Kids, please help out! ().\n question_5233-image_0"}, {"key": "5234", "content": "The teacher distributed some notebooks to the children. If each child got $$2$$ notebooks, there were $$13$$ left over; if each got $$4$$ notebooks, there was $$1$$ left over. There were a total of $$\\text{children}$$, and $$\\text{notebooks}$$."}, {"key": "5235", "content": "The kindergarten gives candy to the award-winning children, if each child is given $$6$$ pieces there would be $$12$$ pieces short, if each child is given $$9$$ pieces there would be $$24$$ pieces short, how many children in total won the awards."}, {"key": "5236", "content": "Xiao Mei needs to follow the path shown in the diagram from point $$A$$ to point $$B$$. Since roadwork is being carried out at point $$C$$ making it temporarily impassable, what is the shortest route for Xiao Mei to reach point $$B$$?\n question_5236-image_0"}, {"key": "5237", "content": "A teacher distributes candies to students. If each student gets $$4$$ candies, there would be $$19$$ candies left. If each student gets $$5$$ candies, there would be $$1$$ candy left. There are in total students."}, {"key": "5238", "content": "Insert \"$$+$$\" or \"$$-$$\" between every two adjacent numbers below to make the equation valid.\n$$3$$\u00ad$$3$$\u00ad$$3$$\u00ad$$3=0$$\n$$6$$\u00ad$$6$$\u00ad$$6$$\u00ad$$6=12$$"}, {"key": "5239", "content": "Eddy put some small balls into boxes. If he puts $$15$$ balls into each box, he is $$10$$ balls short; if he puts $$12$$ balls per box, he ends up with $$5$$ extra balls. There are a total of boxes."}, {"key": "5240", "content": "Fill in the blanks: (1) $$3$$ meters $$=$$ decimeters $$=$$ centimeters. (2) $$7$$ square meters $$=$$ square decimeters $$=$$ square centimeters."}, {"key": "5241", "content": "The image below is a three-order magic square with a magic constant of $$33$$. Please fill in the blanks. What is the number in the bottom-left square? question_5241-image_0"}, {"key": "5242", "content": "Fill in the appropriate numbers in the squares below so that the sum of the three numbers on each row, each column, and each diagonal is all equal to $$24$$ (three numbers have been filled in). What number should be filled in the square with the red circle in the middle? question_5242-image_0"}, {"key": "5243", "content": "The street lights are arranged in the order of red, red, blue, green, yellow, blue, green, yellow, blue, green, yellow... The color of the $$50$$th light should be ( )."}, {"key": "5244", "content": "There is a string of colored lights on the TV tower, arranged in the order of \"red, yellow, green, white\". Can you calculate what color the $$27$$th light is?"}, {"key": "5245", "content": "When numbering the pages of a book, a total of 24 number \"8\"s were used and the last page contains the number \"8\" in its page number. Please, how many pages does this book have?"}, {"key": "5246", "content": "The page numbers of a book range from $$1$$ to $$62$$, which means there are a total of $$62$$ pages. When adding up all the page numbers, one page number was accidentally omitted, and as a result, the sum was $$1939$$. Question: What is the omitted page number."}, {"key": "5247", "content": "A dictionary has a total of $$400$$ pages, using the number \"$$0$$\" a total of times."}, {"key": "5248", "content": "If natural numbers, starting from 1 and excluding 0, are arranged in ascending order without any gaps to form a large number: $$1234567891011121314$$... What is the digit in the 200th position from the left?"}, {"key": "5249", "content": "A book has a total of 440 pages. Among the page numbers from 1 to 440, the digit \"3\" is used a total of times."}, {"key": "5250", "content": "As shown in the figure, the side length of the square is $$5$$ cm, the perimeter of this square is cm.\n question_5250-image_0"}, {"key": "5251", "content": "A square has $$4$$ sides, with the length of one side being $$9$$ cm, so the total length of these $$4$$ sides is cm."}, {"key": "5252", "content": "Popo walked around the school basketball court and found that the basketball court is a rectangle with a perimeter of $$90$$ meters and a width of $$15$$ meters, then the length of this basketball court is meters."}, {"key": "5253", "content": "The perimeter of the rectangle is $$66$$ centimeters, the length is $$3$$ centimeters more than the width, find the length of the rectangle in centimeters."}, {"key": "5254", "content": "Da Bai and Xiao Bai have a total of $$50$$ apples, Da Bai has $$10$$ more apples than Xiao Bai. How many apples does Xiao Bai have?"}, {"key": "5255", "content": "Grandpa is $$75$$ years old this year, and dad is $$30$$ years younger than grandpa. When grandpa was $$60$$ years old, dad was years old."}, {"key": "5256", "content": "There are $$9$$ matches, with two people, A and B, taking turns. It is stipulated that each time one can take $$1$$ or $$2$$ matches, and the person who takes the last match wins. If person A goes first, ( ) has a sure-win strategy."}, {"key": "5257", "content": "Among the two figures below, the one with the larger perimeter is . (Fill in the letter representing the figure name on the line)\n question_5257-image_0"}, {"key": "5258", "content": "The figure below is a side view of a staircase. It is known that each step is $$30$$ cm wide and $$15$$ cm high. The perimeter of this side view is in centimeters.\n question_5258-image_0"}, {"key": "5259", "content": "Using $$8$$ square pieces of paper with a side length of $$3$$ cm to form a rectangle, the minimum perimeter of this rectangle is in centimeters."}, {"key": "5260", "content": "A piece of wire can form a square with a perimeter of $$20$$ cm. If this wire is used to form a rectangle with a width of $$4$$ cm, then the length of this rectangle is cm."}, {"key": "5261", "content": "The side length of a square increases by $$3$$ cm, its perimeter increases by ( ) cm."}, {"key": "5262", "content": "All of the figures below are made up of identical small squares, the perimeter of ( ) is the shortest."}, {"key": "5263", "content": "The four cards are respectively labeled with $$1$$, $$2$$, $$3$$, $$4$$. Select some of the cards with the requirement that the sum of the numbers on the selected cards equals $$6$$. Then, there are several ways to select the cards that meet the requirement.\n question_5263-image_0"}, {"key": "5264", "content": "Using the digits $$0$$, $$4$$, $$9$$, you can form different natural numbers without repeating any digit."}, {"key": "5265", "content": "Using $$3$$, $$0$$, $$5$$, $$2$$, how many distinct two-digit numbers can be formed?"}, {"key": "5266", "content": "Fill in the blanks with appropriate numbers to make the equation valid. question_5266-image_0 What is the first addend?"}, {"key": "5267", "content": "Using $$1$$, $$3$$, $$5$$, several three-digit numbers without repeating digits can be formed. If these three-digit numbers are arranged in ascending order, then the $$4$$th three-digit number is."}, {"key": "5268", "content": "Using the five numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, a four-digit number with no repeating digits can be formed."}, {"key": "5269", "content": "Today, the teacher assigned some mental arithmetic homework. Wei'er was able to solve an average of $$48$$ problems per minute for the first $$5$$ minutes, then solved problems at a pace of $$32$$ per minute for $$13$$ minutes, and finally $$36$$ problems per minute for the last $$7$$ minutes. Therefore, the total number of problems assigned by the teacher was 1"}, {"key": "5270", "content": "When calculating 3 4 8 \u00d7 5 7 1 9 8 3 6, the actual meaning of $$5$$ multiplied by $$348$$ in the vertical calculation is ( )."}, {"key": "5271", "content": "Which group of numbers has a product equal to $$2014$$?"}, {"key": "5272", "content": "The teacher also bought $$220$$ balloons for decorating the classrooms, needing to decorate $$20$$ classrooms. So, how many balloons are needed on average per classroom? But then, $$10$$ more classes were suddenly added, needing to decorate $$10$$ more classrooms. So, about how many balloons are needed on average per classroom now? Can they be exactly divided? If not, how many are left? question_5272-image_0"}, {"key": "5273", "content": "The image below is a $$5\\times 5$$ area with $$5$$ trees planted. Now, it is required to set up tents on the vacant land without trees, and the tents must be next to a tree. No two tents occupying grids can share a common edge. The number of tents in each row is shown on the far right, and the number of tents in each column is shown at the bottom. Is there a tent in the 5th row, 3rd column? ( ).\n question_5273-image_0"}, {"key": "5274", "content": "Jungle Treasure Hunt: We are treasure hunting in the jungle, starting from point $$A$$ to point $$B$$. The journey is full of dangers, luckily, there is a map left by previous explorers for reference. However, we found traps everywhere, and even safe places can only be passed once. Can we find the treasure and return safely?\n question_5274-image_0"}, {"key": "5275", "content": "With $$5$$, $$7$$, $$8$$, three cards can form different three-digit numbers."}, {"key": "5276", "content": "There is a string of colored lights on the TV tower, arranged in the order of \"red, yellow, green, white\". Please calculate, what color is the $$27$$th light?"}, {"key": "5277", "content": "$$1$$, $$2$$, $$3$$, $$1$$, $$2$$, $$3$$, $$1$$, \u2026 what is the $$64$$th number."}, {"key": "5278", "content": "$$3\\times 6=18$$, $$33\\times 66=2178$$, $$333\\times 666=221778$$, $$3333\\times 6666=22217778$$..., $$\\underbrace{33\\cdots 3}_{20 3s}\\times \\underbrace{66\\cdots 6}_{20 6s}=$$ ()\uff0e"}, {"key": "5279", "content": "The result of $$1+2+3+4+5+6+7+8+9$$ is an"}, {"key": "5280", "content": "Calculate: $$17\\times 99=$$."}, {"key": "5281", "content": "Compute:\n$$(1)$$$$67\\times 99=$$\uff0e\n$$(2)$$$$33\\times 102=$$\uff0e"}, {"key": "5282", "content": "$$16\\times 31 \\times 25=$$"}, {"key": "5283", "content": "Calculate: $$55\\times 22+55\\times 77=$$."}, {"key": "5284", "content": "Calculate: $$12\\div (4\\div 5)\\div (5\\div 6)\\div (6\\div 7)=$$."}, {"key": "5285", "content": "$$23\\div 5+41\\div 5+36\\div 5$$=\uff0e"}, {"key": "5286", "content": "Is the sum of the equation $$1+2+3+4+\\cdots +2019+2020$$ odd or even?"}, {"key": "5287", "content": "$$96\\times25\\div8=$$"}, {"key": "5288", "content": "$$1790\\div5\\div2=$$"}, {"key": "5289", "content": "The width of the rectangular green space shown in the picture below needs to be increased to $$24$$ meters, length remains unchanged. The area of the expanded green space is square meters.\n question_5289-image_0"}, {"key": "5290", "content": "As shown in the diagram, rectangle $$ABCD$$ is divided into $$9$$ small rectangles. The area of $$5$$ of these small rectangles is shown in the diagram. The area of rectangle $$ABCD$$ is.\n question_5290-image_0"}, {"key": "5291", "content": "If the perimeter of square $$A$$ is twice the perimeter of square $$B$$, then the side length of square $$A$$ is twice the side length of square $$B$$, and the area of square $$A$$ is four times the area of square $$B$$."}, {"key": "5292", "content": "The first quarter of $$2016$$ has ( ) days."}, {"key": "5293", "content": "The Shanghai Expo started from May 1, 2010, and ended on October 1, 2010. This Expo lasted for a total of days."}, {"key": "5294", "content": "This year's Dragon Boat Festival is on May 30, 2017, which is a Tuesday. Counting from this day, 10 days later is ( )."}, {"key": "5295", "content": "The perimeter of a rectangle is $$20$$ cm, and its width is $$4$$ cm shorter than its length. The area of this rectangle is square centimeters."}, {"key": "5296", "content": "Compute: $$2\\div (5\\div 8)\\div (8\\div 17)\\div (17\\div 20)=$$."}, {"key": "5297", "content": "The number of people in Class B is exactly $$4$$ times the number of people in Class A. If $$30$$ people are transferred from Class B to Class A, then the number of people in both Class A and Class B will be the same. Please state the original number of people in Class A and Class B."}, {"key": "5298", "content": "There are two ropes, the first rope is $$10$$ meters long, and the second rope is $$6$$ meters long. After cutting off the same length from both, the remaining part of the first rope is exactly $$3$$ times the length of the remaining part of the second rope. Find how many meters remain for the first and the second ropes, respectively."}, {"key": "5299", "content": "The image shows a corner of the school playground, and its area is in square meters. (Unit in the image: meters)\n question_5299-image_0"}, {"key": "5300", "content": "Can you calculate this simply? $$1\\times 2\\times 3\\times 4\\times 5\\times 6\\times 7\\times 8\\times 9\\times 10\\div \\left( 24\\times 25\\times 27 \\times 28\\right)=$$"}, {"key": "5301", "content": "Calculate.$$288\\div 24+288\\div 18+288\\div 6=$$."}, {"key": "5302", "content": "Calculate:$$52\\times 49+52\\times 50+52=$$"}, {"key": "5303", "content": "There is a line of colored flags on the sports field, totaling $$234$$ flags, arranged in an order of $$3$$ red flags followed by $$1$$ yellow flag. Among these colored flags, there are red flags and yellow flags."}, {"key": "5304", "content": "In the game Zuma, from the dragon's mouth continuously come many colored dragon balls, first $$4$$ red balls, followed by $$3$$ yellow balls, then $$2$$ green balls, and finally $$1$$ white ball, repeating in this manner. The $$2000$$th dragon ball to come out of the dragon's mouth is ( )."}, {"key": "5305", "content": "In January 2012, there were 4 Saturdays and 5 Sundays. So, what day of the week was the second day of the Chinese New Year (January 24th) in 2012?"}, {"key": "5306", "content": "April 17, 2019, was Wednesday, May 8 was a weekday."}, {"key": "5307", "content": "In the diagram of nine squares below, two numbers have already been filled in. Please fill in seven more non-zero natural numbers so that the product of any row, any column, or any diagonal of three numbers is equal. Then $$A\\times B$$=.\n question_5307-image_0"}, {"key": "5308", "content": "In January 2012, there were 4 Saturdays and 5 Sundays, so the first day of the Chinese New Year (January 23) fell on a _____."}, {"key": "5309", "content": "In the nine squares of the diagram below, two numbers have already been filled in. Please fill in seven more non-zero natural numbers so that the product of any three numbers in a row or column is equal. Then $$A\u00d7B$$=.\n question_5309-image_0"}, {"key": "5310", "content": "In the title image, there are 9 squares, and it is required to fill each square with different numbers so that the sum of the three numbers on each row, each column, and each diagonal line is equal. The question mark represents the number.\n question_5310-image_0"}, {"key": "5311", "content": "The figure below is a third-order magic square, the number at \"$$?$$\" is.\n question_5311-image_0"}, {"key": "5312", "content": "The diagram below is a floor plan of an exhibition hall, which is composed of five exhibition rooms. There is a door connecting every pair of exhibition rooms, and the exhibition hall also has one entrance and one exit. Can a visitor pass through all the doors without repetition and enter through the entrance and exit through the exit? ( )\n question_5312-image_0"}, {"key": "5313", "content": "Observe the statistical chart on the right. The correct statement(s) is (are) ( ).\n\u2460From September to November, the monthly sales volume of Brand A was higher than that of Brand B;\n\u2461From September to November, the profit of Brand A was higher than that of Brand B;\n\u2462From September to November, the average monthly sales volume of both Brand A and Brand B was above $$150$$ units;\n\u2463Based on this estimation, the sales volume in December should be very good.\n question_5313-image_0"}, {"key": "5314", "content": "The teacher bought a total of $$20$$ items including automatic pens and workbooks, spending a total of $$40$$ dollars, with each automatic pen costing $$1$$ dollar and each workbook costing $$3$$ dollars. How many automatic pens and workbooks did the teacher buy?"}, {"key": "5315", "content": "In the cage, there are unicorns (one-legged creatures) and triclops (three-legged creatures) with a total of $30$ creatures. They have a total of $42$ legs. Calculate the number of unicorns and triclops"}, {"key": "5316", "content": "The total value of $$12$$ coins is $$9$$ dimes, which include only two types, $$5$$ cents and $$1$$ dime each. So how many of each type of coin are there?"}, {"key": "5317", "content": "A certain school carried out activities for technology and art interest groups. There were a total of 60 students in the fourth grade. 41 students participated in the technology interest group, 13 students participated in both interest groups, and 7 students did not participate in any. Some students participated in the art interest group."}, {"key": "5318", "content": "Teacher Zhou conducted a questionnaire survey among $$42$$ people. The result shows that $$18$$ people like reading, $$22$$ people like writing, $$16$$ people like recitation, $$6$$ people like both reading and writing, $$8$$ people like both reading and recitation, $$9$$ people like both writing and recitation, and there are $$5$$ people who like all three hobbies. Some people do not have any of these three hobbies."}, {"key": "5319", "content": "In a math competition, there were a total of $$20$$ questions. Each correct answer was awarded $$8$$ points, while each wrong answer or unanswered question resulted in a deduction of $$5$$ points. Xiao Bai ended up with $$69$$ points. How many questions did he get right?"}, {"key": "5320", "content": "Below is a bar chart for the water usage statistics of Xiao Pang's family for the four quarters of $$2017$$: Quarter First Quarter Second Quarter Third Quarter Fourth Quarter Total Water Usage/Ton $$11$$$$14$$$$16$$$$56$$ (1) Xiao Pang's family used more water in the fourth quarter than in the first quarter. (2) Draw a bar chart for the water usage of Xiao Pang's family for the four quarters of $$2017$$. question_5320-image_0"}, {"key": "5321", "content": "Analyze the bar chart as shown, the average monthly car sales volume in the second half of the year, October sales increased by units compared to September. question_5321-image_0"}, {"key": "5322", "content": "A book, on the first day Xiao Bai read half of the book minus $$5$$ pages, and on the second day read half of what was left plus $$6$$ pages, with $$40$$ pages remaining unread. How many pages are there in this book in total?"}, {"key": "5323", "content": "There are two bookshelves, a large one and a small one. The large bookshelf has $$30$$ books and the small bookshelf has $$17$$ books. After removing the same number of books from both shelves, the number of books on the large bookshelf is $$3$$ times plus $$1$$ more than the number of books on the small bookshelf. Calculate how many books are now on the large bookshelf and how many books are on the small bookshelf."}, {"key": "5324", "content": "In a certain month, there are more Mondays than Tuesdays, and more Sundays than Saturdays, then this month has a total of ___ days."}, {"key": "5325", "content": "Newton and Einstein participated in a competition and won many medals. The number of Einstein's medals was 3 times that of Newton's. Later, Einstein gave Newton 20 medals, and as a result, both had an equal number of medals. How many medals does Einstein have now?"}, {"key": "5326", "content": "In January 2012, there were 4 Saturdays and 5 Sundays, so the first day of the Lunar New Year (January 23) in 2012 was on a."}, {"key": "5327", "content": "Xiaoqing and Dapeng originally had $$32$$ chocolates in total. After Xiaoqing gave $$4$$ chocolates to Dapeng, Dapeng had three times as many chocolates as Xiaoqing. Originally, Xiaoqing had pieces of chocolate."}, {"key": "5328", "content": "The perimeter of a rectangle is $$48$$ dm, if both the length and the width are increased by $$8$$ dm, its area increases by square centimeters."}, {"key": "5329", "content": "Students A, B, C, D$$4$$ are lined up in a row for a photo, with A required to be on the far right and B not on the far left. There are a total of different ways to line up."}, {"key": "5330", "content": "There are $$8$$ different technology books and $$5$$ different comic books on the bookshelf, Eddie wants to choose a book to read, he has several different choices; Vi chooses $$2$$ books of different types to read, she has several different choices."}, {"key": "5331", "content": "A large rectangle is divided into four smaller rectangles, the area of three of these rectangles is shown as in the diagram. Then, the area of the unmarked rectangle is. question_5331-image_0"}, {"key": "5332", "content": "$$49\\times 34+49\\times 23+57\\times 51$$=."}, {"key": "5333", "content": "Calculate: $$251-216+149-184$$=."}, {"key": "5334", "content": "The length of a diagonal of a square is $$12$$ cm, the area of this square is square centimeters."}, {"key": "5335", "content": "Wang Lin's family uses three times the amount of water as Zhang Wen's family, and Wang Lin's family uses 20 tons more water than Zhang Wen's family. The water-saving Zhang Wen's family uses ____ tons of water."}, {"key": "5336", "content": "A class has $$56$$ students. There are $$28$$ students participating in the English competition and $$27$$ students participating in the sports competition. If there are $$25$$ students who did not participate in both, then the number of students participating in both the English and sports competitions is."}, {"key": "5337", "content": "Among these $$2008$$ natural numbers from $$1$$ to $$2008$$, the total number of numbers that are exactly multiples of any two of $$3$$, $$5$$, $$7$$ is."}, {"key": "5338", "content": "In the third grade, class three, $$45$$ students participated in a subject competition. After the results were announced, $$10$$ students scored full marks in English, $$3$$ students scored full marks in both English and Chinese, and $$29$$ students did not score full marks in both subjects. Please calculate: how many students scored full marks in Chinese."}, {"key": "5339", "content": "Compiling a book's page numbers used a total of $$492$$ digits, please ask how many pages this book has. Among these page numbers, the digit \"$$5$$\" was used a total of times."}, {"key": "5340", "content": "A book has a total of $$500$$ pages. Among the page numbers from $$1$$ to $$500$$, the digit \u201c$$1$$\u201d is used a total of times."}, {"key": "5341", "content": "The last digit of the result of the expression $$\\left( {{367}^{367}}+{{762}^{762}} \\right)\\times {{123}^{123}}$$ is."}, {"key": "5342", "content": "As shown in the diagram, four small animals keep swapping seats. Initially, the mouse sits in chair number $$1$$, the monkey sits in chair number $$2$$, the rabbit sits in chair number $$3$$, and the cat sits in chair number $$4$$. The first swap is between the front and back rows, the second swap, based on the first one, is between the left and right columns, the third swap is again between the front and back rows, and the fourth swap is again between the left and right columns $$\\cdots \\cdots$$ This continues. After the tenth swap, the cat sits in chair number __, the rabbit sits in chair number __, the monkey sits in chair number __, the mouse sits in chair number __.\n question_5342-image_0"}, {"key": "5343", "content": "The number A is 5 times of number B. If A increases by 16 and B increases by 32, then A becomes 2 times B. What was the original A."}, {"key": "5344", "content": "Fill in a digit in $$\\square$$ so that the number can be divided by $$3$$. What are the possible digits you can fill in?\n$$\\square 732$$"}, {"key": "5345", "content": "Fill in a proper number in $$\\overline{29\\square }$$ so that it is divisible by both $$2$$ and $$3$$. ( )"}, {"key": "5346", "content": "$$\\overline{35\\square73}$$ can be divided by $$11$$, the number in the space is ( )."}, {"key": "5347", "content": "Which one in the picture below is an angle? \uff08 \uff09."}, {"key": "5348", "content": "The corners of a rectangular table are ( )."}, {"key": "5349", "content": "The angle of a right angle is ( )."}, {"key": "5350", "content": "$$72\\div9=$$"}, {"key": "5351", "content": "$$48\\times5\\div8=$$"}, {"key": "5352", "content": "Place appropriate operators and parentheses on the left side of the equation below, the option that makes the equation true is ( ). $$8\\;\\;\\;\\;\\;\\;\\;\\;1\\;\\;\\;\\;\\;\\;\\;\\;5=35$$"}, {"key": "5353", "content": "$$116+57-16=$$."}, {"key": "5354", "content": "When numbering the pages of a book, a total of $$24$$ number \"$$8$$s\" were used and the last page contains the number \"$$8$$.\" May I ask how many pages does this book have?"}, {"key": "5355", "content": "Arrange non-zero natural numbers in ascending order without intervals to form a large number: $$1234567891011121314\\cdots \\cdots $$ What is the $$100$$th digit from the left?"}, {"key": "5356", "content": "A book has a total of 440 pages, among the page numbers from 1 to 440, a total number of the digit \u201c3\u201d is used."}, {"key": "5357", "content": "A book has a total of $$300$$ pages. Among the page numbers $$1\\sim 300$$, the digit \u201c$$5$$\u201d was used a total of times."}, {"key": "5358", "content": "The area of the parallelogram in the diagram below is ( ).\n question_5358-image_0"}, {"key": "5359", "content": "A certain store sold different brands of air conditioners in March and April, with the sales volume as follows in the table. Based on the data in the table, answer the following questions:\nHow many air conditioners were sold in March in total;\nThe difference in the number of Midea brand air conditioners sold between March and April is.\n question_5359-image_0"}, {"key": "5360", "content": "Every student in a certain class has subscribed to at least one video, 25 people subscribed to 'Firework Egg', 30 people subscribed to 'Superhero Adventure', and 10 people subscribed to both. Therefore, the class has people."}, {"key": "5361", "content": "Chickens and rabbits are in the same cage, the number of chickens is three times that of the rabbits, together they have 120 legs, then, there are chickens and rabbits."}, {"key": "5362", "content": "Using the digits $$1$$, $$2$$, $$3$$, you can form different natural numbers without repeating any digit."}, {"key": "5363", "content": "In the equation below, the same letters represent the same digits, and different letters represent different digits. Then $$A=$$, $$B=$$, $$C=$$, $$D=$$. question_5363-image_0"}, {"key": "5364", "content": "In the following long addition, different Chinese characters represent the ten different digits from $$0\\sim9$$. If this long addition is valid, the smallest four-digit number represented by 'listening to the soundless water' is."}, {"key": "5365", "content": "Four people, A, B, C, and D, put in the same amount of money to order the same specification for several New Year gifts. After purchasing the gifts, A, B, C, respectively, got 3, 7, 14 more gifts than D. At settlement, to ensure fairness, those who got more gifts had to pay money to those who got fewer. Each person either paid money or received money. Finally, B paid D $14, and B did not pay A any money. Then, C should pay D an additional amount of money."}, {"key": "5366", "content": "After a student completed their math homework, they accidentally spilled ink on the homework paper (as shown in the figure). Please calculate the number of students who achieved excellent, good, and passing grades respectively, based on the provided conditions, and then complete the statistics chart. (1) The number of students who passed is 1 less than 45 times the number of students who failed; (2) The sum of the number of students with excellent and passing grades is 13 more than the number of students with good grades; (3) The number of students with excellent grades is 12 less than twice the number of students with passing grades. Excellent; Good; Passing. question_5366-image_0"}, {"key": "5367", "content": "As shown in the diagram, it represents Xiao Hua's scores for 4 tests, where $$78$$ is the average score of the first four tests. To increase the average score by $$4$$ points in the 5th test, what is the minimum score that must be achieved in the 5th test? Please draw the line for the 5th test score and the average score line for 5 tests. question_5367-image_0"}, {"key": "5368", "content": "A class has a total of $$30$$ students, among whom $$26$$ can play badminton, $$9$$ can play table tennis, and no one who cannot do both sports, some people in the class can play both badminton and table tennis."}, {"key": "5369", "content": "The brother and his younger brother were $$5$$ years apart last year, and this year their combined ages are $$15$$ years. So, this year the brother is $$10$$ years old, and his younger brother is $$5$$ years old. question_5369-image_0"}, {"key": "5370", "content": "In the same plane, $$8$$ lines can have at most how many intersection points."}, {"key": "5371", "content": "Using $$90$$ chess pieces to form a three-layer hollow square matrix, how many chess pieces are there in the outermost layer."}, {"key": "5372", "content": "Running two laps on a rectangular playground that is $$80$$ meters long and $$40$$ meters wide, in total you have to run ( ) meters."}, {"key": "5373", "content": "The length of a rectangle is $$8$$ meters, and the width is $$4$$ meters, the perimeter of this rectangle is ( ) meters."}, {"key": "5374", "content": "Which of the following is NOT a method to calculate the perimeter of a rectangle ( )."}, {"key": "5375", "content": "As shown in the diagram, there is a rectangular sheet of paper that is $$12$$ cm long and $$10$$ cm wide. If the sheet is cut into two parts along the dotted line, the sum of the perimeters of these two parts is in cm.\n question_5375-image_0"}, {"key": "5376", "content": "Cut the largest possible square from a rectangular piece of paper measuring $$75$$ cm in length and $$48$$ cm in width, then cut another largest possible square from the remaining part, and continue this process repeatedly. The sum of the perimeters of the first $$5$$ squares cut out is in centimeters."}, {"key": "5377", "content": "As shown in the figure, $$8$$ equally sized small rectangles form a large rectangle. It is known that the perimeter of the large rectangle is $$28$$ cm, then the perimeter of the small rectangle is centimeters. question_5377-image_0"}, {"key": "5378", "content": "There is a rectangle shaped paper, if you make $$3$$ vertical cuts, resulting in $$4$$ rectangles whose total perimeter is $$2$$ times the original rectangle's perimeter. Then, if you make $$3$$ horizontal cuts, resulting in $$4$$ rectangles, the total perimeter of these rectangles is what multiple of the original rectangle's perimeter."}, {"key": "5379", "content": "As shown in the figure below, the unit of the marked values is centimeters. The perimeter of this figure is in centimeters.\n question_5379-image_0"}, {"key": "5380", "content": "As shown in the figure, the circumference of the inner square is 24 cm. Based on the numbers given in the diagram, calculate the perimeter of the rectangle in cm. (Unit: cm)\n question_5380-image_0"}, {"key": "5381", "content": "Place the six square sheets of paper with a side length of $$10$$ cm as shown in the diagram. Each small square sheet is covered by a smaller square, whose side length is half of the original square's side length. The perimeter of the outline of the figure in the diagram (the thick lines) is in centimeters.\n question_5381-image_0"}, {"key": "5382", "content": "Select any two from $$0$$, $$2$$, $$3$$, $$7$$ to form different two-digit numbers. Among these two-digit numbers, there are a total of ( ) different odd numbers."}, {"key": "5383", "content": "Among the two-digit numbers formed by the digits $$3$$, $$5$$, $$0$$, $$8$$ on these $$4$$ digit cards, what is the smallest odd number? ( )"}, {"key": "5384", "content": "For the following vertical calculation, the same letter represents the same digit and different letters represent different digits. Assuming no carry over, find the value of $$A+B+C+D$$ ( ).\n question_5384-image_0"}, {"key": "5385", "content": "Fill in a suitable number in the blank of the equation below to make the equation valid. The final result is.\n question_5385-image_0"}, {"key": "5386", "content": "Among the following vertical addition problems, the tens place of the sum is ( ).\n\n\n\n\n\u25a1\n\n\n+\n\u25a1\n\n\n\u25a1\n\u25a1"}, {"key": "5387", "content": "The same letters represent the same numbers, and different letters represent different numbers, so the four-digit number $$\\overline{ABCD}$$ is.\n question_5387-image_0  question_5387-image_1"}, {"key": "5388", "content": "Different shapes represent different numbers, what number does each of the following shapes represent? Please choose the correct answer ( ).\n$$\\begin{matrix}& \u25b2 & 8 \\\\ +&1 & \u25a0 \\\\ \\hline &6 & 4 \\end{matrix}$$\n\u25b2$$=(\\quad )$$\n\u25a0$$=(\\quad )$$"}, {"key": "5389", "content": "The picture on the right is an addition equation of a two-digit number, given that $$A+B+C+D=22$$, then $$X+Y=$$ ( ).\n question_5389-image_0"}, {"key": "5390", "content": "Using an $$8$$ meter long wire to form a square, the perimeter of this square is ( ) meters"}, {"key": "5391", "content": "With $$2$$, $$4$$, $$7$$, $$1$$ forming two-digit numbers without repetition, you can form ( ) numbers."}, {"key": "5392", "content": "If two iron wires of the same length are used to form a rectangle and a square, respectively, then ( )."}, {"key": "5393", "content": "If the side length of a square increases by $$3$$ cm, then its perimeter will increase by ( ) cm."}, {"key": "5394", "content": "In the equation below, four small pieces of paper each cover a number. What is the total sum of the four numbers covered?\n question_5394-image_0"}, {"key": "5395", "content": "As shown in the diagram, the square is divided into four smaller squares, the perimeter of each small square is ( )\uff0e\n question_5395-image_0"}, {"key": "5396", "content": "Among the following multiplication operations, the one with the smallest product is ( )."}, {"key": "5397", "content": "When calculating $$603\\div 2$$, the result of dividing the $$6$$ in the hundreds place by $$2$$ should be written in the (\u3000\u3000) place."}, {"key": "5398", "content": "As shown in the right figure, in the vertical form of $$48\\div 4$$, the number pointed to by the arrow represents ( ).\n question_5398-image_0"}, {"key": "5399", "content": "$$3$$ persons digging a $$3$$ meter long trench requires $$3$$ hours, plan to dig a $$50$$ meter long trench of the same type in $$50$$ hours, according to this calculation, the number of people needed is."}, {"key": "5400", "content": "$$6$$ workers produce $$360$$ machine parts in $$2$$ hours, if the number of workers is doubled and the time increases by $$2$$ hours, then the number of machine parts produced will be ( ) pieces."}, {"key": "5401", "content": "Perform vertical calculations.\n$$3\\times 30=$$  $$2\\times 60=$$  $$4\\times 50=$$"}, {"key": "5402", "content": "When calculating $$46 \\div 2$$ using the column method, usually start with ( )."}, {"key": "5403", "content": "The school is holding a sports meet, and the students have prepared $$96$$ balloons, which can be tied into bunches of $$6$$ each. How many bunches can be made? Xiao Hua has calculated the result using vertical calculation, and the arrow in the calculation points to ( ).\n question_5403-image_0"}, {"key": "5404", "content": "There are a total of $$6$$ pieces of chocolate, fairly distributed to $$3$$ people, each person gets ( ) pieces of chocolate."}, {"key": "5405", "content": "The expression that produces a different result from $$48\\times 60$$ is ( )."}, {"key": "5406", "content": "West Rainbow City is selecting a group of singers. The enrollment threshold was determined based on the audition results, and eventually, $$30$$ out of $$630$$ contestants were admitted. If the average score of all contestants is $$48$$, the average score of the admitted contestants is $$88$$, and the average score of the contestants not admitted is $$32$$ points lower than the enrollment threshold, then the enrollment threshold is __ points."}, {"key": "5407", "content": "Compute: $$\\frac{9}{10}-\\frac{1}{2}=$$; $$\\frac{3}{7}+\\frac{9}{14}=$$; $$\\frac{17}{15}-\\frac{7}{20}=$$\uff0e"}, {"key": "5408", "content": "Calculate: $$1\\frac{1}{2}+2\\frac{1}{4}+3\\frac{1}{8}=$$."}, {"key": "5409", "content": "Calculate: The sum of all proper fractions with a denominator of $$7$$ is."}, {"key": "5410", "content": "The sum of the largest proper fraction and the smallest improper fraction with a unit fraction of $$\\frac{1}{11}$$ is."}, {"key": "5411", "content": "$$\\frac{1}{2}+\\frac{1}{6}+\\frac{2}{15}+\\frac{3}{40}=$$."}, {"key": "5412", "content": "$$20$$ athletes, riding motorcycles and performing along the straight path of the bridge, each motorcycle is $$2$$ meters long, with a distance of $$10$$ meters between two consecutive motorcycles, the length of this motorcade in meters is\uff0e"}, {"key": "5413", "content": "On a circular track with a perimeter of $$400$$ meters at a certain school, a red flag is placed every $$8$$ meters. Then, a yellow flag is placed every $$2$$ meters between two adjacent red flags. The number of red and yellow flags needed should be prepared."}, {"key": "5414", "content": "Walking from the first floor to the third floor requires climbing $$20$$ steps in total. If the number of steps to climb up each floor is the same, then the total number of steps required to go from the first floor to the eighth floor is ."}, {"key": "5415", "content": "Zhi Zhi and Hui Hui went to their teacher's house for a visit, the teacher lives on the $$15$$th floor, both of them started walking up from the first floor at the same pace, when Zhi Zhi reached the $$3$$rd floor, Hui Hui just reached the $$5$$th floor. When Hui Hui reached the teacher's home, Zhi Zhi was on the $$8$$th floor."}, {"key": "5416", "content": "Xiaoming's house has a large clock in the hall, which strikes 5 times at 5 o'clock, and takes 8 seconds to complete. So, when it's 10 o'clock, the clock will strike 10 times, how many seconds it will take to complete (ignoring the time it takes for each strike)."}, {"key": "5417", "content": "The image below shows a $$6\\times 6$$ area with $$7$$ trees planted. It is required to set up tents on the vacant land without trees, with the condition that the tents must be stationed beside a tree. Any two tents should not share a common point, and the number of tents in each row and column must be as indicated to the far left and top, respectively. Question: Is there a tent at row $$5$$, column $$4$$ ( )?\n question_5417-image_0"}, {"key": "5418", "content": "Use $$5$$ identical cups to hold water, with water levels at $$4$$ cm, $$5$$ cm, $$6$$ cm, $$7$$ cm, $$8$$ cm, respectively. The average water level of these $$5$$ cups is ( ) cm."}, {"key": "5419", "content": "Xiao Dong completed $$27$$ problems in $$3$$ hours. At this rate, how many problems can he complete in $$8$$ hours? And how long does it take to complete $$108$$ problems?"}, {"key": "5420", "content": "Among the weights of three people, A, B, and C, A is the lightest and C is the heaviest, so the average weight of these three people is ( )."}, {"key": "5421", "content": "If it takes $$9$$ minutes to saw a wooden stick into $$4$$ segments, then it will take (\u3000\u3000) minutes to saw the same wooden stick into $$7$$ segments."}, {"key": "5422", "content": "A fruit shop mixes $$3$$ kilograms of fruit candies with $$9$$ kilograms of milk candies to make mixed candies. It is known that the fruit candies cost $$7$$ yuan per kilogram and the milk candies cost $$11$$ yuan per kilogram. How much does the mixed candies cost per kilogram?"}, {"key": "5423", "content": "If a $$20$$ meter-long wire is cut into $$4$$ meter-long pieces, it needs to be cut (\u3000\u3000) times."}, {"key": "5424", "content": "Xiao Hong weighs $$30$$ kg, Xiao Huang weighs $$35$$ kg, Xiao Bai weighs $$28$$ kg, their average weight is ( ) kg."}, {"key": "5425", "content": "Calculate: $$1-\\frac{1}{4}+\\frac{3}{4}=$$ ( )."}, {"key": "5426", "content": "As the following picture shows, the numbers in the blanks are all from 2 to 6 (reusable). What is the sum of the numbers in these $$9$$ blanks?\n question_5426-image_0"}, {"key": "5427", "content": "In the calculation below, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers, making the equation valid. So, the four-digit number '\u559c\u7231\u6570\u5b66' is ().\n question_5427-image_0"}, {"key": "5428", "content": "Calculate $$4\\times 139\\times 25$$="}, {"key": "5429", "content": "Calculate $$237\\times 2\\times 5 $$="}, {"key": "5430", "content": "Calculate $$125\\times (8\\times 23)$$="}, {"key": "5431", "content": "Calculate $$\\left( 625\\times 3 \\right)\\times16 $$="}, {"key": "5432", "content": "Calculate: $$25\\times 24$$="}, {"key": "5433", "content": "Calculate: $$84\\times 25$$="}, {"key": "5434", "content": "Compute: $$125\\times 72$$="}, {"key": "5435", "content": "Calculate: $$36\\times (200-1)$$=."}, {"key": "5436", "content": "Calculate: $$(300+2)\\times 23$$=."}, {"key": "5437", "content": "Calculate: $$(400-3)\\times 25$$=."}, {"key": "5438", "content": "Calculate: $$52\\times 101$$=."}, {"key": "5439", "content": "Calculate: $$46\\times 99$$=\uff0e"}, {"key": "5440", "content": "Calculate: $$67\\times 139-67\\times 39$$=\uff0e"}, {"key": "5441", "content": "Calculate: $$35\\times 19+35\\times 82-35$$=\uff0e"}, {"key": "5442", "content": "Calculate $$46\\times 36+63\\times 46+46$$="}, {"key": "5443", "content": "Calculate $$80\\times 95-2\\times 95+95\\times 22$$="}, {"key": "5444", "content": "Calculate: $$28\\times 52+72\\times 21+72\\times 31$$=."}, {"key": "5445", "content": "Calculate: $$29\\times 33+76\\times 53+29\\times 43+76\\times 18$$=\uff0e"}, {"key": "5446", "content": "Calculate: $$99\\times 22+33\\times 34$$="}, {"key": "5447", "content": "Calculate: $$50\\times 13+25\\times 74$$=\uff0e"}, {"key": "5448", "content": "Calculate: $$36\\times 219+64\\times 220$$=."}, {"key": "5449", "content": "Calculate: $$70\\times 1995-3990+1995\\times 32=$$"}, {"key": "5450", "content": "Calculate: $$80\\times 75-150+75\\times 22$$=\uff0e"}, {"key": "5451", "content": "There are two baskets of apples, A and B. Basket A's apples weigh $$156$$ kilograms more than Basket B's apples. Basket A has $$24$$ kilograms less than $$5$$ times the weight of Basket B. How many kilograms of apples are in Basket A? ( )"}, {"key": "5452", "content": "Two wires of equal length, the first one used 149 meters, after the second one used 26 meters, among the remaining meterage, the second one is 4 times the length of the first one. Question: How long were the two wires originally, respectively?"}, {"key": "5453", "content": "$$6$$ years ago, the father's age was $$5$$ times the son's age. In $$6$$ years, the combined age of the father and son will be $$78$$ years. Question: How old is the father this year."}, {"key": "5454", "content": "This year, Xiaobing is $$7$$ years old, Xiaobing's mom is $$35$$ years old, after the year, mom's age will be $$3$$ times that of Xiaobing."}, {"key": "5455", "content": "This year, mom is $$33$$ years older than Fangfang. In $$5$$ years, mom's age will be $$4$$ times Fangfang's age. Find mom's age this year."}, {"key": "5456", "content": "Tian Tian, You You, and Si Si are good friends born in the same year, they all live in the same community and often play with Xiao Xin, the elder brother from the same neighborhood. One day, Xiao Xin tested them by saying: 'My age this year is equal to the sum of your three ages. After $$15$$ years, the sum of your three ages will be twice my age. Do you know how old I am this year?' Please use the knowledge you've learnt in this lesson to help the three good friends solve this problem."}, {"key": "5457", "content": "Currently, the mother's age is exactly 6 times the daughter's age. 9 years later, the mother's age will be 3 times the daughter's age. Therefore, the mother's current age is years old."}, {"key": "5458", "content": "It is known that Dad is $$6$$ years older than Mom. $$2$$ years ago, the sum of their ages was $$7$$ times the age of their son. $$3$$ years later, the sum of their ages will be $$9$$ years more than $$5$$ times the son's age. $$2$$ years ago, Mom's age was years."}, {"key": "5459", "content": "A said to B: 'When I was your current age, you were only $$5$$ years old.' B said to A: 'When I am your current age, you will be $$50$$ years old.' So, A is now __ years old, B is now __ years old."}, {"key": "5460", "content": "As shown in the picture, a large square is formed with $$6$$ identical small rectangles. The perimeter of the large square is $$48$$ centimeters. Then, the perimeter of the small rectangle is centimeters.\n question_5460-image_0"}, {"key": "5461", "content": "As shown in the figure, in a square garden with a side length of $$8$$ meters, there are $$4$$ paths with a width of $$1$$ meter each (the shaded part in the figure). Calculate the area of the garden (the blank part) in square meters. question_5461-image_0"}, {"key": "5462", "content": "As shown in the figure, each of the adjacent sides of a square is increased by $$2$$ cm, and the area is increased by $$40$$ square cm. The perimeter of the original square is in centimeters. question_5462-image_0"}, {"key": "5463", "content": "Given any $$4$$ points on the same plane, how many lines can be determined? Try to draw. ( )"}, {"key": "5464", "content": "In the diagram, there are $$6$$ straight lines and $$11$$ intersections. Remove $$1$$ straight line to decrease the number of intersections by $$5$$. Which line number should be removed?\n question_5464-image_0"}, {"key": "5465", "content": "There are $$5$$ points in the diagram from which $$6$$ straight lines can be drawn. By adding another point to the diagram, if you want to increase the number of different straight lines, how many situations can you think of.\n question_5465-image_0"}, {"key": "5466", "content": "The teacher distributes candies to the students, if each student gets 9 candies, there are 2 short; if each student gets 11 candies, there are 14 short. So, there are a total of students, and the teacher prepared candies."}, {"key": "5467", "content": "The teacher distributes candies to the students. If each student gets 4 candies, there are 17 candies left; if each student gets 7 candies, there are 10 candies short. Hence, there are in total students, and the teacher prepared candies."}, {"key": "5468", "content": "The Monkey King distributes peaches to the little monkeys. If he gives each little monkey $$4$$ peaches, there will be $$5$$ peaches left; if he gives each little monkey $$5$$ peaches, then there will be $$4$$ peaches short. So, how many little monkeys are there in total, and how many peaches did the Monkey King prepare?"}, {"key": "5469", "content": "There are some envelopes and stationery on the desk, if each letter uses $$2$$ pieces of stationery, after using up all the envelopes, there are still $$20$$ pieces of stationery left; if each letter uses $$3$$ pieces of stationery, then after using up all the stationery, there are still $$10$$ envelopes left. So, how many pieces of stationery and how many envelopes are there on the desk."}, {"key": "5470", "content": "The coach distributed some badminton shuttlecocks among several players. Each received $$5$$ shuttlecocks with $$10$$ left over; if the number of players were to triple, and each wanted to receive $$2$$ shuttlecocks, there would be $$8$$ short. Therefore, the coach prepared a total of shuttlecocks."}, {"key": "5471", "content": "Olympic venues implement garbage sorting treatment. Five garbage bins are placed in each place, labeled from left to right as: batteries, plastics, waste paper, cans, non-recyclable, as shown in the figure. Now it is planned to paint the five garbage bins one of the three colors: red, green, blue, with the requirement that adjacent garbage bins must be of different colors, and the garbage bin for recycling waste paper cannot be painted red. There are a total of methods for coloring.\n question_5471-image_0"}, {"key": "5472", "content": "There are $$10$$ stations between Beijing and Guangzhou, among which only two are major stations (excluding Beijing and Guangzhou), and vehicles departing from major stations can have sleeper berths. Thus, the railway bureau needs to prepare different types of sleeper tickets."}, {"key": "5473", "content": "An electronic clock displays the time from $$00:00:00$$ to $$23:59:59$$. The electronic clock changes every $$1$$ second. Over a 24-hour period, there are moments when the time read from left to right and from right to left are in the same numerical order. Find how many seconds there are during these moments."}, {"key": "5474", "content": "Calculate: $$3752\\div \\left(39\\times 2\\right)+5030\\div \\left(39\\times 10\\right)=$$."}, {"key": "5475", "content": "There are four types of calculating devices: $$A$$, $$B$$, $$C$$, and $$D$$. Device $$A$$ multiplies the input number by $$5$$; Device $$B$$ adds $$3$$ to the input number; Device $$C$$ divides the input number by $$4$$; Device $$D$$ subtracts $$6$$ from the input number. These devices can be connected in sequence, such as connecting Device $$A$$ to Device $$B$$ is written as $$A\\bullet B$$, and inputting $$4$$ results in $$23$$. Connecting Device $$B$$ to Device $$A$$ is written as $$B\\bullet A$$, and inputting $$4$$ results in $$35$$. Thus, when the devices $$A\\bullet C\\bullet D$$ are connected in sequence and input $$28$$, the result is ."}, {"key": "5476", "content": "Calculate: $$1\\div (2\\div 3)\\div (3\\div 4)\\div (4\\div 5)\\div \\cdots \\div (2017\\div 2018)=$$."}, {"key": "5477", "content": "Calculate. (1) $$1122\\div (34\\times 11)=$$\uff0e(2) $$6300\\div \\left( 5\\times 3\\times 7 \\right)=$$\uff0e"}, {"key": "5478", "content": "Given an arithmetic sequence, the 5th term is $$34$$, and the 15th term is $$104$$. Find the 10th term of this sequence."}, {"key": "5479", "content": "An arithmetic sequence has a total of $5$ numbers, with a sum of $45$. Then, the third number in this arithmetic sequence is."}, {"key": "5480", "content": "A certain school's fifth-grade class of $$162$$ students go boating. It is known there are large boats that can hold $$7$$ people each, with a rental price of $$100$$ yuan per boat, and small boats that can hold $$5$$ people each, with a rental price of $$75$$ yuan per boat. To ensure every student gets on a boat, the minimum amount these $$162$$ students need to spend on boat rentals is yuan."}, {"key": "5481", "content": "There are five lathes in the workshop that malfunction at the same time. It is known that the repair time for the first to the fifth lathe is sequentially 8 minutes, 20 minutes, 7 minutes, 15 minutes, and 10 minutes. There are two repairmen with the same work efficiency. How should they be arranged to minimize the total duration of repair from start to end? The shortest time in minutes."}, {"key": "5482", "content": "A certain natural gas station (indicated as point $$O$$) needs to install natural gas pipelines to seven residential areas located on a circular line, from $$A$$ to $$G$$. The distance between every two residential areas is shown in the following diagram (unit: kilometers). There are two specifications for the pipelines, thick and thin. The thick pipeline can supply gas to all $$7$$ residential areas, costing $$8000$$ yuan per kilometer, while the thin pipeline can only supply gas to $$1$$ residential area, costing $$3000$$ yuan per kilometer. The junction between thick and thin pipelines must be within the residential areas. Question: How should these two types of pipelines be used together to minimize the cost? The minimum cost is yuan."}, {"key": "5483", "content": "As shown in the diagram: The number labeled on the left of each row and on the top of each column represents the quantity of contiguous black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_5483-image_0"}, {"key": "5484", "content": "As shown in the picture: The numbers marked on the left side of each row and the top of each column represent the amount of consecutive black blocks in that row or column. Children, can you mark all the black blocks based on these numbers? question_5484-image_0"}, {"key": "5485", "content": "As shown in the diagram: the numbers marked on the left of each row and the top of each column represent the quantity of continuous black blocks in that row or column. Kids, can you mark all the black blocks based on these numbers? question_5485-image_0"}, {"key": "5486", "content": "As shown in the diagram: the numbers marked on the left side of each row and on the top of each column represent the number of consecutive black squares in that row or column. Children, can you mark all the black squares based on these numbers? question_5486-image_0"}, {"key": "5487", "content": "As shown in the diagram: The numbers marked on the left of each row and the top of each column represent the count of consecutive black squares in that row or column. Kids, can you mark all the black squares based on these numbers? question_5487-image_0"}, {"key": "5488", "content": "A certain school's third grade has a total of $$123$$ students, all of whom subscribed to one or several (up to $$4$$ kinds) of the following publications: 'Math World', 'Math Enthusiasts', 'Elementary Mathematics Journal', and 'Intellect Horizon'. Therefore, there is at least a group of students who subscribed to the exact same set of publications."}, {"key": "5489", "content": "A deck of poker contains $$54$$ cards, you need to draw at least how many cards to ensure there are at least $$2$$ clubs and $$3$$ hearts."}, {"key": "5490", "content": "There are several red, yellow, and blue balls in a pocket. Xiao Congming and a few other children are playing a game together, each can randomly take out $$2$$ balls from the pocket. No matter how they choose, there will always be two children who take out two balls of the exact same color. There has to be at least one child playing the game."}, {"key": "5491", "content": "There are some balls of the same size and shape in the pocket: there are $$8$$ red balls, $$12$$ yellow balls, $$15$$ white balls, you need to pick at least a certain number of balls to ensure that there are at least $$3$$ balls of one color and $$7$$ balls of another color."}, {"key": "5492", "content": "The kindergarten bought many plastic toys of cows, horses, sheep, and dogs, and each child can choose any two toys, but they cannot be the same. At least a certain number of children must go to pick up the toys to ensure that there are two children who have chosen the same pair of toys."}, {"key": "5493", "content": "A certain school had $$55$$ students participate in a competition. It is known that if the participants are arbitrarily divided into four groups, then there must be one group with more than $$2$$ girls. It is also known that among any $$10$$ participants, there must be at least one boy. Thus, the number of boys participating in the competition is $$46$$ people."}, {"key": "5494", "content": "There are $$4$$ different brands of basketballs, each with $$10$$ balls. You must touch a ball with your eyes closed to ensure that there are $$4$$ balls of the same brand."}, {"key": "5495", "content": "In a math and English test, all participants' scores were natural numbers, with the highest score being $$198$$ and the lowest score $$169$$. No one scored $$193$$, $$185$$, or $$177$$ points, and at least $$6$$ people got the same score. The minimum number of participants in the test."}, {"key": "5496", "content": "Xiaoming walks from home to school. If he walks $$40$$ meters per minute, he will be $$2$$ minutes late; if he walks $$50$$ meters per minute, he will arrive $$4$$ minutes early. The distance from Xiaoming's home to school is meters."}, {"key": "5497", "content": "10 students (including one team leader and 9 team members) formed a team to participate in a math competition and won first place. The organizing committee decided to give each team member a bonus of 200 yuan, and the team leader received 90 yuan more than the average bonus of all 10 players. Thus, the bonus received by the team leader is yuan."}, {"key": "5498", "content": "In an exam, boys scored an average of 2 points higher than the overall average, while girls scored an average of 1 point lower than the overall average. The total score of the boys was 942 points, and the total score of the girls was 1800 points. Find: the number of boys."}, {"key": "5499", "content": "Xiao Bai and Xiao Hua saw a magical insect that doubles in size every hour and can grow to 20 centimeters in 1 day. The time it takes for the insect to grow to 5 centimeters is needed in hours."}, {"key": "5500", "content": "A shepherd herded a flock of sheep across $$10$$ rivers. Each time they crossed a river, one-third of the sheep fell into the water, but he managed to rescue $$3$$ sheep each time. In the end, he counted and found he had $$9$$ sheep left. How many sheep were in the flock before crossing the rivers?"}, {"key": "5501", "content": "Da Mao, Er Mao, and San Mao divide 48 apples among themselves, and the number of apples each person gets equals their age 2 years from now. If San Mao gives half of his apples evenly to Da Mao and Er Mao, then Er Mao divides half of his current apples evenly between Da Mao and San Mao, and finally, Da Mao divides half of his current apples evenly between Er Mao and San Mao, and by then each person has an equal number of apples. Consequently, Da Mao is currently years old, Er Mao is currently years old, San Mao is currently years old."}, {"key": "5502", "content": "A and B each have a certain number of candies, with A having fewer candies than B. Each operation involves the person with more candies giving some to the person with fewer candies, so that the number of candies of the latter is doubled. After $$2017$$ such operations, A has $$10$$ candies, and B has $$8$$ candies. Question: How many candies did each person originally have? A originally had $$*$$ candies, and B originally had $$*$$ candies."}, {"key": "5503", "content": "What is the units digit of $$3\\times 13\\times 23\\times 33\\times \\ldots \\times 2013$$?"}, {"key": "5504", "content": "$$A$$, $$B$$, $$C$$, $$D$$, $$E$$ five lamps each have a pull cord switch. Initially, $$B$$, $$D$$, $$E$$ are on. A child pulls the switches in the order of $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, a total of $$104$$ times. At this point, the lamps that are on are."}, {"key": "5505", "content": "Xiaoxin goes to exercise, the first time he exercises and then goes again after $$1$$ day, the second time after finishing his exercise, he goes again after $$2$$ days, after exercising the third time, he goes again after $$3$$ days. If Xiaoxin's first exercise session is on a Monday, according to the above pattern, Xiaoxin's $$10$$th exercise session would be on a ."}, {"key": "5506", "content": "As shown in the figure, there are $$16$$ chairs arranged in a circle, numbered from $$1$$ to $$16$$ in sequence.$$.$$ Now, a person moves clockwise from the $$1$$st chair for $$328$$ steps, then counter-clockwise for $$485$$ steps, clockwise again for $$485$$ steps, counter-clockwise for $$328$$ steps, and finally clockwise for $$136$$ steps, at this time he arrives at the chair number.\n question_5506-image_0"}, {"key": "5507", "content": "Xiao Ming's birthday is on Tuesday, July 1, 1997. So, by July 1, 2019, when he turns 22 years old, the day of the week will be."}, {"key": "5508", "content": "Boss Wang purchased a batch of clothing in three styles, A, B, and C. Style A costs $$80$$ per set, style B $$50$$ per set, and style C $$20$$ per set. Boss Wang purchased a total of $$47$$ sets of clothing, spending $$2440$$. It is known that the number of style B clothing purchased is twice that of style C. Therefore, A purchased sets, B purchased sets, C purchased sets."}, {"key": "5509", "content": "Lele Department Store entrusted the transport station to deliver $$100$$ vases. Both parties agreed on a freight charge of $$1$$ yuan per vase, but if any were damaged, not only would the freight not be paid, but also a compensation of $$1$$ yuan per broken vase would be required. As a result, the transport station earned a total freight charge of $$92$$ yuan. A total of vases were broken during transportation."}, {"key": "5510", "content": "There are two types of camels: the dromedary, which has one hump on its back, and the Bactrian camel, which has two humps on its back. The dromedary is taller and has longer limbs, allowing it to walk and run in the desert; the Bactrian camel has shorter, thicker limbs, making it more suited to walking on gravel and snow. There is a group of camels with $$23$$ humps and $$60$$ feet in total, thus this group of camels has in total, among which there are Bactrian camels."}, {"key": "5511", "content": "A document requires $$12$$ hours for person A to type alone and $$20$$ hours for person B. Now, after A types alone for some hours, B continues and finishes the typing, taking a total of $$14$$ hours. Hours A spent typing are."}, {"key": "5512", "content": "In a class at the sports meet, there were $$10$$ instances of students finishing in the top three. It is known that first place earns $$9$$ points, second place earns $$5$$ points, third place earns $$2$$ points, and no points are awarded for other places. The class scored a total of $$64$$ points, with the maximum number of instances of first-place finishes being."}, {"key": "5513", "content": "In a forest on the planet $$X$$, there lives a group of rabbits, among which some are rare mutant rabbits. It's known that normal rabbits have one head and four legs, while mutant rabbits have three heads and two legs. Given that all the rabbits combined have $$53$$ heads and $$102$$ legs, then the total number of all rabbits (including mutant rabbits) is."}, {"key": "5514", "content": "$$3$$ large monks and $$5$$ small monks can eat $$12$$ buns in a day, so $$9$$ large monks and $$15$$ small monks can eat buns in a day, $$12$$ large monks and $$20$$ small monks can eat buns in three days."}, {"key": "5515", "content": "A construction team is expected to complete a ditch in $$30$$ days. Initially, $$18$$ people worked for $$12$$ days and completed half of the project. According to this pace, if they want to finish $$9$$ days ahead of schedule, they need to increase the number of people."}, {"key": "5516", "content": "Person A starts from $$A$$ and walks at a constant speed towards $$B$$. At the same time, persons B and C start from $$B$$ and walk at a constant speed towards $$A$$. A and B meet at point $$C$$ along the way. When A and C meet, B just arrives at $$A$$. When A arrives at $$B$$, C also just arrives at $$A$$. If A had started $$5$$ minutes later, A and B would meet $$160$$ meters away from point $$C$$. Therefore, the speed of A is meters per minute."}, {"key": "5517", "content": "The following figure is a square made of $$8$$ rectangles, each measuring $$2$$ cm in length and $$1$$ cm in width. Starting from point $$A$$ and moving along the gridline to point $$B$$ without retracing any part of the path, the maximum length that can be traveled in centimeters is: question_5517-image_0"}, {"key": "5518", "content": "Compute. $$375000000\\div 125\\div 5\\div 25\\div 8\\div 4\\div 2=$$."}, {"key": "5519", "content": "Calculate the following problems. $$8\\div 11+7\\div 33+6\\div 99=$$."}, {"key": "5520", "content": "\"$$\\odot $$\" defines a new operation. It is known that $$1\\odot 4=5$$; $$2\\odot 3=7$$; $$4\\odot 1=17$$; $$3\\odot 2=11$$; $$\\ldots \\ldots $$ (2) $$(1\\odot 10)\\odot 10=$$, $$1\\odot (10\\odot 10)=$$."}, {"key": "5521", "content": "$$30$$ students are lined up from shortest to tallest, with the same height difference between each adjacent pair of students. The total height of the first $$10$$ students is $$1250$$ centimeters, and the total height of the first $$20$$ students is $$2650$$ centimeters. The total height of these $$30$$ students is centimeters."}, {"key": "5522", "content": "In a math test with only $$20$$ questions, earning $$5$$ points for each correct answer and losing $$3$$ points for each wrong answer or unattempted question, Wei Er did not pass the exam. However, she found that she could just pass by getting one less question wrong. She got this many questions correct."}, {"key": "5523", "content": "There are animals with six heads and four feet and birds with four heads and two feet. There are seventy-six heads in total and forty-six feet in total. Question: Count the birds and beasts (from 'Sun Tzu's Mathematical Manual')"}, {"key": "5524", "content": "As shown in the diagram, rhombus paper pieces are pieced together in sequence following a pattern. From the diagram, it is known that there are $$5$$ rhombus paper pieces in the first pattern; there are $$9$$ rhombus paper pieces in the second pattern; there are $$13$$ rhombus paper pieces in the third pattern. Following this pattern, the sixth pattern contains ( ) rhombus paper pieces.\n question_5524-image_0"}, {"key": "5525", "content": "Calculate: $127\\times 13+127\\times 6-127\\times 9=$"}, {"key": "5526", "content": "Calculate: $987\\times 7+13\\times 7=$"}, {"key": "5527", "content": "Calculate: $79+79\\times 83+79\\times 16=$"}, {"key": "5528", "content": "Perform vertical calculation: (4) $$5232 \\div 4=$$."}, {"key": "5529", "content": "Perform vertical calculation: (3) $$1326\\div 6=$$."}, {"key": "5530", "content": "Set up a vertical calculation: (4) $$1917\\div 27=$$."}, {"key": "5531", "content": "Calculate: (1) $$12200\\div 25=$$."}, {"key": "5532", "content": "Calculate: (2) $$3500\\div 25\\div 4=$$."}, {"key": "5533", "content": "Compute: (3) $$6300\\div \\left( 25\\times 9 \\right)=$$."}, {"key": "5534", "content": "Calculate: (4) $$\\left( 72\\times 45 \\right)\\div \\left( 5\\times 8 \\right)=$$."}, {"key": "5535", "content": "First observe, then calculate: $$3\\times 5\\times 7\\times 11\\times 13\\times 17\\div \\left( 51\\times 65\\times 77 \\right)=$$."}, {"key": "5536", "content": "First observe, then calculate the following expressions: (1) $$(130+39)\\div 13=$$."}, {"key": "5537", "content": "First observe, then calculate the following expressions: (2) $$625\\div 5-125\\div 5=$$."}, {"key": "5538", "content": "Calculate: (2)$$73\\div 5+127\\div 5=$$."}, {"key": "5539", "content": "The picture is of an incomplete multiplication long equation, the result of this equation is. question_5539-image_0"}, {"key": "5540", "content": "Enter the appropriate number in the squares in the figure below to make the following division vertical expression valid, the divisor is. question_5540-image_0"}, {"key": "5541", "content": "The figure below is an incomplete division long division, the divisor in this equation is. question_5541-image_0"}, {"key": "5542", "content": "The figure below shows a $$5\\times 5$$ area with $$5$$ trees planted. It is required to set up tents on the empty land without trees, and the tents must be set up beside a tree. Any two tents occupy grids without a common point, and the number of tents in each row is shown on the far right, while the number of tents in each column is shown at the bottom. Then, the tents in the first column are in the row. question_5542-image_0"}, {"key": "5543", "content": "A page from the middle of a book has been torn out, the sum of the remaining page numbers is $$5027$$. The two page numbers on the torn out page are what? (Write from smallest to largest)"}, {"key": "5544", "content": "[Thinking Expansion] In quadrilateral $$ABCD$$, point $$E$$ is the midpoint of side $$AB$$, and point $$F$$ is the midpoint of side $$CD$$. Given that the area of quadrilateral $$ABCD$$ is $$96$$ square centimeters, then the area of the shaded part is square centimeters. question_5544-image_0"}, {"key": "5545", "content": "[Thinking Expansion] As shown in the diagram, a large square and a small square have side lengths of $$4$$ cm and $$3$$ cm, respectively. Therefore, the area of the shaded part is square centimeters. question_5545-image_0"}, {"key": "5546", "content": "[Thinking Extension] There is an arithmetic sequence, the sum of its first $$7$$ terms is $$105$$, and the first term is $$3$$. What is the common difference?"}, {"key": "5547", "content": "[Campus Knowledge] The value of A is $$42.62$$, and the value of B is $$4.1$$ more than that of A, what is the value of B?"}, {"key": "5548", "content": "[Thinking Expansion] As shown in the figure, the area of triangle $$ABC$$ is $$600$$ square centimeters, $$D$$ is the midpoint of $$BC$$, $$ED$$ is twice the length of $$AE$$. Then, the area of triangle $$ABE$$ is square centimeters question_5548-image_0"}, {"key": "5549", "content": "[Thinking Expansion] Eddie, Vera, and Da Kuan agreed to go to the amusement park for fun. The amusement park has a total of $$50$$ attractions. It is known that Eddie participated in $$42$$ attractions, Vera participated in $$35$$ attractions, and Da Kuan participated in $$31$$ attractions, then the minimum number of attractions that Eddie, Vera, and Da Kuan all participated in is ."}, {"key": "5550", "content": "Perform the calculation in column form: $$420\\div 5$$ =$$540\\div 3$$="}, {"key": "5551", "content": "Doctor, Eddie, and Vee pass the ball to each other, starting with Doctor. After $$4$$ passes, Eddie has the ball, showcasing a unique way of passing."}, {"key": "5552", "content": "There is a series of numbers arranged in the order of $$385161713851617138516171\\cdots \\cdots$$. Please answer: (1) What is the 50th number. (2) How many times does the number \u201c1\u201d appear in these 50 numbers. (3) What is the sum of these 50 numbers."}, {"key": "5553", "content": "Given $$7\\times 11\\times 13=1001$$, calculate the value of the following expressions: (1) $$7\\times 9\\times 11\\times 13=$$. (2) $$14\\times 22\\times 26=$$."}, {"key": "5554", "content": "Is the sum of the equation $$1+3+5+7+9$$ odd or even? ( )\uff0e"}, {"key": "5555", "content": "The image below is the calendar for January 2020. Answer the questions and summarize the pattern: (1) The total days from January 1, 2020, to January 22, 2020; (2) The total days from January 5, 2020, to January 15, 2020; (3) The total days from January 5, 2020, to February 10, 2020. question_5555-image_0"}, {"key": "5556", "content": "$$2020$$ year $$10$$ month $$1$$ day is Thursday. Starting from this day, what day of the week is the $$25$$th day?"}, {"key": "5557", "content": "The doctor is conducting an experiment, recording the water temperature at regular intervals, as shown in the table below: Table of Temperature Changes When Heating WaterHeating Time (min)$$0$$$$2$$$$4$$$$6$$$$8$$$$10$$$$12$$Water Temperature ($${}^\\circ \\text{C}$$)$$26$$$$32$$$$50$$$$70$$$$85$$$$90$$$$100$$Based on the data in the table, answer the following questions:(1) The water temperature before heating was $${}^\\circ \\text{C}$$;(2) After heating for $$10$$ minutes, the water temperature reached $${}^\\circ \\text{C}$$;(3) It took minutes to heat the water from $$50{}^\\circ \\text{C}$$ to $$85{}^\\circ \\text{C}$$;(4) Estimate the minutes needed to heat the water to approximately $$60{}^\\circ \\text{C}$$."}, {"key": "5558", "content": "Class 2 needs to decide on a park for the 'Children's Day' outing via voting by all classmates, as shown in the figure. question_5558-image_0 (1) Complete the statistical table: Park NamesPeople's ParkZooBotanical GardenWater ParkNumber of People(2) Class 2 has a total of people;"}, {"key": "5559", "content": "There are a total of $$36$$ rabbits in two cages. If $$8$$ rabbits are taken from the first cage and put into the second cage, then the two cages will have the same number of rabbits. Find the number of rabbits in the first and the second cage initially."}, {"key": "5560", "content": "It is known that the diagonals of the quadrilateral $$ABCD$$ are perpendicular to each other and the area of the quadrilateral is $$80$$ square centimeters. Given $$AC=10$$ centimeters, find the length of $$BD$$ in centimeters. question_5560-image_0"}, {"key": "5561", "content": "As shown in the figure, a large rectangle is divided into $$9$$ small rectangles, among which the area of $$3$$ small rectangles is shown in the figure (unit: square centimeters) (1) Can a small rectangle with an area of $$45$$ and a small rectangle with an area of $$20$$ be translated to form a large rectangle? (2) The area of the rectangle represented by \u201c\u2606\u201d is square centimeters. question_5561-image_0"}, {"key": "5562", "content": "Wang Fang and Li Hua walked away from the same place in opposite directions after training in the evening. Wang Fang walked 64 meters per minute, while Li Hua walked 75 meters per minute. It took Wang Fang 20 minutes to get home, and it took Li Hua a total of 25 minutes to get home. The distance between their homes is in meters."}, {"key": "5563", "content": "Car A and Car B start from the same place at the same time, heading in opposite directions. Car A travels at $$100$$ kilometers per hour, while Car B travels at $$120$$ kilometers per hour. After $$3$$ hours, the distance between Car A and Car B is kilometers. $$100+120\\times 3=460$$ (kilometers)."}, {"key": "5564", "content": "Among the following two equations, the same letters represent the same digits, and different letters represent different digits. Then $$A+B+C+D+E+F+G=$$.\n question_5564-image_0"}, {"key": "5565", "content": "In the following equation, the same letter represents the same number, and different letters represent different numbers. So the sum of $$A$$, $$B$$, $$C$$, $$D$$ is.\n question_5565-image_0"}, {"key": "5566", "content": "In the long division below, the same letters represent the same digit, and different letters represent different digits. Then the four-digit number $$\\overline{tavs}=$$\n question_5566-image_0"}, {"key": "5567", "content": "In the problem below, each Chinese character represents a number. Different characters represent different numbers, and the same characters represent the same number. What numbers do they represent for the equation to hold? Force$$=$$, Struggle$$=$$, Do$$=$$, Olympic$$=$$, Sports$$=$$, Meeting$$=$$, Success$$=$$, Achievement$$=$$ question_5567-image_0"}, {"key": "5568", "content": "Fill in the blanks with appropriate numbers in the equations below so that the equations are valid. Please write out these two equations (addition equation first, then subtraction equation): ;. 6 + 2 6 - 1"}, {"key": "5569", "content": "In the following equation, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers. Find the numbers represented by the Chinese characters that satisfy the equation, and calculate: I $$+$$ love $$+$$ math $$+$$ learning =. question_5569-image_0"}, {"key": "5570", "content": "In the equation below, the Chinese characters \u201c\u7f8e (beautiful), \u4e3d (pretty), \u5c71 (mountain), \u6751 (village), \u4e00 (one), \u8d77 (together), \u62a4 (protect)\u201d represent $$7$$ out of the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, where different characters represent different numbers, making the addition equation correct. The sum of the $$7$$ numbers represented by \u201c\u7f8e, \u4e3d, \u5c71, \u6751, \u4e00, \u8d77, \u62a4\u201d is.\n\n\n\n\n\u7f8e\n\u4e3d\n\u5c71\n\u6751\n\n\n+\n\n\u4e00\n\u8d77\n\u62a4\n\n\n\n2\n0\n0\n6"}, {"key": "5571", "content": "As shown in the diagram, different Chinese characters represent different numbers in the equation. It is known that: \"level$$=5$$\", then the three-digit number represented by \"$$\\overline{study and think}$$\" is.\n question_5571-image_0"}, {"key": "5572", "content": "Among the Chinese characters below, what number does '\u8fd0' represent? $$\\begin{matrix}&&2& 0& 8\\\\- &&\u8fce&\u5965&\u8fd0 \\\\ \\hline&& & \u8fce& \u8fd0\\end{matrix}$$"}, {"key": "5573", "content": "Using the numbers $$1\\sim5$$, complete the vertical form in the figure below. (Each number can only be used once) The minuend is question_5573-image_0"}, {"key": "5574", "content": "As shown in the figure, the same Chinese characters represent the same digit, different Chinese characters represent different digits. All Chinese characters do not equal $$0$$ and do not match any digit already shown in the figure. Then, the four-digit number \"$$\\overline{manySheep}$$\" $$=$$\uff0e\n question_5574-image_0"}, {"key": "5575", "content": "In the equation below, the same letter represents the same number, and different letters represent different numbers. Thus, the number represented by \"$$\\overline{EDCAD}$$\" is. question_5575-image_0 \u200b"}, {"key": "5576", "content": "As shown in the diagram, $$\\square $$, $$\\bigcirc $$, and $$\\triangle $$ each represent different numbers. Please find out what numbers they respectively represent. $$\\square $$=, $$\\bigcirc $$=, $$\\triangle $$= question_5576-image_0"}, {"key": "5577", "content": "Fill in a suitable number in the blank space of the equation below to make the equation valid. The final result is question_5577-image_0"}, {"key": "5578", "content": "A book has a total of $$16$$ pages, using the numbers $$1$$~$$16$$ on the pages for a total of several digits."}, {"key": "5579", "content": "A certain car dealership has $$65$$ cars, among which $$45$$ have air conditioning, $$30$$ have high-quality sound systems, and $$12$$ cars have both air conditioning and high-quality sound systems. The number of cars that have neither air conditioning nor a high-quality sound system is ( ) cars."}, {"key": "5580", "content": "Among the boys in class 1 of grade 4, there are $$16$$ who like playing basketball, $$21$$ who like playing football, $$7$$ who like playing volleyball, $$10$$ who like both basketball and football, $$3$$ who like both basketball and volleyball, $$4$$ who like both football and volleyball, $$3$$ who like all three sports, and $$5$$ who don't like any of the sports. How many boys are there in class 1 of grade 4?"}, {"key": "5581", "content": "Hongqi Primary School class 6 ($$5$$) has $$15$$ people, at least some of them were born in the same month."}, {"key": "5582", "content": "To separate $$7$$ kittens into $$3$$ cages, no matter how it's done, there is always at least one cage containing $$3$$ kittens."}, {"key": "5583", "content": "A book has a total of $$500$$ pages, numbered $$1$$, $$2$$, $$3$$, $$4$$, $$... 499$$, $$500$$. The number \u201c$$2$$\u201d appears a total of times in the page numbers."}, {"key": "5584", "content": "In a box, there are 8 socks each of red, yellow, and blue. What is the minimum number of socks that must be taken out to ensure that there is at least one pair of socks of the same color?"}, {"key": "5585", "content": "The math textbook for the second semester of fourth grade has a total of $$119$$ pages. The number of digits required to print its page numbers is ( )."}, {"key": "5586", "content": "Three teachers read a certain number of books. Teacher Zhang read $$66$$ of them, Teacher Wang read $$40$$ of them, and Teacher Li read $$23$$ of them. There are $$17$$ books that both Teacher Zhang and Teacher Wang have read, $$13$$ books that both Teacher Wang and Teacher Li have read, and $$9$$ books that both Teacher Li and Teacher Zhang have read. All three teachers have read $$6$$ books. Together, these three teachers have read a total of ( ) books."}, {"key": "5587", "content": "There are $$5$$ red balls and $$4$$ white balls in the box. You must take out at least ( ) balls to ensure that there are balls of both colors."}, {"key": "5588", "content": "A book has a total of 600 pages, and among the page numbers from 1 to 600, a total number of '1's used is."}, {"key": "5589", "content": "Teacher Zhou conducted a questionnaire survey among $$42$$ people, with the results showing that $$18$$ people like reading, $$22$$ people like writing, $$16$$ people like reciting, $$6$$ people like both reading and writing, $$8$$ people like both reading and reciting, $$9$$ people like both writing and reciting, and there are $$5$$ people who like all three hobbies. How many people do not like any of these three hobbies ( )."}, {"key": "5590", "content": "A construction site needs $$1080$$ bags of cement, $$3$$ trucks of the same load capacity transported $$4$$ times, just enough to transport half, the remaining half will need an additional truck of the same model to transport, how many more times do they need to transport to finish."}, {"key": "5591", "content": "Count the number of squares in the image below.\n question_5591-image_0"}, {"key": "5592", "content": "Count the number of triangles in the figure below.\n question_5592-image_0"}, {"key": "5593", "content": "Count the number of rectangles in the figure below.\n question_5593-image_0"}, {"key": "5594", "content": "Xiao Su and Xiao Feng played roller skating together. They set off from home at the same time. Xiao Su's speed was $$40$$ meters per minute, and Xiao Feng's speed was $$50$$ meters per minute. Along the way, Xiao Su accidentally took a fall, which delayed her for $$5$$ minutes, and then she continued onward. After a while, she met with Xiao Feng. It is known that it took Xiao Feng $$30$$ minutes from leaving home to the meeting point. Then, the distance between Xiao Su and Xiao Feng's homes is meters."}, {"key": "5595", "content": "Beibei and Huanhuan set off at the same time from two cities that are $$600$$ kilometers apart, and met after $$5$$ hours. Beibei's car travels $$20$$ kilometers per hour faster than Huanhuan's. Huanhuan's car travels kilometers per hour."}, {"key": "5596", "content": "Xiao Ming goes to the park 400 meters away from home to walk the dog. After finishing, she was preparing to go home. At the same time, her mother started from home to the park. Xiao Ming's speed is 10 meters per minute, her mother's speed is 15 meters per minute, and the dog's speed is 30 meters per minute. After meeting the mother, the dog kept running back and forth between Xiao Ming and her mother at the same speed. When Xiao Ming and her mother met, the dog had run a total of meters."}, {"key": "5597", "content": "Locations $$A$$ and $$B$$ are $$400$$ kilometers apart; two cars, one from each location, begin driving towards each other at the same time. The car from $$A$$ travels at $$35$$ kilometers per hour, and the car from $$B$$ at $$45$$ kilometers per hour. A pigeon, flying at a speed of $$50$$ kilometers per hour, departs at the same time as the car from $$A$$ towards the car from $$B$$. Upon encountering car $$B$$, it turns back towards car $$A$$, and upon encountering car $$A$$, it turns back towards car $$B$$, continuing this pattern. When the two cars meet, the pigeon has flown a certain number of kilometers."}, {"key": "5598", "content": "A and B start from two places that are $$794$$ kilometers apart and head towards each other. A travels at $$52$$ kilometers per hour, and B travels at $$42$$ kilometers per hour. A has traveled $$416$$ kilometers when they meet, and B started an hour earlier than A."}, {"key": "5599", "content": "As shown in the diagram, to go from point $$A$$ to point $$B$$ across the room, if it is required to only move from a room with a smaller number to a room with a larger number, there are a total number of different ways to do so.\n question_5599-image_0"}, {"key": "5600", "content": "Eight triangles can divide a plane into a maximum number of parts."}, {"key": "5601", "content": "According to the direction of the arrow in the right figure, from $$2014$$ to $$2015$$ and then to $$2016$$, the direction of the arrow is as shown in the following ( )\uff0e question_5601-image_0"}, {"key": "5602", "content": "The total number of rectangles (including squares) in the picture is.\n question_5602-image_0"}, {"key": "5603", "content": "There are currently $$17$$ matchsticks, used for arranging numbers as shown in the figure, exactly all are used up$$. The largest number that can be formed with distinct digits is question_5603-image_0"}, {"key": "5604", "content": "Now there are $$15$$ matchsticks to arrange numbers as shown in the diagram, using exactly all of the matchsticks.$$.$$ The largest four-digit number that can be formed is question_5604-image_0"}, {"key": "5605", "content": "Count the number of triangles in the picture. question_5605-image_0"}, {"key": "5606", "content": "The construction team repairs the road. If it's rainy, they can repair $$120$$ meters. On sunny days, their work efficiency is higher, repairing $$30$$ more meters than on rainy days. The construction team repairs $$900$$ meters of road in a week. There are days of sunshine."}, {"key": "5607", "content": "A piece of paper, the first time it is torn into $$3$$ small pieces, and thereafter every time one of the $$1$$ pieces is torn into smaller $$3$$ pieces, after several times, there are a total of $$2015$$ pieces of paper."}, {"key": "5608", "content": "A peach garden that is approximately a parallelogram is divided into two parts by a rectangular stone path (as shown in the diagram). It is known that the base of the parallelogram is $$39$$ meters, the height is $$24$$ meters, and the width of the path is $$1$$ meter. If on average each peach tree occupies $$3$$ square meters, this peach garden approximately has peach trees. question_5608-image_0 \u200b"}, {"key": "5609", "content": "Uncle Zhao built a trapezoidal chicken coop against the wall, with the fence around the chicken coop measuring $$22\\text{m}$$ (as shown in the picture), and the area of this chicken coop is $$\\text{m}^2$$.\n question_5609-image_0"}, {"key": "5610", "content": "A book, on the first day Xiao Ming read half of the book minus $$6$$ pages, on the second day he read half of what was left plus $$7$$ pages, and there were still $$45$$ pages left unread. The total number of pages in this book is ___."}, {"key": "5611", "content": "Analyze the bar chart as shown, the average monthly sales volume of cars in the second half of the year, and the percentage increase in sales volume in December compared to November.\n question_5611-image_0"}, {"key": "5612", "content": "There are peach trees, pear trees, and apple trees in the orchard, totaling $$552$$ trees. The number of peach trees is $$12$$ more than double the number of pear trees, and the number of apple trees is $$20$$ less than the number of pear trees. How many peach trees, pear trees, and apple trees are there respectively?"}, {"key": "5613", "content": "Can the figure below be drawn in one stroke, and if not, what is the minimum number of strokes required to draw it?\n question_5613-image_0"}, {"key": "5614", "content": "The gardener plants trees by the river in the order of $$1$$ willow tree, $$2$$ pine trees, $$3$$ poplar trees, $$1$$ willow tree, $$2$$ pine trees, $$3$$ poplar trees$$\\cdots\\cdots$$, totaling $$68$$ trees. How many pine trees were planted in total?"}, {"key": "5615", "content": "As shown in the figure, it is a $$3\\times 3$$ magic square, it is known that the sum of the three numbers in each row, each column, and each diagonal are equal. Then, \"?\" should be filled with.\n question_5615-image_0"}, {"key": "5616", "content": "The sum of $$1+2+3+4+5+6+7+\\cdots+99+100+99+98+97+96+\\cdots +7+6+5+4+3+2+1$$ is. (Fill in 'odd' or 'even')"}, {"key": "5617", "content": "The width of a rectangle is $$5$$ meters. The width of the rectangle remains unchanged, and its length is increased by $$8$$ meters. The area of the rectangle now is increased by square meters compared to the original rectangle."}, {"key": "5618", "content": "In a parking lot, there are currently $$24$$ vehicles, among which cars have $$4$$ wheels and tricycles have $$3$$ wheels. These vehicles together have $$86$$ wheels. How many tricycles are there?"}, {"key": "5619", "content": "A number is 6 more than 4 times $$x$$, this number is represented in an expression containing letters as ( )."}, {"key": "5620", "content": "As shown in the diagram, the eight parts in the picture are to be colored with four different colors: red, yellow, green, blue. Adjacent parts cannot be colored with the same color, whereas non-adjacent parts can use the same color. This picture has a total number of different coloring methods.\n question_5620-image_0"}, {"key": "5621", "content": "In an arithmetic sequence, the first number is $$11$$, and the eleventh number is $$51$$. The difference between two adjacent numbers is ."}, {"key": "5622", "content": "Among nine boxes numbered from $$1\\sim 9$$, there are $$351$$ small glass beads. Except for the box numbered $$1$$, each box contains the same number of beads more than the previous box. (2) If box number $$3$$ contains $$23$$ small glass beads, then box number $$8$$ contains ."}, {"key": "5623", "content": "A regular hexagon with a side length of $$1$$ can be divided into $$6$$ regular triangles with a side length of $$1$$. Therefore, a regular hexagon with a side length of $$5$$ can be divided into how many regular triangles with a side length of $$1$$."}, {"key": "5624", "content": "Teams A, B, C, and D play in a soccer match, with each of the 4 teams playing against the other 3 teams once. According to the rules: the winning team in each match earns 3 points; the losing team earns 0 points; if the teams draw, each team earns 1 point. Known: (1) the total score of these 4 teams in three matches are 4 consecutive odd numbers; (2) Team B has the highest total score; (3) Team D has drawn two matches, one of which is with Team C; Based on the conditions, we can infer: Which team ranks fourth in total score?"}, {"key": "5625", "content": "In a basketball team of six people, the average height of everyone is $$150$$ centimeters. Among them, the average height of $$4$$ team members is $$2$$ centimeters lower than the average height of the whole team. The average height of the other $$2$$ team members is centimeters."}, {"key": "5626", "content": "In several exams, the average score of the whole class was $$90$$ points, the average score of the boys was $$88$$ points, and the average score of the girls was $$95$$ points. It is known that there are $$20$$ boys, find the number of girls."}, {"key": "5627", "content": "A small bug crawls along the edges of a rectangular box with a length of $$6$$ meters, a width of $$4$$ meters, and a height of $$5$$ meters. If it can only move forward and not back, and it can't crawl the same edge twice, then how many meters can it crawl at most? question_5627-image_0"}, {"key": "5628", "content": "As shown in the figure, circles represent rooms, solid lines represent ground passages, and dotted lines represent underground passages. At the beginning, a policeman and a thief are in two different rooms. Each time, the policeman moves to an adjacent room along a ground passage; at the same time, the thief moves to an adjacent room along an underground passage. If after moving $$3$$ times they have not met in any room, how many different routes can they take? question_5628-image_0"}, {"key": "5629", "content": "A long, long time ago, there was a king and a great general of a country both of whom loved horse racing. They agreed to have a race. Each would bring out four horses, ranked first, second, third, and fourth; and the speeds of these eight horses from fastest to slowest were: the king's first-ranked horse, the general's first-ranked horse, the king's second-ranked horse, the general's second-ranked horse, the king's third-ranked horse, the general's third-ranked horse, the king's fourth-ranked horse, the general's fourth-ranked horse. If the king's horses enter in the order of first, second, third, and fourth rank, then the general has a way to arrange the order of his horses to at least win two races."}, {"key": "5630", "content": "As shown, $$ABCDEF$$ is a regular hexagon. A frog starts at the vertex $$A$$, and it can jump to either of the two adjacent vertices each time. If it reaches point $$D$$ within $$4$$ jumps, it stops jumping (for example: $$A-B-C-D$$); if it cannot reach point $$D$$ within $$4$$ jumps, it also stops after making $$4$$ jumps (for example: $$A-B-C-B-A$$). Then, the total number of different possible jumping sequences from the start to the stop is.\n question_5630-image_0"}, {"key": "5631", "content": "Calculate: $$\\left( 1+93+34 \\right)\\times \\left( 93+34+65 \\right)-\\left( 1+93+34+65 \\right)\\times \\left( 93+34 \\right)=$$."}, {"key": "5632", "content": "Calculate: $$\\left( 1000+15+314 \\right)\\times \\left( 201+360+110 \\right)$$$$+\\left( 1000-201-360-110 \\right)\\times \\left( 15+314 \\right)$$=\uff0e"}, {"key": "5633", "content": "Grain silos A, B, and C together stored 1700 tons of rice, among which silo A stored 900 tons less than the combined amount of silos B and C. Silo B stored 300 tons more than silo C. Calculate how many tons of rice were stored in silo B."}, {"key": "5634", "content": "A certain school plans to plant a total of $$240$$ poplar trees, willow trees, and locust trees. It is known that the number of poplar trees is $$3$$ times the number of willow trees plus $$8$$ trees, and the number of locust trees is twice the number of poplar trees minus $$14$$ trees. The original plan was to plant poplar trees, willow trees, and locust trees."}, {"key": "5635", "content": "A set of books is placed on the top and bottom shelves of a school library. If 8 books are removed from the top shelf, the number of books on both shelves becomes equal. If 8 books are removed from the bottom shelf, the number of books on the top shelf becomes twice as many as those on the bottom shelf. How many books were originally on the top and bottom shelves?"}, {"key": "5636", "content": "Warehouse A and B store rice. If Warehouse A gives 300 kg to Warehouse B, then they will have the same amount of rice; if both warehouses sell 200 kg, then the remaining rice in Warehouse A will be three times that in Warehouse B. How much rice did they originally have in total?"}, {"key": "5637", "content": "Harry Potter has a magical type of tree, each of which bears magical fruits. Each tree bears its first magical fruit as soon as it is planted, and then grows one more fruit every night. If he plants several magical trees on the first day, plants $$2$$ times the number of the first day plus $$2$$ trees on the second day, and $$3$$ times the number of the first day plus $$3$$ trees on the third day. After planting on the third day (before the night passes), all magical trees together bear $$277$$ magical fruits, then, the number of trees he planted on the first day is."}, {"key": "5638", "content": "There are two candles of different thickness but the same length. When they are lit at the same time, after $$1$$ hour, the thinner candle has shortened by $$15$$ cm, while the thicker candle has only shortened by $$3$$ cm. At this time, the length of the thicker candle is exactly $$3$$ times that of the thinner candle. Please calculate how many more hours the thicker candle can burn."}, {"key": "5639", "content": "The number of fifth-grade students at a certain school is $$154$$ fewer than the number of sixth-grade students. If another $$46$$ students are transferred to the sixth grade, then the number of sixth-grade students will be $$3$$ times that of the fifth grade. How many students were there originally in the fifth and sixth grades?"}, {"key": "5640", "content": "As shown in the figure, a rectangular vegetable garden is divided into three parts. It is known that the second part is 10 meters wider than the first part, and the area of the second part is 1000 square meters; the third part is 4 meters narrower than the first part, and the area of the third part is 650 square meters. Then, the area of the first part of the land is square meters. question_5640-image_0"}, {"key": "5641", "content": "As shown in the diagram, a rectangle is divided into eight smaller rectangles, five of which have their areas shown in the diagram (unit: square centimeters), and the area of the large rectangle is square centimeters. question_5641-image_0"}, {"key": "5642", "content": "It is known that the area of the large square in the diagram is $$22$$ square centimeters, and the area of the small square is square centimeters. question_5642-image_0"}, {"key": "5643", "content": "$$4$$ identical rectangles and one small square are combined into a large square with an area of $$100$$ square centimeters. Given that the area of the small square is $$36$$ square centimeters, then the length of the rectangle is in centimeters; the width is in centimeters.\n question_5643-image_0"}, {"key": "5644", "content": "Increasing one adjacent side of a square by $$2$$ cm and the other by $$4$$ cm results in an increase of $$50$$ square cm in the area; thus, the area of the original square is square cm. question_5644-image_0"}, {"key": "5645", "content": "A group of monkeys is divided into three teams to pick peaches in the peach garden, with each team having an equal number of monkeys; after completing the picking, the peaches are combined and then divided among the monkeys. If each monkey gets $$5$$ peaches, then $$27$$ are left over; if each monkey gets $$7$$ peaches, then there will be one monkey who doesn't get enough peaches to have $$7$$ (at least $$1$$ short). The total number of peaches picked by the monkeys is."}, {"key": "5646", "content": "The coach bought the team members some towels and mineral water, spending the same total amount on these two items. Each towel cost $$4$$, and each bottle of mineral water cost $$2$$. It is known that each person received $$2$$ towels and $$5$$ bottles of mineral water. In the end, the mineral water was exactly distributed, with $$8$$ towels remaining. How much money did the coach spend in total?"}, {"key": "5647", "content": "A group of children are sharing a pile of candies. The first child took 1 piece, the second child took 2 pieces, the third child took 3 pieces, and so on, until all the candies were distributed. If the candies were distributed evenly, each child would receive exactly 10 pieces. The total number of candies in the pile is ."}, {"key": "5648", "content": "Black and white beads arranged in alternate rows forming an equilateral triangle shape (as shown in the diagram), when there are $$10$$ more white beads than black beads, the total number of white beads used is\uff0e question_5648-image_0"}, {"key": "5649", "content": "Among the integers from $$1$$ to $$2000$$, there are numbers that are multiples of $$3$$ but not multiples of $$5$$."}, {"key": "5650", "content": "As shown in the diagram, the areas of the triangular cardboard, the square cardboard, and the circular cardboard are equal, each being $$60$$ square centimeters. The total area of the shaded parts is $$40$$ square centimeters, the total area covered by the 3 pieces of cardboard is $$100$$ square centimeters, the area of the part overlapped by the 3 pieces of cardboard is square centimeters. question_5650-image_0 \u200b"}, {"key": "5651", "content": "At the New Year's gala, a total of $$100$$ people participated in dance, choir, and music performances. It is known that:\n\u2460$$50$$ people participated in dance, $$40$$ people participated in music;\n\u2461The number of people who only participated in choir is twice the number of those who only participated in dance;\n\u2462$$15$$ people participated in both dance and choir but not in music;\n\u2463The number of people who only participated in music is $$6$$ more than those who participated in both music and choir but not in dance.\nThen, the number of people who participated in both music and choir but not in dance is $$7$$."}, {"key": "5652", "content": "Eddie has a book, starting from page $$1$$, the $$170$$th digit in the page numbers is."}, {"key": "5653", "content": "There is a book, when summing the page numbers of this book, one piece of paper's page number was mistakenly added one more time, resulting in a total of $$2047$$. Thus, the page number that was added extra is the sum."}, {"key": "5654", "content": "There's a sequence: $$1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \\cdots$$, each number $$n$$ is written $$n$$ times, when writing up to $$20$$, the number \u201c1\u201d appears times."}, {"key": "5655", "content": "One side of the path has a total of $$9$$ flags inserted, with one flag inserted every $$4$$ meters, and none at both ends, the total length of this path in meters is. (The width of the flags is negligible)"}, {"key": "5656", "content": "The circular path by the pond, with a total length of $$42$$ meters, requires a trash can to be placed every $$6$$ meters, totaling the number of trash cans needed. (The width of the cans is negligible)"}, {"key": "5657", "content": "As shown in the diagram, there are areas $$A$$, $$B$$, $$C$$, $$D$$, $$E$$. Now using $$5$$ different colors to color these $$5$$ areas, in order to make the colors of adjacent areas different, there are various different coloring methods. question_5657-image_0"}, {"key": "5658", "content": "The diagram below shows a deformed mushroom, divided into six areas. Now, it needs to be colored using four different colors, with the requirement that two adjacent areas (two areas with a common edge are considered adjacent) must be colored differently. If colors can be reused, then there are a total of different coloring methods. question_5658-image_0"}, {"key": "5659", "content": "From $$5$$ bottles of different purified waters, $$2$$ bottles of different colas, and $$6$$ bottles of different juices: pick out $$3$$ bottles of different types of drinks, there are a total of choices."}, {"key": "5660", "content": "Using $$0$$, $$3$$, $$6$$, $$1$$, $$9$$ to form a three-digit number."}, {"key": "5661", "content": "Use $$3$$ different colors to color the areas $$A$$, $$B$$, $$C$$, and $$D$$ in the figure, each area can only use one color, and adjacent areas cannot be the same color. How many different coloring methods are there?\n question_5661-image_0"}, {"key": "5662", "content": "Eddy arranged some chess pieces into a two-layer hollow square. Later, he added $$28$$ more chess pieces, turning the figure into a three-layer hollow square$.$ Initially, Eddy possibly arranged a maximum number of chess pieces."}, {"key": "5663", "content": "Five people compete, each competing in a match, winning a match scores $$2$$ points, drawing scores $$1$$ point, losing scores $$0$$ points; the first place has no draws, the second place has never lost, the five people have different scores, each person's score is ,,,,,."}, {"key": "5664", "content": "Big Fatty, Second Fatty, and Third Fatty ate a total of $$78$$ dumplings. Big Fatty ate three times the amount that Third Fatty ate, and Second Fatty ate twice the amount that Third Fatty ate. So, Big Fatty ate $$.$$ dumplings."}, {"key": "5665", "content": "The sum of numbers A, B, and C is $$40$$. It is known that number A is $$2$$ times number B, and number B is $$3$$ times number C. The value of number B is."}, {"key": "5666", "content": "There are $$100$$ pieces of candy, divided among three kids: A, B, and C. A got $$3$$ more pieces than B, and B got $$5$$ more pieces than C. A got, B got, and C got pieces of candy."}, {"key": "5667", "content": "After making some progress in learning, Eddie designed an intelligent patrol robot to enhance the security of the super-pioneer residence.\nAs shown in the figure, the paths in the garden where the super pioneers are located are composed of some rectangles, as shown below. The intelligent patrol robot must start from point $$A$$, patrol through each section of the road at least once, and then return to point $$A$$. Please estimate the minimum distance it needs to walk in meters.\n question_5667-image_0"}, {"key": "5668", "content": "Please fill in between the four numbers $$5$$, $$11$$, $$7$$, $$7$$ with $$+$$, $$-$$, $$\\times $$, $$\\div $$ or (), in any order. Each number can only be used once, and you can change the order of the numbers, to make their result equal to $$24$$."}, {"key": "5669", "content": "Place the four operation symbols $$+$$, $$-$$, $$\\times$$, $$\\div$$ into the four boxes in the diagram without repetition, so that the results of these equations are all natural numbers, and the sum of the largest and smallest numbers among them is $$15$$. Then, the product of the results of the equations that contain the plus and multiplication symbols is. $$5\\square 1=$$$$6\\square 2=$$$$7\\square 3=$$$$8\\square 4=$$"}, {"key": "5670", "content": "There are $$9$$ numbers, fill in a \"+\" or a \"-\" between every two adjacent numbers, so that the result is $$31$$. The question is: what is the maximum product of all subtracted numbers (numbers preceded by a minus sign)? $$9~~~~8~~~~7~~~~6~~~~5~~~~4~~~~3~~~~~2~~~~1=31$$"}, {"key": "5671", "content": "In the proper places between $$12$$ eights ($$8$$), fill in the operators $$+$$, $$-$$, $$\\times $$, $$\\div $$ or ( ), to make the equation true. $$8$$ $$8$$ $$8$$ $$8$$ $$8$$ $$8$$ $$8$$ $$8$$ $$8$$ $$8$$ $$8$$ $$8=2008$$"}, {"key": "5672", "content": "Dakuan read from page $$35$$ to $$48$$ of a book, Eddie read from page $$80$$ to $$90$$, and Wei'er read from page $$144$$ to $$159$$. In total, they read pages."}, {"key": "5673", "content": "[Warm-up Exercise 3] $$3$$ mice stole $$30$$ ears of corn in $$5$$ days, at this rate, $$10$$ mice would need ___ days to steal $$80$$ ears of corn."}, {"key": "5674", "content": "[Warm-up 1 before class] During the Spring Festival, Xue Xue and his parents go back to their hometown to visit his grandparents, taking a long-distance bus for $$2$$ hours. The speed of the long-distance bus is $$85$$ kilometers per hour. Therefore, the total kilometers Xue Xue travels from home to his grandparents\u2019 house is ____."}, {"key": "5675", "content": "[Warm-up before class 2] Master Wang processed $$60$$ parts in $$2$$ hours. Based on this calculation, he can process parts for $$8$$ hours a day, and if $$360$$ parts are to be processed, it requires hours."}, {"key": "5676", "content": "[Warm-up before class 1] Statistical table of donations for drought areas by two primary schools (each with $$5$$ grades): question_5676-image_0 (1) The total donation of the fifth grade from the two schools was yuan; (2) The first grade of the first school donated the most; (3) The first grade of the second school donated the least; (4) The total donation from the first school was yuan."}, {"key": "5677", "content": "[Pre-class Warm-up 2] The chart below shows the number of students in each class of the third grade at a certain school. According to the statistical chart, the incorrect statement is (). question_5677-image_0"}, {"key": "5678", "content": "[Warm-up Exercise 3] A forest park raised some chickens and rabbits, knowing that the number of rabbits is equal to the number of chickens, they have a total of $$102$$ legs, then there are chickens, and there are rabbits."}, {"key": "5679", "content": "[Warm-up 2] In the 'Celebrating the 70th Anniversary of the Founding of the Nation' knowledge quiz, answering a question correctly earns $$10$$ points, while answering incorrectly deducts $$5$$ points. Congcong attempted $$10$$ questions in total and ended up with $$85$$ points. He answered questions correctly and incorrectly."}, {"key": "5680", "content": "[Warm-up before class 1] A cricket has $$6$$ legs, a spider has $$8$$ legs. There are $$9$$ crickets and spiders in total, with a total of $$60$$ legs. There are $$6$$ crickets and $$3$$ spiders."}, {"key": "5681", "content": "Answer the following questions: (1) Three cards with $$1$$, $$2$$, $$3$$ can form different three-digit numbers. (2) Three cards with $$0$$, $$1$$, $$2$$ can form different three-digit numbers. (3) Three cards with $$1$$, $$3$$, $$6$$ can form different three-digit numbers (cards can be rotated)."}, {"key": "5682", "content": "Autumn has arrived, and the children went to the orchard to pick apples together. (1) Eddie picked $$36$$ apples, Vi picked $$27$$ apples, and Xiaoming picked $$33$$ apples, with an average of apples picked per person. (2) If a total of $$25$$ children participated in this activity and on average, each child picked $$28$$ apples, then everyone picked a total of apples. question_5682-image_0"}, {"key": "5683", "content": "Eddie bought a storybook and read 25 pages each day for the first 4 days, then 40 pages each day for the next 6 days, finishing the book exactly. So, on average, he reads pages per day. question_5683-image_0"}, {"key": "5684", "content": "A certain year's June 5th is a Friday. (Fill in with $$1.2.3.4.5.6.7$$) (1) That year's June 30th is a weekday. (2) That year's August 10th is a weekday."}, {"key": "5685", "content": "$$2021$$ year $$3$$ month $$27$$ day is Saturday, so $$2021$$ year $$3$$ month $$10$$ day is weekday ."}, {"key": "5686", "content": "A three-digit decimal number, with $$5$$ in both the hundreds and hundredths places, and $$0$$ in all other positions, the number is."}, {"key": "5687", "content": "Count, how many triangles are there in the picture below. question_5687-image_0"}, {"key": "5688", "content": "Each bag of flour weighs $$a$$ kilograms, each bag of rice weighs $$b$$ kilograms, $$8$$ bags of flour and $$5$$ bags of rice weigh a total of kilograms."}, {"key": "5689", "content": "The brother is $$14$$ years old this year, and the sister is $$10$$ years old this year. When the sum of the siblings' ages is $$44$$ years old, a year has passed."}, {"key": "5690", "content": "Each helicopter below has its own number, the helicopter with the number $$60$$ is the $$order$$th. question_5690-image_0"}, {"key": "5691", "content": "During the physical education class, the teacher directed everyone to line up, with Vi standing at the beginning of the line, and Edi at the end of the line. Starting from the beginning to the end of the line, each student reported a number that was $$7$$ more than the one before. If Vi reported $$17$$, and Edi reported $$150$$, then the total number of people in the line was\uff0e question_5691-image_0"}, {"key": "5692", "content": "A worker master stacks logs of uniform thickness into the shape below, with each layer having $$1$$ more log than the layer above, totaling $$8$$ layers. (1) The last layer has logs. (2) This stack of logs has a total of logs. question_5692-image_0"}, {"key": "5693", "content": "The sum of the ages of dad and mom this year is $$72$$ years old, dad is $$6$$ years older than mom. Mom's age this year is ."}, {"key": "5694", "content": "The teacher said to Xiao Ming: \"My age 15 years ago was the same as your age 6 years from now. 7 years ago, my age was 8 times your age.\" Xiao Ming is years old this year, the teacher is years old this year."}, {"key": "5695", "content": "Dad is $$36$$ years older than Xiao Ming, and this year Dad's age is $$4$$ times that of Xiao Ming. How old is Dad this year?\nAnswer: This year Dad is $$48$$ years old."}, {"key": "5696", "content": "Mobi and his grandfather are a total of $$70$$ years old this year, the grandfather's age is $$6$$ times that of Mobi. How old is the grandfather and Mobi?"}, {"key": "5697", "content": "A has $$7$$ times more membership points cards than B. After A gives B $$24$$ cards, both have the same number of cards. Originally, A had cards."}, {"key": "5698", "content": "Form a four-digit number with $$0$$, $$4$$, $$9$$, $$2$$, among which the largest is ( )."}, {"key": "5699", "content": "Li Bai goes to buy alcohol with a jug, every encounter with a store doubles it, with flowers he drinks eight liang. Encountering stores and flowers three times, he finishes the jug of alcohol. The jug originally had two liang of alcohol."}, {"key": "5700", "content": "There are a total of $$27$$ birds on three trees, $$2$$ birds flew from the first to the second tree, $$3$$ birds flew from the second to the third tree, and $$4$$ birds flew from the third back to the first tree. At this point, each of the three trees has the same number of birds. Originally, each tree had the same number of birds."}, {"key": "5701", "content": "A, B, and C went fishing together. They put the fish they caught into a basket, lied down to rest on the spot, and all fell asleep. A woke up first, divided the fish in the basket into three equal parts and found one extra fish. He threw the extra fish back into the river and took one portion of fish home. Then B woke up, also divided the existing fish in the basket into three equal parts, found one extra fish, threw the extra fish back into the river, and took one portion of fish home. Finally, C woke up and did the same, also finding one extra fish. The three people caught at least a number of fish."}, {"key": "5702", "content": "The yard originally had a certain number of tons of coal.$$.$$ The first time, half of the original coal was transported out, the second time $$150$$ tons were transported in, the third time $$50$$ tons were transported out, resulting in a remaining $$300$$ tons of coal in the yard."}, {"key": "5703", "content": "Xiao Bai and Xiao Hua encountered a magical bug that doubles in size every hour and can grow to 20 cm in a day. Smart kids, how many hours does it take for the bug to grow to 5 cm?"}, {"key": "5704", "content": "Count the total number of triangles in the picture. question_5704-image_0"}, {"key": "5705", "content": "As shown in the diagram, starting from $$A$$ and walking to $$B$$ following the direction of the arrows, and you can only follow the direction of the arrows, the number of routes from $$A$$ to $$B$$ is.\n question_5705-image_0"}, {"key": "5706", "content": "As shown in the diagram, Sisi starts her journey from home to go to Xueersi school. On the way, she needs to pass through the commercial street to have lunch. So, the shortest route she can choose has several options.\n\n question_5706-image_0"}, {"key": "5707", "content": "As shown, starting from point $$A$$ and walking along the line segments to point $$D$$, and it must pass through point $$B$$ but cannot pass through point $$C$$. The question is how many of the shortest routes there are from point $$A$$ to point $$D$$.\n question_5707-image_0"}, {"key": "5708", "content": "[Warm-up 3 before class] The athlete undergoes long-distance running training. He runs at a speed of 150 meters per minute during the first half of the course and at 100 meters per minute during the second half of the course. Therefore, his average speed throughout the entire long-distance running process is meters per minute."}, {"key": "5709", "content": "[Warm-up 1 before class] Two people, A and B, set off from point $$A$$ at the same time, walking in opposite directions. Person A walks at a speed of $$7$$ meters per second, while person B walks at a speed of $$4$$ meters per second. Half an hour later, the distance between the two is meters."}, {"key": "5710", "content": "There is a $$7\\times 7$$ matrix as shown below. According to the pattern, develop the matrix into a $$99\\times 99$$ matrix. Which letter will be in the bottom right corner of the matrix? $$C$$$$B$$$$A$$$$E$$$$D$$$$C$$$$B$$$$D$$$$A$$$$E$$$$D$$$$C$$$$B$$$$A$$$$E$$$$B$$$$B$$$$A$$$$E$$$$A$$$$E$$$$A$$$$C$$$$C$$$$A$$$$D$$$$E$$$$D$$$$B$$$$D$$$$D$$$$B$$$$C$$$$D$$$$C$$$$C$$$$E$$$$E$$$$A$$$$B$$$$C$$$$B$$$$D$$$$A$$$$B$$$$C$$$$D$$$$E$$$$A$$"}, {"key": "5711", "content": "Two piles of coal, the weight of the first pile is $$5$$ times the weight of the second pile. The first pile used $$36$$ tons, and the second pile used $$4$$ tons. The remaining weight of the first pile is $$3$$ times the weight of the second pile. The original weight of the first pile was tons, and the original weight of the second pile was tons."}, {"key": "5712", "content": "Qingqing needs to cross a small hill from home to school, she walks up the hill at $$50$$ meters per minute, and the speed downhill is $$20$$ meters per minute faster than uphill. The distance from home to school is $$2800$$ meters, and it takes $$50$$ minutes to get to school. It takes minutes to get home from school."}, {"key": "5713", "content": "The distance from the school to the cinema is $$4930$$ meters. Person A and person B run towards each other, with person A running $$40$$ meters per minute and person B running $$50$$ meters per minute. Along the way, person A stops for $$1$$ minute due to loose shoelaces, and person B stops for $$5$$ minutes when encountering an acquaintance. The minutes required for both to meet from the start are."}, {"key": "5714", "content": "Grandpa and grandma walk hand in hand in the park, they start from point $$A$$ and walk forward $$4$$ meters, then turn right $$90$$ degrees and go forward another $$4$$ meters, then turn right $$90$$ degrees and go $$4$$ meters $$\\cdots\\cdots$$ continuing in this pattern, after they have walked $$2004$$ meters, they are meters away from the starting point $$A$$."}, {"key": "5715", "content": "The number of hens in a chicken farm is $$6$$ times the number of roosters. Later, both the number of hens and roosters increased by $$60$$, and the number of hens became $$4$$ times the number of roosters. Then, the original total number of chickens in the chicken farm was"}, {"key": "5716", "content": "Putting $$108$$, $$1008$$, $$10008$$, $$100008$$, $$\\cdots$$, $$100\\cdots 08$$ together in sequence to form a natural number $$108100810008100008\\cdots 100\\cdots 08$$ that is divisible by $$81$$, the sum of the digits of this number is at least."}, {"key": "5717", "content": "Calculate. $$279972\\div 28=$$."}, {"key": "5718", "content": "The school bought $$5$$ boxes of colored chalk and $$10$$ boxes of white chalk, with $$20$$ pieces per box. How many pieces of chalk are there in total? (Calculate using two methods)"}, {"key": "5719", "content": "Calculate (1) $$26\\times 99=$$ (2) $$123\\times 999= $$ (3) $$37\\times 103=$$"}, {"key": "5720", "content": "Fill in the blanks. (1) The perimeter of a square is $$36$$ meters, the side length of this square is meters, and the area of this square is square meters; (2) The area of a rectangle is $$40$$ square meters, the length is $$8$$ meters, the width is meters, and the perimeter of this rectangle is meters."}, {"key": "5721", "content": "Supermarket beverage big promotion, the promoter found that if $$3$$ bottles of black tea and $$8$$ bottles of green tea are packed together, all the drinks will be used up, and the quantity of green tea is $$2$$ times the quantity of black tea plus $$80$$ bottles, black tea has bottles, green tea has bottles."}, {"key": "5722", "content": "There are three trucks, $$A$$, $$B$$, and $$C$$. The cargo loaded on truck $$C$$ is half of that on truck $$B$$, and $$B$$ has $$180$$ grams less cargo than $$A$$. The cargo on $$A$$ is four times that on $$C$$. The combined cargo weight in kilograms for trucks $$A$$ and $$B$$ is."}, {"key": "5723", "content": "Rhinoceroses, antelopes, and peacocks, three types of animals, have a total of $$26$$ heads, $$80$$ legs, and $$20$$ horns. It's known that a rhinoceros has $$4$$ legs and $$1$$ horn, an antelope has $$4$$ legs and $$2$$ horns, and a peacock has $$2$$ legs and no horns. Therefore, there are rhinoceroses, antelopes, and peacocks."}, {"key": "5724", "content": "In mythology, there are $$3$$ types of creatures, namely the Phoenix, Pegasus, and Angel. Among them, the Phoenix has $$2$$ wings and $$2$$ legs, the Pegasus has $$2$$ wings and $$4$$ legs, and the Angel has $$6$$ wings and $$2$$ legs. Now, there are a total of $$20$$ creatures, $$80$$ wings, and $$52$$ legs. So, there are $$4$$ Phoenixes, $$6$$ Pegasuses, and $$10$$ Angels."}, {"key": "5725", "content": "Calculate: $$2020.2-1006.674-(1000.326-652.8)=$$."}, {"key": "5726", "content": "Quick calculation: $$23.56-12.97-(14.56-8.97)$$=."}, {"key": "5727", "content": "A board is nailed with $$16$$ nails, arranged in a 4 by 4 matrix. With rubber bands, a total of different squares can be formed.\n question_5727-image_0"}, {"key": "5728", "content": "Given $${{a}^{n}}=3$$, $${{b}^{n}}=2$$, then $${{({{a}^{2}}{{b}^{3}})}^{n}}=$$."}, {"key": "5729", "content": "Arithmetic sequence: $$1$$, $$4$$, $$7$$, $$10$$, $$\\cdots$$, where $$55$$ is the nth term of this sequence."}, {"key": "5730", "content": "Fill in the blank between two numbers with either \"$$+$$\" or \"$$-$$\" to make the equation valid.\n$$4$$ $$4$$ $$4$$ $$4=8$$"}, {"key": "5731", "content": "Eddie's home has a rectangular flower bed (as shown in the left image below), and Wei's home has a square flower bed (as shown in the right image below). Knowing that the smallest square size in the pictures is the same, whose garden is larger? question_5731-image_0"}, {"key": "5732", "content": "The perimeter of this figure is in centimeters. (Unit: centimeters) question_5732-image_0"}, {"key": "5733", "content": "A primary school held a sports meeting, and the students formed a $$7\\times 7$$ square array to participate in a group calisthenics performance. By reducing one row and one column from this square array, the number of students decreased by ."}, {"key": "5734", "content": "At the end of the month, when the boss calculates everyone's salary, if each person is given $1000, there would be an excess of $10000; if each person is given $1500, there would be a shortfall of $5000. (1) The total difference in the distribution results of the two salary payment methods is dollars. (2) There are employees in the company, and the boss has prepared dollars for paying salaries."}, {"key": "5735", "content": "Ming bought two sets of storybooks. When calculating the price, he mistook the selling price of one set of books as $$266$$ yuan instead of $$226$$ yuan, resulting in a total of $$400$$ yuan. How much are these two sets of books actually in total? question_5735-image_0"}, {"key": "5736", "content": "Divide $$12$$ identical watermelons into $$3$$ piles of different quantities, there are various different ways. question_5736-image_0"}, {"key": "5737", "content": "Four schools participated in the 'Youth Marathon' competition with a total of $$549$$ students. If we add $$2$$ to the number of students from School A, subtract $$2$$ from School B, double the number from School C, and halve the number from School D, then the numbers from the four schools will exactly equal each other. Find out how many students from School A, School B, School C, and School D participated in the event."}, {"key": "5738", "content": "The teacher distributed apples and peaches to the children, with the total number of apples bought being $$2$$ times that of the peaches. After each child received $$5$$ peaches, there were $$15$$ peaches left; by distributing $$14$$ apples per child, there were $$30$$ apples short. The teacher bought a total of peaches and apples."}, {"key": "5739", "content": "Calculate a number in the following manner: $$+2$$, $$\\times 2$$, $$-2$$, $$\\div 2$$, $$+2$$, $$\\times 2$$, $$-2$$, $$\\div 2$$, $$\\cdots \\cdots $$\uff0e(1) If you calculate $$5$$ for $$100$$ times, the result will be."}, {"key": "5740", "content": "Workshop is divided into Group $$A$$ and Group $$B$$. Group $$A$$ has $$3$$ times plus $$4$$ people more than Group $$B$$. If $$8$$ people are moved from Group $$B$$ to Group $$A$$, then Group $$A$$ will have $$5$$ times the number of people in Group $$B$$. Group $$A$$: people, Group $$B$$: people."}, {"key": "5741", "content": "Xiaole needs to cross a hill from home to school, walking uphill at $$35$$ meters per minute and downhill at $$55$$ meters per minute. The distance from home to school is $$1450$$ meters, and it takes $$30$$ minutes to get to school. How many minutes did Xiaole spend walking downhill?"}, {"key": "5742", "content": "Fill in the blanks. (1) The area of a square is $$49$$ square meters, the side length of this square is meters, the perimeter of this square is meters; (2) The area of a rectangle is $$4000$$ square decimeters, the length is $$8$$ meters, the width is meters, the perimeter of this rectangle is meters."}, {"key": "5743", "content": "There are poplar trees, willow trees, and pine trees totaling $$100$$ trees in the park, the number of poplar trees is $$8$$ times the number of pine trees, and the number of willow trees is equal to the number of pine trees, then there are $$10$$ pine trees in the park."}, {"key": "5744", "content": "A traffic coordinator issued $$75$$ tickets in September, which can be categorized into two types: one for illegal parking, and another for running a red light$$.$$ The number of tickets for illegal parking was four times the number of tickets for running a red light, and there were tickets for illegal parking."}, {"key": "5745", "content": "The toy factory produced $$2000$$ more toys in February than in January, and $$3000$$ more toys in March than in February, how many more toys were produced in March compared to January."}, {"key": "5746", "content": "There are $$30$$ coins numbered $$1\\sim 30$$ face up on the table. First, coins numbered as multiples of $$3$$ are flipped over, then those numbered as multiples of $$4$$ are flipped over. In the end, there are still coins facing up."}, {"key": "5747", "content": "It is said that a long time ago, because there were no good measures for pest control, the calculations on a book were often partially eaten by insects. Therefore, when people were reading, they had to figure out, according to the remaining calculations, what the eaten numbers were. These types of problems were later referred to as 'insect-eaten calculations'. Fill in the blanks with appropriate numbers to make the addition problem in the diagram correct; then the largest addend is $$393$$."}, {"key": "5748", "content": "Fill in the appropriate numbers in the blanks to make the vertical calculation in the diagram correct, then the result of the addition is. question_5748-image_0"}, {"key": "5749", "content": "The image contains $$5$$ lines and $$9$$ intersections. If line $$e$$ is removed, there will remain intersections.\n question_5749-image_0"}, {"key": "5750", "content": "The teacher distributes candies to the students. If each person gets $$2$$ candies, there will be $$20$$ candies remaining; if each person gets $$5$$ candies, there will be $$2$$ candies remaining. How many students are there in total, and how many candies did the teacher prepare? question_5750-image_0"}, {"key": "5751", "content": "Vera shared cakes among the children, each child got $$3$$ cakes, leaving an excess of $$12$$ cakes; if each child got $$4$$ cakes, then there would be $$7$$ cakes left over. Thus, there are children and cakes in total."}, {"key": "5752", "content": "The teacher distributes candies to the students. If each student receives $$9$$ candies, there are $$2$$ candies short; if each student receives $$11$$ candies, then there are $$14$$ candies short. Therefore, there are a total of students, and the teacher prepared candies."}, {"key": "5753", "content": "During the nature class, the teacher distributed some leaves to the students. If each person gets $$5$$ leaves, there will be $$3$$ leaves short; if each person gets $$7$$ leaves, then there will be $$25$$ leaves short. There are students, in total there are leaves."}, {"key": "5754", "content": "The teacher distributes candies to the students. If each student gets $$4$$ candies, then there are $$17$$ candies left; if each student gets $$7$$ candies, then there are $$10$$ candies short. Therefore, there are a total of students, and the teacher prepared candies."}, {"key": "5755", "content": "The Monkey King divides peaches among the little monkeys. If he gives each little monkey $$5$$ peaches, then he is short of $$4$$ peaches; if he gives each little monkey $$4$$ peaches, he will have $$5$$ peaches left over. How many little monkeys are there in total, and how many peaches has the Monkey King prepared?"}, {"key": "5756", "content": "Determine the parity of the result of the following equation: $$22\\times 4+33\\times 5+66\\times 8-45\\times 10$$"}, {"key": "5757", "content": "In the new home of the PhD, there is a rectangular living room that is $$5$$ meters long and $$4$$ meters wide, so its area is in square meters. If the floor tiles used have an area of $$10$$ square decimeters each, the number of tiles needed to cover it is ."}, {"key": "5758", "content": "Xiao Ming's ID number is $$331003200405210634$$, and Xiao Ming's birthday is ( )."}, {"key": "5759", "content": "Calculate:\n$$(1)$$ $$36\\times 19+64\\times 19=$$\n$$(2)$$ $$32\\times 25+68\\times 25=$$\n$$(3)$$ $$268\\times 75-68\\times 75=$$"}, {"key": "5760", "content": "If expressed as a fraction, the shaded part of the figure below is ( ) of the entire figure.\n question_5760-image_0"}, {"key": "5761", "content": "Wang Gang went to Wanda to see a movie, he arrived at $$7:15$$, and the movie started at $$8:05$$. He needs to wait for ( ) minutes."}, {"key": "5762", "content": "The number closest to $$9000$$ is (  )\uff0e"}, {"key": "5763", "content": "Elementary School and Xiao Si have a total of $$125$$ books. The number of books in Elementary School is $$2$$ times more than that of Xiao Si, plus $$5$$ books, so Elementary School has books."}, {"key": "5764", "content": "Xiaojun has two routes to go to school. The length of these two routes is, ( )\n question_5764-image_0"}, {"key": "5765", "content": "A class has $$48$$ people. There are $$25$$ people who can play basketball, $$18$$ people who can play volleyball, and $$12$$ people who cannot play either. There are people who can play both basketball and volleyball."}, {"key": "5766", "content": "The full distance of a marathon race is about $$42$$ (__)."}, {"key": "5767", "content": "There are a total of 6 straight lines in the figure. Removing one line to make the number of intersections 7, the removed line is question_5767-image_0"}, {"key": "5768", "content": "Compute: (1) $$23\\times 4\\times 25$$= (2) $$125\\times 13\\times 8$$=\n (3) $$12\\times 25$$= (4) $$48\\times 125$$="}, {"key": "5769", "content": "\u2605\u2605\u25cb\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u25cb\u2605\u2605\u25cb\u25cb\u25cb$$\\dots\\dots $$ The 17th figure in such a sequence is ( )."}, {"key": "5770", "content": "As shown in the picture, there are $$8$$ people in black clothes numbered $$1$$, $$2$$, $$3$$, $$\\cdots \\cdots 8$$, forming a circle to practice passing a box. Starting from the person in black clothes number $$1$$ and passing clockwise $$50$$ times, the box should end up in the hands of the person in black clothes number .\n question_5770-image_0"}, {"key": "5771", "content": "Determine if the following numbers or formulas result in an odd or even number.\n(1)$0$(2)$199$\n(3)$43\\times 5$(4)$0\\times 51$(5)$37+23$"}, {"key": "5772", "content": "A student asked the teacher how old they are, and the teacher said: 'When I was your age, you were just $$3$$ years old; when you are my age, I will be $$39$$ years old.' Therefore, the teacher's age this year is $$27$$ years old."}, {"key": "5773", "content": "Calculate: (1) $$63.375+25.88=$$\uff0e(2) $$33.07-29.677=$$\uff0e"}, {"key": "5774", "content": "$$3+6+9+\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot +36+39=$$."}, {"key": "5775", "content": "Mingming is 6 years old this year, and his mother is 27 years older than Mingming, making his mother's age this year. In 3 years, his mother's age will be times that of Mingming."}, {"key": "5776", "content": "Count, among the following figures there are squares.\n question_5776-image_0"}, {"key": "5777", "content": "A pile of steel pipes, with each layer having one more pipe than the layer above it, the topmost layer has $$5$$ pipes, and the bottommost layer has $$13$$ pipes. The total number of pipes in this pile is ( )."}, {"key": "5778", "content": "Can you represent the quantities asked in the problems below with letters? (1) Mom is $$a$$ years old this year, Mingming is $$b$$ years old this year, Mom is older than Mingming by years. (2) The unit price of a soccer ball is $$a$$ yuan, a basketball is $$b$$ yuan, the school bought $$15$$ soccer balls, $$20$$ basketballs, spending a total of yuan on soccer balls, a total of yuan on basketballs, and a total of yuan for these balls."}, {"key": "5779", "content": "There are $$4$$ residential areas along a road, each area inhabited by a number of students as shown in the following diagram. Now, there is a plan to gather everyone into one of these areas. To minimize the total walking distance for everyone, which area should they gather in? question_5779-image_0"}, {"key": "5780", "content": "Solve the equation.$$8x-32=8-2x$$, $$x=$$."}, {"key": "5781", "content": "Eddie arranged some chess pieces into a two-layer hollow square matrix. Later, he added $$28$$ more chess pieces, turning the figure into a three-layer hollow square matrix.$$ Initially, the minimum number of chess pieces that could have been arranged is."}, {"key": "5782", "content": "Uncle Zhou has a circular fish pond with a circumference of $$140$$ meters. He wants to plant a willow tree every $$5$$ meters along the pond. He needs to plant willow trees."}, {"key": "5783", "content": "The school has a path that is $$60$$ meters long. There are plans to plant trees along one side of the path. A tree will be planted every $$10$$ meters (including both ends), so a total of trees are needed. (The width of the trees is considered negligible)"}, {"key": "5784", "content": "In front of the 'Youth and Children Activity Center', there is a straight road. Trees are planted on one side of the road (not planting trees close to one end of the door), totaling $$30$$ trees, with each tree $$5$$ meters apart from the next. Thus, the length of this road is meters. (The width of the trees is negligible)"}, {"key": "5785", "content": "The distance between two buildings is $$40$$ meters. Planting a cedar tree every $$4$$ meters, a total of cedar trees can be planted. (Ignoring the width of the trees)"}, {"key": "5786", "content": "Eddie, in order to restore the ecology of the Magic Forest, planted $$28$$ trees on one side of a road, it is known that the distance between two adjacent trees is $$3$$ meters. (1) If Eddie plants trees from one end to the other, the length of this road is meters. (2) If he doesn't plant a tree at one end, the length of this road is meters. (3) If no trees are planted at both ends, the length of this road is meters."}, {"key": "5787", "content": "As shown in the figure, an ant starts from the vertex $$P$$ of a pyramid and stops after traversing $$5$$ vertices in sequence along the edges of the pyramid without repeating any vertex. This ant has a total of different ways to do so. question_5787-image_0"}, {"key": "5788", "content": "Fill in the blanks. (1) $$3$$ meters $$=$$ decimeters $$=$$ centimeters. (2) $$7$$ square meters $$=$$ square decimeters $$=$$ square centimeters."}, {"key": "5789", "content": "The following image is the calendar for January 2020, answer the questions and summarize the pattern: question_5789-image_0 (1) From January 1, 2020, to January 22, 2020, there are a total of days; (2) From January 5, 2020, to January 15, 2020, there are a total of days; (3) From January 5, 2020, to February 10, 2020, there are a total of days."}, {"key": "5790", "content": "There is a rectangular piece of paper, length is $$10$$ cm, width is $$5$$ cm, ($$1$$) cut horizontally with scissors once (as shown in the figure), increase by cm; cut vertically once, increase by cm. question_5790-image_0 ($$2$$) Cut horizontally and vertically with scissors two times each, then the sum of the perimeters of all the small rectangles divided is cm."}, {"key": "5791", "content": "Originally, barrels A and B contained the same amount of oil. Now, if $$9$$ kilograms of oil are poured from barrel A into barrel B, then the oil in barrel B is $$4$$ times that in barrel A. How many kilograms of oil are now in barrel A and barrel B, respectively?\n question_5791-image_0"}, {"key": "5792", "content": "As shown in the diagram, in parallelogram $$ABCD$$, $$AE$$ is perpendicular to $$BC$$ at point $$E$$, $$AF$$ is perpendicular to $$CD$$ at point $$F$$, $$BC=12$$ cm, $$AE=6$$ cm, $$CD=9$$ cm. Then, the length of segment $$AF$$ is cm. question_5792-image_0"}, {"key": "5793", "content": "Given in parallelogram $$ABCD$$, $$DE=12\\text{cm}$$, $$DF=9\\text{cm}$$, $$BC=13\\text{cm}$$, the area of the parallelogram is square centimeters.\n question_5793-image_0"}, {"key": "5794", "content": "Eddy wants to buy a staple food combined with a type of drink, altogether there are various ways to make a purchase.\n\n\n\nStaple Food\nDrink\n\n\n question_5794-image_0 question_5794-image_1 \n question_5794-image_2 question_5794-image_3 question_5794-image_4 question_5794-image_5"}, {"key": "5795", "content": "While shopping, Xiaotie bought four items. When calculating the final price, he mistook $$13.21$$ for $$18.21$$, and $$39.08$$ for $$39.68$$. How much difference is there between the price he calculated and the actual amount he should pay?"}, {"key": "5796", "content": "Set up vertical calculation: (1) $$23\\times 14=$$ (2) $$25\\times 41=$$"}, {"key": "5797", "content": "Set up the division as follows: $$408\\div 4$$=$$1216\\div 4$$="}, {"key": "5798", "content": "The Tree Planting Day has arrived, and Xueersi School organized a tree planting activity. If $$5$$ people can plant $$100$$ trees in $$2$$ hours, assuming each person plants the same number of trees per hour: (1) how many trees can $$5$$ people plant in $$1$$ hour? (2) how many trees can $$1$$ person plant in $$2$$ hours? (3) how many trees can $$1$$ person plant in $$1$$ hour?"}, {"key": "5799", "content": "Calculate: $$17\\times 9=$$\uff0e"}, {"key": "5800", "content": "Calculate: $$20\\div 3+40\\div 9+80\\div 9=$$\uff0e"}, {"key": "5801", "content": "It is known that New Year's Day in 1995 was a Saturday, what day of the week was July 1, 1997?"}, {"key": "5802", "content": "A rectangle is $$10$$ cm in length and $$5$$ cm in width, its area is square centimeters. Divide it into $$2$$ identical squares, the perimeter of a square is cm, and the area is square centimeters."}, {"key": "5803", "content": "A PhD owns ducks, which are 32 more in number than the geese he owns. It is known that the number of ducks is 2 more than triple the number of geese. How many ducks are there?"}, {"key": "5804", "content": "As shown in the diagram, by filling each square with distinct natural numbers, it can make the sum of the three numbers in each row, each column, and each diagonal line equal. Therefore, the number in the top-left corner should be.\n question_5804-image_0"}, {"key": "5805", "content": "The image below is a floor plan of a park. To allow visitors to walk through each path once without repetition, the entrance and exit should be set at ( ).\n question_5805-image_0"}, {"key": "5806", "content": "There are $$24$$ cars in the parking lot, including four-wheeled and three-wheeled cars. These cars have a total of $$86$$ wheels. Then, there are ____ three-wheeled cars."}, {"key": "5807", "content": "The fourth grade at Fragrant Grasslands Elementary School has $$58$$ students learning piano, $$43$$ students learning painting, $$37$$ students learning both piano and painting. Ask how many students are only learning piano."}, {"key": "5808", "content": "Given the arithmetic sequence $$3$$, $$7$$, $$11$$, $$15$$, $$\\cdots $$, the $$26$$th term is."}, {"key": "5809", "content": "There are a total of triangles in the right figure.\n question_5809-image_0"}, {"key": "5810", "content": "Calculate: (1) $$18\\times 6=$$ (2) $$108\\times 6=$$"}, {"key": "5811", "content": "The last item in the outdoor expansion is first aid knowledge training. The school prepared some first aid kits. If all were distributed to the third grade, with $$10$$ per class, then $$8$$ would remain; if all were distributed to the fourth grade, with $$12$$ per class, then $$22$$ would be lacking. It is known that there are $$2$$ fewer classes in the third grade than in the fourth grade. (1) The fourth grade has two more classes than the third grade, and these two classes were allocated some first aid kits. (2) There are classes in the third grade, and respectively classes in the fourth grade, with a total of first aid kits."}, {"key": "5812", "content": "Among the figures below, the one with the incorrect height is ( )."}, {"key": "5813", "content": "If the base and height of a parallelogram are each increased to $$2$$ times their original length, its area will be increased by ( ) times."}, {"key": "5814", "content": "As shown in the figure, the side length of the large square is $$8$$ centimeters, and the side length of the small square is $$6$$ centimeters. How many square centimeters is the area of the shaded part in the diagram?\n question_5814-image_0"}, {"key": "5815", "content": "The aquarium prepared $$230$$ kilograms of fish for the $$8$$ walruses in the museum. In the first two days, these $$8$$ walruses ate a total of $$80$$ kilograms of fish. Two days later, $$2$$ of the walruses were transported away. Assuming each walrus eats the same amount of fish every day, the remaining fish can feed the remaining walruses for days."}, {"key": "5816", "content": "It is known that $$3$$ model workers and $$6$$ ordinary workers can produce $$360$$ parts in $$4$$ hours. Now there is a batch of production tasks that requires $$6$$ model workers and $$12$$ ordinary workers to work for $$10$$ hours to complete. If after working for $$3$$ hours, another $$1$$ model worker and $$2$$ ordinary workers join, the task can be completed hours earlier."}, {"key": "5817", "content": "The denominator of $$\\frac{2}{5}$$ plus $$15$$, to keep the fraction the same, the numerator needs to be expanded by ( ) times."}, {"key": "5818", "content": "Cut a piece of iron wire that is $$3$$ meters long into $$5$$ equal parts. Among the following statements, the incorrect one is ( )."}, {"key": "5819", "content": "Xiaoming's younger brother is a triplet. Xiaoming's age this year is equal to the total age of his 3 younger brothers. In 6 years, the total age of the 3 younger brothers will be twice Xiaoming's age. Xiaoming is years old this year."}, {"key": "5820", "content": "The age of the father $$15$$ years ago is the equivalent of the son\u2019s age $$12$$ years later. When the father\u2019s age is $$4$$ times the son\u2019s age, the father is years old."}, {"key": "5821", "content": "A group of soldiers in a certain unit formed a solid square formation while marching. Another team of $$31$$ people joined their square formation, exactly increasing each row and column by one. Now, the total number of people is."}, {"key": "5822", "content": "Black and white beads, one row of black, one row of white, arranged in the shape of an equilateral triangle (as shown in the figure), when there are $$10$$ more white beads than black beads, the total number of white beads used is\uff0e question_5822-image_0"}, {"key": "5823", "content": "A fourth-grade class forms a square formation, with the number of people on the most outer layer being $$40$$ people. It's asked how many people are on each side of the outer layer and how many people are in the entire square formation."}, {"key": "5824", "content": "$$120$$ chess pieces are arranged into a three-layer hollow square matrix, with each side of the innermost layer having several chess pieces."}, {"key": "5825", "content": "Students in fourth grade at Hope Elementary School form a solid square array, and there are still $$5$$ people left. If one row is added both horizontally and vertically to form a slightly larger solid square array, then there would be $$26$$ people missing. There are people in the fourth grade of Hope Elementary School."}, {"key": "5826", "content": "The new semester begins, and Young Pioneers holding flowers form a double-layered square formation around a decorated vehicle, with the outermost layer having $$13$$ people on each side. There are a number of Young Pioneers around the decorated vehicle."}, {"key": "5827", "content": "A team of soldiers arranged in a three-layered hollow square formation will have an excess of $$16$$ people; if another layer of people is added to the hollow part, they will be short of $$28$$ people. This team of soldiers has a total of people, and if they were to form a solid square formation, each side should have people."}, {"key": "5828", "content": "There is an arithmetic sequence of 20 natural numbers with a total sum of 1000. It is also known that each number is 4 more than the previous one. The first number in this arithmetic sequence is."}, {"key": "5829", "content": "A triangle where both acute angles are $$60$$ degrees is ( )"}, {"key": "5830", "content": "The figure is a ( ) triangle.\n question_5830-image_0"}, {"key": "5831", "content": "There are a total of $$30$$ table tennis balls in three boxes. Take out $$3$$ table tennis balls from the first box and put them into the second box. Then, take out $$5$$ table tennis balls from the second box and put them into the third box. At this point, the total number of table tennis balls in the three boxes is the same. So, how many table tennis balls were in the first box?"}, {"key": "5832", "content": "A number, when added to $$5$$, multiplied by $$5$$, subtracted by $$5$$, and then divided by $$5$$, equals $$5$$. This number is."}, {"key": "5833", "content": "A bundle of wire, the first time used more than half of the total length plus $$3$$ meters, the second time used half of the remaining minus $$10$$ meters, the third time used $$15$$ meters, finally remaining $$7$$ meters, this bundle of wire originally had meters."}, {"key": "5834", "content": "Eddie lives on the first floor, and the doctor lives on the tenth floor. Eddie wants to visit the doctor\u2019s house. How many flights of stairs must he climb from the first floor to the tenth floor?"}, {"key": "5835", "content": "Set up a division in column form: (1) $$565\\div 5=$$\uff0e"}, {"key": "5836", "content": "Set up a vertical calculation\uff1a\uff082\uff09$$378\\div 7=$$\uff0e"}, {"key": "5837", "content": "Set up in column form and calculate: (1) $$300\\div 25=$$\uff0e"}, {"key": "5838", "content": "Calculate: (1) $$67000\\div 25=$$\uff0e"}, {"key": "5839", "content": "First observe, then calculate the following expression: (2) $$\\left( 18000-720 \\right)\\div 9=$$."}, {"key": "5840", "content": "First observe, then calculate the following expressions: (1) $$294\\div 7+56\\div 7=$$\uff0e"}, {"key": "5841", "content": "Calculate: (1)$$91\\div 9+89\\div 9=$$."}, {"key": "5842", "content": "Fill in the appropriate numbers in the squares in the diagram below, so that the following division vertical expression is valid. The divisor is. question_5842-image_0"}, {"key": "5843", "content": "Answer the following questions: Fill in the appropriate numbers in the blanks to make the vertical equation in the picture valid. What is the result of the addition? question_5843-image_0"}, {"key": "5844", "content": "The school allocates dormitories for new students. If each room houses $$3$$ people, there will be $$22$$ people left over; if each room houses $$8$$ people, there will be $$1$$ room left empty. How many dormitories are there and how many new students are there? question_5844-image_0"}, {"key": "5845", "content": "A class of students went rowing. They calculated that if each boat seats $$4$$ people, they would need to add one more boat; if each boat seats $$5$$ people, they would need to reduce one boat. Question: How many students are there in the class in total? question_5845-image_0"}, {"key": "5846", "content": "January 1, 2016 was Friday, January 1, 2017 was Sunday."}, {"key": "5847", "content": "[Thinking Expansion] As shown, $$CD=2BD$$, given that the area of triangle $$ABD$$ is $$20$$, then the area of triangle $$ACD$$ is question_5847-image_0"}, {"key": "5848", "content": "[Logical Expansion] A class has $$40$$ people, among which $$32$$ people can play basketball, and $$28$$ people can play football. Then, what is the minimum number of people who can play both sports?"}, {"key": "5849", "content": "[Campus Knowledge] The value of A is $$42.62$$, B is $$4.1$$ more than A, what is the value of B"}, {"key": "5850", "content": "[Thinking Expansion] $$44+46+48+50+52+54+56=$$."}, {"key": "5851", "content": "[Thinking Expansion] As shown in the figure, if the area of the rectangle is $$50$$ square centimeters, then the area of the shaded part is square centimeters. question_5851-image_0"}, {"key": "5852", "content": "[Cognitive Expansion] The length of a rectangle is $$12$$ meters and the width is $$8$$ meters, so the area of the shaded part is square meters. question_5852-image_0"}, {"key": "5853", "content": "In a class, four students compete in a checkers tournament, where every pair of students plays a game against each other. The winner of each game receives $$2$$ points, each player in a draw receives $$1$$ point, and the loser receives $$0$$ points. (2) The maximum and minimum points the first-place winner can get, and the maximum points the last-place winner can get."}, {"key": "5854", "content": "The figure below is a summary table of the results of a teacher grading everyone's essays, where some information has been obscured. Based on the provided conditions, calculate how many people are in the excellent, good, and satisfactory categories respectively? Then complete the summary table. (1) The number of people passing is 1 less than 45 times the number of people failing; (2) The combined number of people with excellent and satisfactory grades is 13 more than the number of people with good grades; (3) The number of people with excellent grades is 12 less than twice the number of people with satisfactory grades. question_5854-image_0 The number of people with excellent grades is ____, the number of people with good grades is ____, and the number of people with satisfactory grades is ___."}, {"key": "5855", "content": "Is the result of the following equation an odd or even number. (2) $522-103\\times 3+98\\times 22-54$"}, {"key": "5856", "content": "Is the result of the following expression odd or even. (1) $36+53\\times 66-47\\times 11$"}, {"key": "5857", "content": "5762,3105,9631,7953,2945,3281, the numbers among these that can be divided by 3 are in total."}, {"key": "5858", "content": "Fill in the $$\\square$$ in each of the following numbers with appropriate digits so that the number is divisible by $$9$$. What are the possible digits for $$\\square$$? Please write out these four numbers respectively.$$\\overline{\\square 162}$$, $$\\overline{5\\square 41}$$, $$\\overline{56\\square 3}$$, $$\\overline{618\\square }$$. "}, {"key": "5859", "content": "Calculate the following question: $$\\underbrace{33\\cdots 3}_{100 3s}\\times \\underbrace{33\\cdots 3}_{100 3s}=$$"}, {"key": "5860", "content": "Starting from $$1$$, natural numbers are arranged according to the rule shown in the figure. By framing $$4$$ numbers with a parallelogram so that their sum is $$842$$, the smallest number in the parallelogram is. question_5860-image_0"}, {"key": "5861", "content": "The teacher distributes strawberries to the children in the class. If each child gets 5 strawberries, there is 1 missing; if each child is to get 6 strawberries, there are 4 missing. How many strawberries are there?"}, {"key": "5862", "content": "As shown in the figure, a city's east-west road intersects with the north-south road at the intersection $$A$$. Person A is at point $$B$$, 560 meters south of intersection $$A$$, and Person B is at intersection $$A$$. Both A and B start moving at the same time with constant speed, A moves north and B moves east. After $$4$$ minutes, the distance of both from $$A$$ is equal. They continue walking for another $$24$$ minutes, and their distances from $$A$$ become equal again. The speed of Person B is in meters/minute. question_5862-image_0"}, {"key": "5863", "content": "Eddy and Will live $$16$$ kilometers apart. Both set off from their homes at the same time, moving in the same direction with Will ahead and Eddy behind. Will travels at $$12$$ kilometers per hour. If Eddy wants to catch up with Will within $$2$$ hours, Eddy's speed must be at least kilometers per hour."}, {"key": "5864", "content": "In the multiplication vertical method shown in the figure, some numbers are covered by triangular pieces of paper. The result of the equation is. question_5864-image_0"}, {"key": "5865", "content": "A number plus $$5$$, multiplied by $$5$$, subtract $$5$$, then divided by $$5$$, the result equals $$5$$, this number is."}, {"key": "5866", "content": "Xiao Ming, Xiao Li, Xiao Jun, and Xiao Hua have heights of $$109$$ cm, $$105$$ cm, $$108$$ cm, and $$118$$ cm, respectively. The average height of the four persons is cm."}, {"key": "5867", "content": "Eddy and Vera prepare to beautify the entire Maze Magic School (1) First, they plant willow trees on one side of a 100-meter-long pedestrian street, planting one every 10 meters, including both ends, totaling willow trees to be planted. (2) The distance between the Sun and Moon teaching buildings is 50 meters, Eddy now plans to plant poplar trees between these two buildings, planting one every 5 meters, totaling poplar trees needed. (3) Vera plants pine trees on one side of the straight road leading to the magic castle gate, the road is 40 meters long, with every two trees spaced 5 meters apart, totaling pine trees to be planted. (4) There is a circular flower bed in the square, with the perimeter of the flower bed being 80 meters. Now, they plan to place a pot of flowers every 8 meters around the flower bed, totaling pots of flowers that can be placed."}, {"key": "5868", "content": "Doctor, Eddie, and Vi pass the ball to each other, starting with the doctor, and after $$4$$ passes. (1) If the ball returns to the doctor's hands, there are different ways to pass the ball. (2) If the ball is passed to Eddie's hands, there are different ways to pass the ball."}, {"key": "5869", "content": "Using these three numbers $$1$$, $$3$$, $$5$$ to form a three-digit number without repeating any digits."}, {"key": "5870", "content": "Perform vertical multiplication for the following problems$$136\\times 123=$$$$155\\times 301=$$"}, {"key": "5871", "content": "In the equation below, different Chinese characters represent different numbers, and the same Chinese characters represent the same number. If \"\u5de7 + \u89e3 + \u6570 + \u5b57 + \u8c1c = 30\", then the five-digit number represented by \"\u5de7\u89e3\u6570\u5b57\u8c1c\" is. question_5871-image_0"}, {"key": "5872", "content": "Set up in vertical form and calculate the following: (1) $$54\\times 3= $$ (2) $$7\\times44=$$"}, {"key": "5873", "content": "Set up the long multiplication: (1) $$45\\times 32=$$\uff0e(2) $$46\\times 35=$$\uff0e(3) $$89\\times 64=$$"}, {"key": "5874", "content": "Arbor Day has come, and the Xueersi School organized a tree planting event. If $$5$$ people can plant $$100$$ trees in $$2$$ hours, assuming each person plants the same number of trees per hour: (1) then how many trees can $$5$$ people plant in $$1$$ hour? (2) How many trees can $$1$$ person plant in $$1$$ hour?"}, {"key": "5875", "content": "Vi plans to study piano, dance, or singing in the next $$5$$ days, learning only one course per day, with no two consecutive days being the same. She plans to study piano on the first day and also piano on the last day. How many total learning plans are there?"}, {"key": "5876", "content": "There is a bamboo in its rapid growth period. The length measured for the first time is $$14$$ centimeters, and each subsequent measurement is $$3$$ centimeters more than the last one. (1) At the time of the fifth measurement, the length of the bamboo is centimeters. (2) At the time of the sixteenth measurement, the length of the bamboo is centimeters. question_5876-image_0"}, {"key": "5877", "content": "Starting from $$1$$, the sequence of consecutive odd numbers $$1$$, $$3$$, $$5$$, $$7$$, $$\u2026\u2026$$, so $$21$$ is the nth number in this sequence."}, {"key": "5878", "content": "Starting from $$2$$, the sequence of consecutive even numbers $$2$$, $$4$$, $$6$$, $$8$$, $$10\\cdots \\cdots $$, then $$36$$ is the nth number in this sequence."}, {"key": "5879", "content": "How many line segments are there in the picture? question_5879-image_0"}, {"key": "5880", "content": "Perform vertical calculation:\n(1) $$132\\times 3=$$(2)$$18\\times 14=$$(3)$$76\\times 36=$$"}, {"key": "5881", "content": "$$2018$$ year $$10$$ month $$10$$ day is Wednesday, $$2028$$ year $$10$$ month $$10$$ day is Tuesday."}, {"key": "5882", "content": "There are a total of $$100$$ RMB notes worth $$5$$ yuan and $$10$$ yuan, with a total value of $$800$$ yuan. How many notes are there of $$10$$ yuan and $$5$$ yuan respectively?"}, {"key": "5883", "content": "A farmer took a basket of duck eggs to market to sell. In the morning, she sold half the number of duck eggs in the basket minus $$10$$, and in the afternoon, she sold half of the remaining plus $$10$$. Finally, $$65$$ eggs were left unsold in the basket. How many duck eggs were there in the basket originally?"}, {"key": "5884", "content": "As shown in the diagram, it is known that the degree of $$\\angle 4$$ is $$3$$ times the degree of $$\\angle 1$$. Therefore, $$\\angle 1=$$$${}^\\circ$$, $$\\angle 2=$$$${}^\\circ$$, $$\\angle 3=$$$${}^\\circ$$, $$\\angle 4=$$$${}^\\circ$$. question_5884-image_0"}, {"key": "5885", "content": "As shown in the figure, a large rectangle is divided into $$3$$ small rectangles and one small square, where the area of the small square is $$16$$ square centimeters, and the areas of the two rectangles are $$28$$ square centimeters and $$70$$ square centimeters, respectively. The area represented by $$A$$ for the rectangle is ( ) square centimeters.\n question_5885-image_0"}, {"key": "5886", "content": "In the diagram below, two adjacent sides are perpendicular to each other, so the perimeter of this shape is in centimeters. (Unit: centimeters) question_5886-image_0"}, {"key": "5887", "content": "[Warm-up before class 1] The shortest route from $$A$$ to $$B$$. question_5887-image_0"}, {"key": "5888", "content": "[Warm-up 3 before class] As shown in the diagram, starting from point $$A$$ and walking along the segment to point $$D$$, and must pass through point $$B$$, but cannot pass through point $$C$$. How many are there for the shortest route from point $$A$$ to point $$D$$? question_5888-image_0"}, {"key": "5889", "content": "[Warm-up before class 2] As shown in the figure, it is made up of two squares, with the side length of the smaller square being $$\\text{a}$$ centimeters, and the side length of the larger square being $$\\text{b}$$ centimeters. When $$\\text{a}=2$$ and $$\\text{b}=4$$, the area of the shaded part is in square centimeters. question_5889-image_0"}, {"key": "5890", "content": "[Warm-up 1 before the class] The figure below is a parallelogram, with an area of $$70$$ square centimeters given. The length of $$AE$$ is $$5$$ centimeters, and the length of $$AF$$ is $$7$$ centimeters. The perimeter of this parallelogram is in centimeters. question_5890-image_0"}, {"key": "5891", "content": "[Warm-up before class 3] As the figure shows, the area of the trapezoid is. question_5891-image_0"}, {"key": "5892", "content": "[Warm-up before class 2] The distance from the school to the cinema is $$4930$$ meters. Person A and Person B run towards each other; Person A runs $$40$$ meters per minute and Person B runs $$50$$ meters per minute. Along the way, Person A stops for $$1$$ minute to tie his shoelaces, and Person B stops for $$5$$ minutes to talk to an acquaintance. The time it takes for the two to meet from the start is minutes."}, {"key": "5893", "content": "Locations A and B are $$500$$ kilometers apart. Xiao Zhang first sets off on a motorcycle from location A, and $$1$$ hour later, Xiao Li starts driving a car from location A, with both arriving at location B at the same time. The initial speed of the motorcycle is $$80$$ kilometers per hour, which later reduces to $$60$$ kilometers per hour. The speed of the car is $$100$$ kilometers per hour, but the car stopped for $$2$$ hours en route. Xiao Zhang's motorcycle reduced speed $$1$$ hour after he set off."}, {"key": "5894", "content": "The People's Liberation Army conducts field training exercises. On sunny days, they walk $$35$$ kilometers per day, and on rainy days, they walk $$28$$ kilometers per day. Over $$11$$ days, they walked a total of $$350$$ kilometers. There were a total of sunny days during this period."}, {"key": "5895", "content": "$$3$$ monkeys can eat $$18$$ peaches in $$2$$ days, at this rate, $$6$$ monkeys can eat how many peaches in $$6$$ days."}, {"key": "5896", "content": "On a bookshelf, the first layer holds $$52$$ books, the second and third layers together hold $$70$$ books, the fourth layer holds $$46$$ books, average books per layer."}, {"key": "5897", "content": "$$49\\times 34+49\\times 23+57\\times 51$$=.$$22\\times 31+66\\times 23$$=."}, {"key": "5898", "content": "A and B had a total of $$114$$ passengers. After arriving at a certain place, $$20$$ people boarded ship A, and $$8$$ people disembarked from ship B. At this point, the number of people on ship A was exactly double the number of people on ship B. The original number of passengers on ship A was."}, {"key": "5899", "content": "Using $$9$$ matchsticks, place a number in each box within a square frame, such that all digits in the two numbers formed are distinct. The largest possible sum these two numbers can achieve is, and the smallest is. question_5899-image_0"}, {"key": "5900", "content": "After dividing each side of an equilateral triangle into five equal parts and then connecting the corresponding line segments, the following figure is obtained. How many triangles are there in the figure? question_5900-image_0"}, {"key": "5901", "content": "$$147\\div 7 $$="}, {"key": "5902", "content": "In the vertical addition shown below, the same Chinese characters represent the same digits, and different characters represent different digits. Then, the three-digit number represented by $$\\overline{\u597d\u672a\u6765}$$ is.\n question_5902-image_0"}, {"key": "5903", "content": "For the series $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$19$$,$$\\cdots$$, the $$10$$th number is, $$49$$ is the nth number of this series."}, {"key": "5904", "content": "Summation of an arithmetic sequence. $$1+2+3+4+5+6+\\cdots \\cdots +98+99$$=."}, {"key": "5905", "content": "Nan Nan has $$75$$ toy cars, Bei Bei has $$45$$ toy cars. If Bei Bei gives some toy cars to Nan Nan so that Nan Nan has $$3$$ times as many toy cars as Bei Bei."}, {"key": "5906", "content": "Calculate: $$63\\times36+64\\times63= $$\uff08 \uff09\uff0e"}, {"key": "5907", "content": "There are $$5$$ different pencil cases, $$4$$ different pencils, and $$3$$ different pens. Taking one of each to form a set of study tools, the maximum number of different sets of study tools that can be formed is."}, {"key": "5908", "content": "Huanhuan's number of cards is 3 times that of Lele's. If Huanhuan gives Lele 10 cards, they will have the same number of cards. How many cards did Huanhuan originally have, and how many did Lele have?"}, {"key": "5909", "content": "As shown in the diagram, there is a shortest path from $$A$$ to $$B$$, not passing through $$C$$.\n question_5909-image_0"}, {"key": "5910", "content": "The kindergarten gives candies to the winning children. If each child is given $$6$$ candies, there would be $$2$$ candies short. If each child is given $$8$$ candies, there would be $$10$$ candies short. How many children are there in total, and how many candies in total?"}, {"key": "5911", "content": "The school allocates dormitories for new students. If each room accomodates $$3$$ people, there will be $$22$$ people left over; if each room accomodates $$8$$ people, there will be $$1$$ room empty. Question: How many dormitory rooms are there, and how many new students are there? question_5911-image_0"}, {"key": "5912", "content": "The kindergarten distributes a basket of apples to the children. If each child in the senior class receives $$5$$ apples, there are $$10$$ apples left; if each child in the junior class receives $$8$$ apples, there are $$2$$ apples short. Knowing that there are $$3$$ more children in the senior class than in the junior class, then the total number of apples in this basket is, and the total number of children in both senior and junior classes is."}, {"key": "5913", "content": "In a parking lot, there were parked sedans (four wheels) and motorcycles (two wheels) totaling $$32$$ vehicles, with a total of $$108$$ wheels. Find the number of motorcycles; number of sedans."}, {"key": "5914", "content": "Complete the following questions: (1) Among any $$367$$ people born in the same year, are there any who have the same birthday?"}, {"key": "5915", "content": "The simplified calculation of $700\\div4\\div25$ is ( )."}, {"key": "5916", "content": "$136\\div5+364\\div5$ for simple calculation is ( )."}, {"key": "5917", "content": "$72\\div\\left( 6\\times5\\right)\\times5$ Simplified calculation is ( )\uff0e"}, {"key": "5918", "content": "The side length of the square is $$3$$ cm, the area of this square is square centimeters; the length of the rectangle is $$6$$ cm, and the width is $$4$$ cm, the area of this rectangle is square centimeters."}, {"key": "5919", "content": "The area of a square is $$36$$ square centimeters, then its side length is centimeters, and its perimeter is centimeters."}, {"key": "5920", "content": "Xiao Li and Xiao Wang have a total of $$97$$ apples, Xiao Wang has $$3$$ times less than Xiao Li minus $$3$$, so Xiao Wang has $$72$$ apples."}, {"key": "5921", "content": "Xiaobai wants to place $$18$$ identical model cars onto a $$3$$-tier shelf, with at least $$5$$ on each tier, there are different methods of arrangement."}, {"key": "5922", "content": "Split $$13$$ into the sum of three different non-zero natural numbers, but the three natural numbers can only be chosen from $$1\\sim 8$$, and there are a total of different ways to split."}, {"key": "5923", "content": "Distribute $$8$$ tanks among three kids, Xiao Xiao, Zhong Zhong, and Da Da, with each child getting at least one tank. How many methods are there?"}, {"key": "5924", "content": "Three pirates divide $$20$$ gold coins. If each pirate gets at least $$5$$ coins, there are a total of different ways to divide them."}, {"key": "5925", "content": "How many ways can $$15$$ identical balls be divided into three piles, with each pile having at least $$3$$ balls?"}, {"key": "5926", "content": "Split $$14$$ into the sum of three different non-zero natural numbers, how many different splitting methods are there?"}, {"key": "5927", "content": "$$37\\times 23+69\\times 63+46\\times 37=$$."}, {"key": "5928", "content": "Solve the equation: $$2(x-2)+2=x+1$$. The solution of the equation is $$x=$$."}, {"key": "5929", "content": "Given $$7x-13-2x=35+2x$$, then $$x=$$."}, {"key": "5930", "content": "The combined age of the siblings this year is $$25$$ years, the brother is $$3$$ years older than the sister, the brother is $$14$$ years old this year, the sister is $$11$$ years old this year."}, {"key": "5931", "content": "This year, the elder sister is $$13$$ years old, and the younger brother is $$10$$ years old, when the sum of their ages reaches $$101$$ years, the elder sister will be $$52$$ years old, and the younger brother will be $$49$$ years old."}, {"key": "5932", "content": "This year, Aunt Zhang's age is 5 times that of Xiao Hong. 3 years later, the sum of their ages is 54 years. Xiao Hong is ___ years old this year."}, {"key": "5933", "content": "Put all $$7$$ identical lollipops into two different boxes, with no box being empty. Then, there are a total of different ways to do so. question_5933-image_0"}, {"key": "5934", "content": "Do mental calculation, and discuss any patterns you observe.\n($$1$$) $$2\\times 3=$$.\n($$2$$) $$2\\times 30=$$.\n($$3$$) $$2\\times 300=$$.\n($$4$$) $$20\\times 300=$$."}, {"key": "5935", "content": "Solve the following problems: (1) A doctor wants to buy a set of books to donate to children. The set consists of $$20$$ books, each costing $$15$$ dollars. How much money should the doctor prepare to buy the books? (2) The doctor also wants to buy some milk for the children, each carton of milk costs $$40$$ dollars, and he plans to buy $$150$$ cartons. How much money should the doctor prepare to buy the milk?"}, {"key": "5936", "content": "Set up the calculation vertically: (1) $$45\\times 32=$$\uff0e(2) $$46\\times 35=$$\uff0e(3) $$89\\times 64$$=\uff0e(4) $$132\\times 21$$=\uff0e"}, {"key": "5937", "content": "List and calculate vertically: (1) The age of an ancient tree is $$276$$ years old, Xiaoming's age is $$12$$ years old, how many times the age of the ancient tree is Xiaoming's age? (2) At the National Day parade, a rectangular marching formation had $$350$$ people, looking from the side each row had $$25$$ people, how many rows were there in total?"}, {"key": "5938", "content": "Given that the quotient of a division equation is $$22$$, now we multiply the dividend by $$4$$, and divide the divisor by $$2$$. Using the newly obtained dividend divided by the newly obtained divisor, the quotient is."}, {"key": "5939", "content": "Eddie went shopping and found the pricing of the items as follows. (1) If Eddie wants to buy 10 pencils, how much money would he need? (2) The store has a new batch of ice pops. Eddie found that there are 5 ice pops in a box, which was too many. He plans to buy only 1 ice pop, how much money should he pay? And how much if he wants to buy 2 ice pops? question_5939-image_0"}, {"key": "5940", "content": "Eddie and Vee noticed that the doctor was working very hard, so they decided to help with the household chores. (1) Eddie is very good at washing dishes, he can wash $$42$$ dishes in $$6$$ minutes, at this rate, he can wash dishes in $$8$$ minutes. (2) Vee is also good at washing dishes, she can wash $$25$$ dishes in $$5$$ minutes, at this rate, she wants to wash $$30$$ dishes, needing minutes."}, {"key": "5941", "content": "In order to enhance their literary literacy, Eddie and Viola copied ancient poems together. Each of them copied a five-character quatrain as shown in the pictures below. Can you find any characteristics about the number of characters per line in the five-character quatrain? Eddie wants to know how many characters they have copied in total. Can you think of a good way to help him? question_5941-image_0 question_5941-image_2"}, {"key": "5942", "content": "To welcome new students, the Xueersi Restaurant has launched a new grilled chicken leg machine. It is known that $$3$$ machines can grill $$600$$ chicken legs in $$4$$ days, based on this speed calculate .(1)$$1$$ machine can grill how many chicken legs in $$1$$ day.(2)$$5$$ machines can grill how many chicken legs in $$1$$ day.(3)$$5$$ machines can grill how many chicken legs in $$3$$ days."}, {"key": "5943", "content": "Let's calculate everyone's New Year's money! (1) In 2018, the average amount of New Year's money for three students was $$120$$ yuan. After adding Eddie's New Year's money, the average amount for four students became $$150$$ yuan, and Eddie's New Year's money was yuan. (2) In 2019, the average amount of New Year's money for four students was $$160$$ yuan. After removing Vi's New Year's money, the average amount for three students became $$150$$ yuan, and Vi's New Year's money was yuan."}, {"key": "5944", "content": "As shown in the diagram, walking in a straight line from $$P$$ to $$Q$$ (crossing through the interior is allowed), there are several different shortest paths.\n question_5944-image_0"}, {"key": "5945", "content": "As shown in the figure, from point $$A$$ to point $$B$$, if it is required to pass through point $$C$$ or $$D$$ to find the shortest route, there is one.\n question_5945-image_0"}, {"key": "5946", "content": "Determine which of the following figures can be drawn with one stroke. question_5946-image_0"}, {"key": "5947", "content": "Eddie is organizing his desk, dividing $$9$$ identical pencils into $$3$$ piles, there are a total of different ways to do this."}, {"key": "5948", "content": "Eddie is cleaning his desk, dividing $$12$$ identical erasers into $$3$$ piles of different quantities, there are a total of different ways to do so."}, {"key": "5949", "content": "Calculate: $$125\\times 16\\times 5$$="}, {"key": "5950", "content": "Calculate: $$125\\times (30+8)$$=."}, {"key": "5951", "content": "Calculate: $$37\\times 101=$$."}, {"key": "5952", "content": "Calculate: $$23\\times 99 =$$."}, {"key": "5953", "content": "Calculate: $$12\\times 37+24\\times 45-36\\times 9$$="}, {"key": "5954", "content": "Calculate: $$42\\times 36+58\\times 37$$="}, {"key": "5955", "content": "This year Bao Bao is $$15$$ years old, her father is $$45$$ years old, please ask: When Bao Bao was how old, her father\u2019s age was $$4$$ times that of Bao Bao."}, {"key": "5956", "content": "The teacher distributes candy to the students, if each student gets $$2$$ candies, then there will be $$20$$ candies left over; if each student gets $$5$$ candies, then there will be $$2$$ candies left over. So, there are a total of students, and the teacher prepared candies. question_5956-image_0"}, {"key": "5957", "content": "Young pioneers go to plant trees; if each digs $$5$$ tree holes, there are still $$3$$ tree holes left undug; if among them two people each dig $$4$$ tree holes, and the rest each dig $$6$$ tree holes, then all the tree holes are exactly dug. There are in total young pioneers, and there are tree holes to be dug."}, {"key": "5958", "content": "A grade has a total of $$150$$ people. When dividing into classes, it was found that no matter how the division is done, the class with the most students will always have at least $$22$$ people. Therefore, the maximum number of classes is ( )."}, {"key": "5959", "content": "Four soccer teams play a single round-robin tournament, with every two teams playing against each other. If a game is drawn, each team gets $$1$$ point, otherwise, the winning team gets $$3$$ points, and the losing team gets $$0$$ points. At the end of the tournament, the total points of all teams are exactly four consecutive natural numbers. Question: What is the total score of the team that lost to the first-placed team?"}, {"key": "5960", "content": "When Eddie was multiplying two integers, he mistook the ones digit of one factor as $$4$$ instead of $$1$$, resulting in a product of $$525$$. Vera was also performing this multiplication and she mistook the same ones digit $$4$$ as $$8$$, resulting in a product of $$700$$. The correct product for this multiplication should be."}, {"key": "5961", "content": "When doing a division arithmetic problem, the dividend $$137$$ was mistakenly seen as $$173$$. After finishing, the new quotient is $$3$$ more than the correct quotient, with the remainder unchanged. Then, in the correct division equation, what is the divisor"}, {"key": "5962", "content": "[Warmup 3 before class] A construction site needs $$1080$$ bags of cement, $$3$$ trucks with the same load carried it in $$4$$ trips, which was exactly half the needed amount. The remaining amount is transported by adding one more truck of the same model, and it still needs times to finish transporting."}, {"key": "5963", "content": "[Warm-up 2 before class] The Hongguang brigade plows the fields with tractors, $$2$$ tractors for $$3$$ hours plow $$75$$ mu of land. Based on this calculation, $$4$$ tractors for $$5$$ hours will plow mu of land."}, {"key": "5964", "content": "[Pre-class Warm-up 1] During the Spring Festival, Xue learns to visit his grandparents' home with his parents. First, they need to take a high-speed train for $$3$$ hours, then transfer to a long-distance bus for $$2$$ hours. Knowing that the speed of the high-speed train is $$315$$ kilometers per hour, and the speed of the long-distance bus is $$86$$ kilometers per hour. Then, the total distance from Xue's home to his grandparents' home is kilometers."}, {"key": "5965", "content": "We can use matchsticks to form the numbers $$0\\sim 9$$. (1) If you are given $$20$$ matchsticks (all to be used), the largest number that can be formed is, and the smallest number that can be formed is. question_5965-image_0"}, {"key": "5966", "content": "Using $$19$$ matchsticks (all used up), the largest and smallest numbers that can be made with each digit being different are, respectively. question_5966-image_0"}, {"key": "5967", "content": "Using $$8$$ matchsticks, place a number in each square within the frame. The number can be single or multiple digits, can be the same or different, the ultimate addition equation formed, the biggest result is, the smallest is. question_5967-image_0"}, {"key": "5968", "content": "Eddy and Vera are preparing to visit Grandma Li at the nursing home, as shown in the following figure: (3) In the evening, a heavy rain fell near the city center, and the nearby roads were impassable. Please ask how many shortest routes there are to the nursing home. question_5968-image_0"}, {"key": "5969", "content": "In a series of numbers, $$2$$, $$8$$, $$14$$, $$\\cdots \\cdots$$, $$62$$, each number is $$6$$ more than the previous one, this series of numbers has a total of."}, {"key": "5970", "content": "A movie theater has a total of $$11$$ rows of seats, with each row having $$2$$ more seats than the row in front of it. The first row has $$10$$ seats. question_5970-image_0 (1) The last row has ____ seats. (2) This theater has a total of ____ seats."}, {"key": "5971", "content": "Find the pattern and fill in the number. $$3$$, $$6$$, $$9$$, $$12$$,, $$18$$, $$21$$."}, {"key": "5972", "content": "Find the pattern: $$1$$, $$1$$, $$2$$, $$3$$, $$5$$, $$8$$, $$13$$, $$21$$,,, $$89$$. ( )"}, {"key": "5973", "content": "As shown in the figure, a certain city's east-west road and north-south road intersect at intersection $$A$$. Person A is at point $$B$$, 560 meters south of intersection $$A$$, and person B is at intersection $$A$$. Person A moves northward, and person B moves eastward at a uniform speed. After $$4$$ minutes, the distance of both persons from $$A$$ becomes equal. After continuing to walk for another $$24$$ minutes, the distance of both persons from $$A$$ once again becomes equal. The speed of person A is meters/minute. question_5973-image_0"}, {"key": "5974", "content": "Find the units digit of the following result: $$8+88+888+\\cdots +\\underbrace{888\\cdots 88}_{101 eights}$$, the units digit is."}, {"key": "5975", "content": "Fei is $$5$$ years old this year, and her father is $$30$$ years old. When Fei is $$10$$ years old, her father will be years old."}, {"key": "5976", "content": "To install railings around a square flower bed, $$24$$ meters of railing is needed. The length of the side of the flower bed is meters."}, {"key": "5977", "content": "The perimeter of the rectangle in the figure below is centimeters.\n question_5977-image_0"}, {"key": "5978", "content": "The perimeter of the figure below is in centimeters. Unit: (cm)\n question_5978-image_0"}, {"key": "5979", "content": "The blank part in the picture is a safe area, and the shaded area has 3 mines. Please mark them with 'X'. What is the cell in the third row and fourth column? question_5979-image_0"}, {"key": "5980", "content": "There are $$48$$ peaches, divided equally among $$4$$ monkeys, how many peaches does each monkey get? Xiao Liang calculated the result using the vertical method, the \"$$4$$\" that the arrow points to in the vertical method represents ( ).\n question_5980-image_0"}, {"key": "5981", "content": "In the vertical format of $$738\\div 2$$, this step indicated by the arrow means ( )\uff0e\n question_5981-image_0"}, {"key": "5982", "content": "In the decimal $$12.345$$, $$1$$ is in the tens place, representing $$1$$ ten; $$2$$ is in the ones place, representing $$2$$ ones; $$3$$ is in the tenths place, representing $$3$$ tenths; $$4$$ is in the hundredths place, representing $$4$$ hundredths; $$5$$ is in the thousandths place, representing $$5$$ thousandths."}, {"key": "5983", "content": "Move the decimal point of $$21.045$$ two places to the left, (expand or reduce) it to the original, it becomes."}, {"key": "5984", "content": "A square with a side length of $$10$$ cm. A small square with a side length of $$2$$ cm is cut from it (two methods of cutting as shown in the figure below), what is the perimeter of the remaining shape?\n question_5984-image_0 question_5984-image_1"}, {"key": "5985", "content": "Eddie is running around a rectangular playground, which is $$28$$ meters long and $$15$$ meters wide. What is the perimeter of this playground?\nquestion_5985-image_0"}, {"key": "5986", "content": "The combined age of the two brothers this year is $$20$$ years old, and the older brother is $$4$$ years older than the younger brother, so the age of the younger brother this year is."}, {"key": "5987", "content": "There are $$32$$ matchsticks on the table, person A and person B take turns to remove $$1$$ to $$3$$ matchsticks each time. It is stipulated that the one who takes the last matchstick wins. If both sides adopt the best strategy, should person A choose to go first or second to win, and how?"}, {"key": "5988", "content": "Xiao Si and Xiao Xue are good friends. It is known that the sum of their ages next year is twice the age of Xiao Si last year. The year before last, Xiao Xue's age was half that of Xiao Si. Calculate the current ages of Xiao Si and Xiao Xue."}, {"key": "5989", "content": "Uncle Zhang and Uncle Li have a combined age of $$56$$ years. When Uncle Zhang was half the age of Uncle Li's current age, Uncle Li's age at that time was the same as Uncle Zhang's current age. So, how old is Uncle Zhang now?"}, {"key": "5990", "content": "In a kindergarten, $$378$$ kids form several circles (one circle within another) to play a game. It is known that there are $$22$$ people in the innermost circle and $$62$$ people in the outermost circle. If the difference in the number of people between two adjacent circles is the same, then the difference between two adjacent circles is ____ people."}, {"key": "5991", "content": "The 6th term of an arithmetic sequence is 17, and the sum of the first 5 terms is 40. Find the sum of the first 18 terms."}, {"key": "5992", "content": "There are a total of $$11$$ numbers in a sequence, with the middle number being the largest. Counting forward from the middle number, each number is $$2$$ smaller than the previous one; counting backward from the middle number, each number is $$3$$ smaller than the previous one. It is known that the sum of these $$11$$ numbers is $$200$$. What is the middle number?"}, {"key": "5993", "content": "In the final math exam of the first class of the third grade, the scores of the top $$10$$ students just form an arithmetic sequence. It is known that the full score of the exam is $$100$$ points, everyone's score is an integer, and the students who ranked $$3$$rd, $$4$$th, $$5$$th, and $$6$$th together scored $$354$$ points. It is also known that Xiao Yue scored $$96$$ points. Then, the student who ranked $$10$$th scored $$72$$ points."}, {"key": "5994", "content": "A magician performs a magic trick. At the beginning, there are $$3$$ ping pong balls in the box on the table. The first time, he takes out $$1$$ ball from the box, turns it into $$3$$ balls and then puts them all back into the box; the second time, he takes out $$2$$ balls from the box, turns each ball into $$3$$ balls, and then puts them all back into the box...the tenth time, he takes out $$10$$ balls from the box, turns each ball into $$3$$ balls, and then puts them all back into the box. Please calculate how many ping pong balls are there in the box in total now."}, {"key": "5995", "content": "For the sequence $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$19$$ $$\\cdots$$, the $$10$$th number is, $$49$$ is the which number in this sequence, the difference between the $$100$$th number and the $$50$$th number is."}, {"key": "5996", "content": "In an isosceles triangle $$ABC$$, where one angle is $$30{}^\\circ $$, the other two angles of triangle $$ABC$$ are degrees and degrees or degrees and degrees (filled in from smallest to largest)."}, {"key": "5997", "content": "In triangle $$ABC$$, $$\\angle A=40\u00b0$$, $$\\angle B=50\u00b0$$, what is $$\\angle C$$ = degrees?"}, {"key": "5998", "content": "The New Year has arrived, Xiaoyue and Dayue have prepared a total of less than $$20$$ candies. Dayue first gave some of his candies to Xiaoyue, at this time the number of Xiaoyue's candies was $$3$$ times that of Dayue's. Later, Xiaoyue returned three times the number of candies Dayue gave him, at this time the number of Dayue's candies was $$3$$ times that of Xiaoyue's. So, originally, Xiaoyue and Dayue had a total of candies."}, {"key": "5999", "content": "There is a sequence of numbers: $$1$$, $$1$$, $$2$$, $$3$$, $$5$$, $$8$$, $$\\cdots$$, starting from the third number, each number is the sum of the two preceding ones. The remainder of the $$2015$$th number divided by $$7$$ is."}, {"key": "6000", "content": "A three-digit number divided by $$28$$, leaves a remainder of $$7$$. Among such three-digit numbers, the largest is."}, {"key": "6001", "content": "The remainder of the result of $$2015+2016+2017+2018$$ divided by $$12$$ is."}, {"key": "6002", "content": "The remainder is when the product of $$71427$$ and $$19$$ is divided by $$7$$."}, {"key": "6003", "content": "The sum of numbers A and B is $$1088$$. Dividing number A by number B gives a quotient of $$11$$ and a remainder of $$32$$. Then, number A is, and number B is."}, {"key": "6004", "content": "Among all numbers greater than $$35$$, there is a number whose remainder and quotient are equal when divided by $$7$$."}, {"key": "6005", "content": "In $$1995$$, $$1998$$, $$2000$$, $$2001$$, and $$2003$$, if the sum of some of these numbers gives a remainder of $$7$$ when divided by $$9$$, then group these numbers together. There are a total of groups like this."}, {"key": "6006", "content": "There are ten balls numbered from $$1$$ to $$10$$ in a box. Xiao Hong takes out nine balls from the box in three turns. If from the second turn, the sum of the numbers of the balls taken out each time is more than twice the sum of the previous time plus one, then the number of the remaining ball is (please fill in from smallest to largest)."}, {"key": "6007", "content": "It is known that a natural number $$p$$ leaves a remainder when divided by $$16$$ and $$19$$, and the sum of the quotient and the remainder when $$p$$ is divided by $$16$$ is equal to the sum of the quotient and the remainder when $$p$$ is divided by $$19$$. If $$300\\leqslant p\\leqslant 700$$, then the total number of such $$p$$ is ."}, {"key": "6008", "content": "Among all the natural numbers in $$2017$$, there is an integer $$x$$ such that $$3^x$$ and $$x^2$$ have the same remainder when divided by $$5$$."}, {"key": "6009", "content": "The remainder of $$\\underbrace{6666\\cdots 66}_{1995 \\text{ sixes}}\\div 7$$ is."}, {"key": "6010", "content": "As shown in the diagram, in the parallelogram $$ABCD$$, $$BC=10$$ cm. A line through point $$A$$ and perpendicular to $$BC$$ meets it at point $$E$$, and a line through point $$A$$ and perpendicular to $$CD$$ meets it at point $$F$$, $$AE=12$$ cm, $$CD=15$$ cm. The length of the line segment $$AF$$ is cm.\n question_6010-image_0"}, {"key": "6011", "content": "As shown in the figure, quadrilateral $$ABCD$$ is a parallelogram, and quadrilateral $$ABCE$$ is a trapezoid. It is known that the area of the parallelogram $$ABCD$$ is $$72$$ square centimeters, and $$BC=12$$ centimeters. $$DE$$ is $$2$$ times that of $$AE$$. Calculate the area of the trapezoid $$ABCE$$ in square centimeters.\n question_6011-image_0"}, {"key": "6012", "content": "As shown in the diagram, two right trapezoids of equal height are combined into a rectangle. It is known that the area of the right trapezoid $$ABCD$$ is $$30$$. Then, the area of the right trapezoid $$BCEF$$ is.\n question_6012-image_0"}, {"key": "6013", "content": "The side length of each cell (small square) in the picture is $$2$$ centimeters$$. The area of the trapezoid is in square centimeters.\n question_6013-image_0"}, {"key": "6014", "content": "Parallelograms have: . Trapeziums have: . (Fill in the sequence numbers)\n question_6014-image_0"}, {"key": "6015", "content": "Calculate the following: $$\\underbrace{88\\cdots 8}_{10\\, eights}\\times \\underbrace{99\\cdots 9}_{10\\, nines}=$$"}, {"key": "6016", "content": "There are a bunch of chess pieces. Vera arranges them on the table according to the pattern of \"four black and five white\", as seen in the figure below. A total of $$72$$ chess pieces are arranged, (2) How many of the $$72$$ chess pieces are white? question_6016-image_0"}, {"key": "6017", "content": "There are a bunch of chess pieces, arranged by Wei on the table in the pattern of 'four black, five white', as shown in the figure below. A total of $$72$$ pieces were arranged. (1) What color is the $$20th$$ piece? question_6017-image_0"}, {"key": "6018", "content": "The doctor asked Da Kuan to plant a row of trees on one side of the road. Initially, Da Kuan planted $$5$$ poplar trees in a row, but the doctor said, 'This is not the right way to plant. You should plant according to the order of $$3$$ willow trees, $$1$$ pine tree, and then again $$3$$ willow trees, $$1$$ pine tree $$\\cdots \\cdots $$.' After that, Da Kuan continued to plant according to this pattern. In the end, Da Kuan planted a total of $$187$$ trees. question_6018-image_0 \u200b\u200b\u200b\u200b (1) How many trees are repeated once? (2) How many trees are there in total following the pattern? These patterned trees can be divided into the same groups, with remaining trees. (3) How many pine trees are there, and how many willow trees are there?"}, {"key": "6019", "content": "The area of a square is $$81$$ square meters, and the side length is meters. question_6019-image_0"}, {"key": "6020", "content": "There are so many visitors to Monkey Mountain today. Wei counted a total of $$50$$ people including the elderly, youths, and children. Among them, the number of youths is twice that of the elderly, and the number of children is three times that of the elderly plus $$2$$ more persons. So, how many are the elderly, youths, and children, respectively?"}, {"key": "6021", "content": "There are three people: A, B, and C. A is $$12$$ years older than B. C is $$15$$ years older than A. C's age is $$4$$ times the age of B. The ages of A:B:C are respectively:"}, {"key": "6022", "content": "Dr. and Da Kuan's homes are $$650$$ meters apart. Dr. walks at $$60$$ meters per minute, and Da Kuan walks at $$70$$ meters per minute. Both start from their homes at the same time and walk towards each other on the same road. After $$3$$ minutes, the distance between the two is meters."}, {"key": "6023", "content": "The turtle wants to go to the beach to bask in the sun. The uphill distance is $$300$$ meters, and the downhill distance is also $$300$$ meters. The speed uphill is $$10$$ meters/minute, and the speed downhill is $$15$$ meters/minute. The turtle's average speed to the destination is meters/minute. question_6023-image_0"}, {"key": "6024", "content": "Xiaoming has to walk $$1.5$$ kilometers from school to home. One day after school, he left and had walked $$0.3$$ kilometers before returning to school to get his math book, and then he went home. question_6024-image_0 (1) This day, he walked more kilometers than usual to get home; (2) This day, he walked a total of kilometers to get home."}, {"key": "6025", "content": "Da Mao, Er Mao, and San Mao pass the ball to each other, starting with Da Mao, passing it $$3$$ times, how many different ways of passing are there?"}, {"key": "6026", "content": "Doctor, Eddie, and Vi pass the ball to each other, starting with the Doctor, after $$4$$ passes. (1) If the ball returns to Doctor's hands, there are several different ways to pass the ball. (2) If the ball is passed to Eddie's hands, there are several different ways to pass the ball."}, {"key": "6027", "content": "As shown in the figure, $$ABCDEF$$ is a regular hexagon. A frog starts at the vertex $$A$$. It can jump to one of the two adjacent vertices each time. If it can jump to point $$D$$ within $$4$$ moves, it will stop jumping (for example: $$A-B-C-D$$); if it cannot reach point $$D$$ within $$4$$ moves, it will also stop after completing $$4$$ moves (for example: $$A-B-C-B-A$$). How many different jumping patterns could the frog possibly have from start to stop? question_6027-image_0"}, {"key": "6028", "content": "As shown in the diagram, an ant starts from the apex $$P$$ of a pyramid and proceeds to cover all $$5$$ vertices along the edges of the pyramid without retracing its path and then stops. How many different routes can the ant take? question_6028-image_0"}, {"key": "6029", "content": "Find the pattern and fill in the blanks. $$37\\times 3=111$$$$37\\times 6=222$$$$37\\times 9=$$$$37\\times 27=$$"}, {"key": "6030", "content": "Column subtraction calculation: (1) $$600\\div25\\div4=$$ (2) $$1500\\div \\left(15\\times25\\right)=$$ (3) $$800\\div \\left(200\\div125\\right)=$$"}, {"key": "6031", "content": "For Children's Day, the teacher prepared $$24$$ cakes to be distributed evenly among the $$12$$ students in the class. Finding that it was not enough, they bought an additional $$36$$ cakes. Thus, each student received cakes. question_6031-image_0"}, {"key": "6032", "content": "Based on the following $$4$$ simple statistical tables, create a compound statistical table and answer the questions (each person can only choose one group). question_6032-image_0 (1) Draw the compound statistical table and add a total row and column in the table. (2) These $$4$$ groups have a total of people, with an average of male students per group and female students per group. (3) After the male students give females students people, the number of male and female students becomes the same."}, {"key": "6033", "content": "The school organized a picking activity, with a total of $$46$$ people participating. There were $$18$$ people who picked only cherries, $$7$$ people who picked both cherries and apricots, and $$6$$ people who picked neither cherries nor apricots. Question: How many people picked only apricots?"}, {"key": "6034", "content": "Among these natural numbers from $$1\\sim 60$$: (1) How many are multiples of $$2$$? (2) How many are multiples of $$3$$? (3) How many are multiples of both $$2$$ and $$3$$?"}, {"key": "6035", "content": "A certain English test consisted of two parts. As a result, 12 students from Grade 3 Class 3 scored full marks, 25 students answered the first part correctly, and 19 students made mistakes in the second part. Question: How many students in Grade 3 Class 3 made mistakes in both parts?"}, {"key": "6036", "content": "There are two piles of chess pieces, A and B, with pile A having more pieces than pile B. Now move the pieces as follows: the first time, take out the same number of pieces from pile A as there are in pile B and put them into pile B; the second time, take out the same number of pieces from pile B as the remaining in pile A and put them into pile A; the third time, again take out the same number of pieces from pile A as the remaining in pile B and put them into pile B. After moving three times like this, the number of pieces in both piles A and B are exactly $$32$$ each. How many pieces were originally in pile A and pile B, respectively."}, {"key": "6037", "content": "A and B have several pieces of candy each, and each operation involves the person with more candy giving some to the person with less candy, doubling the amount of candy the latter has. After three such operations, A has $$5$$ pieces of candy, and B has $$12$$ pieces of candy. The number of pieces A started with is, and the number B started with is."}, {"key": "6038", "content": "There is a bunch of chess pieces. After dividing them into three equal parts, there is one piece left. Take away two parts and the one left, and then divide the remaining chess pieces into three equal parts, there is still one piece left. Take away two parts and the one left again, and finally, after dividing the remaining chess pieces into three equal parts once more, there is still one piece left. How many chess pieces were there at least originally?"}, {"key": "6039", "content": "Please identify the pattern of each term in the following expressions and fill in the blank: The $$1$$st term is $$1\\times 2$$, the $$2$$nd term is $$2\\times 3$$, the $$3$$rd term is $$3\\times 4$$, $$ \\cdots $$ then the $$n$$th term is."}, {"key": "6040", "content": "The area of the figure below is.\n question_6040-image_0"}, {"key": "6041", "content": "A rectangle has an area of $$72\\text{c}{{\\text{m}}^{2}}$$, with a length of $$9\\text{cm}$$ and a width of $$\\text{cm}$$."}, {"key": "6042", "content": "As shown in the figure, in a rectangular garden with a length of $$10$$ meters and a width of $$7$$ meters, a rectangular shaded path with a width of $$2$$ meters is constructed (the shaded part in the figure), and the area of the garden (the blank part) is in square meters.\n question_6042-image_0"}, {"key": "6043", "content": "How many different natural numbers without repeated digits can be composed of the digits $$0$$, $$3$$, $$5$$?"}, {"key": "6044", "content": "Based on the provided arithmetic operation, '\u5b66' represents , '\u4e60' represents . question_6044-image_0"}, {"key": "6045", "content": "This year, Ningning is $$9$$ years old, mom is $$34$$ years old, when mom is $$52$$ years old, Ningning will be ____\uff0e question_6045-image_0"}, {"key": "6046", "content": "Among the following statements, the correct one is ( )."}, {"key": "6047", "content": "The upper base of a trapezoid is $$3$$ meters, the lower base is $$5$$ meters, and the height is $$4$$ meters. Its area is ( ) square meters."}, {"key": "6048", "content": "The sum of the top and bottom bases of a trapezoid is $$42$$ cm, and its height is $$5$$ cm. The area of this trapezoid is ( ) cm2."}, {"key": "6049", "content": "The area of the parallelogram in the diagram is ( ) $$\\text{c}{{\\text{m}}^{2}}$$. question_6049-image_0"}, {"key": "6050", "content": "As shown in the diagram, a frog jumps on five points marked with numbers on a circle. If it stops on an odd number, it will jump two points clockwise next time; if it stops on an even number, it jumps one point counterclockwise the next time. If the frog starts jumping from $$1$$, where does it stop after $$2018$$ jumps? question_6050-image_0"}, {"key": "6051", "content": "During physical education class, 20 children hold hands to form a circle and play a game, there are ( ) gaps."}, {"key": "6052", "content": "In a certain place, there are four different denominations of coins, as shown in the pictures. Assuming you have exactly one of each denomination. The question is how many different sums of money can you create."}, {"key": "6053", "content": "Class A and Class B have $$20$$ and $$30$$ students, respectively. It is known that the average score of Class A is $$93$$, and the overall average score of the two classes is $$90$$. What is the average score of Class B?"}, {"key": "6054", "content": "Four students have an average of $$40$$ scorecards each, the $$5th$$ student has $$10$$ more cards than the average number of cards of these four students, find the average number of cards for these five students."}, {"key": "6055", "content": "On one side of a road that is $$2700$$ meters long, a pine tree is planted every $$10$$ meters, and between every two adjacent pine trees, a willow tree is planted every $$2$$ meters. How many willow trees were planted?"}, {"key": "6056", "content": "The circus bought some red, yellow, and blue balloons to decorate the circular stage. A red balloon was tied at equal intervals, exactly using up the $$40$$ red balloons purchased. Then, a yellow balloon was tied exactly in the middle of every two adjacent red balloons, resulting in a shortage of $$3$$ yellow balloons. Finally, a blue balloon was tied between every two adjacent balloons, perfectly using up all the blue balloons. So, how many yellow and blue balloons did the circus buy, respectively?"}, {"key": "6057", "content": "The circus bought some red, yellow, and blue balloons to decorate the circular stage with a circumference of $$30$$ meters. Starting from a point on the stage (which is tied with a balloon), a red balloon is tied every $$2$$ meters, and just enough red balloons were used. A yellow balloon is tied every $$3$$ meters, and it was found that there were $$3$$ yellow balloons short. Finally, a blue balloon is tied between every two adjacent balloons (no blue balloon is tied at the positions where red and yellow overlap), and just enough blue balloons were used. So, the number of red, yellow, and blue balloons that the circus bought were respectively,,,, pieces."}, {"key": "6058", "content": "Cinderella attended the prince's ball. The clock in the hall struck 3 times at 3 o'clock, taking 6 seconds to do so (ignoring the time taken to strike). Therefore, when it strikes 12 times at 12 o'clock, since Cinderella must leave the ball before the 12 strikes are finished, she has seconds to escape from the start of the first strike at 12 o'clock."}, {"key": "6059", "content": "There is a rope $$100$$ cm long. Starting from the left end, make a mark every $$3$$ cm, and starting from the right end, make a mark every $$5$$ cm as well. Then cut the rope where there are marks. How many pieces has the rope been cut into?"}, {"key": "6060", "content": "Perform vertical calculation: (2) $$784\\div 56=$$."}, {"key": "6061", "content": "Set up division in a column: (3) $$3016 \\div 26=$$."}, {"key": "6062", "content": "Calculate: (2) $$27000\\div 4\\div 25=$$."}, {"key": "6063", "content": "Calculate: (3) $$4200\\div (25\\times 7)=$$."}, {"key": "6064", "content": "Calculate: (4) $$(54\\times 24)\\div (9\\times 4)=$$."}, {"key": "6065", "content": "If a straight line is added to the graph, the number of new intersections can be increased. question_6065-image_0"}, {"key": "6066", "content": "Determine which of the following figures can be drawn with one stroke."}, {"key": "6067", "content": "Judge the following pictures, those that can be drawn with one stroke are: question_6067-image_0"}, {"key": "6068", "content": "It is said that a long time ago, because there were no good measures to prevent insects, the calculations on books were often partially eaten by insects. Therefore, when reading books, people had to figure out, based on the remaining calculations, which numbers were eaten by the insects. Later, people referred to this type of problem as 'insect-eaten calculation'. In the addition calculation below, the breakthrough can be in units, because 'the more you add, the smaller it gets'; it can also be in tens, because 'something comes from nothing,'."}, {"key": "6069", "content": "In the following equation, the same symbol represents the same number, and different symbols represent different numbers. Based on this equation, it can be inferred: $$\\square +\\bigcirc +\\triangle +$$\u2606$$=$$."}, {"key": "6070", "content": "(1) The school organizes a charity sale, and Wei is in charge of selling goods. Wei sells $$25$$ boxes of apples, with each box containing $$36$$ apples, and each apple priced at $$4$$ yuan. How much money did Wei make in total? question_6070-image_0 \u200b(2) Please simplify the following calculations: \u2460$25\\times6\\times4$=\u2461$8\\times9\\times125$="}, {"key": "6071", "content": "Calculate: (1)$$25\\times 28$$=(2)$$125\\times 64$$=(3)$$125\\times 16\\times 5$$="}, {"key": "6072", "content": "Cascade subtraction calculation: (1) $$(144\\div 36)\\times (36\\div 9)\\times (9\\div 3)=$$ (2) $$2 \\div \\left( {5 \\div 7} \\right) \\div \\left( {7 \\div 11} \\right) \\div \\left( {11 \\div 16} \\right) \\div \\left( {16 \\div 35} \\right) =$$"}, {"key": "6073", "content": "The school organized a picking activity, with a total of $$46$$ people participating. $$18$$ people only picked cherries, $$7$$ people picked both cherries and apricots, and $$6$$ people picked neither cherries nor apricots. Question: How many people picked only apricots?"}, {"key": "6074", "content": "To write $$10$$ as the sum of $$3$$ natural numbers: (1) Is $$10=0+5+5$$ feasible? (2) There are several different ways."}, {"key": "6075", "content": "Place $$10$$ identical radishes into three identical baskets, each basket must be filled, and each basket can hold a maximum of $$5$$ radishes. How many different ways are there to do this?"}, {"key": "6076", "content": "Calculate: $$88\\times 39+22\\times 44$$=."}, {"key": "6077", "content": "Count the number of rectangles (including squares) in the image below. question_6077-image_0"}, {"key": "6078", "content": "In the long division shown in the right figure, the dividend is .\n question_6078-image_0"}, {"key": "6079", "content": "There is an intersection (as shown below), where Party A is $$880$$ meters south of the intersection, moving north at a speed of $$120$$ meters per minute. Meanwhile, Party B is at the intersection, moving east at a speed of $$100$$ meters per minute. After a number of minutes, Party A and Party B are at the same distance from the intersection for the first time. question_6079-image_0"}, {"key": "6080", "content": "There is a crossroad (as shown below), where person A is 880 meters south of the crossroads, moving north at a speed of 120 meters per minute. At the same time, person B is at the crossroads, moving east at a speed of 100 meters per minute. After some minutes, for the second time, the distances of A and B from the crossroad are equal. question_6080-image_0"}, {"key": "6081", "content": "The school allocates rooms for the students. If each room houses 5 people, then there are 10 people who don't have a place to stay; if each room houses 8 people, then 1 room will be vacant. Ask how many students there are and how many rooms there are."}, {"key": "6082", "content": "Determine from the diagrams below, the number that can be drawn in one stroke is. question_6082-image_0"}, {"key": "6083", "content": "As shown in the figure below, there are four islands A, B, C, D, interconnected by nine bridges. If one more bridge is added, tourists can walk across all nine bridges once without repeating. question_6083-image_0"}, {"key": "6084", "content": "The image below shows the character \"\u5c71\" (meaning 'mountain') written by Mr. Wang with a brush. Please calculate the perimeter of this \"mountain\". \n question_6084-image_0"}, {"key": "6085", "content": "Fang Fang likes playing with puzzles. The picture below is a piece of the puzzle. Please calculate the perimeter of this puzzle piece in centimeters.\n question_6085-image_0"}, {"key": "6086", "content": "The figure below shows a $$7\\times 7$$ area with $$9$$ trees planted. Now it is required to pitch tents on the empty land without trees, and it is required that the tents must be pitched next to a tree. Any two tents occupying squares do not share a common point, and the number of tents in each row is as shown on the far right, and the number of tents in each column is as shown at the bottom. Then, the tent in the $$1^{st}$$ column is in which row. question_6086-image_0"}, {"key": "6087", "content": "Autumn has arrived, and the children went to the orchard to pick apples together. (1) Eddie picked $$36$$ apples, Vi picked $$27$$ apples, and Xiaoming picked $$33$$ apples, with an average of apples picked per person. (2) If a total of $$25$$ children participated in this activity, and on average each child picked $$28$$ apples, then everyone picked a total of apples. question_6087-image_0"}, {"key": "6088", "content": "One day, Jojo and his classmate agreed to meet at a certain point between them. Jojo walks 65 meters per minute, and his classmate walks 45 meters per minute. They set off at the same time and are still 43 meters apart after 50 minutes. Thus, the original distance between Jojo and his classmate is meters."}, {"key": "6089", "content": "Vehicles A and B start from two cities that are $$40$$ kilometers apart, traveling in opposite directions. Vehicle A travels at $$35$$ kilometers per hour, and Vehicle B travels at $$40$$ kilometers per hour. After $$5$$ hours, the distance between vehicles A and B is kilometers."}, {"key": "6090", "content": "Using the digits $$1$$, $$3$$, and $$5$$, a number of different natural numbers can be formed without repeating any digits."}, {"key": "6091", "content": "A circular artificial lake has a circumference of about $$600$$ meters. A tree is planted every $$4$$ meters around the lake. The total number of trees that can be planted is ."}, {"key": "6092", "content": "For Children's Day, balloons are to be arranged on both sides of the hallway. It is known that balloons are placed at both ends of each side of the hallway, with one balloon placed every 6 meters in the middle, totaling 12 balloons, and the length of the hallway in meters."}, {"key": "6093", "content": "Answer the following questions: (1) Using the cards $$1$$, $$2$$, $$3$$, different three-digit numbers can be formed. (2) Using the cards $$0$$, $$1$$, $$2$$, different three-digit numbers can be formed. (3) Using the cards $$1$$, $$3$$, $$6$$, different three-digit numbers can be formed (cards can be rotated)."}, {"key": "6094", "content": "Complete the following questions. (1) How many different three-digit numbers can be formed using the digits $$1$$, $$2$$, $$3$$? (2) How many different three-digit numbers can be formed using the digits $$0$$, $$3$$, $$6$$? (3) How many different three-digit numbers, without repeating any digits, can be formed using the digits $$1$$, $$3$$, $$6$$?"}, {"key": "6095", "content": "[Warm-up 2] Da Bai and Xiao Ming start walking towards each other at the same time from two places $$1000$$ meters apart. Da Bai walks $$47$$ meters per minute, and Xiao Ming walks $$53$$ meters per minute. The second time they are $$100$$ meters apart is after they start."}, {"key": "6096", "content": "[Warm-up 3 before class] Xiaobai and Xiaohua live $$100$$ meters apart. Xiaobai walks $$4$$ meters per minute, and Xiaohua walks $$6$$ meters per minute. They both start from their homes at the same time, walking in opposite directions on the same road. After $$5$$ minutes, the distance between them is meters."}, {"key": "6097", "content": "A slow vehicle travels from Place A to Place B at a speed of 40 kilometers per hour. After traveling for 5 hours, a fast vehicle starts from Place A towards Place B at a speed of 90 kilometers per hour. The fast vehicle catches up with the slow vehicle at the midpoint between Place A and Place B. The distance between Place A and Place B is in kilometers."}, {"key": "6098", "content": "Arithmetic sequence: $$2$$, $$5$$, $$8$$, $$11$$, $$14$$, ......, the $$21$$st number is."}, {"key": "6099", "content": "The school held a sports meeting. According to statistics, 12 students from Class 1 of Grade 4 participated in the long jump competition, 24 students participated in the tug-of-war competition, 8 students participated in both events, and there were 3 students who did not participate in either event. So, in total, how many students are there in Class 1 of Grade 4."}, {"key": "6100", "content": "A survey of the entire class found that there are $$20$$ people who can swim, $$25$$ people who can play basketball, and $$5$$ people who can do both. Knowing that everyone can do at least one of the activities, the total number of people in the class is."}, {"key": "6101", "content": "There are a total of $$20$$ bicycles and tricycles in the shed, with $$50$$ wheels in total, then the number of bicycles and tricycles is: "}, {"key": "6102", "content": "In a certain math competition, there were a total of $$10$$ questions. Each correct answer awarded $$8$$ points, while each wrong answer deducted $$5$$ points. Xiao Yu ended up with $$41$$ points, which means he answered some questions correctly."}, {"key": "6103", "content": "There are a total of $$12$$ vans and buses with four wheels and six wheels respectively parked in the parking lot, making up a total of $$58$$ wheels. How many buses are there in total?"}, {"key": "6104", "content": "A group of children are playing a game of throwing sandbags. They are divided into two groups, Group A and Group B, with a total of $$140$$ sandbags. If Group A gives Group B $$5$$ sandbags, and then Group B gives Group A $$8$$ sandbags, at this point, the number of sandbags each group has becomes equal. Group A originally had sandbags, and Group B originally had sandbags."}, {"key": "6105", "content": "Distribute 7 identical apples among three people: A, B, and C, with each person getting at least one apple. There are different methods in total for doing so."}, {"key": "6106", "content": "The diagram below requires at least the number of strokes. question_6106-image_0"}, {"key": "6107", "content": "Dividing 6 identical glass balls into 2 piles, there are several different ways to do it."}, {"key": "6108", "content": "A rectangle is divided into nine parts, and the perimeters of some of the smaller rectangles are marked on the diagram. What is the perimeter of the larger rectangle. \n question_6108-image_0"}, {"key": "6109", "content": "Sum this sequence: $$6+14+\\cdots +78+86+94$$=\uff0e(A total of $$12$$ numbers)"}, {"key": "6110", "content": "The perimeter of the rectangle below is in centimeters. question_6110-image_0"}, {"key": "6111", "content": "There is a square pool, with a pathway 1 meter wide surrounding it on all four sides. The area of the pathway is 40 square meters. Calculate the area of the middle part of the pool (blank part) in square meters. question_6111-image_0"}, {"key": "6112", "content": "One rectangle partially overlaps with another rectangle, and the length and width of both rectangles are marked on the diagram. The area of the non-overlapping shaded part differs. question_6112-image_0"}, {"key": "6113", "content": "As shown in the diagram, four identical small rectangles are combined to form a large rectangle. It is known that the perimeter of this large rectangle is 28 cm. The perimeter of the small rectangle is in cm. question_6113-image_0"}, {"key": "6114", "content": "Liu Gang, Ma Hui, and Li Qiang each have a sister, making a total of six people participating in a mixed doubles table tennis competition. It was stipulated in advance that siblings could not team up. In the first game, Liu Gang and Xiao Li played against Li Qiang and Xiao Ying; in the second game, Li Qiang and Xiao Hong played against Liu Gang and Ma Hui's sister. Therefore, Liu Gang's sister is, Ma Hui's sister is, Li Qiang's sister is.\n$$1$$\uff0eXiao Li\uff1b$$2$$\uff0eXiao Ying\uff1b$$3$$\uff0eXiao Hong\uff0e"}, {"key": "6115", "content": "A revealed his exam score to B, C, and D, but the rest of the people kept their scores hidden. B thought: 'At least two of us four have the same score.' C thought: 'My score is not the lowest.' D thought: 'My score is not the highest,' so the highest score among B, C, and D is ( )."}, {"key": "6116", "content": "Xu, Wang, Chen, and Zhao are the carpenter, turner, electrician, and fitter at the factory respectively. They are all fans of Chinese chess.\n\u2460 The electrician only plays chess with the turner\n\u2461 Wang and Xu often play chess with the carpenter\n\u2462 Xu and the electrician have won and lost against each other\n\u2463 Chen has won against the fitter\nSo, who is the carpenter, the turner, the electrician, and the fitter.\n$$1$$\uff0eXu\n$$2$$\uff0eWang\n$$3$$\uff0eChen\n$$4$$\uff0eZhao"}, {"key": "6117", "content": "Calculate: $12\\times 8+45\\times 8+23\\times 8=$"}, {"key": "6118", "content": "Calculate: $439\\times 18-339\\times 18=$"}, {"key": "6119", "content": "Calculate: $11\\times 9+49\\times 9=$"}, {"key": "6120", "content": "A quadrilateral that has only one pair of parallel sides is ( )."}, {"key": "6121", "content": "As shown in the figure, the area of the trapezoid is ( ). (Unit: $$\\rm cm$$)\n question_6121-image_0"}, {"key": "6122", "content": "As shown in the figure, the vertex of the angle is, and the sides are and ;\nRepresent the angle in different ways: ,,,.\n question_6122-image_0"}, {"key": "6123", "content": "As shown in the figure, lines $$AB$$ and $$CD$$ intersect at point $$O$$, $$OE$$ bisects $\\angle AOC$, $$\\angle BOC-\\angle BOD=20{}^\\circ $$. Therefore, $$\\angle BOE$$ =\u00b0. question_6123-image_0"}, {"key": "6124", "content": "A guard of honor formed by $$35$$ people is arranged into $$5$$ rows and $$7$$ columns. The average age of the $$7$$ columns is respectively $$9$$, $$11$$, $$10$$, $$15$$, $$12$$, $$9$$, $$11$$. The average age of the first $$4$$ rows is respectively $$12$$, $$9$$, $$14$$, $$11$$. What is the average age of the last row?"}, {"key": "6125", "content": "Mom wants to put a rectangular carpet in the bedroom. Fill in the blanks with an expression containing letters. \n question_6125-image_0 \nThe area of the entire combined rectangular carpet: Length $$\\times $$ Width $$= $$($$+ $$)$$\\times $$. \nIt can also be represented as the total sum of two carpets areas: $$ + $$."}, {"key": "6126", "content": "The park is planted with many phoenix trees and cedars, it is known there are $$m$$ phoenix trees, and the number of cedars is $$3$$ times the number of phoenix trees plus $$7$$; cedars planted; the total number of phoenix trees and cedars is.\n question_6126-image_0"}, {"key": "6127", "content": "It is stipulated that the operation represented by $$\\odot$$ is as follows, $$a\\odot b=8\\times a-b$$, calculate: $$5\\odot 10=$$."}, {"key": "6128", "content": "Let $$a\\bullet b=a+b\\div 2$$, compute $$10\\bullet 8=$$."}, {"key": "6129", "content": "Define a new operation $$*a=a+1$$, for example, $$*3=3+1=4$$. Then $$*99=$$."}, {"key": "6130", "content": "Answer the following questions: Fill in the blanks with appropriate numbers to make the vertical addition in the figure correct. What is the result of the addition? question_6130-image_0"}, {"key": "6131", "content": "In the equation below, different Chinese characters represent different numbers, and the same Chinese characters represent the same number, making the equation valid. Therefore, the four-digit number \u201c$$\\overline{{Beautiful Future}}$$\u201d is. $$\\begin{matrix}&& &&Future \\\\& &&Beautiful & Future \\\\&& Good&Beautiful&Future\\\\+&Beautiful&Good&Beautiful&Future\\\\\\hline &8&1&0&2\\end{matrix}$$"}, {"key": "6132", "content": "In the vertical addition equation below, the same Chinese characters represent the same digit, and different Chinese characters represent different digits. What digit does '\u597d' represent? ( ). Student good student + three good student 3022"}, {"key": "6133", "content": "As shown in the figure, the numbers in the spaces are from $$2\\sim6$$ (which can be reused). Therefore, the sum of the numbers in these $$9$$ spaces is: question_6133-image_0"}, {"key": "6134", "content": "In the equation below, different Chinese characters represent different numbers, and the same Chinese characters represent the same number. If clever $$+$$ solution $$+$$ number $$+$$ character $$+$$ puzzle $$= 30$$, then the five-digit number represented by 'clever solution number character puzzle' is. question_6134-image_0"}, {"key": "6135", "content": "In the following equation, different Chinese characters represent different numbers, and the same Chinese characters represent the same number. Find the number that each Chinese character represents to satisfy the equation, and calculate:(Wei$$+$$Lai$$+$$Ke)$$\\times $$Qi=\uff0eQiKeQiLaiKeQi+WeiLaiKeQi2030"}, {"key": "6136", "content": "In the subtraction equation below, each letter represents a number, with different letters representing different numbers. The result of $$D+G$$ is definitely not question_6136-image_0"}, {"key": "6137", "content": "In the following vertical arithmetic, different Chinese characters represent ten different numbers from $$0\\sim9$$. For the arithmetic to hold, the minimum four-digit number represented by 'listening to the silent water' is\uff0e question_6137-image_0"}, {"key": "6138", "content": "A square piece of paper has a side length of $$1$$ decimeter, it can be divided into small squares with a side length of $$1$$ centimeter. question_6138-image_0"}, {"key": "6139", "content": "Third-grade students set out for a spring outing from school, walking at 72 meters per minute. After 15 minutes, the school needed to urgently inform the students about something, so they sent Teacher Li to catch up with the students on a bicycle, starting from the school at a speed of 132 meters per minute. How many minutes does Teacher Li need to catch up? If Teacher Li wants to catch up in 9 minutes, how many meters per minute does he need to travel."}, {"key": "6140", "content": "There are two pieces of wood with the same thickness. The first one was sawed into $$3$$ segments, taking $$6$$ seconds. The second one is sawed into $$4$$ segments, taking seconds."}, {"key": "6141", "content": "There is a series of numbers: $$3$$, $$5$$, $$1$$, $$4$$, $$2$$, $$8$$, $$5$$, $$7$$, $$1$$, $$4$$, $$2$$, $$8$$, $$5$$, $$7$$, $$\\cdots$$ (2) The sum of the first $$20$$ numbers is."}, {"key": "6142", "content": "Calculate: $$34\\times 12=$$"}, {"key": "6143", "content": "There is a sequence of numbers: $$3$$, $$5$$, $$1$$, $$4$$, $$2$$, $$8$$, $$5$$, $$7$$, $$1$$, $$4$$, $$2$$, $$8$$, $$5$$, $$7$$, $$\\cdots$$ (1) The $$20$$th number is."}, {"key": "6144", "content": "There is a rectangular playground with a length of $$60$$ meters and a width of $$45$$ meters. Eddie ran around the playground for one lap and ran meters. The playground is covered with green grass, and the area of the grass field is square meters at this time."}, {"key": "6145", "content": "September $$10$$th is Teachers' Day, this year's Teachers' Day is on Thursday. Teacher Gua's birthday is $$9$$th September $$27$$th, this year Teacher Gua's birthday is on a week."}, {"key": "6146", "content": "(Stage Test) Calculate in a simpler way: $25\\times(40+4)=$"}, {"key": "6147", "content": "Calculate using a simple method: $2000\\div125\\div8=$"}, {"key": "6148", "content": "There is a string of colored lights arranged in the order of 'Red, Yellow, Yellow, Green, Blue, Red, Yellow, Yellow, Green, Blue $\\cdots\\cdots$', the color of the $77^{th}$ light is."}, {"key": "6149", "content": "Figure ($$1$$) contains a square; Figure ($$2$$) contains a square.\n question_6149-image_0 question_6149-image_1"}, {"key": "6150", "content": "Li Ming is $$9$$ years old this year, the sum of the ages of his father and mother is $$81$$ years old, then the sum of their ages a year later is $$120$$ years old."}, {"key": "6151", "content": "The formation of Grade 3, Class 2 is a square, with 36 people on the outermost layer, and each side of the outermost layer has people. question_6151-image_0"}, {"key": "6152", "content": "$$32.8+1.02-6.3=$$\uff0e"}, {"key": "6153", "content": "The third grade class 1 participates in a summer camp camping, if each tent houses $$4$$ people, then there are $$10$$ people without tents to live in. If each tent houses $$6$$ people, then there is one extra tent without occupants. There are people in the third grade class 1."}, {"key": "6154", "content": "Xiao Gang's mother is $$24$$ years older than Xiao Gang. $$2$$ years ago, their combined age was $$50$$ years old. What is the mother's age this year?"}, {"key": "6155", "content": "Class 1 of Grade 3 has $$81$$ students, who are arranged in a solid square formation. There are people on the outermost layer. If one more layer is added, more people will be needed."}, {"key": "6156", "content": "As shown in the figure, $$\\angle 1=\\angle 2=30{}^\\circ $$, $$\\angle 3=\\angle 4=\\angle 5=$$ degrees. question_6156-image_0"}, {"key": "6157", "content": "Eddie is $$8$$ years old this year, he asked the doctor how old he is this year, and the doctor said: \"When you are as old as me, I was already $$86$$ years old.\" So, the doctor is $$47$$ years old this year."}, {"key": "6158", "content": "Given an arithmetic sequence $$5$$, $$8$$, $$11$$, $$14$$, ..., the $$10$$th number is, and the sum of these $$10$$ numbers is."}, {"key": "6159", "content": "Eddie has to follow the route in the picture, starting from the school to the museum. Since the city center is under construction and impassable, there's a shortest route for Eddie to get to the museum. question_6159-image_0"}, {"key": "6160", "content": "There is a triangle in the right picture.\n question_6160-image_0"}, {"key": "6161", "content": "12 identical erasers, divided into $$2$$ groups of different quantities, there are a total of different ways to divide."}, {"key": "6162", "content": "There are some rabbits and chickens in the zoo, with chickens being $$20$$ more than the rabbits. There are a total of $$208$$ legs. Rabbits have $$,$$ chickens have $$.$$"}, {"key": "6163", "content": "A square piece of paper has a side length of $$1$$ decimeter. How many small squares with a side length of $$1$$ centimeter can it be divided into? question_6163-image_0"}, {"key": "6164", "content": "Xiao Ming has to walk $$1.5$$ kilometers from school to home. One day after school, he walked $$0.3$$ kilometers from school, then went back to school to get his math book, and then went home. question_6164-image_0 (1) This day he walked more kilometers to get home than usual. (2) This day he walked a total of kilometers to get home."}, {"key": "6165", "content": "Dian Dian reads a storybook, the first day he read $$30$$ pages, starting from the second day, the number of pages read each day was $$4$$ pages more than the previous day, and on the last day, he read $$70$$ pages, just finishing the book. So, the entire book has pages. question_6165-image_0"}, {"key": "6166", "content": "Vera walks to school, covering $$70$$ meters per minute. $$12$$ minutes after leaving home, Vera's father realizes that her pencil case was forgotten at home. He immediately rides his bicycle after her at a speed of $$280$$ meters per minute. How many minutes after Vera's father starts chasing does he catch up with her, and how far are they from home when he catches up?"}, {"key": "6167", "content": "A certain two-digit decimal, when rounded and truncated to one decimal place, results in two one-digit decimals whose sum is $$29.1$$. The maximum value of the original two-digit decimal is."}, {"key": "6168", "content": "Count the number of squares in the picture. Below is Little Confused's method, could you judge whether it's correct? If not, please correct it.\n question_6168-image_0 \n$$3\\times 3-1=8$$ (squares)."}, {"key": "6169", "content": "Three people are to split 342 apples evenly, and the apples are pre-packed as shown in the following diagram: there are 3 large boxes, each containing 100 apples, 4 small boxes, each containing 10 apples, and 2 individual apples. Students, how would you help them split the apples evenly? In the end, each person gets a certain number of apples. question_6169-image_0"}, {"key": "6170", "content": "Using $$1$$, $$2$$, $$0$$, ( ) different two-digit numbers can be formed."}, {"key": "6171", "content": "A three-digit number divided by $$51$$, the quotient is exactly $$3$$ times the remainder. The largest such number is."}, {"key": "6172", "content": "There is a sequence of numbers: $$1$$, $$3$$, $$9$$, $$25$$, $$69$$, $$189$$, $$517$$, $$\\cdots$$ where the first number is $$1$$, the second is $$3$$, and starting from the third, each number is exactly twice the sum of the previous two numbers plus $$1$$. Then, the remainder of the $$2008$$th number divided by $$6$$ is."}, {"key": "6173", "content": "A natural number divided by $$39$$, leaves a remainder of $$15$$. The sum of the dividend, divisor, quotient, and remainder is $$1749$$. Find the dividend."}, {"key": "6174", "content": "The upper base of a trapezoid is $$4$$ cm, the lower base is $$6$$ cm, and the height is $$3$$ cm. If you make a single straight cut, the area of the largest parallelogram that can be obtained is in square centimeters."}, {"key": "6175", "content": "As shown in the figure, two parallelograms $$ABEF$$ and $$CDFG$$ are divided from trapezoid $$ABCD$$, where the area of $$ABEF$$ is $$60$$ square meters, and the length of $$AF$$ is $$10$$ meters, the length of $$FD$$ is $$4$$ meters, the length of $$EG$$ is twice that of $$BE$$, and the area of trapezoid $$ABCD$$ is square meters.\n question_6175-image_0"}, {"key": "6176", "content": "Among the figures below, the number of them with the correct height drawn is ( ). question_6176-image_0 question_6176-image_1 question_6176-image_2"}, {"key": "6177", "content": "According to the trapezoid area formula, fill in the blanks.\n(1) The top base of the trapezoid is $$4$$, the bottom base is $$15$$, the height is $$10$$, the area of the trapezoid is.\n(2) The area of the trapezoid is $$88$$, the top base is $$10$$, the bottom base is $$12$$, the height of the trapezoid is.\n(3) The area of the trapezoid is $$72$$, the top base is $$7$$, the height is $$8$$, then the bottom base is."}, {"key": "6178", "content": "Among the following figures, the correct area calculation formula is ( )."}, {"key": "6179", "content": "The area of a parallelogram is $$48$$ square centimeters, the height is $$12$$ centimeters, the base is ( )."}, {"key": "6180", "content": "The area of the parallelogram in the image below is ( )\uff0e\n question_6180-image_0"}, {"key": "6181", "content": "The brother is $$14$$ years old this year, and the sister is $$10$$ years old this year. When the combined age of the siblings reaches $$44$$ years, a year has passed."}, {"key": "6182", "content": "Count the triangles in the following picture. question_6182-image_0"}, {"key": "6183", "content": "$$A$$, $$B$$, $$C$$ three children pass the ball to each other, starting with $$A$$ for the first pass, and after $$3$$ passes, the ball just returns to $$A$$'s hands, so there are a total of various different ways of passing."}, {"key": "6184", "content": "In the shaded part of the diagram, which squares can be definitively determined as safe zones, mark them with \"$$\\bigcirc $$\", what is the status of the first row third column (  ).\n question_6184-image_0"}, {"key": "6185", "content": "The figure below is a $$6\\times 6$$ area, planted with $$7$$ trees. Now it is required to set up tents on the vacant land without trees, and the tents must be set up beside a tree. Any two tents do not share a common point, and the number of tents in each row is as shown on the far left. Is there a tent at the 1st column of the 6th row? ( )\n question_6185-image_0"}, {"key": "6186", "content": "Within $$20$$, the largest odd number is."}, {"key": "6187", "content": "There is a number that, when added to an odd number, results in an even number, and when added to an even number, results in an odd number. What number could it be?"}, {"key": "6188", "content": "Categorize the number: $$365$$ is."}, {"key": "6189", "content": "Determine the category of the number: $$36$$ is."}, {"key": "6190", "content": "Classify the number: $$73$$ is."}, {"key": "6191", "content": "Classify the number: $$2020$$ is."}, {"key": "6192", "content": "Person A says: \"Today is Tuesday.\" Person B says: \"Today is not Tuesday.\" If what Person A says is true, then what Person B says is ( )."}, {"key": "6193", "content": "Person A says: 'Today is Tuesday.' Person B says: 'Today is Wednesday.' If what Person A said is wrong, then what Person B said is ( )."}, {"key": "6194", "content": "Wang Ping, Song Dan, and Han Tao, three elementary school students, are all Young Pioneers officers: one is the head of the brigade, one is the head of the squadron, and one is the head of the team. In a math test, the scores of these three were:\n\u2460 Han Tao scored better than the head of the brigade.\n\u2461 Wang Ping's score was different from that of the head of the squadron.\n\u2462 The head of the squadron scored worse than Song Dan.\nBased on the scores of these three people, can you determine who is the head of the brigade?"}, {"key": "6195", "content": "Little White Rabbit, Little Black Rabbit, Little Flower Rabbit, and Little Gray Rabbit had a race. After the race ended, Little White Rabbit, Little Black Rabbit, Little Flower Rabbit spoke the following lines, while Little Gray Rabbit didn't speak. \nLittle White Rabbit: Little Flower Rabbit ranked $$1$$st, I ranked $$3$$rd;\nLittle Black Rabbit: I ranked $$1$$st, Little Gray Rabbit ranked $$4$$th;\nLittle Flower Rabbit: Little Gray Rabbit ranked $$2$$nd, I ranked $$3$$rd.\nAfter the race results were announced, it was found that they all were only half right, and Little White Rabbit ranked the following place."}, {"key": "6196", "content": "When Xiao Dong, Xiao Xi, Xiao Nan, and Xiao Bei, four children, were playing together, they found a red scarf and gave it to their teacher. The teacher asked who found it?\nXiao Dong said: 'It's not Xiao Xi.'\nXiao Xi said: 'It's Xiao Nan.'\nXiao Nan said: 'Xiao Dong is wrong.'\nXiao Bei said: 'Xiao Nan is also wrong.'\nOnly one of them is right, that person is ()."}, {"key": "6197", "content": "Please perform a simple calculation: $16\\times2+16\\times8=$."}, {"key": "6198", "content": "Please fill each cell in a $3\\times3$ grid without repetition with the numbers $$2$$~$$10$$, so that the sum of every row, every column, and both diagonals are equal. What is the sum of all these numbers?"}, {"key": "6199", "content": "Please fill each cell of a $3\\times3$ grid with the numbers $$2$$~$$10$$ without repeating any number, so that the sum of the numbers in each row, each column, and each diagonal is equal. What is the magic sum?"}, {"key": "6200", "content": "In the nine squares in the picture, the sum of the three numbers in each row, each column, and each diagonal is equal, then $$A=$$.\n question_6200-image_0"}, {"key": "6201", "content": "There are a total of $$88$$ peach trees and pear trees in the orchard. The number of peach trees is twice the number of pear trees. There are pear trees."}, {"key": "6202", "content": "Xiaohong and Xiaolv have a total of $$38$$ scorecards. If Xiaohong gives Xiaolv $$5$$ cards, Xiaolv's scorecards will be $$3$$ times Xiaohong's minus $$6$$ cards. How many scorecards did each originally have?"}, {"key": "6203", "content": "Car A and Car B originally had a total of $$430$$ passengers. After arriving at a destination, $$50$$ passengers got off Car A, and $$20$$ passengers got on Car B. At this point, the number of passengers in Car A was exactly $$3$$ times that of Car B. Therefore, the original number of passengers in Car A was."}, {"key": "6204", "content": "As shown in the figure, how many birds need to stand on the right side of the seesaw to balance it (fill in the quantity in the brackets in the figure).\n question_6204-image_0"}, {"key": "6205", "content": "Fill in the blank, the weight of $$1$$ sheep equals the weight of mice.\n question_6205-image_0"}, {"key": "6206", "content": "The weight of 1 pineapple plus 1 pear equals the weight of 6 apples, the weight of 2 pears equals the weight of 4 apples, then the weight of 1 pineapple equals the weight of how many apples."}, {"key": "6207", "content": "1 apple plus $$3$$ pears, total is $$14$$ yuan, $$1$$ apple plus $$1$$ pear is $$10$$ yuan. 1 apple costs yuan."}, {"key": "6208", "content": "The weight of 3 apples equals the weight of $$1$$ Hami melon and $$3$$ oranges, the weight of $$1$$ Hami melon and $$2$$ apples equals the weight of $$6$$ oranges, then the weight of $$5$$ apples equals the weight of $$9$$ oranges."}, {"key": "6209", "content": "The weight of $$1$$ sheep is equal to the weight of $$8$$ rabbits, and the weight of $$1$$ rabbit is equal to the weight of $$2$$ roosters. Therefore, the weight of $$1$$ sheep is equal to the weight of roosters."}, {"key": "6210", "content": "The doctor bought 2 jin of beef and 1 jin of lamb for the first time, spending 100 yuan. The price of 5 jin of beef and 10 jin of lamb is the same. Question: The price of 1 jin of beef is yuan, and the price of 1 jin of lamb is yuan."}, {"key": "6211", "content": "The weight of $$10$$ rabbits is equivalent to the weight of $$3$$ geese, the weight of $$6$$ geese is equivalent to the weight of $$1$$ lamb, $$1$$ rabbit weighs $$1$$ kilogram, $$1$$ lamb weighs kilograms."}, {"key": "6212", "content": "Xuexue and Sisi had some Da Bai Tu milk candies. Initially, the number of Da Bai Tu milk candies Xuexue had was $$6$$ times that of Sisi. Later, both of them got $$40$$ more candies each, and as a result, the number of Da Bai Tu milk candies Xuexue had became $$2$$ times that of Sisi. How many Da Bai Tu milk candies did they have in total originally?"}, {"key": "6213", "content": "Xiao Hong has 5 times as many books as Xiao Ming. If Xiao Hong gives Xiao Ming 16 books, then they will have the same number of books. Originally, how many books did Xiao Ming have?"}, {"key": "6214", "content": "A pile of apples is divided among three people: A, B, and C, each receiving an equal amount. Later, A gives B $$2$$ apples, B gives C $$6$$ apples, and then C gives A $$8$$ apples. At this point, the number of apples A has is exactly twice the number that C has. How many apples does B have now?"}, {"key": "6215", "content": "Eddy prepares snacks for the children, dividing the snacks into $$5$$ portions. The $$1$$st portion has $$2$$ pieces, the $$2$$nd portion has $$2$$ pieces, the $$3$$rd portion has $$3$$ pieces, the $$4$$th portion has $$5$$ pieces, and the $$5$$th portion has $$3$$ pieces. Vera thinks it's best if each portion is the same. According to Vera's method, how many pieces should each portion have?"}, {"key": "6216", "content": "The area of the square is $$64$$ square meters, the side length of this square is meters."}, {"key": "6217", "content": "There are a total of $$20$$ chickens and rabbits together, locked in the same cage, and altogether there are $$50$$ legs. Assuming all these $$20$$ animals are chickens, then there would be a total of legs."}, {"key": "6218", "content": "There are a total of $$20$$ chickens and rabbits together, kept in the same cage, with a total of $$50$$ legs in the cage. Assuming all these $$20$$ are chickens, then there would be a total of $$2\\times 20=40$$ (legs); the difference from the actual total number of legs is 50-40=10 (legs); 1 rabbit has 4 legs and $$1$$ chicken has 2 legs, so the difference is 4-2=2 (legs); hence, there are rabbits; there are chickens."}, {"key": "6219", "content": "There are a total of $$20$$ chickens and rabbits in the same cage, with a total of $$50$$ legs in the cage. Assuming all $$20$$ are chickens, there would be a total of $$2\\times 20=40$$ (legs); the difference from the actual total number of legs is 50-40=10 (legs); 1 rabbit has 2 more legs than $$1$$ chicken."}, {"key": "6220", "content": "A little white rabbit is selling mushrooms. Before selling, the mushrooms weighed $$40$$ kilograms. After a little gray rabbit bought more than half by $$2$$ kilograms, how many kilograms of mushrooms does the little white rabbit have left?"}, {"key": "6221", "content": "There are two piles of chess pieces, pile A has $$25$$ pieces, and pile B has $$10$$ pieces, how many pieces need to be moved from pile A to pile B in order to double the number of pieces in pile B?"}, {"key": "6222", "content": "Groups A, B, and C have a total of 120 books. If group B borrows 20 books from group A and then lends 9 books to group C, the number of books held by groups A, B, and C becomes the same. How many books did groups A, B, and C originally have respectively? \uff08 \uff09"}, {"key": "6223", "content": "After selling half of the fish in a basket, and then selling half of the remaining fish, there are still $$35$$ kilograms left. How many kilograms of fish were originally in the basket?"}, {"key": "6224", "content": "School entrances are decorated with square flowerbeds, using a total of $$144$$ pots of flowers, arranged into (   ) rows and (   ) columns."}, {"key": "6225", "content": "The students participated in a calisthenics competition, forming a solid square formation with $$8$$ people per row and $$8$$ people per column. How many students are there in the square formation in total?"}, {"key": "6226", "content": "Drying a handkerchief requires $$2$$ clips, so drying $$8$$ handkerchiefs requires at least clips; currently having $$8$$ clips, the maximum number of handkerchiefs that can be dried is ."}, {"key": "6227", "content": "( ) \u00f7 $$4 = 5$$\u2026\u2026$$2$$\n$$43$$ \u00f7 ( ) $$= 4$$\u2026\u2026$$7$$"}, {"key": "6228", "content": "If $$\\triangle \\div 7=\\bigcirc \\cdots\\cdots\\square $$, the largest number that should be filled in $$\\square $$ is ( )."}, {"key": "6229", "content": "When Qiangqiang was doing addition, he accidentally mistook a tens digit $$8$$ for $$3$$, so the result will be ( )."}, {"key": "6230", "content": "When Xiaopei was doing addition, she accidentally mistook a digit in the addend from $$3$$ to $$5$$, then the result will ( )."}, {"key": "6231", "content": "A subtraction equation, if the tens digit of the minuend is changed from $$8$$ to $$3$$, then the difference will be ( )."}, {"key": "6232", "content": "In a subtraction equation, if the unit digit of the subtrahend is changed from $$2$$ to $$6$$, then the difference will ( )."}, {"key": "6233", "content": "As shown in the figure, how many different shortest routes are there from point $$A$$ to point $$B$$ along the line segment? question_6233-image_0"}, {"key": "6234", "content": "Place roses into some vases. If each vase holds $$8$$ flowers, then $$15$$ flowers are missing; if each vase holds $$6$$ flowers instead, then $$1$$ flower is missing. (1) The total number of vases is . (2) The total number of roses is ."}, {"key": "6235", "content": "How many different ways are there to divide $$8$$ watermelons of the same size into $$3$$ piles? question_6235-image_0 \u200b\u200b\u200b"}, {"key": "6236", "content": "Tian Tian, You You, and Si Si were born in the same year and are good friends. They all live in the same community and often play with Xiao Xin, an older boy from their neighborhood. One day, Xiao Xin tested them, saying: 'My age this year is equal to the sum of your three ages. In $$15$$ years, the sum of your three ages will be twice my age. Do you know how old I am this year?' Use the knowledge from this lesson to help the three friends solve this problem. Xiao Xin is $$15$$ years old this year."}, {"key": "6237", "content": "The combined age of father, brother, and sister is $$64$$ years old. When the father's age was $$3$$ times the brother's age, the sister was $$9$$ years old; when the brother's age was twice the sister's age, the father was $$34$$ years old. Now the brother is years old, the sister is years old, and the father is years old."}, {"key": "6238", "content": "When dad was celebrating his 50th birthday, my younger brother said: 'When I reach the age my older brother is now, the sum of our ages at that time will equal dad's age then.' So, how old is my older brother this year?"}, {"key": "6239", "content": "One year ago, the sum of the parents' ages was 7 times the sum of the two brothers' ages. Four years later, the sum of the parents' ages will be 4 times the sum of the two brothers' ages. It is known that the father is 2 years older than the mother, who is $$ years old this year."}, {"key": "6240", "content": "Fifth-grade students are divided into two teams to participate in the school's broadcast exercises competition, forming two solid square formations, Alpha and Beta. The number of people on each side of the outer layer of the Alpha formation equals $$8$$. If the two teams are combined, they can be reorganized into a hollow Gamma square formation, where the number of people on each side of the outer layer of the Gamma formation is $$4$$ more than that of the Beta formation. The number of people in the Alpha formation exactly fills the hollow of the square formation. A total of people participated in the broadcast exercises competition of the fifth grade."}, {"key": "6241", "content": "A team of soldiers formed into a three-layer hollow square formation exceeds by $$16$$ people. If another layer is added to the hollow part, there are $$28$$ fewer people. The total number of soldiers in this team is. If they were to form a solid square formation, the outermost layer should have the number of people on each side."}, {"key": "6242", "content": "12 teams participate in a soccer match, with each pair of teams playing one match. In each match, the winning team receives 3 points, the losing team receives 0 points, and in the event of a draw, both teams receive 1 point. After the matches are completed, the maximum possible difference in points between the third and fourth teams, ranked from highest to lowest in points, is ."}, {"key": "6243", "content": "Four football teams participate in a round-robin tournament, where a win awards 3 points, a draw awards 1 point, and a loss awards 0 points. There is a team that has never won but still ranks first. Do you think this is possible? If so, please cite a scenario where this occurs; if not, please explain why."}, {"key": "6244", "content": "As shown in the diagram, fill the numbers $$1\\sim 12$$ into the grid below, with the requirement that for adjacent squares (squares sharing a common edge are considered adjacent), the number on the right must be greater than the number on the left, and the number on top must be greater than the number below. There are several ways to fill in the numbers to meet these criteria.\n question_6244-image_0"}, {"key": "6245", "content": "As shown in the figure, in rectangle $$ABCD$$, $$AB=12$$cm, $$BC=8$$cm, one side of parallelogram $$BCEF$$, $$BF$$, intersects $$CD$$ at point $$G$$. If the area of trapezoid $$CEFG$$ is $$64$$ square cm, then the length of $$DG$$ is in cm. question_6245-image_0"}, {"key": "6246", "content": "The number of fruit candies Huanhuan has is $$11$$ times the number of hard candies he has. After buying $$12$$ more of each, the number of fruit candies is $$3$$ times the number of hard candies. How many fruit candies did Huanhuan originally have?"}, {"key": "6247", "content": "Two groups of students participate in voluntary labor, the number of students in team $$A$$ is three times that of team $$B$$, and the number of students in team $$B$$ is $$110$$ less than four times that of team $$A$$. How many students in total participated in the voluntary labor?"}, {"key": "6248", "content": "Xiaoduan and Xiaowang ran together, Xiaoduan said: 'You ran so far, three times my total distance is still 120 meters less than yours.' Xiaowang said: 'Actually, twice my total distance is 740 meters more than yours.' So, the total distance both of them ran was meters."}, {"key": "6249", "content": "There is a sequence of numbers arranged in the order $$11428571142857114\\cdots \\cdots $$, totaling $$100$$ numbers. (1) The number of occurrences of the digit $$1$$. (2) The sum of these numbers."}, {"key": "6250", "content": "The width of a rectangle is $$5$$ cm, and its length is twice the width. The perimeter of this rectangle is (\u3000\u3000) cm."}, {"key": "6251", "content": "In the right figure, if more color blocks are filled, the colored part will constitute $$\\frac{7}{8}$$ of this shape.\n question_6251-image_0"}, {"key": "6252", "content": "$$2021$$ year $$3$$ month $$27$$ day is Saturday, so what day of the week is $$2021$$ year $$3$$ month $$10$$ day?"}, {"key": "6253", "content": "As shown in Figure (1), the numbers marked on the left of each row and the top of each column represent the count of continuous black blocks in that row or column. Kids, these numbers can serve as our breakthrough. question_6253-image_0 question_6253-image_1"}, {"key": "6254", "content": "The older brother and the younger brother were $$5$$ years apart last year. This year, the sum of their ages is $$15$$ years. Therefore, this year the older brother is $$10$$ years old, and the younger brother is $$5$$ years old. question_6254-image_0"}, {"key": "6255", "content": "My younger sister is $$5$$ years old this year. My older sister said to her, 'When you are as old as I am now, I will be $$17$$ years old!' So, how old is the older sister this year."}, {"key": "6256", "content": "The Arbor Day has arrived, and the Xueersi School organizes a tree planting activity. If $$5$$ people plant $$100$$ trees in $$2$$ hours, assuming each person plants the same number of trees per hour: (1) then $$5$$ people plant trees in $$1$$ hour\uff0e(2) then $$1$$ person plants trees in $$1$$ hour\uff0e"}, {"key": "6257", "content": "Below is the menu of a fast food restaurant, Lulu plans to order one main dish, one snack, and one drink. How many different combinations can she choose from? question_6257-image_0"}, {"key": "6258", "content": "The hotel has a total of $$3$$ rooms to choose from. Eddie, Vi, and Da Kuan each choose a room, how many different selection schemes are there in total? question_6258-image_0"}, {"key": "6259", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$BC$$ at point $$E$$. Given that the area of the parallelogram $$ABCD$$ is $$48$$ square centimeters and $$AE=8$$ centimeters, what is the length of $$AD$$ in centimeters? question_6259-image_0"}, {"key": "6260", "content": "At the award ceremony of the robot programming competition, Eddie asked the teacher, 'How many points did I get?' The teacher said, 'After subtracting $$6$$ from your score, dividing by $$2$$, then adding $$10$$ and finally multiplying by $$2$$, the result is exactly $$100$$ points.' Eddie scored in this competition."}, {"key": "6261", "content": "Li Bai took a jug to buy wine, whenever he encountered a shop he would double his purchase, and whenever he saw flowers he would drink eight liangs (a traditional unit of weight). After three encounters with shops and flowers, he drank up all the wine in his jug. Originally, there were two liangs of wine in the jug."}, {"key": "6262", "content": "Xuexue and Sisi were playing when they encountered a little fairy. They asked the fairy: \"You must be younger than $$100$$ years old!\" To their surprise, the fairy shook his head and said: \"You do the math! Add $$75$$ to my age, then divide by $$5$$, then subtract $$15$$, and finally multiply by $$10$$, and it exactly makes $$2000$$ years old.\" Kids, do you know how old the fairy is now?"}, {"key": "6263", "content": "Set up vertical calculations for the following problems: (1) $$54\\times 3= $$ (2) $$7\\times44=$$ (3) $$8\\times112=$$ (4) $$304\\times 3=$$"}, {"key": "6264", "content": "Calculate in column form. (1) $$8.4+2.8=$$ (2) $$7.2-4.5=$$"}, {"key": "6265", "content": "The shortcut for $$76\\times 99$$ is ( )."}, {"key": "6266", "content": "As shown in the diagram, starting from point $$A$$ to point $$B$$, take the shortest route, but make sure not to pass through $$C$$. There are several different ways to go about this. Please explain to your mom and dad how you think about it!\n question_6266-image_0"}, {"key": "6267", "content": "Can you fill in $$+$$, $$-$$, $$\\times $$, $$\\div $$, $$\\left( {} \\right)$$ at the appropriate places to make the equation correct?\n question_6267-image_0"}, {"key": "6268", "content": "Given that the diagonals of quadrilateral $$ABCD$$ are perpendicular to each other, and the area of the quadrilateral is $$80$$ square centimeters. It is known that $$AC=10$$ centimeters, find the length of $$BD$$ in centimeters. question_6268-image_0"}, {"key": "6269", "content": "Mingming bought two sets of storybooks, and when calculating the price, he mistook one set of books' price from $$226$$ to $$266$$, resulting in a total of $$400$$. What is the actual total price of these two sets of books? question_6269-image_0"}, {"key": "6270", "content": "When Dakuan was adding a three-digit number to another three-digit number, he mistook the tens digit $$4$$ in one of the addends, resulting in a sum that was $$30$$ less than the correct answer. What did Dakuan mistake the $$4$$ for?"}, {"key": "6271", "content": "Set up long division calculations and check problems (2) and (3). (1) $$48\\div 4=$$\uff0e(2) $$69\\div 3=$$\uff0e(3) $$845\\div 4=$$$$\\cdots \\cdots $$\uff0e"}, {"key": "6272", "content": "The little monkeys in the Huaguo Mountain are eating peaches. $$6$$ little monkeys eat $$180$$ peaches in $$3$$ days. If each monkey eats the same amount of peaches every day, then $$7$$ monkeys can eat how many peaches in $$4$$ days."}, {"key": "6273", "content": "At the sports meet, Class 1 of the third grade had $$10$$ boys and $$8$$ girls participating, with the average score of the boys being $$14$$ points and the average score of all the participating students in Class 1 being $$10$$ points, the average score of the girls was points."}, {"key": "6274", "content": "In addition to passive defense measures, the doctor also developed a bionic robot\u2014Type $$A$$ Anteater. In a test, the Type $$A$$ Anteater, after moving up, down, left, and right several times, returned to the starting point, forming a mountain shape with a missing corner. How many meters did it travel in total? question_6274-image_0"}, {"key": "6275", "content": "Using the digits $$1$$, $$2$$, $$3$$, you can form different natural numbers without repeating any digit."}, {"key": "6276", "content": "The professor teaches Eddie and Will about the concept of 'turning'. \nThe professor said: 'For a sequence of numbers, if there are three numbers $$abc$$ arranged in order, and either $$a>b$$, $$c>b$$ or $$a < b$$, $$c < b$$, we say that a turn has occurred.'\nEddie said: 'I get it, for example, there are no turns in $$4321$$, but there is one turn in $$1243$$.'\nWill said: 'Right, and for example, there are two turns in $$1324$$.'\nThe professor said: 'Fantastic! It seems you both have mastered it very well. Now I am going to test you. If we arrange $$1$$, $$2$$, $$3$$, $$4$$ in a row, the number of arrangements that exactly have two turns is.'"}, {"key": "6277", "content": "In the equation below, different Chinese characters represent different numbers, and the same Chinese characters represent the same number. If clever$$+$$solution$$+$$number$$+$$character$$+$$puzzle$$=30$$, then the five-digit number represented by \"clever solution number character puzzle\" is. question_6277-image_0"}, {"key": "6278", "content": "A fruit store mixes $$2$$ kilograms of crispy candy with $$3$$ kilograms of fruit candy to make mixed candy. It is known that the crispy candy sells for $$16$$ yuan per kilogram, and the fruit candy sells for $$6$$ yuan per kilogram. How much should the mixed candy be sold for per kilogram?"}, {"key": "6279", "content": "The doctor wants to make a wooden stool. He first saws a piece of wood into $$4$$ parts, which took him $$12$$ minutes. If he wants to saw another piece of wood into $$8$$ parts, it will take minutes. (Assuming the time taken for each sawing is the same)"}, {"key": "6280", "content": "As shown in the diagram, the side length $$DC=15$$ cm of the parallelogram $$ABCD$$, the height $$AE=6$$ cm from this side, a segment $$AF$$ divides this parallelogram into two parts, the difference in their areas is $$18$$ square centimeters. Please, what is the area of trapezium $$ABCF$$ in square centimeters. question_6280-image_0"}, {"key": "6281", "content": "$$A$$, $$B$$, $$C$$, $$D$$ are from China, Japan, the United States, and France respectively, each person has $$1$$ occupation. It is known: (1) $$A$$ and the Chinese person are doctors; (2) $$B$$ and the French person are teachers; (3) $$C$$ has a different occupation from the Japanese person; (4) $$D$$ cannot treat illnesses. Then, what nationality is $$B$$?"}, {"key": "6282", "content": "$$A$$, $$B$$, $$C$$, and $$D$$ are from China, Japan, the USA, and France, respectively, each having $$1$$ occupation. It is known that: ($$1$$) $$A$$ and the Chinese person are doctors; ($$2$$) $$B$$ and the French person are teachers; ($$3$$) $$C$$ has a different occupation from the Japanese person; ($$4$$) $$D$$ cannot treat patients. Then, what nationality is $$A$$?"}, {"key": "6283", "content": "$$A$$, $$B$$, $$C$$, and $$D$$ are from China, Japan, the United States, and France respectively, and each person has $$1$$ occupation. It is known that: ($$1$$) $$A$$ and the person from China are doctors; ($$2$$) $$B$$ and the person from France are teachers; ($$3$$) $$C$$ and the person from Japan have different occupations; ($$4$$) $$D$$ cannot treat patients. So, what is $$C$$'s nationality?"}, {"key": "6284", "content": "$$A$$, $$B$$, $$C$$, and $$D$$ are from China, Japan, the United States, and France respectively, each with $$1$$ occupation. It is known that: (1) $$A$$ and the Chinese person are doctors; (2) $$B$$ and the French person are teachers; (3) $$C$$ and the Japanese person have different occupations; (4) $$D$$ cannot treat illnesses. What nationality is $$D$$?"}, {"key": "6285", "content": "During the physical education class, $$20$$ kids hold hands to form a circle and play a game, the number of intervals is ( )."}, {"key": "6286", "content": "[Warm-up 1 before class] Point A and point B are $$140$$ kilometers apart. Eddie drove a car from point A to point B in $$5$$ hours. At this speed, it took $$6$$ hours to drive from point B to point C. The distance between point B and point C is kilometers."}, {"key": "6287", "content": "The figure shows an incomplete vertical multiplication operation, where we now know that one of the digits is $$8$$, and the result of this multiplication is. question_6287-image_0"}, {"key": "6288", "content": "Arrange natural numbers starting from $$1$$ into an array, and place a $$3\\times3$$ box in the array. The sum of the $$9$$ numbers enclosed by the box could be ().\n question_6288-image_0"}, {"key": "6289", "content": "There were a pile of peaches, the first monkey took half of them and then put back $$1$$ peach; the second monkey took half of the remaining ones and then put back $$1$$ peach; the third monkey took half of the remaining ones and then put back $$1$$ peach$$\\cdots \\cdots $$and so on, until the $$2018$$th monkey took half of the remaining ones and then put back one, and then there were $$2$$ peaches left. How many peaches were there originally."}, {"key": "6290", "content": "Place '+$$' in the right places to make the equation true (adjacent numbers can form one number). $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$=$$ $$42$$"}, {"key": "6291", "content": "$$35$$ apples are to be distributed among $$3$$ children, not necessarily in equal amounts, but each person must receive an even number of apples. Is it possible? ( )."}, {"key": "6292", "content": "Eddie and Dengdeng have a total of $$56$$ marbles, the number of Eddie's marbles is $$6$$ times that of Dengdeng's. Eddie has some marbles, and Dengdeng has some marbles."}, {"key": "6293", "content": "Divide $$15$$ identical balls into three piles, with each pile having at least $$3$$ balls, there are ways to do this."}, {"key": "6294", "content": "Xiaobai wants to put $$18$$ identical car models onto a shelf with $$3$$ layers, with at least $$5$$ on each layer, there are different ways to arrange them."}, {"key": "6295", "content": "The prizes prepared by the teacher for the fun sports day are lollipops. The teacher wants to divide $$8$$ identical lollipops into $$3$$ piles, there are a total of different ways to do this."}, {"key": "6296", "content": "Distribute $$8$$ tanks to three kids, Xiao Xiao, Zhong Zhong, and Da Da, with each getting at least one tank, there is a certain method."}, {"key": "6297", "content": "Teacher FaFa distributes chicken legs, each person gets $$4$$, then $$20$$ are left, each person gets $$6$$, then $$8$$ are left. How many people are there? How many chicken legs are there?"}, {"key": "6298", "content": "As shown in the figure, the streets of a city form a square grid. A postal worker needs to travel from $$A$$ through $$P$$ to $$B$$. By taking the shortest route, there are a total of different ways to do so.\n question_6298-image_0"}, {"key": "6299", "content": "Insert '+', '-', '\\times', '\\div', and parentheses between the two numbers below to make the following equation true. The correct option among the following is ().\n$$5$$\u3000 $$5$$\u3000 $$5$$\u3000 $$5$$\u3000 $$5$$ = $$1$$"}, {"key": "6300", "content": "Using the four numbers $$2$$, $$3$$, $$5$$, $$6$$, and filling in between them with $$+$$, $$-$$, $$\\times $$, $$\\div $$ and ( ), make the result equal to $$24$$ (each number can only be used once)."}, {"key": "6301", "content": "Distributing a plate of oranges among the children, if each gets $$4$$, there are $$10$$ extra; if each gets $$6$$, there are $$4$$ short. This plate of oranges has how many oranges?"}, {"key": "6302", "content": "There are $7$ identical cakes to be distributed among $3$ children, with each child getting at least one cake. There are a total of different ways to do this."}, {"key": "6303", "content": "How many different ways can $$12$$ identical watermelons be divided into $$3$$ piles of different quantities?"}, {"key": "6304", "content": "As shown in the picture, Eddie's home and school are as illustrated. Then, the shortest path Eddie can take from school to home has a total of ____.\n question_6304-image_0"}, {"key": "6305", "content": "As shown in the figure, is there a shortest route along the line segment from $$A$$ to $$B$$ without passing through $$C$$?\n question_6305-image_0"}, {"key": "6306", "content": "Distribute a plate of cherries among the children, if each child gets $$10$$, there will be $$5$$ short; if each child gets $$16$$, there will be $$41$$ short. This plate of cherries has $$.$$"}, {"key": "6307", "content": "As shown in the figure, this is a parallelogram vegetable garden, its area is square meters. question_6307-image_0"}, {"key": "6308", "content": "As shown in the figure, there are areas $$A$$, $$B$$, $$C$$, $$D$$, $$E$$. Now, using $$5$$ different colors to color these $$5$$ areas, to ensure adjacent areas have different colors, there are several different coloring methods. question_6308-image_0"}, {"key": "6309", "content": "As shown in the diagram: the numbers marked on the left of each row and at the top of each column represent the number of consecutive black squares in that row or column. Based on these numbers, we can know that there are a total of ( ) black squares.\n question_6309-image_0"}, {"key": "6310", "content": "[Pre-class Warm-Up 2] A book has $$35$$ pages, and the page numbers from 1 to 35 use a total number of digits."}, {"key": "6311", "content": "[Warm-up before class 1] 'Journey to the West' is one of the Four Great Classical Novels of Chinese literature. It describes the story of Sun Wukong, Zhu Bajie, and Sha Wujing who protect Tang Seng on his journey to the West to obtain sacred texts. They face eighty-one difficulties, defeat demons along the way, and eventually obtain the real scriptures. The children's version of 'Journey to the West' has $$202$$ pages. How many pages are there from page $$32$$ to page $$187$$?"}, {"key": "6312", "content": "[Warm-up Exercise 3] The number of digits used in the page numbers of a novel during printing is $$210$$. This novel has a total of pages."}, {"key": "6313", "content": "[Warm-up 3] On a hot summer day, several kids went to a beverage store, each ordering at least one cold drink. Among them, $$6$$ people ordered popsicles, $$6$$ people ordered soda, $$4$$ people ordered Sprite. There were $$3$$ people who ordered both popsicles and soda, $$1$$ person who ordered both popsicles and Sprite, and $$1$$ person who ordered both soda and Sprite; there was $$1$$ person who ordered all three. So, in total, there were kids who went to the beverage store."}, {"key": "6314", "content": "[Warm-Up 1] In order to enrich their knowledge, the shrimp and the crab went to the library to read books. After a month, the shrimp read a total of $$48$$ books, and the crab read a total of $$32$$ books. They read $$12$$ books in common, so they actually read a total of books."}, {"key": "6315", "content": "[Pre-class Warm-Up 2] The Super Power Squad has $$25$$ members, each member knows at least one skill out of invisibility or shapeshifting. Among them, $$14$$ people know invisibility, $$18$$ people know shapeshifting. Therefore, the number of people who know both skills is."}, {"key": "6316", "content": "Fill in each blank with a number in the equation below so that the equation holds. Then, the divisor is. question_6316-image_0"}, {"key": "6317", "content": "Calculate: $$1998+199.8+19.98+1.998+2.222=$$"}, {"key": "6318", "content": "Calculate: $$63.981-\\left( 19.52+1.3145 \\right)+41.7-0.09=$$."}, {"key": "6319", "content": "Calculate: (1) $139.05 + 8.74 + 47.26 - 32.1 - 75.05=$ (2) $321.19 - 5.552 - 121.448 + 67.81=$"}, {"key": "6320", "content": "A board is nailed with $$8$$ nails, arranged in a dot matrix of two rows and four columns, a total of different triangles can be formed with rubber bands.\n question_6320-image_0"}, {"key": "6321", "content": "$$16$$ nails are used to create a dot matrix with both horizontal and vertical spacings of $$1$$ cm. Using a rubber band to encompass several nails, shapes such as triangles, squares, trapezoids, etc., can be formed. How many squares can be formed? question_6321-image_0"}, {"key": "6322", "content": "On a wooden board with $$13$$ nails (as shown in the bottom left image), using rubber bands to loop around several of the nails, various shapes such as triangles, squares, trapezoids, and so on can be formed (as shown in the bottom right images). Please answer: How many squares can be formed. question_6322-image_0"}, {"key": "6323", "content": "Count the number of rectangles (including squares) in the image. question_6323-image_0"}, {"key": "6324", "content": "Count, how many triangles are there in total in the picture on the right? question_6324-image_0"}, {"key": "6325", "content": "The total number of squares in the figure below. question_6325-image_0"}, {"key": "6326", "content": "The right figure is half a square, it is divided into small isosceles right triangles, in the figure, there are squares, and there are triangles. question_6326-image_0"}, {"key": "6327", "content": "Xiaoming's younger brother is a triplet. Xiaoming's age this year is equal to the total age of his 3 younger brothers. In 6 years, the total age of the 3 younger brothers will be twice Xiaoming's age. How old is Xiaoming this year?"}, {"key": "6328", "content": "Old trees, big trees, and small trees were chatting. The old tree said: 'The small tree has grown for a number of days, and the big tree has grown for that many weeks; the small tree has grown for a number of months, and I have grown for that many years. Together, we are a total of 1000 years old.' Please ask, the age of the old tree this year, the age of the big tree this year, and the age of the small tree."}, {"key": "6329", "content": "There are three people: A, B, and C. When A's age is twice B's age, C is $$22$$ years old; when B's age is twice C's age, A is $$31$$ years old; when A is $$60$$ years old, C is years old."}, {"key": "6330", "content": "Three years ago, the sum of the ages of Xiaozhi's parents was 8 times that of Xiaozhi's; six years later, the sum of the ages of the parents will be 3 years less than 5 times that of Xiaozhi. How old is Xiaozhi this year? If the father is 6 years older than the mother, and the father's age was 10 times that of Xiaozhi's age several years ago."}, {"key": "6331", "content": "Both brothers thought only they aged a year as time passed and others did not grow up. One day, the older brother said to the younger brother: 'In $$3$$ years, my age will be twice yours.' The younger brother said: 'That's wrong, in $$3$$ years, I will be the same age as you.' At this time, the older brother is years old, the younger brother is years old."}, {"key": "6332", "content": "The total current age of father, brother, and sister is $$64$$ years. When the father's age was $$3$$ times the brother's age, the sister was $$9$$ years old; when the brother's age was $$2$$ times the sister's age, the father was $$34$$ years old. Now, the father's age is, the brother's age is, the sister's age is."}, {"key": "6333", "content": "When A is as old as B, A's age is 3 times that of B; when B reaches A's current age, A is 15 years less than twice the age of B. So now, A is ___ years old, B is ___ years old."}, {"key": "6334", "content": "The age of the father 15 years ago is equal to the age of the son 12 years later. When the age of the father is 4 times the age of the son, the father is years old."}, {"key": "6335", "content": "In kindergarten, $$378$$ children are forming several circles (one circle inside another) to play a game. It is known that there are $$22$$ people in the innermost circle and $$62$$ people in the outermost circle. If the difference in the number of people between two adjacent circles is constant, then the difference in the number of people between two adjacent circles is."}, {"key": "6336", "content": "A sequence of numbers has $$11$$ numbers in total, with the middle number being the largest. Counting from the middle number forwards, each number is $$2$$ less than the previous one; counting backwards from the middle number, each number is $$3$$ less than the previous one. It is known that the sum of these $$11$$ numbers is $$200$$. What is the middle number?"}, {"key": "6337", "content": "A magician performs a magic trick. At the beginning, there are $$3$$ ping pong balls in a box on the table. For the first time, he takes out $$1$$ ball from the box, transforms it into $$3$$ balls, and then puts them all back into the box; the second time, he takes out $$2$$ balls from the box, transforms each ball into $$3$$ balls, and puts all of them back into the box... On the tenth time, he takes out $$10$$ balls from the box, transforms each ball into $$3$$ balls, and puts them all back into the box. Could you please calculate how many ping pong balls are there in the box now."}, {"key": "6338", "content": "In the final math exam of Grade 3 Class 1, the scores of the top $$10$$ students exactly form an arithmetic sequence. Knowing that the perfect score is $$100$$ points, all students' scores are integers, and the total score of the $$3^{rd}$$, $$4^{th}$$, $$5^{th}$$, and $$6^{th}$$ students together is $$354$$ points. Knowing also that Xiao Yue scored $$96$$ points, the score of the $$10^{th}$$ student was $$72$$ points."}, {"key": "6339", "content": "The 6th number in an arithmetic sequence is 17, the sum of the first 5 numbers is 40, then the sum of the first 18 numbers is."}, {"key": "6340", "content": "For the sequence $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$19$$ ... , the $$10$$th number is, $$49$$ is the $$n$$th number of this sequence, the difference between the $$100$$th number and the $$50$$th number is ."}, {"key": "6341", "content": "A square wall is tiled with small square tiles in two colors: red and green. From the outside in, the outermost layer is tiled with red tiles, the second layer with green tiles, the third layer with red tiles, the fourth layer with green tiles, and so on alternately, using a total of $$400$$ tiles. Which color of tile is more numerous on this wall? How many more tiles of one color are there compared to the other?"}, {"key": "6342", "content": "$$120$$ chess pieces are arranged into a three-layer hollow square matrix, with each side of the innermost layer having a chess piece."}, {"key": "6343", "content": "A troop of soldiers forming a three-layer hollow square will have an excess of $$16$$ people; if another layer of people is added to the hollow part, there will be $$28$$ people less, how many people are there in this troop of soldiers? If they form a solid square, how many people should be on each side?"}, {"key": "6344", "content": "The new semester begins, and the Young Pioneers holding flowers formed a square formation of two layers on each side around a decorated vehicle, with the outermost layer having $$13$$ people on each side. There are a number of Young Pioneers around the decorated vehicle."}, {"key": "6345", "content": "Beads of two colors, black and white, arranged in rows to form an equilateral triangle shape (as shown), with one row of black beads followed by one row of white beads. When the number of white beads exceeds the number of black beads by $$10$$, the total number of white beads used is\uff0e question_6345-image_0"}, {"key": "6346", "content": "A group of fourth-grade students in a school is arranged in a square formation, with the number of people in the outermost layer being $$40$$ people. Hence, each side of the outermost layer of the square formation has people, and in total, the squere formation has people."}, {"key": "6347", "content": "A certain troop of soldiers formed a solid square formation during a march, another team with a total of $$31$$ people joined their formation, making it so that there was exactly one more rank added both horizontally and vertically, now there are a total number of soldiers."}, {"key": "6348", "content": "Hope Elementary School's fourth graders form a solid square formation, with $$5$$ people left over. If one row is added both horizontally and vertically to form a slightly larger solid square, then $$26$$ people are missing. How many people are in the fourth grade of Hope Elementary School?"}, {"key": "6349", "content": "Based on the rules of the 24-point game, combine the following 3, 5, 7, 9 to make 24. Among the options below, the correct option is ( )."}, {"key": "6350", "content": "[Pre-class Warm-up 2] Master Wang processed $$60$$ parts in $$2$$ hours, based on this calculation, he can process parts for $$8$$ hours a day."}, {"key": "6351", "content": "[Warm-up Activity 3] $$3$$ mice ate $$30$$ ears of corn in $$5$$ days. At this rate, how many days will it take for $$10$$ mice to eat $$80$$ ears of corn?"}, {"key": "6352", "content": "[Warm-up 1 before class] During the Spring Festival, Xue Xue and his parents went back to their hometown to visit his grandparents. It takes $$2$$ hours by long-distance bus, and the speed of the bus is $$85$$ kilometers per hour. So, the total distance from Xue Xue's home to his grandparents' home is kilometers."}, {"key": "6353", "content": "Below is a table and graph showing the number of students from each grade participating in the paper-cutting interest class at a certain school.\n\n\nNumber of students from each grade participating in the paper-cutting interest class\n\n\n\nFirst Grade\nSecond Grade\nThird Grade\nFourth Grade\n\n\n\n\nNumber of People\n60\n90\n55\n95\n\n\n\n question_6353-image_0 \u200b\nEach grid in the graph represents a person."}, {"key": "6354", "content": "Below is the statistical table and graph of the number of students from each grade participating in the papercutting interest class at a certain school.\n\n\nNumber of students from each grade participating in the papercutting interest class\n\n\n\nFirst Grade\nSecond Grade\nThird Grade\nFourth Grade\n\n\n\n\nNumber of People\n60\n90\n55\n95\n\n\n\n question_6354-image_0 \u200b\nThe number of students from the third grade participating in the papercutting interest class is less than that of the second grade."}, {"key": "6355", "content": "[Warm-up before class 1] A statistical table for donations to drought areas by two primary schools (each with $$5$$ grades): question_6355-image_0 (1) The total donation by the fifth grades of both schools is yuan; (2) The first grade of the first primary school donated the most; (3) The second primary school's first grade donated the least; (4) The total donation of the whole first primary school is yuan."}, {"key": "6356", "content": "There are now $$5$$ chocolate gift boxes, each containing $$12$$ chocolates. The teacher wants to distribute them evenly among $$6$$ students. So, each student gets pieces of chocolate. question_6356-image_0"}, {"key": "6357", "content": "Starting from $$1$$, the sequence of consecutive odd numbers $$1$$, $$3$$, $$5$$, $$7$$, $$\u2026\u2026$$, then $$21$$ is the nth number in this sequence."}, {"key": "6358", "content": "$$1+2+3+4+5+6+7+8+9=$$"}, {"key": "6359", "content": "$$1+3+5+7+9+11+13=$$"}, {"key": "6360", "content": "To enlarge $$29.3$$ by $$10$$ times, just move the decimal point ( ) place(s)."}, {"key": "6361", "content": "Arithmetic sequence summation: $$1+3+5+7+\\cdot \\cdot \\cdot +97+99=$$."}, {"key": "6362", "content": "Uncle Zhang and Uncle Li have a combined age of $$56$$ years. When Uncle Zhang was half the age of Uncle Li's current age, Uncle Li was the age that Uncle Zhang is now. How old is Uncle Zhang now?"}, {"key": "6363", "content": "Given $$A=11(x+3)-7$$, $$B=21+21x-8(15+2x)\\div 4$$, $$C=9+3(2x+5)-37$$, if $$x=2105$$, then $$A-B+C=$$."}, {"key": "6364", "content": "If $$5^{m}=6$$ and $$5^{n}=3$$, find the value of $$5^{3m-2n}$$."}, {"key": "6365", "content": "Transform a solid square matrix with $$16$$ pieces on each side into a four-layer hollow square matrix with the same total number of pieces. How many pieces are there on each side of the outermost layer of this hollow square matrix?"}, {"key": "6366", "content": "A said to B: 'When I was your current age, you were only $$5$$ years old.' B said to A: 'When I am your current age, you will be $$50$$ years old.' So, the current age of A and B are."}, {"key": "6367", "content": "A said to B, \"When I was your age, your age was half of my age this year.\" B said to A, \"When I reach your current age, your age will be double my age this year minus 7.\" So, currently, A is __ years old, B is __ years old."}, {"key": "6368", "content": "The Monkey King divided peaches among the little monkeys. If he gave each little monkey $$4$$ peaches, there would be $$5$$ peaches left; if he gave each little monkey $$5$$ peaches, the peaches would be exactly distributed. So, how many little monkeys were there, and how many peaches did the Monkey King prepare?"}, {"key": "6369", "content": "Divide $$9$$ identical candies among Eddie, Vi, and Da Kuan, such that each person gets at least one candy. How many ways can this be done? question_6369-image_0"}, {"key": "6370", "content": "$$352\\times 68$$ in vertical calculation, calculating \u201c$$2\\times 6$$\u201d actually is ( )."}, {"key": "6371", "content": "When calculating $$643\\times 58$$ using the vertical method, the step $$5\\times 6$$ represents ( )."}, {"key": "6372", "content": "Grade six with $$270$$ people went to the park for a trip, rented a total of $$10$$ vehicles. Each large bus seats $$30$$ people, each small bus seats $$20$$ people, all busses were exactly full, ( ) large buses were rented."}, {"key": "6373", "content": "The farm raises a total of $$210$$ chickens and rabbits. It is known that the number of chicken feet is $$2$$ times the number of rabbit feet, and there are chickens."}, {"key": "6374", "content": "A parking lot has a total of $$24$$ vehicles, among which cars have $$4$$ wheels and tricycles have $$3$$ wheels. Together, these vehicles have $$88$$ wheels. Therefore, there are ( ) tricycles."}, {"key": "6375", "content": "The average of three numbers is $$120$$, after adding another number, the average of the four numbers becomes $$150$$. What is the number added?"}, {"key": "6376", "content": "In an exam, the average score of the boys was $$3$$ points lower than the overall average score, and the average score of the girls was $$4$$ points higher than that of the boys. The total score for the boys was $$1232$$ points, and for the girls it was $$3888$$ points. How many girls were there?"}, {"key": "6377", "content": "A school has $$100$$ students participating in a math competition, with an average score of $$63$$ points. Among them, the average score of male students is $$60$$ points, and that of female students is $$70$$ points. Thus, there are more male students than female students by a count of."}, {"key": "6378", "content": "A fruit store mixes $$3$$ kilograms of fruit candy with $$9$$ kilograms of milk candy to make mixed candy. Knowing that fruit candy costs $$7$$ per kilogram and milk candy costs $$11$$ per kilogram, then the cost per kilogram of the mixed candy is\uff0e"}, {"key": "6379", "content": "Several children are measuring their heights. If Eddie grows by $$10\\rm cm$$ and everyone else remains the same, then their average height would increase by $$2\\rm cm$$. Therefore, there are a total of children."}, {"key": "6380", "content": "Eddie took several exams, and on the last exam, he found that: if he scored $$97$$ on this exam, then his average score would be $$90$$; if he scored $$71$$ on this exam, then his average score would be $$88$$. Eddie took a total of exams."}, {"key": "6381", "content": "Eddie participated in a shooting competition, where he fired a total of $$10$$ shots, hitting the target with each shot as shown by the \u201c\u00d7\u201d in the figure. The numbers in the figure indicate the points that can be earned by hitting each part of the target. Eddie\u2019s average score for this shooting was points.\n question_6381-image_0"}, {"key": "6382", "content": "During the final exams, Xiao Hua's average score for Chinese, Math, and Music was $$98$$ points. After the English score was announced, the average score for all four subjects dropped by $$6$$ points. Xiao Hua's English score was points."}, {"key": "6383", "content": "Count separately, how many squares are there in each of the two pictures? (1) _ question_6383-image_0 \u200b (2) _ question_6383-image_1"}, {"key": "6384", "content": "Count the total number of squares in the picture. question_6384-image_0"}, {"key": "6385", "content": "The park has planted many phoenix trees and cedars, with the number of phoenix trees known to be $$m$$. The number of cedars is $$3$$ times the number of phoenix trees plus $$7$$ more. Cedar trees planted are; the total number of phoenix trees and cedar trees is\uff0e question_6385-image_0"}, {"key": "6386", "content": "There is a bamboo in its vigorous growth period. The first measurement of its length is $$14$$ cm, and each subsequent measurement is $$3$$ cm more than the previous one. (1) At the time of the 5th measurement, the length of the bamboo is in cm. (2) At the time of the 31st measurement, the length of the bamboo is in cm. question_6386-image_0"}, {"key": "6387", "content": "Students, can you quickly calculate $$1+2+3+4+5+6+7$$ equals to\uff0e question_6387-image_0"}, {"key": "6388", "content": "Uncle Zhang's farm has some chickens and rabbits. If putting a chicken and a rabbit together in one cage requires $$100$$ cages, then the total number of chickens and rabbits at Uncle Zhang's farm is, and the total number of chicken and rabbit legs is.\n question_6388-image_0"}, {"key": "6389", "content": "The teacher distributes candies to the students, and if each student is given $$2$$ candies, there will be $$20$$ candies left; if each student is given $$5$$ candies, there will be $$2$$ candies left. Therefore, there are a total of students, and the teacher prepared candies. question_6389-image_0"}, {"key": "6390", "content": "The teacher distributes candies to the students. If each student receives $$4$$ candies, there are $$17$$ left over; if each student receives $$7$$ candies, there are $$10$$ short. So, there are a total of students, and the teacher prepared candies."}, {"key": "6391", "content": "Uncle Zhou has a circular fish pond with a circumference of $$140$$ meters. He wants to plant a willow tree every $$5$$ meters around the pond. He needs to plant willow trees."}, {"key": "6392", "content": "The school has a path that is $$60$$ meters long and plans to plant trees on both sides of the path. A tree will be planted every $$10$$ meters, including at both ends, requiring a total number of trees to be planted. (The width of the trees is negligible)"}, {"key": "6393", "content": "Xiaoming started doing his extracurricular homework at $$4:50$$ and finished at $$5:40$$. It took Xiaoming a total of ( ) minutes to do his extracurricular homework."}, {"key": "6394", "content": "Big Fat ate a number of buns that were 3 times as many as Little Fat plus 10 more. Knowing that Big Fat ate 50 more buns than Little Fat, how many buns did Big Fat eat?"}, {"key": "6395", "content": "As shown in the figure, the perimeter of the large square is $$36$$ cm, the perimeter of the small square is $$16$$ cm, half of the area of the small square overlaps with the large square. The perimeter of the figure formed by these two squares is cm.\n question_6395-image_0"}, {"key": "6396", "content": "After folding a ribbon three times, each segment is $$12$$ cm long, the original length of this ribbon in centimeters is."}, {"key": "6397", "content": "$$30$$ decimeters $$=$$ meters\n$$2$$ meters $$2$$ centimeters $$=$$ centimeters\n$$4000\\text{c}{{\\text{m}}^{2}}=$$ $$\\text{d}{{\\text{m}}^{2}}$$\n$$6500\\text{d}{{\\text{m}}^{2}}=$$ $${{\\text{m}}^{2}}$$"}, {"key": "6398", "content": "Moby participates in a fitness program, engaging in one of the following activities each day: running, swimming, or jumping rope, without choosing the same activity on two consecutive days. On the first day, Moby chooses jumping rope, and on the fourth day, jumping rope is chosen again. Hence, there are a total of different situations for the four days of activities."}, {"key": "6399", "content": "A and B are playing a table tennis match, it's decided that whoever wins three games first will be the winner. The first game was won by A, but in the end, B emerged victorious, there are a total of different situations."}, {"key": "6400", "content": "There are $$120$$ lamps lined up in a row, initially all turned on. For the first time, starting from the first lamp on the left, every second lamp is toggled (i.e., toggling the $$1st, 4th, 7th\u2026$$ lamps). The second time, starting from the first lamp on the right, every fifth lamp is toggled; the number of lamps that were toggled both times and the number of lamps that remain lit are."}, {"key": "6401", "content": "There are $$8$$ types of plants growing along the riverbank, and the number of fruits they bear differs by $$1$$ between any two adjacent types of plants. Question: Is it possible for there to be a total of $$225$$ fruits on the $$8$$ types of plants? Explain your reasoning."}, {"key": "6402", "content": "Xiao Ming counts in a cycle from $$1\\ to 5$$, and Xiao Hua counts in a cycle from $$1\\ to 6$$. When both have counted 600 numbers, the sum of the numbers counted by Xiao Hua is more than that counted by Xiao Ming."}, {"key": "6403", "content": "There is a sequence of numbers: $$9286\\cdots \\cdots $$Starting from the third number, each number is the units digit of the product of its preceding two numbers. Then, the sum of the first $$100$$ numbers is."}, {"key": "6404", "content": "There are two identical rectangles, length $$10$$ cm, width $$6$$ cm, if they are stacked together as shown in the diagram, what is the perimeter of the shape in centimeters? question_6404-image_0"}, {"key": "6405", "content": "The figure below is made up of five identical rectangles forming a larger rectangle. It is known that the perimeter of the larger rectangle is $$18$$ centimeters. The area of the smaller rectangle is in square centimeters.\n question_6405-image_0"}, {"key": "6406", "content": "Using two rectangles of length $$8$$ cm and width $$4$$ cm to form a square, the perimeter of the formed square is in centimeters, and the area is in square centimeters.\n question_6406-image_0 question_6406-image_1"}, {"key": "6407", "content": "Putting two identical rectangles together (as shown in the figure), the perimeter compared to the sum of the perimeters of the original two rectangles ()\uff0e question_6407-image_0"}, {"key": "6408", "content": "There is a book of $$300$$ pages. If any $$22$$ pages are torn from it, can the sum of all the page numbers on these $$22$$ pages be $$1999$$? (Answer yes or no)"}, {"key": "6409", "content": "Write the natural number $$1-811$$ on the blackboard, each time arbitrarily erasing two numbers, then writing down their sum or difference, and repeat this operation. After several times, only one number remains on the blackboard. Please state whether the result is an odd or even number."}, {"key": "6410", "content": "Is the result of the expression $$1123+3025-62\\times 101+33\\times 123$$ odd or even? ( )"}, {"key": "6411", "content": "Calculate: $$99\\times 22+33\\times 34=$$\uff0e"}, {"key": "6412", "content": "Calculate: $$43\\times 27+43\\times 21+48\\times 57=$$."}, {"key": "6413", "content": "Compute: $$5\\times 25\\times 125\\times 64$$=."}, {"key": "6414", "content": "Calculate: $$111\\times 4\\div 9\\times 3\\div 74\\times 2=$$."}, {"key": "6415", "content": "$(1)3600\\div \\left( 25\\times 3 \\right)=$\n$(2)\\left( 360\\times 75 \\right)\\div \\left( 150\\times 12 \\right)=$"}, {"key": "6416", "content": "Students from three sixth-grade classes at a school went out to plant trees. It's known that within one hour, $$5$$ female students can plant $$3$$ trees, and $$3$$ male students can plant $$5$$ trees. The number of students in each class is shown in the following figure, so the class that planted the most trees is class $$2$$.\n question_6416-image_0"}, {"key": "6417", "content": "Tourists want to walk along the forest path as shown in the figure below, covering all paths. The shortest total distance is.\n question_6417-image_0"}, {"key": "6418", "content": "As shown in the diagram below, there are four islands $$A$$, $$B$$, $$C$$, and $$D$$, connected by seven bridges. Can a visitor traverse all seven bridges once without repeating any bridge?\n question_6418-image_0"}, {"key": "6419", "content": "In the nine squares shown below, three numbers have been filled in. Please fill in another six numbers so that the product of the three numbers in any row or column is equal. Then, $$a\\times c=$$.\n question_6419-image_0"}, {"key": "6420", "content": "There is a magic square as shown in the figure, then $$a=$$.\n question_6420-image_0"}, {"key": "6421", "content": "In the matrix shown in the following figure, the sum of the numbers in each row, each column, and each diagonal line is the same. However, only $$7$$ specific numbers are given in the figure. Therefore, the number that should be filled in at position $$A$$ is.\n question_6421-image_0"}, {"key": "6422", "content": "At a cinema, Type A tickets cost $$24$$ per ticket, and Type B tickets cost $$18$$ per ticket. If a class of $$35$$ students buys both types of tickets and exactly spends $$750$$, then Type A tickets purchased were."}, {"key": "6423", "content": "There are $$28$$ motorcycles and cars in total in the parking lot, with a total of $$64$$ wheels. How many cars are there?"}, {"key": "6424", "content": "This year, the father's age is 5 times that of his son. The combined age of the father and son in 3 years is 54 years old. So, the father's age this year is ___ years. question_6424-image_0"}, {"key": "6425", "content": "The speed of a maglev train is $$430$$ km/h. Before entering the station, the speed decreases by $$m$$ km/h every minute. After $$5$$ minutes, the speed decreases by km/h; after $$5$$ minutes, the speed is km/h. $$\\left( m<{}43 \\right)$$ question_6425-image_0"}, {"key": "6426", "content": "Represent the total cost of buying $$n$$ footballs and $$m$$ basketballs with an expression containing letters. When $$n=4$$ and $$m=5$$, the total cost of buying the footballs and basketballs is yuan. question_6426-image_0 question_6426-image_1"}, {"key": "6427", "content": "(1) The first grade class one performs a march in step. The formation requires: 5 people per row, a total of 5 rows, with people from class one participating. (2) Removing a row and a column results in fewer people. question_6427-image_0"}, {"key": "6428", "content": "The solid square formation of the third grade, class three, has a total of $$56$$ people on the outermost layer. This square formation has a total of people. question_6428-image_0"}, {"key": "6429", "content": "Fourth-grade students formed a three-layer hollow square formation to perform a magic trick, with 18 people on each side of the outermost layer. (1) The number of people in the outermost layer; (2) The total number of people in the second layer; (3) The total number of people in the square formation;"}, {"key": "6430", "content": "At the closing ceremony of the art festival, volunteers used beautiful flowers to congratulate the performers. In the open space in front of the gymnasium, they arranged a hollow square formation of flower beds. The outermost layer had $$12$$ pots of flowers on each side, with a total of $$3$$ layers, requiring a total of flower pots."}, {"key": "6431", "content": "Using $$96$$ chess pieces to form a three-layer hollow square matrix, (1) the difference in the number of chess pieces between adjacent layers. (2) The outermost layer has chess pieces."}, {"key": "6432", "content": "Among the natural numbers sequence $$1$$, $$2$$, $$3$$, $$\\cdots$$, $$1000$$, there are a number of natural numbers that can be divided by $$5$$ or $$11$$."}, {"key": "6433", "content": "There are $$100$$ lamps numbered from $$1$$ to $$100$$, all turned on and lined up. During the first round, switches of lamps numbered with multiples of $$3$$ are toggled once. In the second round, switches of lamps numbered with multiples of $$5$$ are toggled once. How many lamps remain lit?"}, {"key": "6434", "content": "A survey of the whole class found that 16 students can swim, 21 can play basketball, 10 can do both, and 8 can do neither, making the total number of students in the class."}, {"key": "6435", "content": "There is a straight line in the image below, with intersecting points question_6435-image_0"}, {"key": "6436", "content": "Increasing the length of a rectangle by $$5$$ meters and the width by $$8$$ meters yields a square whose area is $$181$$ square meters larger than the original rectangle. Calculate the side length of this square in meters. question_6436-image_0"}, {"key": "6437", "content": "There are $$6$$ bags, each with balls of the same color, including a total of $$4$$ colors. The number of balls in the $$6$$ bags are $$11$$, $$15$$, $$17$$, $$24$$, $$33$$, and $$37$$, respectively. Among these balls, the number of white balls is twice that of black balls, and there are as many red balls as white balls. One of the bags contains green balls, and the total number of green balls in this bag is $$17$$."}, {"key": "6438", "content": "The teacher distributes candies to the students, if each student gets 9 candies, there are 2 less; if each student gets 11 candies, there are 14 less. So, in total there are students, and the teacher has prepared candies."}, {"key": "6439", "content": "Column subtraction calculation: (1) $$999\\div 27$$=\uff0e(2) $$3300\\div 55$$=\uff0e"}, {"key": "6440", "content": "A square piece of paper has a side length of $$1$$ decimeter, it can be divided into small squares with a side length of $$1$$ centimeter. question_6440-image_0"}, {"key": "6441", "content": "A car travels from Place A to Place B at a speed of $$60$$ kilometers per hour, taking $$5$$ hours to arrive. To arrive in $$4$$ hours, the hourly speed needed is kilometers."}, {"key": "6442", "content": "Han Han and Qiao Qiao live 800 meters apart. Both start from their homes at the same time and walk towards each other on the same road. Han Han walks at 36 meters per minute, and Qiao Qiao walks at 44 meters per minute. After 4 minutes, the distance between them is meters."}, {"key": "6443", "content": "Running Man is running a certain distance at a constant speed of $$300$$m/min and can finish the entire distance in $$3$$ hours. If he ran at a constant speed of $$360$$m/min, how many minutes less would it take him to run this distance? A person runs at a speed of $$300$$ meters per minute and completes the run in $$3$$ hours. Assuming he increases his speed to $$360$$ meters per minute, how many minutes would he save compared to before?"}, {"key": "6444", "content": "Da Mao and Er Mao's houses are $$500$$ meters apart. Da Mao walks at $$34$$ meters per minute, and Er Mao walks at $$45$$ meters per minute. Both leave their homes at the same time and walk in opposite directions on the same road. After $$4$$ minutes, the distance between them is meters."}, {"key": "6445", "content": "Dongdong's home is $$1000$$ meters away from the school. To reach the school in $$20$$ minutes, Dongdong needs to walk meters per minute."}, {"key": "6446", "content": "A group of foreign tourists visited Wuhan, with $$18$$ people visiting the Yellow Crane Tower, $$20$$ people visiting the East Lake, and $$12$$ people visited both attractions. This group of tourists totals people."}, {"key": "6447", "content": "Calculate the following: $$471471471471\\div 157157157157=$$."}, {"key": "6448", "content": "This year, the father's age is $$4$$ times the age of the daughter. In $$18$$ years, the father's age will be $$2$$ times the age of the daughter. Question: What are the current ages of the father and the daughter, respectively?"}, {"key": "6449", "content": "Please find the pattern for each term in the following sequence and fill in the blank: (2) The first term is $$1$$, the second term is $$8$$, the third term is $$27$$, the fourth term is $$64$$, $$ \\cdots $$ then the tenth term is."}, {"key": "6450", "content": "Based on the statistical table, solve the following problems.\n question_6450-image_0 \nIn the first half of the year, the average monthly production of Factory A is, and the average monthly production of Factory B is."}, {"key": "6451", "content": "As shown in the diagram, in a shooting competition, $$5$$ balloons are arranged in three rows. The requirement is to burst the balloons following the rules below: first, select a row, and then one must burst the lowest unburst balloon in that row. Following this rule, there are several different sequences to burst all five balloons. question_6451-image_0 \u200b"}, {"key": "6452", "content": "Using $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ to form a five-digit number (numbers can be reused), and the difference (larger minus smaller) between any two adjacent digits is $$1$$. How many such five-digit numbers are there?"}, {"key": "6453", "content": "As shown in the figure, $$ABCDE$$ is a regular pentagon, Eddie starts at vertex $$A$$, and he can jump to one of the two adjacent vertices each time. If he arrives at point $$D$$ within $4$ jumps, he stops jumping; if he cannot reach $$D$$ within $4$ jumps, he also stops after $4$ jumps. Thus, the total number of different possible jumping methods from start to stop is.\n question_6453-image_0"}, {"key": "6454", "content": "Tian Tian likes to eat xiaolongbao, cornbread, and osmanthus cake. He only eats one type each day and does not eat the same type on two consecutive days. Assuming he eats xiaolongbao on the first day and also on the fourth day, then there are several different arrangement plans for these four days. (Assume xiaolongbao is $$A$$, cornbread is $$B$$, and osmanthus cake is $$C$$)"}, {"key": "6455", "content": "In the table shown in the picture, form a pair of words with the two characters above and below in each column, for example, the first group of words is (\u5e8a\u6211), the second group of words is (\u524d\u4eec), then the 50th group of words is. \u5e8a\u524d\u660e\u6708\u5149\u5e8a\u524d\u660e\u6708\u5149\u5e8a\u524d\u660e\u6708\u5149...\u6211\u4eec\u5b66\u800c\u601d\u6210\u5c31\u7f8e\u597d\u672a\u6765\u5b66\u800c\u601d\u6210\u5c31\u7f8e\u597d\u672a\u6765\u5b66\u800c\u601d\u6210\u5c31\u7f8e\u597d\u672a\u6765..."}, {"key": "6456", "content": "There are $$9$$ coins on the table. You flip $$6$$ of them at the same time. After several flips, all the coins are flipped over. The possible number of flips could be."}, {"key": "6457", "content": "Calculate $$7485+343\\times 141-17\\times 232-119\\times 120+2014$$, Eddie calculated the result as $$39639$$. Can you determine if his calculation is correct?"}, {"key": "6458", "content": "Calculate: $$5\\times 25\\times 125\\times 64$$=\uff0e"}, {"key": "6459", "content": "Calculate: $$38\\times 1717+34\\times 3131=$$."}, {"key": "6460", "content": "Compute: $$2017\\times 20162015-2015\\times 20162017$$=."}, {"key": "6461", "content": "Xiao Tie has $$20$$ cards, Xiao Zin has $$25$$ cards, after Xiao Tie gives some cards to Xiao Zin, the number of cards Xiao Zin has becomes twice the number of Xiao Tie's cards."}, {"key": "6462", "content": "Da Bai and Xiao Bai planted a total of $$32$$ trees, Da Bai planted $$2$$ times more trees than Xiao Bai plus $$2$$ more trees, so how many trees did Xiao Bai plant."}, {"key": "6463", "content": "Xiao Ming and Xiao Hong had a total of $$103$$ pieces of candy. Xiao Ming ate $$3$$ pieces, and Xiao Hong bought $$5$$ more. At that time, the number of candies Xiao Ming had was $$4$$ times that of Xiao Hong's. So, how many pieces of candy did Xiao Ming originally have?"}, {"key": "6464", "content": "Each child in senior kindergarten class receives $$17$$ picture cards, while each child in junior kindergarten class receives $$13$$ picture cards. The number of children in the junior class is $$2$$ times that of the senior class. The junior class receives $$126$$ more picture cards in total than the senior class. How many children are there in the junior class?"}, {"key": "6465", "content": "In the Asian Cup final, the number of Chinese journalists was 3 times that of foreign journalists. After the match, 180 Chinese journalists left the venue, and 40 foreign journalists left. The remaining numbers of Chinese and foreign journalists were equal. How many Chinese journalists were there originally?"}, {"key": "6466", "content": "A large and a small monkey went to pick peaches from a tree. It is known that the larger monkey picked 53 more peaches than the smaller monkey, and the number of peaches picked by the larger monkey is 3 more than 3 times the number picked by the smaller monkey. So, the larger monkey picked peaches, and the smaller monkey picked peaches."}, {"key": "6467", "content": "In a certain year, there are $$53$$ Fridays and $$53$$ Saturdays, then March $$1$$ of that year is a ."}, {"key": "6468", "content": "Given that a normal year has $$53$$ Sundays, what day of the week was January $$1$$ of this year? (Enter a number between $$1$$-$$7$$)"}, {"key": "6469", "content": "$$2019$$ year $$2$$ month $$1$$ day is Friday, the third to last day of the month is a Thursday."}, {"key": "6470", "content": "A certain unit adopts a five-day work week, meaning work from Monday to Friday with the weekend, Saturday and Sunday, off. It is known that a certain month has $$31$$ days, and an employee, Xiao Wang, of the unit took $$9$$ days off in that month (there were no other holidays in the month). Which day of the week could the 6th of the month possibly be among the following four options? ( )"}, {"key": "6471", "content": "Students A, B, and C take turns to get milk for Grandma Li every morning. If Student A gets the milk for the first time on Monday, then the $$100$$th time Student A gets the milk will be on what day of the week. (Please fill in the number)"}, {"key": "6472", "content": "Our country took back the sovereignty over Hong Kong on July 1, 1997, which happened to be a Tuesday. Then, on the tenth anniversary, July 1, 2007, the day of the week was."}, {"key": "6473", "content": "January 1, 2012 was a Sunday, May 1, 2019 was a Wednesday."}, {"key": "6474", "content": "A certain month has five Saturdays, and the date of the last Saturday is an even number. The day of the week for the 1st of this month is."}, {"key": "6475", "content": "The following image is a third-order magic square. Then $$a+h=$$.\n question_6475-image_0"}, {"key": "6476", "content": "The following image is an incomplete fourth-order magic square. Therefore, A=, B=. question_6476-image_0"}, {"key": "6477", "content": "In the nine squares shown in the image, four numbers have already been filled in. Please fill in five more natural numbers so that the product of any three numbers in any row or column is equal. Then, the sum of all the numbers you have filled in is. question_6477-image_0"}, {"key": "6478", "content": "Complete the blanks based on the picture.\n\u2460 The number of female students waiting is the highest;\n\u2461 There are $$27$$ male students in the class;\n\u2462 There are a total of $$3$$ students in the class who failed, which accounts for $$\\frac{3}{46}$$ of the total number of students in the class.\n question_6478-image_0"}, {"key": "6479", "content": "A statistical table of the weather conditions in a certain region for the months of May and September.\n question_6479-image_0 \nMay has the fewest days, September has the most days, September has fewer cloudy days than May, May has more sunny days than September; May has a total of days, including days of rain."}, {"key": "6480", "content": "The figure below cannot be drawn with one stroke. Please add one line to make it possible to draw the figure with one stroke, the correct option is ( ).\n question_6480-image_0"}, {"key": "6481", "content": "The figure below is a plan view of a park's paths, where the numbers indicate the length of the paths (in meters). $$A$$ and $$B$$ are the entrance and exit of the park, respectively. Entering from the entrance, walking through all the paths, and then exiting from the exit, the shortest distance is meters. question_6481-image_0"}, {"key": "6482", "content": "Determine which of the following figures cannot be drawn in one stroke ( ).\n question_6482-image_0"}, {"key": "6483", "content": "In a quiz competition, the rules are: earn $$10$$ points for each correct answer, lose $$6$$ points for each wrong answer. Contestant number one attempted $$10$$ questions and ended up with $$36$$ points, how many questions did he answer correctly?"}, {"key": "6484", "content": "A table tennis match sold tickets at $$30$$, $$40$$, and $$50$$ each for a total of $$200$$ tickets, generating an income of $$7800$$ dollars. The number of tickets sold at $$40$$ and $$50$$ dollars was equal, and the number of tickets sold at $$30$$ dollars was."}, {"key": "6485", "content": "The Ministry of Health surveyed whether $$120$$ kinds of food contain vitamins $$A$$, $$C$$, and $$E$$. The results are: $$62$$ kinds contain vitamin $$A$$, $$90$$ kinds contain vitamin $$C$$, and $$68$$ kinds contain vitamin $$E$$. There are $$48$$ kinds that contain both vitamins $$A$$ and $$C$$, $$36$$ kinds that contain both vitamins $$A$$ and $$E$$, $$50$$ kinds that contain both vitamins $$C$$ and $$E$$, and $$25$$ kinds that contain all three vitamins. Question: ($$1$$) How many kinds of food do not contain any of these three vitamins? ($$2$$) How many kinds of food contain only vitamin $$A$$?"}, {"key": "6486", "content": "In the series of natural numbers $$1$$, $$2$$, $$3$$, $$\\cdots$$, $$1000$$, the number of natural numbers that cannot be divided by $$3$$ or $$5$$ is ."}, {"key": "6487", "content": "Li Bai takes a jug to buy wine, doubling the amount at each shop, and drinks eight liang when seeing flowers. Encountering shops and flowers three times, he drinks up all the wine in the jug. Originally, the jug had ( ) liang of wine."}, {"key": "6488", "content": "There are two baskets of apples, basket A and basket B, with a different number of apples in each. Some apples are moved from basket A to basket B, causing the number of apples in basket B to double. Then, some apples are moved from basket B back to basket A, causing the number of apples in basket A to also double. At this point, both baskets have $$20$$ apples each. Originally, basket A had __ apples, and basket B had __ apples."}, {"key": "6489", "content": "A and B have a certain number of candies, with A having more than B. Each operation involves the person with more candies giving some candies to the person with fewer candies, such that the number of candies of the person with fewer candies doubles. After $$2019$$ such operations, A has $$8$$ candies. B has $$14$$ candies. How many candies did A originally have?"}, {"key": "6490", "content": "A decimal number, first move the decimal point one place to the left, then increase it by $$1000$$ times, to get $$123$$. What was the original decimal number?"}, {"key": "6491", "content": "$$1.34+5.41+7.25=$$."}, {"key": "6492", "content": "$$2.7896$$ rounded to three decimal places is."}, {"key": "6493", "content": "To arrange $$4.2$$, $$4.23$$, $$4.32$$, $$4.4$$ from largest to smallest is:\n$$>$$$$>$$$$>$$\uff0e"}, {"key": "6494", "content": "There is a line segment in the figure below.\n question_6494-image_0"}, {"key": "6495", "content": "There is a line segment in the picture. question_6495-image_0"}, {"key": "6496", "content": "As shown in the picture, there are $$10$$ nails on a board, and the distance between any two adjacent nails is equal. Using these nails as vertices, you can stretch out a rubber band to form a number of equilateral triangles.\n question_6496-image_0"}, {"key": "6497", "content": "The number of triangles in the figure below is.\n question_6497-image_0"}, {"key": "6498", "content": "Given $${{3}^{m}}=4$$, $${{3}^{3m}}=$$."}, {"key": "6499", "content": "Fill in the blanks: (1) For the arithmetic sequence $$3$$, $$7$$, $$11$$, $$15$$, $$\\ldots$$, the $$26$$th number is. (2) For the arithmetic sequence $$2$$, $$6$$, $$10$$, $$14$$, $$\\ldots$$, $$42$$ is the nth number of this sequence. (3) For the arithmetic sequence $$5$$, $$10$$, $$15$$, $$20$$, $$\\ldots$$, $$80$$, this sequence has a total of numbers."}, {"key": "6500", "content": "Answer the following questions. (1) Knowing that the 6th and 10th terms in an arithmetic sequence are 38 and 62 respectively, the difference between two adjacent numbers is, and the first number is. (2) An arithmetic sequence has a total of 15 numbers, where the 2nd number is 8 and the 5th number is 26, the last number is."}, {"key": "6501", "content": "In nine boxes numbered from $$1$$ to $$9$$, there are a total of $$351$$ grains of rice. It is known that each box contains more grains of rice than the one before it by the same amount. If box number $$1$$ contains $$11$$ grains of rice, how many more grains does each subsequent box contain compared to the one before it?"}, {"key": "6502", "content": "It is known that the sum of the first $$15$$ numbers of an arithmetic series is $$450$$, and the sum of the first $$25$$ numbers is $$1250$$. The difference between two adjacent numbers in this series is, and the first number is."}, {"key": "6503", "content": "It is known that the sum of the first $$15$$ numbers of an arithmetic sequence is $$450$$, and the sum of the first $$20$$ numbers is $$750$$. The difference between two consecutive numbers in this sequence is ___, and the first number is ___."}, {"key": "6504", "content": "In a math competition, the scores of the eight students who won the first prize just form an arithmetic sequence, with a total score of $$656$$, and the score of the first prize exceeds $$90$$ points (out of a total of $$100$$ points). It is known that the scores of the students are integers, then the score of the third place is."}, {"key": "6505", "content": "Arithmetic sequence calculation: $$357+352+347+\\cdots+22=$$\uff0e"}, {"key": "6506", "content": "Given the sum of the first $$13$$ numbers in an arithmetic sequence is $$390$$, and the sum of the first $$21$$ numbers is $$882$$, what is the difference between two consecutive numbers in this sequence. What is the first number."}, {"key": "6507", "content": "The sequence $$1$$, $$4$$, $$7$$, $$10$$, $$\\cdot \\cdot \\cdot \\cdot \\cdot \\cdot$$, $$97$$, $$100$$ is an arithmetic sequence. The $$20$$th term is, $$100$$ is the nth term, the sum of all numbers in this sequence is."}, {"key": "6508", "content": "After inserting $$10$$ numbers between $$124$$ and $$245$$ to form an arithmetic sequence, among these $$10$$ numbers, the smallest number is, and the largest number is."}, {"key": "6509", "content": "Xiaoming wants to put $$210$$ chess pieces into several boxes, placing $$1$$ piece in the first box, $$2$$ pieces in the second box, $$3$$ pieces in the third box, and so on, in such a way that the pieces exactly fill up the boxes. How many boxes did Xiaoming use?"}, {"key": "6510", "content": "Insert the operators $$+$$, $$-$$, $$\\times$$, $$\\div$$, or () between the adjacent numbers on both sides of the equation to make the equation valid. $$5\\;\\;\\;\\;\\;\\;\\;\\;4\\;\\;\\;\\;\\;\\;\\;\\;3\\;\\;\\;\\;\\;\\;\\;\\;2\\;\\;\\;\\;\\;\\;\\;\\;1=6\\;\\;\\;\\;\\;\\;\\;\\;4$$"}, {"key": "6511", "content": "Fill in the appropriate place with \"$$+$$\" or \"$$-$$\" (you may leave spaces between two numbers) in the equation below to make the equation valid. $$7$$$$8$$$$9$$$$1$$$$2$$$$1$$$$3$$$$1$$$$4 = 48$$"}, {"key": "6512", "content": "Using the four digits $$2$$, $$3$$, $$5$$, $$6$$, insert $$+$$, $$-$$, $$\\times $$, $$\\div $$ or ( ), so that the result equals $$24$$ (each digit can only be used once)."}, {"key": "6513", "content": "Fill in the appropriate operators and parentheses in the question below to make the equation correct: $$1$$ $$2$$ $$3$$ $$4$$ $$5$$$$=$$$$20$$."}, {"key": "6514", "content": "Wei'er wants to go from home to Xueersi, but she does not know the total number of ways to take the shortest route. Kids, hurry up and help out! question_6514-image_0"}, {"key": "6515", "content": "Answer the following questions: (1) In the diagram, the shortest road from point A to point B has ____ roads. question_6515-image_0 (2) As shown in the diagram, from $$A$$ to $$B$$, if it's required to only move right or down, there are ____ different routes. question_6515-image_1"}, {"key": "6516", "content": "In the right figure, connect adjacent letters with horizontal or vertical line segments, when walking along these line segments, exactly spells out \"APPLE\". The total number of paths is . question_6516-image_0"}, {"key": "6517", "content": "As shown in the diagram, walking from $$P$$ to $$Q$$ along the arrows, there are several different shortest paths.\n question_6517-image_0"}, {"key": "6518", "content": "A bee starts from location $$A$$ and goes back home to location $$B$$. It can only move to an adjacent beehive on the right side (right, upper right, lower right) and is not allowed to go backwards. There are a total of methods to go home. question_6518-image_0"}, {"key": "6519", "content": "Using $$3$$, $$3$$, $$3$$, $$4$$, $$4$$ and one each of \u201c$$+$$, $$-$$, $$\\times $$, $$\\div $$\u201d to form an equation (without parentheses, positions of numbers can be exchanged), what is the largest result obtainable?"}, {"key": "6520", "content": "Please randomly insert $$+$$, $$-$$, $$\\times$$, $$\\div$$, or () between each pair of the numbers $$1$$, $$2$$, $$4$$, $$6$$, in such a way that the result of the expression equals $$24$$. The positions of the numbers can be changed. The correct answer is ()."}, {"key": "6521", "content": "Please fill in \"$$+$$\" or \"$$-$$\" between the two adjacent numbers below to make the equation valid. The correct answer is ( ). $$11$$ $$10$$ $$9$$ $$8$$ $$7$$ $$6$$ $$5$$ $$4$$ $$3$$ $$2$$ $$1=0$$"}, {"key": "6522", "content": "A customer at a dollar store (where all items are priced at no more than $$100$$) bought a sunflower for $$27.5$$ and a pillow. When checking out, the cashier misread the decimal point of the pillow's price, totaling $$76.5$$. Consequently, the customer paid with a counterfeit $$100$$ bill, which the cashier did not detect and gave change as usual before the customer left$.$ At closing time, the cashier found out the bill was counterfeit and could not be used, and submitted it to the bank$.$ Please, smart kids, calculate the total loss of the careless cashier."}, {"key": "6523", "content": "Count the number of line segments and triangles in the figure below. question_6523-image_0"}, {"key": "6524", "content": "Given $$A=a+b$$, $$B=a-b$$, $$C=2a$$, $$D={{b}^{2}}$$. When $$a=4$$, $$b=3$$, calculate $$A+B-C+D=$$."}, {"key": "6525", "content": "In the right figure, connect adjacent letters with horizontal or vertical line segments. How many routes exactly spell out \"APPLE\" when walking along these segments? question_6525-image_0"}, {"key": "6526", "content": "A bee starts from $$A$$ and returns home to $$B$$. It can only crawl to an adjacent hive on the right side (right, upper right, or lower right) without backing up. How many ways are there for it to return home? question_6526-image_0"}, {"key": "6527", "content": "Warehouse A and B together have 80 bags of rice. Moving 10 bags from warehouse A to B, warehouse A still has 2 more bags than B. How many bags of rice did warehouse A and B originally have?"}, {"key": "6528", "content": "Among the three-digit numbers formed with the digits $$1$$, $$0$$, $$8$$, the difference between the largest and the smallest number is."}, {"key": "6529", "content": "Person A and Person B start from point $$A$$ simultaneously, walking in opposite directions. Person A walks at a speed of $$7$$ meters per second, and Person B walks at a speed of $$4$$ meters per second. After half an hour, the distance between the two people is meters."}, {"key": "6530", "content": "An athlete undergoes long-distance running training, running $$150$$ meters per minute for the first half of the distance, and $$100$$ meters per minute for the second half. The average speed of the entire long-distance running process is meters per minute."}, {"key": "6531", "content": "Count, the total number of line segments in the picture.\n question_6531-image_0"}, {"key": "6532", "content": "Choice: There is a triangle in the picture. question_6532-image_0"}, {"key": "6533", "content": "This year, the father is $$40$$ years old, and his daughter is $$7$$ years old. In a few years, the father's age will be $$4$$ times the daughter's age."}, {"key": "6534", "content": "Express the following relationships with equations containing letters: (1) A worker plans to finish wallpapering in $$a$$ days. If they wallpaper $$4$$ meters each day, and actually take $$8$$ days more than planned, the actual number of days taken to wallpaper and the total length of the wallpaper in meters are; (2) Xiaohong and her dad are assembling furniture with screws. Each box contains $$m$$ screws, Xiaohong used $$5$$ boxes plus $$3$$ extra screws, and her dad used $$8$$ boxes, the total number of screws used by both of them is. When $$m=6$$, the total number of screws used by both of them is. question_6534-image_0"}, {"key": "6535", "content": "Auntie Wang from the kindergarten wants to buy $$100$$ toy models, she brought $$4000$$ yuan, she can buy ( )."}, {"key": "6536", "content": "Walking from the first floor to the fourth floor requires climbing a total of $$48$$ steps. If the number of steps per floor is the same, how many steps are needed to go from the first floor to the sixth floor?"}, {"key": "6537", "content": "On one side of a $$20$$ meter alley, a lantern is installed every $$5$$ meters, with lanterns at both ends. Now, if one wants to place a flag between every two lanterns, how many flags should be prepared? ( )"}, {"key": "6538", "content": "Find two integers such that their sum is $$264$$ and their difference is $$57$$. Do such numbers exist? ( )"}, {"key": "6539", "content": "Xiaobai wants to place $$18$$ identical car models on a $$3$$-layer shelf, with at least $$5$$ on each layer; there are various different ways to do so."}, {"key": "6540", "content": "Three pirates split $$20$$ gold coins. If each pirate gets at least $$5$$ gold coins. There are a total of different ways to split the coins."}, {"key": "6541", "content": "Distribute $$8$$ tanks among three children: Xiao Xiao, Zhong Zhong, and Da Da, with each child receiving at least one tank. There is a certain method."}, {"key": "6542", "content": "Xiao Wanzi has many sets of clothes, with $$10$$ tops, $$8$$ pairs of trousers, and $$6$$ pairs of leather shoes. He needs to choose one from each category to match for going out. In total, there can be different combinations."}, {"key": "6543", "content": "As shown, quadrilateral $$ABCD$$ is a rhombus, given $$AC=18$$ and $$BD=6$$. The area of the rhombus is. (Hint: The diagonals of a rhombus are perpendicular to each other.)\n question_6543-image_0"}, {"key": "6544", "content": "$$4$$ students invite Teacher Wang to line up with them for a photo. If Teacher Wang can only stand in the very middle, then there are a total of different ways of arranging them."}, {"key": "6545", "content": "There are $$58$$ students learning piano, $$43$$ students learning painting, and $$37$$ students learning both piano and painting in the fourth grade of Fangcao Elementary School. The question is how many students are learning only piano."}, {"key": "6546", "content": "After diligent care, Huaguo Mountain achieved a bountiful harvest of peaches. If all the peaches are distributed among the big monkeys, each getting 8 peaches, there will be 8 peaches left; if all are given to the small monkeys, with each getting 15 peaches, there will be a shortage of 7 peaches. It is known that there are 6 more big monkeys than small monkeys. So, in total, there are $$128$$ peaches."}, {"key": "6547", "content": "$$(207\\times 203+20214+2142+21420+14202)\\div 9=$$."}, {"key": "6548", "content": "If $$A=(1+2+3+\\cdots \\cdots +2020)\\times (2+3+4+\\cdots \\cdots +2021)$$, $$B=(2+3+4+\\cdots \\cdots +2020)\\times (1+2+3+\\cdots \\cdots +2021)$$, then the larger one between $$A$$ and $$B$$ is."}, {"key": "6549", "content": "There is a rectangular piece of paper with a length of $$10$$ cm and a width of $$8$$ cm. If it is cut with scissors $$3$$ times (as shown in the figure), then the sum of the perimeters of these $$6$$ rectangles is in cm.\n question_6549-image_0"}, {"key": "6550", "content": "As shown in the figure, the areas of the two parallelograms are $$20$$ and $$15$$ respectively, the difference in area of the two shaded parts is. question_6550-image_0"}, {"key": "6551", "content": "Given in parallelogram $$ABCD$$, the diagonals $$AC$$ and $$BD$$ intersect at point $$O$$, $$AC=10$$, $$BD=8$$. If $$AC\\bot BD$$, then the area of parallelogram $$ABCD$$ is. question_6551-image_0"}, {"key": "6552", "content": "As shown in the figure (unit: cm), two identical right trapezoids overlap each other. If one of the right trapezoids is translated in the direction of $$AD$$, then the area of the shaded part is. question_6552-image_0"}, {"key": "6553", "content": "The area within a parallelogram is marked on the diagram, calculate the area at the question mark. question_6553-image_0"}, {"key": "6554", "content": "The uncle is skilled in planting flowers, and he has a parallelogram-shaped flower bed as shown in the image below. He plans to leave a rectangular path that is $$1\\text{m}$$ wide in the middle for the convenience of arranging the flowers, and the rest will be planted with roses. As shown in the image, each square meter can accommodate $$6$$ rose bushes, and this piece of land can total plant rose bushes.\n question_6554-image_0"}, {"key": "6555", "content": "Two identical right-angled triangles overlap as shown in the diagram below (unit: cm), find the area of the shaded part.\n question_6555-image_0"}, {"key": "6556", "content": "A large parallelogram, with sides of length $$2$$ cm, is assembled from several parallelograms and triangles (as shown in the right figure). Given that the perimeter of the large parallelogram is $$244$$ cm, then there are ( ) parallelograms.\n question_6556-image_0"}, {"key": "6557", "content": "The area of the shaded part is in square centimeters. (unit cm) question_6557-image_0"}, {"key": "6558", "content": "As shown in the figure, the area of the large square is $$9$$ and the area of the small square in the middle is $$1$$. Alpha, Beta, Gamma, and Delta are four trapezoids. Therefore, the sum of the areas of Beta and Delta is. question_6558-image_0"}, {"key": "6559", "content": "The numbers in the picture respectively represent the areas of two parallelograms and one triangle, the area of another triangle is. question_6559-image_0"}, {"key": "6560", "content": "After filling in appropriate numbers in each cell of the $$3\\times 4$$ grid shown in the figure, it is possible to make the sum of the numbers filled in each row equal, and the sum of the numbers filled in each column equal as well. Some numbers have already been filled in, and the number filled in the cell marked with the symbol \u201c*\u201d is. question_6560-image_0"}, {"key": "6561", "content": "There are two people, A and B, playing a rock-paper-scissors game. It is stipulated that the first to win $$2$$ rounds will be the winner. Question: at the time when a winner is determined, how many possible scenarios are there?"}, {"key": "6562", "content": "Radish Head planted a total of $$126$$ radishes, the number of white radishes is $$2$$ times the number of green radishes, and the number of carrots is $$2$$ times the number of white radishes, find the number of green radishes."}, {"key": "6563", "content": "Originally, there were some wine in the jar. When the wine was increased to $$2$$ times its original amount, the total weight of the jar and the wine was $$8$$ kilograms; when the wine was increased to $$5$$ times its original amount, the total weight of the jar and the wine was $$17$$ kilograms. How many kilograms was the original wine?"}, {"key": "6564", "content": "Huanhuan and Lele have a total of $$15$$ candies, and the number of candies Huanhuan has is $$2$$ times that of Lele's. So, how many candies does Lele have?"}, {"key": "6565", "content": "If 12 people are transferred from workshop A to workshop B, then the number of people in the two workshops will be equal. If 18 people are transferred from workshop B to workshop A, then the number of people in workshop A will be 4 times that of workshop B. Originally, workshop A had people."}, {"key": "6566", "content": "When two numbers are divided the quotient is $$4$$ with a remainder of $$5$$, and the difference between these two numbers is $$95$$. Then, the dividend is, and the divisor is."}, {"key": "6567", "content": "In the senior class of the kindergarten, each child receives $$17$$ pictures, and in the junior class, each child receives $$13$$ pictures. The number of children in the junior class is $$2$$ times that of the senior class. The junior class received $$126$$ more pictures in total than the senior class. So, how many children are there in the junior class?"}, {"key": "6568", "content": "Eddy and Weir participated in a typing contest. Together, they typed $$300$$ characters in $$2$$ minutes. It is known that Eddy types $$20$$ more characters per minute than Weir. How many characters does Eddy type per minute, and how many does Weir type per minute?"}, {"key": "6569", "content": "Doudou's total number of scorecards is $$2$$ times that of Mimi's and $$3$$ times that of Lili's. It is known that Doudou has $$40$$ more cards than Lili. Then, Mimi has __ cards."}, {"key": "6570", "content": "$$2018$$ year $$3$$ month $$20$$ day is Tuesday, based on this calculation, $$2018$$ year $$7$$ month $$28$$ day is Saturday (  )."}, {"key": "6571", "content": "There are $$26$$ bricks, 2 brothers were competing to carry them. The younger brother rushed ahead, just arranged the bricks, when the older brother arrived. The older brother thought the younger brother had too many, so he took half from the younger brother for himself. The younger brother thought he could manage, and took half back from the older brother. The older brother felt he had too little, so the younger brother had to give the older brother $$5$$ more bricks, making the older brother take $$2$$ more bricks than the younger brother. Initially, the younger brother planned to carry bricks."}, {"key": "6572", "content": "As shown in the diagram, fold point $$C$$ of rectangle $$ABCD$$ along $$BD$$ to $$C'$$, where $$\\angle BDC=58{}^\\circ $$. Find the degree of $$\\angle ABE$$.\n question_6572-image_0"}, {"key": "6573", "content": "As shown in the diagram, line segments $$a$$ and $$d$$, $$b$$ and $$e$$, $$c$$ and $$f$$ sharing the same endpoint $$A$$ are perpendicular to each other, respectively. The angle between $$a$$ and $$b$$ is $$30{}^\\circ$$, and the angle between $$e$$ and $$f$$ is $$45{}^\\circ$$. Thus, the degree of the angle between $$c$$ and $$d$$ is\uff0e question_6573-image_0"}, {"key": "6574", "content": "Given $$\\angle A$$ and $$\\angle B$$ are complementary, and $$\\angle A$$ is twice $$\\angle B$$, then $$\\angle A$$ is degrees.\n"}, {"key": "6575", "content": "Simplify the following expressions:\n$$a+a+a=$$\uff1b$$a\\times b\\times x=$$\uff0e\n$$a\\times b-c\\times d=$$\uff1b$$5\\left( x+y \\right)=$$\uff0e\n$$3a\\times \\left( m+n \\right)=$$\uff1b$$\\left( 3a+2b \\right)\\times y=$$\uff0e"}, {"key": "6576", "content": "Given $$a=5$$, $$b=3$$, calculate the following problems. If $$A=a+b$$, $$B=a-b$$, $$C=ab$$, $$D={{b}^{2}}$$, then $$A+B$$=, $$C-A$$=, $$AB+D$$=, $${{A}^{2}}-2C$$=."}, {"key": "6577", "content": "Given $$x+3y=5$$, then $$9y+3x+7=$$."}, {"key": "6578", "content": "Given $$3^{m}=4$$, $$3^{n}=5$$, find $$3^{2m+4n}=$$."}, {"key": "6579", "content": "Please fill in the blanks with $$+$$, $$-$$, $$\\times $$, $$\\div $$, or (), in any order among the four numbers $$1$$, $$7$$, $$13$$, $$13$$. The numbers can be rearranged, and each number must be used exactly once, to achieve a result of $$24$$. The correct answer is ()."}, {"key": "6580", "content": "Insert \"$$+$$\" between the following numbers (two adjacent numbers can be combined into one number) to make the equation correct. $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6=84$$, the correct answer is ( )."}, {"key": "6581", "content": "According to the rules, the symbol \"$$\\nabla $$\" represents the operation of choosing the larger number between two numbers, for example: $$5\\nabla 3=3\\nabla 5=5$$, the symbol \"$$\\triangle $$\" represents the operation of choosing the smaller number between two numbers, for example: $$5\\triangle 3=3\\triangle 5=3$$, calculate: $$\\left( 2\\nabla 1 \\right)\\triangle 10$$=."}, {"key": "6582", "content": "If $$a\\And b=a+b\\div 4$$, for example $$1\\And 12=1+12\\div 4=4$$, then $$4\\And 20=$$."}, {"key": "6583", "content": "Use the symbol \"$$\\to $$\" to represent the height relationship between the children, where the arrow points to the taller child. Thus, both \"Beibei $$\\to $$ Jingjing\" and \"Jingjing $$\\leftarrow $$ Beibei\" mean \"Jingjing is taller than Beibei\". Determine who among the five children in the diagram below is the tallest.\n question_6583-image_0"}, {"key": "6584", "content": "If it is specified that $$a\\forall b=a+b\\div a$$, then $$\\left( 1\\forall 2 \\right)\\forall 3=$$."}, {"key": "6585", "content": "Define two operations '#' and '$$\\Delta$$' as follows:\n    a#b represents 3 times the smaller of the two numbers $$a$$ and $$b$$, a$$\\Delta$$b represents 5 times the larger of the two numbers $$a$$ and $$b$$.\n    For example: $$4\\#5=4\\times 3=12,4\\Delta 5=5\\times 5=25$$. Calculate: $$\\left[\\left(6\\#5\\right)+\\left(3\\Delta 8\\right)\\right]\\times\\left[\\left(4\\Delta 2\\right)-\\left(2\\#7\\right)\\right]$$=."}, {"key": "6586", "content": "\"$$\\odot$$\" represents a new operator. It is known that $$1\\odot 4=1\\times 2\\times 3\\times 4=24$$; $$2\\odot 3=2\\times 3\\times 4=24$$; $$3\\odot 2=3\\times 4=12$$; $$\\cdots$$, according to this rule: $$2\\odot 4=$$; $$4\\odot 2=$$."}, {"key": "6587", "content": "Divide $$15$$ identical balls into three piles, with each pile having at least $$3$$ balls, there are several ways to do this."}, {"key": "6588", "content": "Eddie and Vera prepare to beautify the entire Mais Magic School (1) First, they plant willow trees on one side of a 100-meter-long pedestrian street, planting one every 10 meters, including at both ends, for a total of trees needed. (2) The distance between the Sun and Moon teaching buildings is 50 meters, Eddie now plans to plant poplar trees between these two buildings, planting one every 5 meters, totaling trees needed. (3) Vera plans to plant pine trees on one side of the straight road leading to the magic castle's gate, this road is 40 meters long, with every two trees being 5 meters apart, totaling trees needed."}, {"key": "6589", "content": "As shown in the diagram, in parallelogram $$ABCD$$, draw $$AE$$ perpendicular to $$DC$$ at point $$E$$, given $$AB=5$$ cm, and $$AE=3$$ cm, find the area of parallelogram $$ABCD$$ in square centimeters. question_6589-image_0"}, {"key": "6590", "content": "Peipei climbs from the $$6$$th floor to the $$8$$th floor in $$4$$ minutes. Using the same speed, how many minutes does it take for her to climb from the $$1$$st floor to the $$6$$th floor."}, {"key": "6591", "content": "$$8$$ students form a circle to play a game of catch with a handkerchief, as shown in the diagram, starting with student number $$1$$: question_6591-image_0 (2) First, pass clockwise $$1993$$ times, then counterclockwise $$2020$$ times, the handkerchief should be in the hands of student number ."}, {"key": "6592", "content": "The perimeter of the figure below is in centimeters.\n question_6592-image_0"}, {"key": "6593", "content": "8 students form a circle to play a game of passing a handkerchief, as shown in the figure, starting from student number 1: question_6593-image_0 (1) Passing clockwise 138 times, the handkerchief should be in the hands of student number ."}, {"key": "6594", "content": "Xiao Ke's average score in a test for Chinese, Mathematics, and English was $$94$$ points, with the average score for Chinese and Mathematics being $$95$$ points. Therefore, Xiao Ke's English score was points."}, {"key": "6595", "content": "3 little monks can copy $$48$$ pages of scriptures in $$5$$ days, at this rate, $$9$$ little monks can copy how many pages of scriptures in $$10$$ days."}, {"key": "6596", "content": "Calculate: $$505\\div 6=$$."}, {"key": "6597", "content": "Calculate: $$78\\times 24=$$."}, {"key": "6598", "content": "If a number is divided by $$21$$, the quotient is $$12$$, and the remainder is $$3$$, then the number equals."}, {"key": "6599", "content": "Xiao Hong has $$4$$ reward cards, Qisi has $$10$$ reward cards, so how many cards does Qisi need to give Xiao Hong so that they both have the same number of cards."}, {"key": "6600", "content": "The precipitation of a place in the last four months of last year is as follows, the average monthly precipitation in this place during these four months is ( ) mm.\n question_6600-image_0"}, {"key": "6601", "content": "During the addition of two three-digit numbers, Dakuan misread the tens digit $$4$$ of one addend, resulting in an answer $$30$$ less than the correct answer. What did Dakuan mistakenly read $$4$$ as?"}, {"key": "6602", "content": "When Xiao Hui was doing addition, he mistook the unit digit of one of the addends as $$9$$ instead of $$6$$, and the tens digit as $$3$$ instead of $$8$$, resulting in a calculated total of $$90$$. What should the correct result be?"}, {"key": "6603", "content": "Dazhuang was too careless when copying a number, missed out the last $$0$$, as a result, the written number was $$504$$ smaller than the original, (1) The original number is a multiple of the wrong number. (2) The original number is."}, {"key": "6604", "content": "Given $$A=a+b$$, $$B=a-b$$, $$C=2a$$, $$D={{b}^{2}}$$. When $$a=4$$, $$b=3$$, calculate $$A+B-C+D$$=."}, {"key": "6605", "content": "There are a bunch of chess pieces. Veil arranges them on the table according to the pattern of 'four black and five white', as shown in the figure below. A total of $$72$$ chess pieces are arranged. (1) How many chess pieces are repeated once, forming a group? Please circle it. question_6605-image_0"}, {"key": "6606", "content": "There is a set of Go pieces. Wei'er placed two black pieces first, and then followed a sequence of three black and two white pieces, placing a total of $$66$$ pieces. Question: What color is the $$35th$$ piece?"}, {"key": "6607", "content": "$$6$$ classmates form a circle to play a game of passing a handkerchief. As illustrated, starting from classmate $$1$$, it is passed clockwise $$20$$ times, then counter-clockwise $$3$$ times, whose hand is the handkerchief in? question_6607-image_0"}, {"key": "6608", "content": "The Ph.D. has $$7$$ ducks, and the number of chickens is $$4$$ times the number of ducks. (1) Draw a line segment diagram to represent the relationship between the number of chickens and ducks. (2) The total number of chickens and ducks raised by the Ph.D. is $$.$$"}, {"key": "6609", "content": "Please answer the following questions: (1) The figure below is part of a 3x3 magic square, $$X=$$\uff0e question_6609-image_0 question_6609-image_2 \u200b(2) The figure below is part of a 3x3 magic square, $$A=$$\uff0e question_6609-image_4 \u200b(3) The figure below is part of a 3x3 magic square, $$B=$$\uff0e"}, {"key": "6610", "content": "Last year, the grandfather was $$48$$ years older than the grandson, this year the grandfather's age is $$3$$ times that of the grandson (1) The grandfather is older than the grandson by years. (2) This year, the grandfather's age is years. question_6610-image_0"}, {"key": "6611", "content": "There is a rectangular piece of paper, the length is $$10$$ cm, and the width is $$5$$ cm, (1) cut horizontally with scissors once (as shown in the picture), adding cm; cut vertically once, adding cm. question_6611-image_0 (2) Cut horizontally and vertically with scissors twice each, then the sum of the perimeters of all the small rectangles divided is cm."}, {"key": "6612", "content": "There are two stations, east and west, in a certain town. The east station has $$84$$ buses, and the west station has $$56$$ buses. Some buses are transferred from the west station to the east station, making the number of vehicles at the east station $$4$$ times that of the west station. (1) The total number of buses at the two stations is. (2) When the number of vehicles at the east station is $$4$$ times that of the west station, the west station has buses. (3) The west station needs to transfer buses to the east station to make the number of vehicles at the east station $$4$$ times that of the west. question_6612-image_0 \u200b"}, {"key": "6613", "content": "Originally, Class B had $$6$$ times more books than Class D. Now, after giving $$20$$ books to Class D, Class B has $$5$$ books less than Class D. (1) How many more books did Class B have than Class D originally? (2) How many books did Class B and Class D originally have respectively?"}, {"key": "6614", "content": "As shown in the diagram, there are $$7$$ nails on a wooden board. A total number of different isosceles right-angled triangles can be formed using rubber bands (requirement: the vertices of the triangle must be on the nails).\n question_6614-image_0"}, {"key": "6615", "content": "On a wooden board, there are $$13$$ nails (as shown below). By using rubber bands to loop around some of these nails, shapes like triangles, squares, trapezoids, etc., can be formed. Please answer: how many squares can be formed. question_6615-image_0"}, {"key": "6616", "content": "Please find the pattern for each item in the following expressions and fill in the blank: (1) The first item is $$\\frac{3}{4}$$, the second item is $$\\frac{6}{7}$$, the third item is $$\\frac{9}{10}$$, $$ \\cdots $$ then the nth item is."}, {"key": "6617", "content": "In a plane, $$n$$ rectangles can divide the plane into a maximum number of parts."}, {"key": "6618", "content": "On the plane, $$n$$ ellipses can divide the plane into several parts."}, {"key": "6619", "content": "One triangle and $$3$$ rectangles in the same plane can divide this plane into at most parts."}, {"key": "6620", "content": "$$3$$ triangles and $$2$$ circles in the same plane can divide the plane into at most parts."}, {"key": "6621", "content": "Using $$14$$ matchsticks, place a number in each square within a box, making two numbers where all digits are different, the maximum result of the addition equation is, and the minimum is. question_6621-image_0"}, {"key": "6622", "content": "Using $$15$$ matchsticks, place a number in each square within a frame, forming three numbers where all digits are different, making the result of the addition the largest possible and the smallest possible. question_6622-image_0"}, {"key": "6623", "content": "[Warm-up 1] We can use matchsticks to form the numbers $$0\\sim 9$$. If you are given $$11$$ matchsticks and use them all: (1) The largest three-digit number you can form is. (2) The smallest three-digit number you can form is."}, {"key": "6624", "content": "[Warm-up Exercise 2] We can use matchsticks to form the numbers $$0\\sim 9$$. If you are given $$10$$ matchsticks (all to be used), the largest number that can be formed is, and the smallest number that can be formed is. question_6624-image_0"}, {"key": "6625", "content": "[Warm-up before class 3] With $$10$$ matchsticks (using all of them), the smallest number that can be formed with each digit being different is. question_6625-image_0"}, {"key": "6626", "content": "6 natural numbers: 234, 530, 658, 54367, 90816, 342125.\n(1) The number that can be divided by 2 is ___, the number that can be divided by 5 is ___.\n(2) The number that can be divided by 4 is ___, the number that can be divided by 25 is ___.\n(3) The number that can be divided by 8 is ___. The number that can be divided by 125 is ___"}, {"key": "6627", "content": "$$\\overline{173\\square }$$ is a four-digit number. The teacher fills in two digits into this $$\\square $$ one after another, and the resulting two four-digit numbers can respectively be divided by $$9$$ and $$11$$. The sum of the two digits filled in by the teacher is."}, {"key": "6628", "content": "Calculate: (1) $$\\frac{1}{5}+\\frac{2}{5}=$$\uff0e(2) $$\\frac{2}{9}+\\frac{4}{9}=$$\uff0e(3) $$\\frac{3}{7}-\\frac{2}{7}=$$\uff0e(4) $$\\frac{5}{6}-\\frac{1}{6}=$$\uff0e"}, {"key": "6629", "content": "Trees are planted on both sides of a $$50$$ meter long road, with a tree planted every $$5$$ meters, including at both ends, totaling the number of trees that can be planted. (The width of the tree is negligible)"}, {"key": "6630", "content": "Chang Hao and Gu Li competed in a Go game, the one who wins three games first will claim the victory of the match. If Chang Hao eventually wins, then there are several possible scenarios for the progress of the match."}, {"key": "6631", "content": "$$(56\\div5)\\div(28\\div15)=$$"}, {"key": "6632", "content": "$$999\\times44\\div66=$$"}, {"key": "6633", "content": "A ray $$OA$$, if two more rays $$OB$$ and $$OC$$ are drawn from point $$O$$, making $$\\angle AOB=72{}^\\circ $$, and $$\\angle BOC$$ is $$3$$ times $$\\angle AOC$$, then the degree of $$\\angle BOC$$ is $${}^\\circ$$ or $${}^\\circ$$\uff0e(Fill in from smallest to largest)"}, {"key": "6634", "content": "As shown in the diagram, it is known that $$\\angle ACE=4\\angle ECB$$. Then, the degree of $$\\angle DCE$$ is $${}^\\circ$$. question_6634-image_0"}, {"key": "6635", "content": "The image contains an acute angle, and an obtuse angle. question_6635-image_0"}, {"key": "6636", "content": "As shown in the figure, $$OB$$ bisects $$\\angle AOC$$, and $$\\angle 4=4\\angle 2$$, $$\\angle 3=3\\angle 2$$. Find $$\\angle 1=$$$${}^\\circ$$, $$\\angle 2=$$$${}^\\circ$$, $$\\angle 3=$$$${}^\\circ$$, $$\\angle 4=$$$${}^\\circ$$\uff0e question_6636-image_0"}, {"key": "6637", "content": "As shown in the figure, the vertex $$O$$ of $$\\angle AOB$$ is on line $$l$$. It is known that the sum of all angles less than a straight angle in the figure is $$400$$ degrees, then $$\\angle AOB$$ is ____ degrees. question_6637-image_0"}, {"key": "6638", "content": "As shown in the figure, $$\\angle AOD=7\\angle BOC$$, then the degree of $$\\angle DOC$$ is $${}^\\circ$$\uff0e question_6638-image_0"}, {"key": "6639", "content": "A said to B: \"My current age is twice your age when I was your current age; when you reach my current age, the sum of our ages will be $$81$$ years,\" A's current age is years, and B's current age is years."}, {"key": "6640", "content": "Given the sum of the first $$15$$ numbers of an arithmetic sequence is $$450$$, and the sum of the first $$20$$ numbers of the sequence is $$750$$, what is the $$13$$th number of the sequence?"}, {"key": "6641", "content": "Compute: $$432\\div (8\\times 9)=$$\uff0e\n$$21\\times 15\\div 5=$$\uff0e\n$$(54\\times 24)\\div (9\\times 4)=$$\uff0e"}, {"key": "6642", "content": "At the end of the year shopping festival, mom is preparing to buy new appliances for the home, a soy milk maker for $$198$$ yuan, a vacuum cleaner for $$369$$ yuan, mom should approximately prepare (  ) yuan."}, {"key": "6643", "content": "Calculate: (1) $$23\\times 4\\times 25=$$\uff0e\n(2) $$125\\times 13\\times 8=$$\uff0e\n(3) $$12\\times 25=$$\uff0e\n(4) $$48\\times 125=$$\uff0e\n(5) $$125\\times (80+4)=$$\uff0e\n(6) $$(100-8)\\times 25=$$\uff0e"}, {"key": "6644", "content": "Dr. Zhang's ID number is $$420111198005122683$$, Dr. Zhang's gender is , the date of birth is ."}, {"key": "6645", "content": "The following image shows an incomplete 4x4 magic square. Fill in $$A$$ and $$B$$ in the blanks accordingly. (Fill in the order) question_6645-image_0"}, {"key": "6646", "content": "The numbers marked in the below figure represent the length of each side, in centimeters. Its perimeter is in centimeters. question_6646-image_0"}, {"key": "6647", "content": "A vegetable plot, shaped as shown in the figure, is known to have $$a=b=30$$ meters, $$c=12$$ meters, the perimeter of this plot is meters. question_6647-image_0"}, {"key": "6648", "content": "A large rectangle is divided into $$16$$ smaller rectangles, with the perimeter of $$4$$ pieces already marked. Then the perimeter of the large rectangle is in centimeters. question_6648-image_0"}, {"key": "6649", "content": "A large rectangle has been divided into several smaller rectangles. If the perimeters of some of these smaller rectangles are given (as shown in the diagram, in centimeters), then the perimeter of the largest rectangle is. question_6649-image_0"}, {"key": "6650", "content": "Two squares of the same size are combined into a rectangle, and the perimeter of the rectangle is $$6$$ cm less than the sum of the perimeters of the original two squares. The perimeter of one of the original squares is in cm."}, {"key": "6651", "content": "$$8$$ identical small rectangles form a large rectangle. The perimeter of the large rectangle is $$84$$ cm, and the perimeter of the small rectangle is in cm. question_6651-image_0"}, {"key": "6652", "content": "Using a rectangle of length $$9$$ cm and width $$3$$ cm to form the shape below, the perimeter of the obtained shape is in centimeters. question_6652-image_0"}, {"key": "6653", "content": "According to the pattern, what is the next term for each of the following series? And what is the nth term? (1) 4, 7, 10, 13, ... (2) 2, 5, 4, 10, 6, 15, ... (3) 3, 5, 9, 15, 23, ..."}, {"key": "6654", "content": "Han Lei insists on reading every day, and the number of pages he reads each day increases successively, with the difference in the number of pages read between two consecutive days being equal. It is known that on the $$2$$nd day he read $$5$$ pages, and on the $$9$$th day he read $$26$$ pages, completing a book in $$10$$ days. (1) The total number of pages read on the $$2$$nd and $$9$$th days is . (2) Thus, the total number of pages in this book is ."}, {"key": "6655", "content": "Classes A and B went tree planting together, with Class A having $$6$$ groups and Class B having $$4$$ groups. It is known that on average, each group in Class A planted $$9$$ trees, and together, both classes averaged $$7$$ trees per group. (1) The total number of trees planted by Class A. (2) The total number of trees planted by both classes. (3) The total number of trees planted by Class B. (4) On average, the number of trees planted per group by Class B."}, {"key": "6656", "content": "The teacher places $$12$$ identical flowers into three vases of red, yellow, and blue, with at least one flower in each vase, there are different ways to do so. question_6656-image_0"}, {"key": "6657", "content": "There are three different denominations of coins in a place, as shown in the figure, supposing you have exactly the following four coins. You can form several different amounts of money. question_6657-image_0"}, {"key": "6658", "content": "Perform calculations vertically: (1) $$23\\times 14=$$ (2) $$25\\times 41=$$"}, {"key": "6659", "content": "Set up the division vertically: (1) $$420\\div 5$$ = (2) $$540\\div 3$$ ="}, {"key": "6660", "content": "The array in the figure is made up of $$77$$ even numbers, among which $$20$$, $$22$$, $$24$$, $$36$$, $$38$$, $$40$$, these six numbers are enclosed by a parallelogram, and their sum is $$180$$. After translating this parallelogram up and down, left and right, it encloses another six numbers in the array, and if the sum of these six numbers is $$660$$. Then, the number located at the top left corner of the parallelogram is.\n question_6660-image_0"}, {"key": "6661", "content": "Observe the calendar below, frame five numbers with a cross. If the sum of the five numbers is $$80$$, then the number in the middle is.\n question_6661-image_0"}, {"key": "6662", "content": "As shown in the diagram, starting from $$9$$, consecutive natural numbers are filled into a table according to a rule. The questions are:\n(1) In which row and column should $$135$$ be placed;\n(2) What is the number in the $$25$$th row and $$3$$rd column.\n question_6662-image_0"}, {"key": "6663", "content": "Starting with $$1$$, arrange the consecutive natural numbers as shown in the diagram, and frame five numbers with a cross. The sum of these five numbers equals: ( )\n question_6663-image_0"}, {"key": "6664", "content": "Starting from $$1$$, consecutive natural numbers are arranged according to the rules as shown below. By striking out five numbers with the \"$$X$$\" as shown in the figure, so that the sum of these five numbers equals $$240$$, the largest of these five numbers is.\n question_6664-image_0"}, {"key": "6665", "content": "As shown in the figure, arrange the even numbers $$2$$, $$4$$, $$6$$, $$8\\ldots $$, into $$5$$ columns. The columns from left to right are the $$1st$$, $$2nd$$, $$3rd$$, $$4th$$, and $$5th$$ columns, respectively. Please answer:\n($$1$$) In which row and column is $$100$$?\n($$2$$) What number is in the $$20th$$ row and $$2nd$$ column?\n question_6665-image_0"}, {"key": "6666", "content": "Starting from the natural number $$1$$, arrange according to the pattern shown in the figure below. Define the position in the figure at row $$m$$, column $$n$$ as $$\\left(m, n\\right)$$, such as the position of the natural number $$8$$ is $$\\left(2, 3\\right)$$, then the position of the natural number $$176$$ is recorded as.\n. question_6666-image_0"}, {"key": "6667", "content": "As shown in the figure, consecutive natural numbers starting from $$1$$ are filled into a table according to a pattern. $$100$$ should be placed at the row and column; the number at the $$15$$th row and $$4$$th column is.\n question_6667-image_0"}, {"key": "6668", "content": "Calculate: $$572=$$$$_{12}$$$$=$$$$_{16}$$."}, {"key": "6669", "content": "A certain print shop's printer broke, it can only print $$0$$ and $$1$$, so when it prints page numbers, they can only be $$1$$, $$10$$, $$11$$, $$100$$, $$101\\ldots \\ldots $$, so the $$100$$th page number is."}, {"key": "6670", "content": "Calculate in base 7 $${{\\left( 314 \\right)}_{7}}\\times {{\\left( 233 \\right)}_{7}}=\uff08$$$$\uff09_{7}$$."}, {"key": "6671", "content": "Calculate: $${{(567)}_{10}}=$$()$$_{8}$$$$=$$()$$_{5}$$$$=$$()$$_{2}$$."}, {"key": "6672", "content": "$$\\frac{1}{2}\\times \\frac{3}{4}\\times \\frac{5}{6}\\times \\cdots \\times \\frac{2017}{2018}\\times \\frac{4}{2015}\\times \\frac{6}{2013}\\times \\frac{8}{2011}\\times \\cdots \\frac{2016}{3}=$$\uff0e"}, {"key": "6673", "content": "Calculate: $$\\left( 1+\\frac{11}{31}+\\frac{13}{34}+\\frac{15}{37} \\right)\\times \\left( \\frac{9}{28}+\\frac{11}{31}+\\frac{13}{34}+\\frac{15}{37} \\right)$$\n$$-\\left( 1+\\frac{9}{28}+\\frac{11}{31}+\\frac{13}{34}+\\frac{15}{37} \\right)\\times \\left( \\frac{11}{31}+\\frac{13}{34}+\\frac{15}{37} \\right)=$$."}, {"key": "6674", "content": "Calculate: $$\\frac{1}{4-\\dfrac{1}{3+\\dfrac{1}{2-\\dfrac{1}{1+\\dfrac{1}{2}}}}}$$=\uff0e"}, {"key": "6675", "content": "Calculate: $$\\left( \\frac{1}{3}+\\frac{1}{5}+\\frac{1}{7}+\\frac{1}{9} \\right)\\times \\left( \\frac{1}{5}+\\frac{1}{7}+\\frac{1}{9}+\\frac{1}{11} \\right)$$$$-\\left( \\frac{1}{3}+\\frac{1}{5}+\\frac{1}{7}+\\frac{1}{9}+\\frac{1}{11} \\right)$$$$\\times \\left( \\frac{1}{5}+\\frac{1}{7}+\\frac{1}{9} \\right)$$=\uff0e"}, {"key": "6676", "content": "Calculate: $$\\dfrac{2\\dfrac{2}{3}+1\\dfrac{3}{5}+1\\dfrac{1}{7}+\\dfrac{8}{9}}{\\dfrac{1}{3}+\\dfrac{1}{5}+\\dfrac{1}{7}+\\dfrac{1}{9}}=$$."}, {"key": "6677", "content": "Second grade chorus formation, with a total of $$81$$ people, needs to add one more row and one column, how many more people are needed. question_6677-image_0"}, {"key": "6678", "content": "Grandpa is $$74$$ years old this year. When Grandpa was as old as Dad is now, Dad was only $$18$$ years old. So, how old is Dad this year? question_6678-image_0"}, {"key": "6679", "content": "Place $$10$$ identical radishes into three identical baskets, where each basket must contain some, and each basket can contain up to $$5$$ radishes. In total, there are different ways to do this."}, {"key": "6680", "content": "The number of people in Class B is exactly $$4$$ times the number of people in Class A. If $$30$$ people are transferred from Class B to Class A, then the number of people in Class A and Class B will be the same. Class B originally had people."}, {"key": "6681", "content": "$$49\\times 34+49\\times 23+57\\times 51$$=.$$22\\times 31+66\\times 23$$=."}, {"key": "6682", "content": "Class 2 needs to choose a park to visit for the Children's Day outing, and the voting results of the whole class are shown in the figure. question_6682-image_0 (3) Estimate where Class 2 will eventually go for the outing based on the voting results. question_6682-image_1"}, {"key": "6683", "content": "Divide $$6$$ identical erasers among $$3$$ kids, with each kid getting at least one eraser, there are different ways of division. question_6683-image_0"}, {"key": "6684", "content": "Xiao Mao and Da Mao each have some candies. If Da Mao gives Xiao Mao 6 candies, then Da Mao will have 2 fewer candies than Xiao Mao. If Xiao Mao gives Da Mao 6 candies, then Da Mao will have 4 more candies than three times the amount of Xiao Mao\u2019s candies. (1) When the number of Da Mao's candies is more than three times that of Xiao Mao\u2019s candies by 4, Da Mao has more candies than Xiao Mao by __(candies). (2) Originally, Da Mao had __(candies), and Xiao Mao had __(candies)."}, {"key": "6685", "content": "While patrolling, the police found a thief who was stealing. They were $$560$$ meters apart. At this point, the thief ran away at a speed of $$200$$ meters per minute, and the police chased at a speed of $$240$$ meters per minute. One minute later, their distance was reduced by meters. question_6685-image_0"}, {"key": "6686", "content": "The police found a thief stealing while on patrol, they were $$560$$ meters apart. At this time, the thief fled at a speed of $$200$$ meters per minute, while the police chased at a speed of $$240$$ meters per minute. Can the police catch the thief? question_6686-image_0"}, {"key": "6687", "content": "On a plane, $$2$$ points can determine $$1$$ straight line. Then $$3$$ points can determine ( ) straight lines."}, {"key": "6688", "content": "Using $$14$$ matchsticks, place a number in each square within a box to form two numbers, among which all the digits are distinct, to form an addition equation with the maximum and minimum possible results. question_6688-image_0"}, {"key": "6689", "content": "Definition: $$a\\Delta b=a\\times b-3\\times b, a\\Theta b=4\\times a-b\\div a$$\uff0eCalculate: $$\\left( 4\\Delta 3 \\right)\\Delta \\left( 2\\Theta 6 \\right)=$$\uff0e"}, {"key": "6690", "content": "It is known that the symbol $$\\theta$$ defines a new operation, and it satisfies $$10\\theta 1=31$$, $$1\\theta 10=13$$, $$100\\theta 1=301$$, $$1\\theta 100=103$$. Then, $$10\\theta 5=$$, $$5\\theta 10=$$."}, {"key": "6691", "content": "A primary school held a sports meeting, and the students formed a square formation to participate in a group exercise performance, forming a square formation of $$7$$ rows and $$7$$ columns. If one row and one column are removed, how many people need to be removed?"}, {"key": "6692", "content": "There is a team of soldiers, formed into a solid square formation. The outermost layer has a total of $$76$$ people. How many people are there in this square formation in total."}, {"key": "6693", "content": "A group of students are arranged in a three-layer hollow square formation, with 9 additional people. If the hollow part increases by two layers, there will be 15 fewer people. There are students."}, {"key": "6694", "content": "The operation represented by $$\\odot$$ is defined as follows, $$a\\odot b=8\\times a-b$$. Calculate: (1) $$\\left( 4\\odot 2 \\right)\\odot 3$$; (2) $$4\\odot \\left( 2\\odot 3 \\right)$$."}, {"key": "6695", "content": "Generally, we believe that whoever is pointed at by a handgun is in danger. Therefore,\nRule: police question_6695-image_0 thief $$=$$ police, police question_6695-image_1 thief $$=$$ thief.\nHence: (hunter question_6695-image_2 rabbit) question_6695-image_3 (goat question_6695-image_4 cabbage) $$=$$ ( )."}, {"key": "6696", "content": "$$a\\vee b$$ represents the larger of the two numbers $$a$$ and $$b$$, $$a\\wedge b$$ represents the smaller of the two numbers $$a$$ and $$b$$. Then $$\\left( 2006\\vee 2008 \\right)\\wedge \\left( 2007\\vee 2009 \\right)$$ equals ( )."}, {"key": "6697", "content": "Through any two points on a plane, you can draw ( ) straight line(s)."}, {"key": "6698", "content": "Two line segments, one measuring $$10$$ cm and the other $$8$$ cm, are joined end to end. Their total length is ( )."}, {"key": "6699", "content": "A square, adding up its four sides, the unit of the result could be ( )."}, {"key": "6700", "content": "Answer the following questions: (1) Eddie used a 28 centimeters long ribbon to exactly frame a photo of a Big Eye Monster with a colorful edge. The side length of this square frame is centimeters. question_6700-image_0 question_6700-image_2 (2) Vee used a 40 centimeters long ribbon to exactly frame a photo of a Big Eye Monster with a colorful edge. The width of this rectangular frame is 5 centimeters, and the length of this frame is centimeters."}, {"key": "6701", "content": "The perimeters of these two shapes are, respectively, (unit: centimeters) question_6701-image_0"}, {"key": "6702", "content": "The perimeter of this shape is (unit: cm) question_6702-image_0"}, {"key": "6703", "content": "The perimeter of the figure below is. question_6703-image_0"}, {"key": "6704", "content": "Complete the following questions: (1) A certain animated series has a total duration of $$540$$ minutes, with each episode lasting $$20$$ minutes. This animated series has a total of __ episodes. (2) A pearl necklace factory receives $$410$$ pearls per day, and it takes $$40$$ pearls to make one necklace. How many pearl necklaces can this factory produce at most per day? Are there any pearls left over, and if so, how many are left over?"}, {"key": "6705", "content": "Set up and calculate vertically: (1) The age of an ancient tree is $$276$$ years, Xiao Ming's age is $$12$$ years, the age of this ancient tree is times the age of Xiao Ming. (2) In the National Day military parade, a rectangular formation of the marching team has $$350$$ people, if there are $$25$$ people per row, then there are total rows."}, {"key": "6706", "content": "To welcome new students, the Xueersi restaurant launched a new roasted chicken leg machine. It is known that $$3$$ machines can roast $$600$$ chicken legs in $$4$$ days, calculating at this speed. (1) The number of chicken legs roasted by $$1$$ machine in $$1$$ day. (2) The number of chicken legs roasted by $$5$$ machines in $$1$$ day. (3) The number of chicken legs roasted by $$5$$ machines in $$3$$ days."}, {"key": "6707", "content": "A doctorate wants to plant a pine tree every $$10$$ meters on one side of an acceleration track with a total length of $$2700$$ meters (planting at both ends), and plant a willow tree every $$2$$ meters between two adjacent pine trees. The number of willow trees planted."}, {"key": "6708", "content": "On one side of the road, there is a poplar tree every $$8$$ meters. Xiaoluo rides a bicycle from school to home (the speed of riding remains the same). It takes $$1$$ minute to ride from the $$1$$st tree to the $$6$$th tree. It took Xiaoluo a total of $$10$$ minutes to ride from school to home. The distance from Xiaoluo's home to the school is meters. (The width of the trees is negligible)"}, {"key": "6709", "content": "(1)When planting trees on one side of a road that is $$72$$ meters long, with trees at both ends, a total of $$9$$ trees were planted. The distance between each pair of adjacent trees is the same, with one tree planted every few meters. (The width of the trees is negligible) (2)When planting trees on both sides of a road that is $$63$$ meters long, without trees at both ends, a total of $$16$$ trees were planted. Trees are planted at equal intervals, with one tree planted every few meters. (The width of the trees is negligible)"}, {"key": "6710", "content": "$$123+58+47=$$"}, {"key": "6711", "content": "A string of beads, arranged in the order of $$3$$ black beads, $$2$$ white beads, $$3$$ black beads, $$2$$ white beads... Thus, the color of the $$38^{th}$$ bead is."}, {"key": "6712", "content": "Xiaomei has a box of black and white beads, and she arranges the beads as follows: (1) The 18th bead should be this color; (2) There are a total of white beads among the first 20 beads. question_6712-image_0"}, {"key": "6713", "content": "Black pearls and white balls total $$101$$, strung together in the following arrangement: ... In this string of pearls, the last pearl should be of color, and this color of pearls totals in the string."}, {"key": "6714", "content": "Among integers, numbers that can be divided by $$2$$ are called even numbers, and those that cannot be divided by $$2$$ are called odd numbers. Can you quickly judge which of the following numbers are odd and which are even? $$8$$, $$5$$, $$17$$, $$54$$, $$894$$, $$271$$, $$9865$$, $$9752$$, $$15782$$, $$94113$$, $$18929$$ The number of odd numbers is."}, {"key": "6715", "content": "Determine the parity of the results of the following expressions: ($$1$$) $$58+96$$ ($$2$$) $$73+122$$ ($$3$$) $$35+49$$ ($$4$$) $$84-18$$ ($$5$$) $$515-232$$ ($$6$$) $$189-45$$ ($$7$$) $$437+2782-399-413+1015$$ The expressions that result in an odd number are: ."}, {"key": "6716", "content": "Determine the parity of the results for the following expressions: $$\uff081\uff092\\times 37$$$$\uff082\uff094\\times 54$$$$\uff083\uff093\\times 53$$$$\uff084\uff093\\times 44$$ The number of expressions that result in an odd number is:"}, {"key": "6717", "content": "Calculate (1) 26$$\\times$$99= (2) 123$$\\times$$999= (3) 37$$\\times$$103="}, {"key": "6718", "content": "Calculate: $$800\\div 25\\div 8=$$\uff0e"}, {"key": "6719", "content": "The area of a square is $$81$$ square meters, the side length is meters. question_6719-image_0"}, {"key": "6720", "content": "(2) $$1200$$ $$\text{cm}^2$$ = $$\text{dm}^2$$; $$3800$$ $$\text{dm}^2$$ = $$m^2$$."}, {"key": "6721", "content": "Unit conversion: (1) $$5{{\\text{m}}^{2}}=$$$$\\text{d}{{\\text{m}}^{2}}$$; $$3\\text{d}{{\\text{m}}^{2}}=$$$$\\text{c}{{\\text{m}}^{2}}$$."}, {"key": "6722", "content": "Everyone arrived at the deer park again. Eddie counted and found there were a total of $$24$$ deer, including sika deer and giraffes, and the number of sika deer was $$4$$ less than $$3$$ times the number of giraffes. So, how many sika deer and giraffes did Eddie see respectively? Sika Deer: ____ Giraffes: ____"}, {"key": "6723", "content": "There are three types of monkeys on Monkey Mountain, which are the golden snub-nosed monkey, the macaque, and the black leaf monkey. There are a total of $$56$$ monkeys, and the number of golden snub-nosed monkeys is $$2$$ times that of macaques, while the number of black leaf monkeys is $$4$$ times that of macaques. So, how many monkeys are there of each type? Golden snub-nosed monkeys: ____ Macaques: ____ Black leaf monkeys: ____"}, {"key": "6724", "content": "Today, there are so many tourists visiting Monkey Mountain. Wei counted them all, including elderly people, youths, and children, totaling $$50$$ people. Among them, the number of youths is $$2$$ times the number of elderly, and the number of children is $$3$$ times the number of elderly plus $$2$$ people. So, how many elderly people, youths, and children are there respectively? Elderly: people Youths: people Children: people"}, {"key": "6725", "content": "The professor came to the tropical fish aquarium with Eddie and Vi. In one of the aquariums, there lived $$37$$ fish in total, in three different colors. Eddie noticed that the number of red fish was twice that of the blue ones, and the number of green fish was three times that of red ones plus one more. How many fish are there of each color? Red: fish Blue: fish Green: fish"}, {"key": "6726", "content": "As shown in the figure, there are three circles $$A$$, $$B$$, and $$C$$ on the same straight line. A frog jumps back and forth among these three circles. It starts from $$A$$ and after jumping 4 times, it returns to $$A$$ with different ways of jumping. \n question_6726-image_0"}, {"key": "6727", "content": "$$A$$, $$B$$, $$C$$, $$D$$ four people are playing a passing game. Initially, the ball is with $$A$$, who can pass it to $$B$$, $$C$$, or $$D$$. The question is, after $$3$$ passes, how many scenarios are there for the ball to return to $$A$$."}, {"key": "6728", "content": "Fill in the blanks in the diagram with appropriate numbers to make it a 3x3 magic square. question_6728-image_0 The second number in the third row is:"}, {"key": "6729", "content": "Fill in the appropriate numbers in the squares in the diagram to make it a three-order magic square. question_6729-image_0 The second number in the third row is:"}, {"key": "6730", "content": "In the figure below, there are a total of triangles. question_6730-image_0"}, {"key": "6731", "content": "As shown in the diagram, there is a line segment.\n question_6731-image_0"}, {"key": "6732", "content": "The following picture requires at least pens to complete. question_6732-image_0"}, {"key": "6733", "content": "The following is a floor plan of a children's park. The entrance/exit should be located at point or point to ensure that every path can be walked without repetition. question_6733-image_0"}, {"key": "6734", "content": "To draw the image below in one stroke, the starting point is, and the end point is. question_6734-image_0"}, {"key": "6735", "content": "The classmates of Class 1, Grade 3 headed to the zoo after getting their mineral water. They saw the zookeeper distributing work uniforms to the staff. If each person is given $$2$$ pieces, there would be $$20$$ pieces left; if each person is given $$4$$ pieces, there would be $$4$$ pieces left. Thus, there are a total of workers, and the zookeeper prepared pieces of clothing."}, {"key": "6736", "content": "Students of Class 2, Grade 3 set off towards the monkey mountain after getting their bottled water. They saw the Monkey King distributing peaches to the little monkeys. If each little monkey gets $$4$$ peaches, there will be $$5$$ peaches left. However, if each little monkey gets $$5$$ peaches, there would be a shortage of $$4$$ peaches. So, how many little monkeys are there, and how many peaches did the Monkey King prepare? question_6736-image_0"}, {"key": "6737", "content": "The Young Pioneers' expansion mission is to plant trees. If every Young Pioneer digs $$5$$ tree pits, there will be $$3$$ tree pits short; if every Young Pioneer digs $$6$$ tree pits, there will be $$13$$ tree pits short. There are a total of Young Pioneers, and a total of tree pits need to be dug."}, {"key": "6738", "content": "30 students from Class 3, Grade 3, participate in the Chinese interest group, and 45 students participate in the Math interest group, with 20 students participating in both groups. There are students in this class who have participated in interest groups."}, {"key": "6739", "content": "The first class of the third grade has $$47$$ students. Each student has participated in at least one of the interest groups, either drawing or singing. There are $$20$$ students who have joined the drawing interest group, $$10$$ students have joined both groups, and some have joined the singing interest group."}, {"key": "6740", "content": "The school organized a picking activity, with a total of $$46$$ participants. There were $$18$$ people who picked only cherries, $$7$$ people who picked both cherries and apricots, and $$6$$ people who picked neither cherries nor apricots. Question: How many people picked only apricots."}, {"key": "6741", "content": "Grade 3 Class 3 has $$12$$ people who can both play basketball and play soccer, $$25$$ people can play basketball, $$19$$ people can't play soccer, then the number of people in Grade 3 Class 3 who can't play either basketball or soccer is."}, {"key": "6742", "content": "Each student in first class of grade four has bought at least one book. There are $$30$$ students who bought storybooks, $$12$$ students who bought comic books, and $$6$$ students who bought both. How many students are in the class."}, {"key": "6743", "content": "A class has $$40$$ students, $$15$$ students join the math group, $$18$$ students join the composition group, and there are $$10$$ students who join both groups. There are students who join neither group."}, {"key": "6744", "content": "There are some pancakes in the basket, Da Mao ate half of it plus half a pancake, Er Mao then ate half of the remaining plus half a pancake, San Mao also ate half of the remaining plus half a pancake, and in the end, only $$2$$ were left. Please guess: how many pancakes were originally in the basket."}, {"key": "6745", "content": "There were $$24$$ birds on three trees. $$3$$ birds flew from the first tree to the second tree, and $$5$$ birds flew from the second tree to the third tree. Eventually, the number of birds on the three trees became equal. How many birds were there on each tree originally? First tree: birds Second tree: birds Third tree: birds"}, {"key": "6746", "content": "Compare the sizes of the following two numbers:\n$$32.107$$$$32.170$$;\n$$7.0899$$$$11.0019$$;\n$$198.1611$$$$198.1601$$;\n$$7.6785$$$$767.85$$\uff0e"}, {"key": "6747", "content": "To expand $$9.3936$$ by a thousand times its original value, you only need to move the decimal point places, resulting in ."}, {"key": "6748", "content": "Calculate: $$1.03\\times 1000=$$; $$9.35\\div100=$$."}, {"key": "6749", "content": "Xiao Ai, Xiao Pi, and Xiao Si are comparing their heights. It is known that Xiao Ai is taller than Xiao Pi, and Xiao Si is taller than Xiao Ai. Therefore, their heights from tallest to shortest are ( )."}, {"key": "6750", "content": "As shown in the figure, it is known that $$\\angle 2=124{}^\\circ $$, $$\\angle 1$$=\u00b0. question_6750-image_0"}, {"key": "6751", "content": "Which of the following images can be used to draw a $$75{}^\\circ $$ angle."}, {"key": "6752", "content": "There is a small ball in the box. Three kids guess the color. Damao says, \"The ball is red.\" Ermou says, \"My thought is the same as Damao.\" Xiaomao says, \"The ball is green.\" Only one person guesses wrong, so the color of the ball is red."}, {"key": "6753", "content": "A, B, and C are teaching Mathematics, Chinese, and Science in schools located in Nanjing, Suzhou, and Wuxi respectively. It is known that: (1) A does not work in Nanjing, and B does not work in Suzhou. (2) The person working in Nanjing does not teach Science. (3) The person working in Suzhou teaches Mathematics. (4) B does not teach Chinese. Question: Where is A working and what subject does he teach? Where is B working and what subject does he teach? Where is C working and what subject does he teach?"}, {"key": "6754", "content": "After graduation, three classmates chose different professions, among them one became a journalist. Once when asked about their professions, A said: \"I am a journalist.\" B said: \"I am not a journalist.\" C said: \"A is lying.\" If only one of their statements is true, then who is the journalist (fill in A or B or C)."}, {"key": "6755", "content": "Zhengnan's father is $$50$$ years old this year, and Zhengnan is $$14$$ years old. When Zhengnan was a certain age, his father's age was exactly $$5$$ times the age of Zhengnan."}, {"key": "6756", "content": "As shown in the figure, please fill in the appropriate numbers in the blanks in the diagram to make the multiplication vertical equation valid. The result of this multiplication equation is 4 0 \u00d7 9 4 7 8"}, {"key": "6757", "content": "Given a sequence $$5$$, $$11$$, $$17$$, $$23$$, $$29$$, $$\\cdots$$, then the 31st number in this sequence is."}, {"key": "6758", "content": "Given a sequence of numbers $$4$$, $$7$$, $$10$$, $$13$$, $$16$$, $$\\cdots$$, then the 11th number in this sequence is."}, {"key": "6759", "content": "There is a series of numbers $$2$$, $$6$$, $$10$$, $$14\\cdots $$, $$122$$, then this series has a total of numbers."}, {"key": "6760", "content": "The arithmetic sequence $$4$$, $$7$$, $$10$$, $$13$$, $$\\cdots $$, $$604$$. $$604$$ is the number in this sequence."}, {"key": "6761", "content": "Arithmetic sequence $$4$$, $$7$$, $$10$$, $$13$$, $$\\cdots$$, $$604$$. The $$301$$st number is."}, {"key": "6762", "content": "Compute: $$3+6+9+12+\\cdots +57=$$\uff0e"}, {"key": "6763", "content": "Calculate: $$4+11+18+25+\\cdots +74=$$."}, {"key": "6764", "content": "Bit by bit, read a storybook. On the first day, $$30$$ pages were read. Starting from the second day, the number of pages read each day was $$4$$ pages more than the previous day. On the last day, $$70$$ pages were read, just enough to finish the book. Then, the total number of pages in this book is."}, {"key": "6765", "content": "Find the pattern and fill in the numbers: $$24$$, $$21$$, $$18$$, , , $$9$$\uff0e"}, {"key": "6766", "content": "Fill in the appropriate number in the $$\\square$$ of the multiplication vertical format below to make the vertical format valid, where one digit of the multiplier is . question_6766-image_0"}, {"key": "6767", "content": "In the number puzzle below, $$a=$$. 3 7 \u00d7 a 1 a 8"}, {"key": "6768", "content": "Carefully observe the calendar in the figure below, and write the answers to the questions on the line. question_6768-image_0 (1) August 6, 2020, is a week_____, and this month has ____ Saturdays. (2) August 2020 has ____ Tuesdays."}, {"key": "6769", "content": "To want to calculate multiplication first, parentheses must be added ( )."}, {"key": "6770", "content": "Using the four numbers $$2$$, $$3$$, $$5$$, $$6$$, insert $$+$$, $$-$$, $$\\times $$, $$\\div $$ or ( ) between them to make the result equal to $$24$$ (each number can only be used once). The correct answer is ( )."}, {"key": "6771", "content": "Insert a \u201c+\u201d or \u201c-\u201d between each pair of the following numbers to make the equation valid.\n$$6\\bigcirc5\\bigcirc4\\bigcirc3\\bigcirc2\\bigcirc1\uff1d1$$"}, {"key": "6772", "content": "Fill in \"$$+$$, $$-$$, $$\\times$$, $$\\div$$\" and parentheses among the numbers below to make the following equation true. The correct option is ( ).\n$$6$$ $$6$$ $$6$$ $$6$$ = $$8$$"}, {"key": "6773", "content": "Using the four numbers $$3$$, $$9$$, $$9$$, $$5$$, insert $$+$$, $$-$$, $$\\times $$, $$\\div $$, and ( ) between them, so that the result equals $$24$$ (each number can only be used once) ( )."}, {"key": "6774", "content": "As shown in the figure, from point $$A$$ to point $$B$$, there are a total of different shortest routes. question_6774-image_0"}, {"key": "6775", "content": "Wei Er wants to go from home to Xueersi, please help Wei Er count, in total there are several different shortest routes. question_6775-image_0"}, {"key": "6776", "content": "As shown in the diagram, there is the shortest path from $$A$$ to $$B$$ along the line segment, not passing through $$C$$. question_6776-image_0"}, {"key": "6777", "content": "As shown in the diagram, all the small segments in the diagram are of equal length. There are a total of $$3$$ shortest routes from point $$A$$ to point $$B$$. question_6777-image_0"}, {"key": "6778", "content": "Xiao Ming has two routes from home to school. The correct statement is ( ). question_6778-image_0"}, {"key": "6779", "content": "Chickens and rabbits are in the same cage, with a total of $$42$$ feet and $$11$$ heads. There are several chickens and several rabbits."}, {"key": "6780", "content": "In a parking lot, there are sedans (four wheels) and motorcycles (two wheels) adding up to a total of $$32$$ vehicles, with a total of $$108$$ wheels. Therefore, the number of sedans and the number of motorcycles are."}, {"key": "6781", "content": "There are $$100$$ pieces of RMB in denominations of $$5$$ yuan and $$10$$ yuan, with a total value of $$800$$ yuan. There are pieces of $$5$$ yuan RMB and pieces of $$10$$ yuan RMB."}, {"key": "6782", "content": "The school held a science and knowledge quiz with a total of $$10$$ questions. Correct answers were awarded $$3$$ points each, while incorrect answers resulted in $$1$$ point being deducted. Xiao Jun answered all the questions and scored $$18$$ points. He got __ questions right."}, {"key": "6783", "content": "There are two types of camels: the dromedary, which has only one hump, and the Bactrian camel, which has two humps. The dromedary is taller with longer limbs, capable of walking and running in the desert; the Bactrian camel has shorter, thicker limbs, more suited for walking on gravel and snow. A group of camels has $$23$$ humps and $$60$$ feet; therefore, this group of camels totals, among which there are Bactrian camels."}, {"key": "6784", "content": "Crickets and spiders together have $$6$$ heads, $$40$$ legs, crickets have count, spiders have count. (Crickets have $$6$$ legs, spiders have $$8$$ legs)"}, {"key": "6785", "content": "There are $$10$$ chickens and $$2$$ rabbits in the cage, with a total number of legs."}, {"key": "6786", "content": "Chickens and rabbits in the same cage, there are a total of $$3$$ animals, $$10$$ legs, thus there are rabbits."}, {"key": "6787", "content": "Chickens and rabbits in the same cage, there are $$5$$ chickens, the rest are rabbits, a total of $$18$$ legs, so there are rabbits."}, {"key": "6788", "content": "Calculate:\n$$364-(476-187)+213-\\left( 324-236 \\right)-150$$=\uff0e"}, {"key": "6789", "content": "Calculate: $$207+205+203+201+199+197+195+193$$=."}, {"key": "6790", "content": "$$643-(318-57\uff09-82$$=."}, {"key": "6791", "content": "$$22\\times 84+84\\times 77+84=$$"}, {"key": "6792", "content": "Xiao Ming's window is made of a large rectangle pieced together from $$6$$ identical small rectangles, with each small rectangle being $$60$$ cm in length. Recently, he wanted to add a windproof sealing strip around the outer perimeter of the window. (1) The width of the small rectangle is cm. (2) The total length of the sealing strip needed is cm."}, {"key": "6793", "content": "In the figure below, only three numbers are marked (unit: centimeters). Based on these three numbers, it can be known that its perimeter is centimeters. question_6793-image_0"}, {"key": "6794", "content": "A rectangle is $$12$$ meters long and $$4$$ meters wide, its perimeter is ( ) meters."}, {"key": "6795", "content": "There are a total of $$50$$ apricot and cypress trees in the park, with the number of apricot trees being $$5$$ more than $$4$$ times the number of cypress trees. How many apricot trees are there?"}, {"key": "6796", "content": "In the park, there are $$50$$ more apricot trees than cypress trees, and the number of apricot trees is $$3$$ times that of cypress trees. How many cypress trees are there?"}, {"key": "6797", "content": "Splicing two squares with a side length of $$5$$ cm into a rectangle, the perimeter of the resulting rectangle is cm."}, {"key": "6798", "content": "There were $$9$$ birds on the tree, and then another $$12$$ birds flew in. Now, the number of birds on the left side is twice the number on the right side. How many birds are there on the branches on the left side now?"}, {"key": "6799", "content": "Vehicle A and Vehicle B initially had a total of $$43$$ passengers. After reaching a certain place, $$5$$ passengers got off from Vehicle A and $$2$$ passengers got on Vehicle B. At this time, the number of people in Vehicle A was exactly $$3$$ times the number of people in Vehicle B. The original number of passengers in Vehicle A, the original number of passengers in Vehicle B. question_6799-image_0"}, {"key": "6800", "content": "Initially, barrels A and B contained equal amounts of oil. Now, after transferring $$12$$ kilograms of oil from barrel A to barrel B, the amount of oil in barrel B is $$4$$ times that in barrel A. Now, barrel A has kilograms of oil, and barrel B has kilograms of oil."}, {"key": "6801", "content": "Originally, the number of books in Class A was $$6$$ times that of Class B. Now, Class A gives $$30$$ books to Class B, and at this time, Class A still has $$5$$ more books than Class B. Initially, Class A had books, and Class B had books."}, {"key": "6802", "content": "Originally, Class C had $$6$$ times more books than Class D. Now, Class C gives $$20$$ books to Class D, and as a result, Class C has $$5$$ books less than Class D. (1) How many more books did Class C originally have than Class D?"}, {"key": "6803", "content": "( ) Class B originally had a number of books, and Class D originally had a number of books."}, {"key": "6804", "content": "The textile factory has an equal number of male and female employees. If $$40$$ male employees are transferred out and $$60$$ female employees are transferred in, at this time the number of female employees is $$5$$ times the number of male employees. Then, the original number of male employees in the textile factory was."}, {"key": "6805", "content": "Xiaoqing and Dapeng originally had a total of $$44$$ pieces of chocolate. After Xiaoqing gave Dapeng $$6$$ pieces, at this time, the number of chocolates Dapeng had was $$3$$ times the amount Xiaoqing had. Xiaoqing now has pieces of chocolate."}, {"key": "6806", "content": "Below is a fast food restaurant menu, Lulu plans to order one main course, one snack, and one drink. She has several different combination options. question_6806-image_0"}, {"key": "6807", "content": "Vera has $$3$$ different dresses, $$4$$ different tops, $$3$$ different pants, $$2$$ different pairs of shoes in her wardrobe, she has a total of different outfit combinations. question_6807-image_0"}, {"key": "6808", "content": "Mase Hotel has a total of $$4$$ rooms to choose from. Eddie, Vi, Da Kuan, and the Doctor each choose one room. There are a total of different choices. question_6808-image_0"}, {"key": "6809", "content": "Xiaowanzi has many clothes, including $$2$$ hats, $$5$$ tops, $$8$$ pairs of pants, and $$3$$ pairs of leather shoes. Every time she goes out, she chooses one item from each category of clothing (including hats) to match. Thus, a total of different combinations can be formed."}, {"key": "6810", "content": "Xiaoming is buying a birthday present for his mom, there are $$4$$ types of small potted plants, $$6$$ types of postcards, and $$8$$ types of small dolls available in the store. Therefore, Xiaoming has several different choices."}, {"key": "6811", "content": "Four classmates stand in a row to take a photo, in total they can take different kinds of photos (photos taken from different positions are also different)."}, {"key": "6812", "content": "A number divided by $$7$$ gives a quotient of $$19$$, with a remainder. $$\\bigcirc \\div 7=19\\cdots \\cdots \\square $$, the maximum remainder is, and at this point, the dividend is."}, {"key": "6813", "content": "In a division equation without a remainder, the dividend is $$4$$ times the divisor. The sum of the dividend, divisor, and quotient is $$434$$. Then, the dividend is."}, {"key": "6814", "content": "When two numbers are divided, the quotient is $$9$$ with a remainder of $$6$$; knowing the sum of these two numbers is $$126$$, then the dividend is."}, {"key": "6815", "content": "The number A $$\\div $$ the number B $$=14\\cdots \\cdots 20$$, when both the number A and the number B are increased by a factor of $$3$$, the remainder is ( )."}, {"key": "6816", "content": "There is a square paper with a side length of $$10$$ cm, which was cut horizontally $$2$$ times and vertically $$3$$ times into $$12$$ small rectangles. The total perimeter of these $$12$$ small rectangles is equal to cm.\n question_6816-image_0"}, {"key": "6817", "content": "Teacher Wei Dong, Teacher Xiao Miao, Teacher You Zi, and $$\rm WC$$ Teacher line up to take a photo, with Teacher Xiao Miao standing in the first position on the left, there are a total of ways to line up."}, {"key": "6818", "content": "$$9.5+0.8=$$."}, {"key": "6819", "content": "$$3.1+6.5=$$\uff0e"}, {"key": "6820", "content": "Calculate: $$6.8-7.5+3.2-2.5=$$."}, {"key": "6821", "content": "Calculate: $$3.17+7.48+0.83-3.48=$$."}, {"key": "6822", "content": "Calculate: $$3.71+(10.36+6.29)-(3.36+5.14)=$$\uff0e"}, {"key": "6823", "content": "Mingming bought two sets of storybooks. When calculating the price, he mistook the selling price of one set of the books as $$266$$ yuan instead of $$226$$ yuan, resulting in a total calculation of $$400$$ yuan. The actual total price of these two sets of books is. question_6823-image_0"}, {"key": "6824", "content": "When Dawid was adding a three-digit number to another three-digit number, he mistook the tens digit of one of the addends for $$4$$, resulting in a result that was $$30$$ less than the correct answer. Therefore, Dawid mistook $$4$$ for."}, {"key": "6825", "content": "While calculating a subtraction problem, Eddie mistakenly wrote the tens digit of the minuend as $$3$$ instead of $$9$$, and the ones digit as $$8$$ instead of $$6$$, resulting in an outcome of $$201$$. The correct difference should be."}, {"key": "6826", "content": "When Mei Mei was doing addition, she mistook one of the tens digits in the addends for $$6$$, and the result was $$30$$ more than the correct answer. What did Mei Mei mistakenly think the $$6$$ was?"}, {"key": "6827", "content": "When Lili was doing addition, she misread one of the digits in the ones place of an addend as $$9$$, resulting in an answer that was $$3$$ less than the correct result. What did Lili misread the $$9$$ as?"}, {"key": "6828", "content": "The second-grade solid choir formation has a total of $$121$$ people. (1) This formation has rows and columns. (2) Adding one more row and one column, the number of people increases by."}, {"key": "6829", "content": "Niu Niu arranged the chess pieces into a solid square formation, using a total of $$64$$ pieces, with the same number of pieces on each side of the outer layer."}, {"key": "6830", "content": "Divide $$15$$ chili peppers into $$5$$ equal parts, each part has\uff0e\n question_6830-image_0"}, {"key": "6831", "content": "$$74\\div 8=9\\cdots \\cdots $$\uff0e"}, {"key": "6832", "content": "The picture below is a $$5\\times 5$$ area with $$5$$ trees planted. Now it is required to set up tents on the vacant land without trees. Furthermore, tents must be set up next to a tree, any two tents must not share a common point, and the number of tents in each row and column must be as indicated on the far left and top, respectively. Is there a tent at the ? position? () question_6832-image_0"}, {"key": "6833", "content": "The figure below shows a $$5\\times 5$$ area with $$5$$ trees. Now, it is required to set up tents on the blank spaces where no trees are planted, and the tents must be set up next to the trees. No two tents can share a common point, and the number of tents in each row is as shown on the far left, and the number of tents in each column is as shown on the top. Is there a tent in the 5th row, 3rd column ( )? question_6833-image_0"}, {"key": "6834", "content": "In the minefield below, there may be mines in the spaces. Based on the numbers in the squares, find the position of the mines. Is there a mine in the location marked with a question mark ( )? question_6834-image_0"}, {"key": "6835", "content": "Eddie practiced running, for the first $$3$$ days he ran an average of $$400$$ meters per day, for the next $$2$$ days he ran an average of $$700$$ meters per day, over these $$5$$ days his daily average running distance was meters."}, {"key": "6836", "content": "Among the following equations, the ones with an odd sum are ( )."}, {"key": "6837", "content": "With the numbers $$2$$, $$3$$, $$4$$, $$7$$, different two-digit numbers can be formed. (Numbers can be reused)"}, {"key": "6838", "content": "Among the three athletes, A, B, and C, one is a shot put athlete, one is a volleyball athlete, and one is a basketball athlete. Now it is known that:\n$$\\left( 1 \\right)$$ Athlete A is the youngest;\n$$\\left( 2 \\right)$$ The shot put athlete is C's brother;\n$$\\left( 3 \\right)$$ C is a female athlete, and she is older than the basketball athlete.\nSo, A is a ( ) athlete."}, {"key": "6839", "content": "The school organized a \"Love Labor, Establish New Trends\" activity, where students $$ABC$$ eagerly volunteered to do good for the school. One day, a student cleaned the classroom ahead of time, and when the teacher asked who did it, the result was: $$A$$ said: \"It was $$B$$ who did it\"; $$B$$ said: \"It wasn't me who did it\"; $$C$$ said \"It wasn't me who did it\". If it is known that among these three people two told lies and one told the truth, then the good deed was done by ( )."}, {"key": "6840", "content": "After a cognitive competition, four students A, B, C, and D guessed who among them could win a prize. A said: 'If I can win a prize, B will also win a prize.' B said: 'If I can win a prize, then C will also win a prize.' C said: 'If D doesn't win a prize, then it's impossible for me to win a prize.' In fact, only one of them did not win a prize and what A, B, and C said were all true. So the student who didn't win the prize is."}, {"key": "6841", "content": "There are two shelves of books, with a total of $$48$$ books. After taking away $$12$$ books from the first shelf, the number of books on the second shelf is $$2$$ times that on the first shelf plus another $$6$$ books. Then, the second shelf has ( ) books."}, {"key": "6842", "content": "Xiaoqing and Dapeng originally had a total of $$32$$ pieces of chocolate. After Xiaoqing gave $$4$$ pieces to Dapeng, Dapeng's amount of chocolate was $$3$$ times that of Xiaoqing's. Originally, Dapeng had $$20$$ pieces of chocolate."}, {"key": "6843", "content": "Fill in the blank: .\n question_6843-image_0"}, {"key": "6844", "content": "Look at the picture below, to balance the seesaw, you need to stand only a small bird on the right side.\n question_6844-image_0"}, {"key": "6845", "content": "The number of fruit candies in Huanhuan's hand is $$5$$ times that of the hard candies. After buying $$6$$ more of each, the number of fruit candies is $$3$$ times that of the hard candies. How many fruit candies did Huanhuan originally have?"}, {"key": "6846", "content": "The passengers of a large bus are 3 times the passengers of a small bus plus 4 more people. If the large bus has 20 more passengers than the small bus, then the small bus has ____ passengers."}, {"key": "6847", "content": "The right side is a statistical graph of the extracurricular books read by four classmates in May. Among the following statements, the wrong one is (). question_6847-image_0"}, {"key": "6848", "content": "The diagram shows the heights of four classmates. The chart does not include the students' names. It is known that Xiao Gang is the tallest, Xiao Li is the shortest, and Xiao Ming is taller than Xiao Hong. What is Xiao Hong's height? question_6848-image_0"}, {"key": "6849", "content": "Dapeng is saving money. After his mom gave him $$36$$ today, his current money amounts to $$4$$ times his original amount. Dapeng originally had yuan."}, {"key": "6850", "content": "There are a total of $$75$$ apples and oranges in the fruit store, with apples being $$11$$ more than oranges. There are $$x$$ apples."}, {"key": "6851", "content": "Runners A and B are responsible for carrying the torch from place $$A$$ to place $$B$$. Runner A starts from place $$A$$ and passes the torch to runner B along the way; after receiving the torch, runner B continues to jog towards place $$B$$. It is known that the distance between place $$A$$ and place $$B$$ is $$2400$$ meters, and runner A ran $$600$$ meters more than runner B. How many meters did runner A run? ( )"}, {"key": "6852", "content": "Xiao Yong has a total of $$22$$ white and black rabbits. If he buys another $$4$$ white rabbits, then the number of white and black rabbits will be the same. The number of black rabbits Xiao Yong has is ."}, {"key": "6853", "content": "Two baskets of fruit have a total weight of $$150$$ kilograms, the first basket is $$10$$ kilograms lighter than the second basket, the first basket of fruit weighs kilograms."}, {"key": "6854", "content": "One day, the little rabbit went to the little monkey's house to invite him to go to the library to read books together. However, one cannot get from the little rabbit's house to the little monkey's house directly; one must pass through the park (as shown in the figure below). Children, try to find out, there are several ways to get from the little rabbit's house to the little monkey's house.\n question_6854-image_0"}, {"key": "6855", "content": "Using $$\\boxed{5}\\boxed{7} \\boxed{9}$$ three cards, you can form different two-digit numbers. (The cards can be rotated)"}, {"key": "6856", "content": "Solve the following problems in columnar form: $$ (1) 54\\times 3= $$$$ (2) 7\\times44=$$$$ (3) 8\\times112=$$$$ (4) 304\\times 3=$$"}, {"key": "6857", "content": "Perform vertical multiplication:$$\uff081\uff0923\\times 14=$$$$\uff082\uff0925\\times 41=$$"}, {"key": "6858", "content": "Perform the calculation in vertical form: $$\uff081\uff09308\\times 201=$$$$\uff082\uff09203\\times 207=$$"}, {"key": "6859", "content": "Calculate using vertical method: $$17\\times 209$$=\uff0e"}, {"key": "6860", "content": "To make the quotient of $$528\\div \\square $$ a three-digit number (where $$\\square $$ is a single-digit number), $$\\square $$ can be filled with; to make it a two-digit number, $$\\square $$ can be filled with."}, {"key": "6861", "content": "The children went to the orchard to pick apples together. There were $$7$$ students who picked $$42$$, $$42$$, $$41$$, $$40$$, $$40$$, $$39$$, and $$36$$ apples respectively.\u2460 There were a total of $$7$$ students, and they picked apples in total\u2461On average, each person picked apples.\u2462 Through calculation, you found that: the average $$=$$ total \u00f7 number of items."}, {"key": "6862", "content": "Autumn has arrived, and the children went to the orchard to pick apples together. (1) Eddie picked $$36$$ apples, Vi picked $$27$$ apples, and Xiaoming picked $$33$$ apples, averaging each person picked apples. (2) If a total of $$25$$ children participated in this activity, and on average each child picked $$28$$ apples, then everyone picked a total of apples. question_6862-image_0"}, {"key": "6863", "content": "Four students each have an average of $$40$$ credit cards, the fifth student has $$10$$ more cards than the average number of cards of these four students, the average number of cards for these five students is."}, {"key": "6864", "content": "At the sports meet, Class 1 of Grade 3 had $$10$$ boys and $$8$$ girls participating. It is known that the average score of the boys was $$14$$ points, and the average score for all the participating students of Class 1 was $$10$$ points. The average score of the girls was points."}, {"key": "6865", "content": "Eddie took $$110$$ dollars to the store to buy snacks. He spent $$37$$ dollars on snacks at the store, and on his way home, he found $$27$$ dollars on the ground. Please ask how much money Eddie has left."}, {"key": "6866", "content": "$$(1) 29+299+2999+29999=$$ $$(2) 21+201+2001+20001=$$"}, {"key": "6867", "content": "There is a sequence of numbers, $$2$$, $$2$$, $$4$$, $$2$$, $$8$$, $$5$$, $$7$$, $$2$$, $$2$$, $$4$$, $$2$$, $$8$$, $$5$$, $$7$$, $$\\cdots$$ $$\\cdots$$ (1) The $$100$$th number is. (2) How many $$2$$s are there in the first $$100$$ numbers. (3) The sum of the first $$100$$ numbers is."}, {"key": "6868", "content": "In the table shown in the image, form a word pair with the top and bottom character of each column. For example, the first pair of words is (spring\u6295), the second pair of words is (wind\u6211). Then, the $$48$$th pair of words is. Spring wind flowers grass fragrance spring wind flowers grass fragrance spring wind flowers grass fragrance$$......$$Peach to me in return for plum peach to me in return for plum$$......$$"}, {"key": "6869", "content": "Is the sum of the equation $$1+2+3+4+\\cdots +2019+2020$$ odd or even? Why?"}, {"key": "6870", "content": "Find the pattern, fill in the blanks. $$37\\times 3=111$$$$37\\times 6=222$$$$37\\times$$ 9=$$37\\times $$27="}, {"key": "6871", "content": "Striped calculation: (1) $$140\\times18\\div14$$ ="}, {"key": "6872", "content": "(2) $$3900\\times15\\div13$$="}, {"key": "6873", "content": "(2) $$1500\\div \\left(25\\times15\\right)$$="}, {"key": "6874", "content": "(1) $$600\\div25\\div4$$="}, {"key": "6875", "content": "(3) $$800\\div \\left(200\\div125\\right)$$="}, {"key": "6876", "content": "(2) $$2 \\div \\left( {5 \\div 7} \\right) \\div \\left( {7 \\div 11} \\right) \\div \\left( {11 \\div 16} \\right) \\div \\left( {16 \\div 35} \\right) $$="}, {"key": "6877", "content": "(2) $$294\\div 7+56\\div 7$$="}, {"key": "6878", "content": "Column separation calculation: $$20\\div 3+40\\div 9+80\\div 9$$="}, {"key": "6879", "content": "(2) The perimeter of a rectangle is $$40$$ meters, and the length is $$12$$ meters. The area of this rectangle is square meters."}, {"key": "6880", "content": "Fill in the blank. (1) The perimeter of a square is $$36$$ meters, the side length of this square is meters, and the area of this square is square meters;"}, {"key": "6881", "content": "(2) The area of a rectangle is $$4000$$ square decimeters, the length is $$8$$ meters, the width is meters, and the perimeter of this rectangle is meters."}, {"key": "6882", "content": "Fill in the blank. (1) The area of a square is $$49$$ square meters, the side length of this square is meters, and the perimeter of this square is meters;"}, {"key": "6883", "content": "Carefully observe the line graph, and fill in the blanks based on the information from the line graph: (1) The quantity of peaches is times that of apples. (2) There are more peaches than apples by . (3) The total of both fruits is . question_6883-image_0"}, {"key": "6884", "content": "The group then arrived at the elephant pavilion. There are a total of $$22$$ elephants, divided into two categories: Asian elephants and African elephants, with the African elephants outnumbering the Asian elephants by $$3$$ times plus $$2$$ more elephants. So, how many African elephants and Asian elephants are there respectively? African elephants: ; Asian elephants: ."}, {"key": "6885", "content": "Xiao Ai has raised $$20$$ rabbits at home, the number of baby rabbits is $$4$$ times the number of adult rabbits, there are adult rabbits, and there are baby rabbits."}, {"key": "6886", "content": "There are poplar trees, willow trees, and pine trees in the park. The number of willow trees is $$2$$ times that of pine trees, and the number of poplar trees is $$3$$ times that of willow trees, so poplar trees are $$6$$ times that of pine trees."}, {"key": "6887", "content": "The feeding group raised $$20$$ chickens, among which the number of hens is $$3$$ times the number of roosters. There are  roosters and  hens."}, {"key": "6888", "content": "Farm A harvested 80 million tons more sorghum than Farm B, and the sorghum harvested by Farm A was 5 times that of Farm B. How much sorghum did Farm A and Farm B each harvest? question_6888-image_0 A: million tons B: million tons"}, {"key": "6889", "content": "Farm A harvested 50 million tons of corn more than Farm B, and the corn harvested by Farm A was 20 million tons more than 3 times that of Farm B. How much corn did Farms A and B each harvest? question_6889-image_0 A: million tons B: million tons"}, {"key": "6890", "content": "Wei plans to study piano, dance, or singing in the next $$5$$ days, taking only one course each day, with no two consecutive days being the same. She plans to study piano on the first day, and also piano on the last day, so there are a total of learning schemes."}, {"key": "6891", "content": "The picture below has nine spaces, and each space is required to be filled with distinct numbers so that the sum of the three numbers in each row, each column, and each diagonal is equal. The value of $$x$$ is. question_6891-image_0"}, {"key": "6892", "content": "The image below is part of a three-order magic square, $$X=$$\uff0e question_6892-image_0"}, {"key": "6893", "content": "(1) There is a line segment in the picture. \\\\ question_6893-image_0 \\\\\\\\\\\\(2) There is a triangle in the picture. question_6893-image_1"}, {"key": "6894", "content": "(1) There is a line segment in the figure below. question_6894-image_0"}, {"key": "6895", "content": "Diagram ($$1$$) has a triangle, and diagram ($$2$$) has a triangle. question_6895-image_0"}, {"key": "6896", "content": "There is a triangle in the picture.\n question_6896-image_0"}, {"key": "6897", "content": "(1) There is a square in the following figure. question_6897-image_0"}, {"key": "6898", "content": "Max Elementary School allocates expansion base dormitories for the third grade. If each dormitory houses 4 people, it lacks 2 people. If each dormitory houses 7 people, it lacks 41 people. Therefore, there are dormitories and a total of people in the third grade."}, {"key": "6899", "content": "Maze Elementary School allocates expansion dormitories for the third grade. If each dormitory houses $$6$$ people, there are $$14$$ extra people. If each dormitory houses $$7$$ people, the last $$1$$ person lives alone in a dormitory. Hence, there are dormitories, and the third grade has a total of people."}, {"key": "6900", "content": "A and B each have a certain number of candies. Each operation consists of the person with more candies giving some candies to the person with fewer candies, so that the number of candies of the person with less doubles. After three such operations, A has $$5$$ candies, and B has $$12$$ candies. What was the original number of candies for both? A: pieces, B: pieces"}, {"key": "6901", "content": "As shown in the figure, $$\\angle 1=35^\\circ $$, then $$\\angle 2=$$$$^\\circ $$\uff0e question_6901-image_0"}, {"key": "6902", "content": "Among the statements made by the following $$4$$ people, only one is true. Who is the thief? A says: $$B$$ is the thief; B says: $$D$$ is the thief; C says: $$B$$ is lying; D says: It's not me."}, {"key": "6903", "content": "When Little Treasure asked his sister's age, she said: 'When I was your age, you were just $$3$$ years old; when you are my age, I will already be $$30$$ years old.' The sister is $$21$$ years old this year."}, {"key": "6904", "content": "As shown in the figure, fill in the blanks with appropriate numbers to make the multiplication vertical method valid. The product is question_6904-image_0"}, {"key": "6905", "content": "As shown in the figure, fill in the appropriate numbers in the boxes in the diagram to make the vertical multiplication equation valid. The sum of the numbers filled in the $$4$$ boxes is.\n question_6905-image_0"}, {"key": "6906", "content": "Fill in each box below with an appropriate number to make the multiplication statement true. What is the three-digit multiplier in the equation?\n question_6906-image_0"}, {"key": "6907", "content": "Fill in the appropriate numbers in the boxes to make the vertical operation valid. The product should be. question_6907-image_0"}, {"key": "6908", "content": "As shown in the diagram, fill in the blanks with appropriate numbers to make the multiplication vertical expression valid. Then, the product of this equation is.\n question_6908-image_0"}, {"key": "6909", "content": "As shown in the figure, please fill in the appropriate number in the blank space in the figure to make the multiplication vertical equation correct. The result of this multiplication equation is 3 0 9 \u00d7 9 8"}, {"key": "6910", "content": "Arithmetic sequence $$9$$, $$12$$, $$15$$, $$18$$, $$\\cdots$$, where $$42$$ is the nth number of the sequence."}, {"key": "6911", "content": "One year, June 5th is a Friday. That year, June 30th is a weekday."}, {"key": "6912", "content": "$$2021$$ year $$3$$ month $$27$$ day is Saturday, then $$2021$$ year $$3$$ month $$10$$ day is."}, {"key": "6913", "content": "New Year's Day ($$1$$ January) in $$2012$$ was a Sunday; New Year's Day in $$2018$$ was on a weekday."}, {"key": "6914", "content": "Fill in the appropriate arithmetic operator on the line below to make the equation true: $$18$$$$122=2196$$."}, {"key": "6915", "content": "In the diagram, the shortest road from point A to point B has a total of. question_6915-image_0"}, {"key": "6916", "content": "As shown in the diagram, starting from point $$A$$ and moving along the segment to point $$B$$, it is mandatory to pass through point $$B$$, but cannot pass through point $$C$$. How many shortest routes are there from point $$A$$ to point $$D$$? question_6916-image_0"}, {"key": "6917", "content": "In a parking lot, there are sedans (four wheels) and motorcycles (two wheels) totaling $$32$$ vehicles, with a total of $$108$$ wheels. How many sedans and motorcycles are there?"}, {"key": "6918", "content": "Dragonflies have $$6$$ legs and $$2$$ pairs of wings; cicadas have $$6$$ legs and $$1$$ pair of wings. Together, dragonflies and cicadas have a total of $$210$$ legs and $$55$$ pairs of wings. How many of each are there?"}, {"key": "6919", "content": "A cricket has $$6$$ legs, a spider has $$8$$ legs. There are a total of $$10$$ creatures, crickets and spiders combined, with $$68$$ legs in total. There are crickets and spiders."}, {"key": "6920", "content": "For the fun sports meet, the prizes prepared by the teacher are lollipops. The teacher wants to divide $$8$$ identical lollipops into $$3$$ piles, there are a total of different methods of dividing."}, {"key": "6921", "content": "Xiaoming's window is made up of $$6$$ identical small rectangles combined into a large rectangle, each small rectangle is $$60$$ centimeters long. Recently, he wanted to put a windproof sealing strip around the outer edge of the window. (1) The width of the small rectangle is centimeters. (2) The total length of the sealing strip needed is centimeters. question_6921-image_0"}, {"key": "6922", "content": "Class A and Class B went to the orchard to pick apples. The number of apples picked by Class A was 4 times that of Class B. If Class A gave 90 apples to Class B, then both classes would have the same number of apples. How many apples did Class A and Class B pick respectively?"}, {"key": "6923", "content": "There are $$2$$ storybooks, $$3$$ popular science books, and $$3$$ comic books on the bookshelf. In total, there are several different ways to pick one book from the shelf"}, {"key": "6924", "content": "There are $$3$$ storybooks, $$2$$ popular science books, and $$2$$ comic books on the bookshelf. Take one book of each type, there are a total of different methods to choose"}, {"key": "6925", "content": "Calculate, the dividend in the following equation should be. $$\\square\\div 7=4\\cdots \\cdots 2$$"}, {"key": "6926", "content": "Xiaoling has $$5$$ different tops, $$4$$ different pants, and $$6$$ different pairs of leather shoes. She picks one of each category to wear each time she goes out. There are a total of different combinations that can be formed."}, {"key": "6927", "content": "Xiao Qi, Xiao Ling, Xiao Jun, and Xiao Li $$4$$ classmates line up to take a photo, with Xiao Qi definitely standing on the far right. There are different kinds of arrangements."}, {"key": "6928", "content": "There are $$5$$ different toys and $$7$$ different comic books in the store, you want to pick a birthday present for your good friend from them, there are several choices."}, {"key": "6929", "content": "When two numbers are divided, the quotient is $$4$$ with a remainder of $$8$$. The sum of the dividend, divisor, quotient, and remainder equals $$415$$. What is the dividend?"}, {"key": "6930", "content": "Calculate .16+28+22+54="}, {"key": "6931", "content": "Calculate 1.6+2.7+5.4="}, {"key": "6932", "content": "Calculate: $$1.9+1.99+1.999=$$."}, {"key": "6933", "content": "Calculate: $$10.36-(3.36+5.14)=$$."}, {"key": "6934", "content": "Xiaoshuai made a mistake in a subtraction problem due to carelessness. He mistook the units digit of the subtrahend for $$8$$ instead of $$6$$, and the tens digit for $$3$$ instead of $$1$$, resulting in a difference of $$47$$. So, the correct answer is."}, {"key": "6935", "content": "When doing a subtraction problem, the units digit of the minuend was mistakenly viewed as $$8$$ instead of $$4$$, and the tens digit was mistakenly viewed as $$4$$ instead of $$8$$, resulting in a difference of $$125$$. Therefore, the correct result should be."}, {"key": "6936", "content": "The second class of the first grade performed martial arts, with a total of $$81$$ people participating. They formed a square matrix."}, {"key": "6937", "content": "The solid choir formation of the second grade has a total of $$121$$ people, (1) this formation has rows and columns. (2) Adding one more row and one column, the number of people needed to be added is."}, {"key": "6938", "content": "Eddie went to the store to make purchases and found the pricing of the goods as follows. question_6938-image_0 (1) If Eddie wants to buy 10 pencils, then Eddie will need to spend money (2) The store has gotten a new batch of popsicles, Eddie found that one box has 5 popsicles, which is too many for him, so he plans to buy only 1 popsicle, needing to pay money. If he wants to buy 2 popsicles, he needs to pay money."}, {"key": "6939", "content": "Eddie and Will saw that the doctor was working very hard, so they decided to help the doctor with the housework. (1) Eddie is very good at washing dishes, he can wash 42 dishes in 6 minutes, at this rate, he can wash dishes in 8 minutes. (2) Will is also good at washing dishes, she can wash 25 dishes in 5 minutes, at this rate, to wash 30 dishes, she needs minutes."}, {"key": "6940", "content": "The Tree Planting Day has arrived, and the Xueersi School organized a tree planting activity. If $$5$$ people can plant $$100$$ trees in $$2$$ hours, and if each person plants the same number of trees per hour: (1) then $$5$$ people plant trees in $$1$$ hour. (2) then $$1$$ person plants trees in $$2$$ hours. (3) then $$1$$ person plants trees in $$1$$ hour."}, {"key": "6941", "content": "As shown in the figure, there are a total of $$100$$ trees, with a gap. question_6941-image_0"}, {"key": "6942", "content": "In order to restore the ecology of the magical forest, Eddie planted $$28$$ trees on one side of a road. It is known that the distance between two adjacent trees is $$3$$ meters. (1) If Eddie plants trees from one end to the other, the length of this road is meters. (2) If one end is not planted with trees, the length of this road is meters. (3) If both ends are not planted with trees, the length of this road is meters."}, {"key": "6943", "content": "(2)$$\\left( 2400-666 \\right)\\div 6$$="}, {"key": "6944", "content": "There are three people: A, B, and C. A is 12 years older than B, C is 15 years older than A, and C's age is 4 times that of B's age. How old is each, A, B, and C? A: years, B: years, C: years"}, {"key": "6945", "content": "(2) If the ball is passed to Eddie, there is a different way of passing."}, {"key": "6946", "content": "(2) There is a triangle in the following figure. question_6946-image_0"}, {"key": "6947", "content": "There are two piles of chess pieces, A and B, with pile A having more pieces than pile B. Now, the pieces are moved as follows: For the first move, take the same number of chess pieces from pile A and put them into pile B as there are in pile B; For the second move, take the same number of chess pieces from pile B and put them into pile A as there are left in pile A; For the third move, again take the same number of chess pieces from pile A and put them into pile B as there are left in pile B. Following this method of moving, after three moves, both piles A and B end up with exactly $$32$$ pieces each. How many chess pieces did pile A and pile B originally have? A: pieces  B: pieces"}, {"key": "6948", "content": "A farmer selling watermelons, the first time sold half plus half a watermelon from the cart, and the second time sold half plus half of the remaining watermelons. By then, there were $$25$$ watermelons left in the cart. How many watermelons were there originally in the farmer's cart."}, {"key": "6949", "content": "Class A and Class B each want to plant a certain number of trees. If Class A gives the same number of trees to Class B and then Class B gives the same number of trees it has at that time back to Class A, both classes will then have exactly 28 trees. How many trees did Class A and Class B originally have?"}, {"key": "6950", "content": "An angle has a vertex and edges."}, {"key": "6951", "content": "Move the decimal point of $$21.045$$ two places to the left, reducing it to its original size, becoming. question_6951-image_0"}, {"key": "6952", "content": "Move the decimal point of $$0.505$$ three places to the right and then two places to the left, the resulting number compared to $$0.505$$ is ( )."}, {"key": "6953", "content": "As shown in the figure, it is known that the degree of $$\\angle 1$$ is twice the degree of $$\\angle 2$$. What are the degrees of $$\\angle 1$$, $$\\angle 2$$, $$\\angle 3$$, and $$\\angle 4$$ respectively? $$\\angle 1$$ is degrees, $$\\angle 2$$ is degrees, $$\\angle 3$$ is degrees, $$\\angle 4$$ is degrees question_6953-image_0"}, {"key": "6954", "content": "As shown in the diagram, it is known that $$\\angle 1=36{}^\\circ $$, $$\\angle 2=3\\angle 4$$. What are the degrees of $$\\angle 2$$, $$\\angle 3$$, $$\\angle 4$$, and $$\\angle 5$$ respectively? $$\\angle 2$$ is degree $$\\angle 3$$ is degree $$\\angle 4$$ is degree $$\\angle 5$$ is degree question_6954-image_0"}, {"key": "6955", "content": "Compare the sizes of the three angles below and measure their degrees. question_6955-image_0 From left to right, the degrees of the three angles are ( )."}, {"key": "6956", "content": "After the exam, Lele said: \"I did not score $$100$$ points.\" If this statement is false, then which of the following statements is correct?"}, {"key": "6957", "content": "Xiao Dong, Xiao Nan, and Xiao Xi all wore sun hats to attend the summer camp, their hats were red, yellow, and purple respectively. It's known that Xiao Dong did not wear a yellow hat, and Xiao Nan neither wore a yellow nor a purple hat. The color of the hat Xiao Dong wore is ."}, {"key": "6958", "content": "Among three people, A, B, and C, there is $$1$$ priest, $$1$$ liar, and $$1$$ gambler. The priest never lies, the liar always lies, and the gambler sometimes tells the truth and sometimes lies. A says: 'I am the priest.' B says: 'I am the liar.' C says: 'I am the gambler.' Question: Among the three people A, B, and C, who is the priest, the liar, and the gambler."}, {"key": "6959", "content": "There are three individuals: A, B, and C. Their places of origin are one of Liaoning, Guangxi, and Shandong, and their professions are one of the following: teacher, worker, and actor. It is known that: (1) Person A is not from Liaoning, and person B is not from Guangxi; (2) The person from Liaoning is not an actor, and the person from Guangxi is a teacher; (3) Person B is not a worker. The question is: What are the places of origin and professions of A, B, and C?"}, {"key": "6960", "content": "In the garden, there are three types of plants: sunflowers, lilies, and peonies. It is observed that they bloom each week according to the following patterns: (1) Within a week, only one day will all three flowers bloom simultaneously; (2) No flower can bloom for three consecutive days; (3) Within a week, any two flowers will only have one day when they both do not bloom; (4) Sunflowers do not bloom on Tuesday, Thursday, and Sunday; (5) Lilies do not bloom on Thursday and Saturday; (6) Peonies do not bloom on Sunday; then on which day of the week do all three flowers bloom together."}, {"key": "6961", "content": "Tang Seng and his three disciples are cooking. One of them fetches water, one heats water, one washes vegetables, and one washes rice. It is known that:\n(1) Tang Seng neither fetches water nor washes rice;\n(2) Wukong neither washes vegetables nor fetches water;\n(3) If Tang Seng does not wash vegetables, then Sha Seng will not fetch water;\n(4) Bajie neither fetches water nor washes rice.\nSo, who is heating the water?"}, {"key": "6962", "content": "On Monday, the class teacher discovered that a piece of window glass in the classroom had been shattered, so they sought out three students from the class, Qiangqiang, Mingming, and Liangliang, to inquire about the situation.\nQiangqiang said: \"It was Mingming who broke it.\" \nMingming said: \"I didn't break it.\" \nLiangliang said: \"I didn't break it either.\" \nOnly one of these three students told the truth, and the one who broke the glass is among them. Thus, the glass was broken by."}, {"key": "6963", "content": "Compare the following numbers: $$33.217$$$$33.270$$; $$7.899$$$$11.9$$; $$98.1611$$$$98.1602$$; $$9.6785$$$$967.85$$."}, {"key": "6964", "content": "Among the figures below, figure\uff08 \uff09cannot find a $$135{}^\\circ $$ angle."}, {"key": "6965", "content": "This year, the father's age is 5 times that of his son. The sum of their ages in 3 years will be 54 years old. Therefore, the father's age this year is ___ years old."}, {"key": "6966", "content": "Grandfather is $$74$$ years old this year. When grandpa was as old as dad is now, dad was only $$18$$ years old. So how old is dad this year?"}, {"key": "6967", "content": "When the elder brother was as old as the younger brother is now, the younger brother was only $$4$$ years old; when the younger brother becomes as old as the elder brother is now, the elder brother will already be $$64$$ years old. So, how old is the elder brother this year."}, {"key": "6968", "content": "This year my sister is $$13$$ years old, my brother is $$10$$ years old. When the sum of their ages reaches $$101$$ years, the sister will be years old, and the brother will be years old."}, {"key": "6969", "content": "In the multiplication long form shown in the figure, some numbers are covered by triangular paper pieces. What is the result of the equation. question_6969-image_0"}, {"key": "6970", "content": "The following figure shows an incomplete multiplication equation. Now it is known that one of the digits is $$8$$, and the result of this equation is. question_6970-image_0"}, {"key": "6971", "content": "Complete the following multiplication long multiplication number puzzle, then the sum of the two factors is.\n question_6971-image_0"}, {"key": "6972", "content": "As shown in the diagram, a large square with a perimeter of $$20$$ centimeters is cut along the dotted lines into $$9$$ smaller rectangles, whose total perimeter is in centimeters. question_6972-image_0"}, {"key": "6973", "content": "Originally, Class C had 6 times as many books as Class D. After giving 20 books to Class D, Class C ended up having 5 books less than Class D. Class C originally had books, and Class D originally had books."}, {"key": "6974", "content": "There are $$84$$ cars at the East station and $$36$$ cars at the West station. Now, transferring cars from the East station to the West station can make the number of cars at the East station double that of the West station."}, {"key": "6975", "content": "The sum of the dividend, divisor, quotient, and remainder in a certain division equation is $$115$$. If both the dividend and the divisor are doubled, the sum of the dividend, divisor, quotient, and remainder in the resulting division equation is $$223$$. Therefore, the quotient in the original equation is."}, {"key": "6976", "content": "Peppa and George originally had a total of $$56$$ chocolates. After Peppa gave George $$5$$ chocolates, Peppa had 6 times as many chocolates as George. How many chocolates did Peppa originally have?"}, {"key": "6977", "content": "The students of Class 1, Grade 3 participated in the radio calisthenics competition, and arranged themselves into a solid square formation, with each row and each column having $$5$$ students, the square formation in total has students."}, {"key": "6978", "content": "Third-grade students participated in a broadcast gymnastics competition, forming a square formation as shown in the following image. Can you quickly count how many people there are?\n question_6978-image_0"}, {"key": "6979", "content": "At the closing ceremony of the art festival, volunteers used beautiful flowers to congratulate the performers, setting up a hollow square flower bed on the open ground in front of the gymnasium, with the outermost layer having $$12$$ pots of flowers on each side, totally $$3$$ layers, requiring a total number of flower pots"}, {"key": "6980", "content": "As shown in the diagram, it is a parallelogram, then the area of the following figure is square centimeters.\n question_6980-image_0"}, {"key": "6981", "content": "As shown in the figure, in parallelogram $$ABCD$$, it is known that $$AB=24$$, $$DE=10$$, $$DF=30$$, find $$BC=$$.\n question_6981-image_0"}, {"key": "6982", "content": "In the equation $$\\square \\div 5=21\\cdots \\cdots \\square $$, what is the maximum possible dividend ()?"}, {"key": "6983", "content": "Dividing two numbers, the quotient is $$10$$ with a remainder of $$2$$, and the sum of the dividend and the divisor is $$57$$. Then, the dividend is ( )."}, {"key": "6984", "content": "Answer the following questions. During PE class, Eddie runs around a rectangular playground: question_6984-image_0 \u200b\u2460This rectangular playground has a total of ____ sides. \u2461If the playground is $$100$$ meters long and $$50$$ meters wide, the perimeter of this playground is ____ meters. \u2462From the above calculation, you have discovered: The perimeter of a rectangle = (length $$+$$ width) $$\\times$$ ."}, {"key": "6985", "content": "$$123+58+47=$$"}, {"key": "6986", "content": "Xiaomei has a box of black and white beads. She arranged the beads in the following way: (1) The 18th bead should be of color; (2) There are a total of white beads in the first 20 beads. question_6986-image_0"}, {"key": "6987", "content": "Determine the parity of the results of the following expressions: (1) $$12\\times 34$$ (2) $$21\\times 37$$ (3) $$16\\times 33$$ (4) $$11\\times 13\\times 15\\times 17\\times 19\\times 21\\times 12\\times 23$$ (5) $$31\\times 33\\times 35\\times 37\\times 41\\times 43\\times 45\\times 47$$ The results that are odd numbers are."}, {"key": "6988", "content": "(2) $$1500\\div \\left(15\\times25\\right)$$="}, {"key": "6989", "content": "(2) The area of a rectangle is $$40$$ square meters, its length is $$8$$ meters, and its width is meters, the perimeter of this rectangle is meters."}, {"key": "6990", "content": "Farm A harvested $$50$$ million tons more of wheat than Farm B, and the wheat harvested by Farm A was $$10$$ million tons less than $$4$$ times that of Farm B. How much wheat did Farm A and B each harvest? question_6990-image_0 A: million tons B: million tons"}, {"key": "6991", "content": "Some three-digit numbers have this characteristic: the difference between two adjacent digits is $$1$$, such as $$121$$, $$345$$, etc. Then, the total number of three-digit numbers that meet this requirement and have each digit less than $$4$$ is."}, {"key": "6992", "content": "The image below is a part of the three-order magic square, $$X=$$\uff0e question_6992-image_0"}, {"key": "6993", "content": "The picture below is a 3x3 magic square, please fill in the \u203b. question_6993-image_0"}, {"key": "6994", "content": "Fill in the appropriate numbers in the squares below, so that the sum of the three numbers on each row, each column, and each diagonal equals $$24$$ (three numbers are already filled out). What number should be filled in the square with a red circle in the middle? question_6994-image_0"}, {"key": "6995", "content": "(2) There is a square in the diagram below. question_6995-image_0 \u200b"}, {"key": "6996", "content": "(1) In the $$4\\times 2$$ grid below, there is a square. question_6996-image_0"}, {"key": "6997", "content": "(2) In the below $$6\\times 3$$ grid, there is a square. \u200b question_6997-image_0 \u200b"}, {"key": "6998", "content": "There is a square in the picture. question_6998-image_0"}, {"key": "6999", "content": "There is a triangle in the image below. question_6999-image_0"}, {"key": "7000", "content": "The image below is a plan of a park. To ensure that visitors can walk through every path without repetition, if the entrance is located at point $$B$$, the exit should be set at. question_7000-image_0"}, {"key": "7001", "content": "The figure below has a singularity. question_7001-image_0"}, {"key": "7002", "content": "A survey of the whole class found that there are $$30$$ people who can swim, $$35$$ people who can play basketball. There are $$20$$ people who can do both. The total number of people in this class is."}, {"key": "7003", "content": "Blue and red beads, each person chooses at least one type, a total of $$20$$ people, among which $$16$$ people chose blue beads, $$12$$ people chose red beads. Question: how many people chose both types of beads."}, {"key": "7004", "content": "A farmer sold eggs. The first time, she sold more than half of the eggs in the basket by $$1$$, and the second time, she sold more than half of the remaining eggs by $$2$$. At that time, there were $$3$$ eggs left in the basket. How many eggs were originally in the basket?"}, {"key": "7005", "content": "As shown in the figure, it is known that $$\\angle 1=56{}^\\circ $$, $$\\angle 2$$=\u00b0. question_7005-image_0"}, {"key": "7006", "content": "Which angle cannot be formed using a set of set squares? ( )"}, {"key": "7007", "content": "Anan, Ningning, and Pangpang compete to see who is the most handsome. Among them, only one is the handsomest. Each of them made a statement: (1) Anan said: 'Definitely, I am the most handsome with my outstanding appearance.' (2) Ningning modestly said: 'I am not the handsomest.' (3) Pangpang said: 'Anan is lying.' Through verification of the facts, only one of them told the truth, then: who is the most handsome among them."}, {"key": "7008", "content": "The Little Math Cup \"Strongest Champion\" Challenge is in full swing, unfortunately, just the day before the competition, the trophy was lost! The organizers brought in the strongest detective who then questioned four suspects: Baby, Benben, Congcong, and Beibei. Baby said: Benben stole it; Benben said: Beibei stole it; Congcong said: Benben is lying; Beibei said: Anyway, it wasn't me who stole it. If only one person is telling the truth, then who stole the trophy."}, {"key": "7009", "content": "$$ABC$$Three classmates chose different professions after graduation. One of them became a journalist. Once, when asked about their professions, $$A$$ said: 'I am a journalist.' $$B$$ said: 'I am not a journalist.' $$C$$ said: '$$A$$ is lying.' If only one of their statements is true, then the journalist is (fill in $$A$$ or $$B$$ or $$C$$)."}, {"key": "7010", "content": "As shown in the figure, there is a shortest route along the line segment from $$A$$ through $$C$$ to $$B$$. question_7010-image_0"}, {"key": "7011", "content": "There are three digit cards $$1$$, $$4$$, $$9$$, how many different two-digit numbers can be formed? (Cards cannot be rotated for use)"}, {"key": "7012", "content": "Divide $$12$$ watermelons of the same size into $$3$$ piles of different quantities, there are several different ways of doing so. question_7012-image_0"}, {"key": "7013", "content": "Divide $$6$$ identical erasers among $$3$$ children, with each child getting at least one eraser, there are different ways to do this. question_7013-image_0"}, {"key": "7014", "content": "There are $$12$$ identical roses to be divided into two piles, there are a total of different ways of dividing them."}, {"key": "7015", "content": "Divide $$14$$ scorecards into two piles, with at least $$3$$ cards in each pile, there are a total of several ways."}, {"key": "7016", "content": "Calculate:\n(1) $$25\\times108=$$\n(2) $$69\\times102=$$\n(3) $$83\\times99=$$"}, {"key": "7017", "content": "Answer the following questions. There is a physical education class in today's schedule, and Wei'er hands him a square handkerchief: question_7017-image_0 \u200b\u2460This handkerchief has a total of sides.\u2461Eddie measured the length of each side and found that the side length is $$2$$ meters, the perimeter of this square handkerchief is meters\uff0e\u2462Through the above calculations, you have discovered: the perimeter of a square $$=$$ side length $$\\times$$."}, {"key": "7018", "content": "As shown in the figure, there are a total of $$100$$ trees with a gap. question_7018-image_0"}, {"key": "7019", "content": "As shown in the figure, there are a total of $$100$$ trees, with intervals. question_7019-image_0"}, {"key": "7020", "content": "Edi and Vier are preparing to beautify the entire Mage Magic School (1) First, they plant willow trees on one side of a 100-meter long pedestrian street, planting one every 10 meters, with one at each end, for a total of trees to be planted. (2) The distance between the Sun and the Moon teaching buildings is 50 meters, and Edi now plans to plant poplar trees between these two buildings, planting one every 5 meters, for a total of poplar trees needed. (3) Vier plans to plant pine trees along one side of the straight road leading to the gate of the Magic Castle, this road is 40 meters long, with a gap of 5 meters between every two trees, for a total of pine trees to be planted. (4) There is a circular flowerbed in the square with a circumference of 80 meters, now they plan to place a pot of flowers every 8 meters around the flowerbed, for a total of pots of flowers that can be placed."}, {"key": "7021", "content": "Calculate: $$\uff081\uff0930-29+28-27+26-25+24-23+22-21+20-19+18-17$$=$$\uff082\uff0920+21-22+23-24+25-26+27-28+29-30+31-32+33$$=$$\uff083\uff09100-99+98-97+96-95+\\cdots+4-3+2-1$$="}, {"key": "7022", "content": "Calculate: $$\uff081\uff0960-59-58+57+56-55-54+53+52-51-50+49+48-47-46+45$$=$$\uff082\uff09100+10-11-12+13+14-15-16+17+18-19-20+21+22-23-24+25$$=$$\uff083\uff09102-101+100-99-98+97+96-95-94+93+\\cdots +8-7-6+5+4-3-2+1$$="}, {"key": "7023", "content": "Calculate: $$168-\uff08136+111\uff09+143-\uff08254-211\uff09+\uff08132+137\uff09$$="}, {"key": "7024", "content": "Arrange some natural numbers in a row from left to right, so that the sum of any five consecutive numbers is equal to $$15$$. Given that the first number equals $$1$$, the second number equals $$2$$, the third number equals $$3$$, and the fourth number equals $$4$$, then: (1) The first ten numbers in this sequence are. (2) The hundredth number equals."}, {"key": "7025", "content": "Parking lots A, B, C, and D have $$10$$, $$7$$, $$5$$, $$4$$ cars parked in them respectively. Moving one car from the lot with the most cars to each of the other three lots is called one adjustment. After $$2020$$ such adjustments, the number of cars parked in lot A is."}, {"key": "7026", "content": "Write three integers $$1$$, $$3$$, $$5$$ on the blackboard, then erase one and replace it with the sum of the other two. Continue this process, can you eventually get $$10$$, $$12$$, $$14$$?"}, {"key": "7027", "content": "Calculate the following expressions using the distributive property: (1) $$\\left( 140+77 \\right)\\div 7$$="}, {"key": "7028", "content": "Column subtraction calculation: (1) $$91\\div 5+9\\div 5$$="}, {"key": "7029", "content": "In the Disability Sports Arena, Eddie's team and Vi's team have the same number of people. 20 people from Vi's team moved to Eddie's team, as a result, the number of people in Eddie's team became 3 times that of Vi's team. How many people were originally in Eddie's team and Vi's team? Eddie's team: people, Vi's team: people"}, {"key": "7030", "content": "Class A and Class B have the same number of students. If 18 students are transferred from Class A to Class B, then the number of students in Class B will be exactly 4 times the number of students in Class A. How many students were there originally in each class? Class A: students Class B: students"}, {"key": "7031", "content": "Eddy and Ergin $$PK$$, Ergin's energy value is $$62$$, Eddy's energy value is $$38$$. After the first round, both consumed the same amount of energy value, Ergin's remaining energy value is 3 times that of Eddy's. How much energy value do Eddy and Ergin have left now? Eddy: Ergin: question_7031-image_0"}, {"key": "7032", "content": "Eddie and Vi had a table tennis match, with the rule that whoever wins three games first will win the match. Then, there are possibilities for the process of the match."}, {"key": "7033", "content": "After filling in each square of the 3$$\\times$$4 grid as shown in the figure with appropriate numbers, it can make the sum of the numbers filled in each row equal and the sum of the numbers filled in each column also equal. Now some numbers have already been filled in, so the sum of the numbers filled in each row is. question_7033-image_0 \u200b"}, {"key": "7034", "content": "(2) There is a square in the diagram below. question_7034-image_0"}, {"key": "7035", "content": "As shown in the figure, there are a total of triangles in the picture. question_7035-image_0"}, {"key": "7036", "content": "The figure below cannot be drawn with one stroke. By adding a line between the points ( ), it can be turned into a one-stroke figure.\n question_7036-image_0"}, {"key": "7037", "content": "The figure below cannot be drawn with one stroke. By removing a line between the points ( ), it can be transformed into a figure that can be drawn with one stroke.\n question_7037-image_0"}, {"key": "7038", "content": "An English test consisted of two parts. As a result, 12 students in Class 3 Grade 3 got full marks. 25 students got the first part right, and 19 students made mistakes in the second part. Question: How many students in Class 3 Grade 3 made mistakes in both parts?"}, {"key": "7039", "content": "The image below is the calendar for April 2016. Based on the information provided by this calendar, you can calculate that April 4, 2015, was a weekday. (Fill in the number) question_7039-image_0"}, {"key": "7040", "content": "The school held a science and knowledge quiz competition with a total of $$10$$ questions. Answering a question correctly earns $$3$$ points, while answering incorrectly deducts $$1$$ point. Xiao Jun answered all the questions and scored $$18$$ points. He answered correctly questions."}, {"key": "7041", "content": "Write $$10$$ as the sum of $$3$$ natural numbers, there are a total of different ways."}, {"key": "7042", "content": "Given a three-digit number, the sum of the digits is $$4$$. There are a total of such three-digit numbers."}, {"key": "7043", "content": "Given a three-digit number, the sum of the digits is $$24$$. There are a total of such three-digit numbers."}, {"key": "7044", "content": "There is a rectangular piece of paper, with a length of $$10$$ cm and a width of $$5$$ cm. (1) Cut horizontally with scissors once (as shown in the picture), increase by centimeters; cut vertically once, increase by centimeters. question_7044-image_0 (2) Cut horizontally and vertically with scissors 5 times each, then the sum of the perimeters of all the small rectangles formed is centimeters."}, {"key": "7045", "content": "As shown in the diagram, there is a rectangle piece of paper that is $$12$$ cm long and $$10$$ cm wide, cut the paper into two parts along the dashed lines parallel to the sides. (1) The total length of the vertical dashed lines is $$10$$ cm, and the total length of the horizontal dashed lines is $$15$$ cm. (2) The sum of the perimeters of these two parts is $$94$$ cm. question_7045-image_0"}, {"key": "7046", "content": "$$7.48+3.17-2.35+0.53-3.48+1.65+5.3$$="}, {"key": "7047", "content": "Clever calculation. $$0.8+9.8+99.8+999.8$$="}, {"key": "7048", "content": "Person A and person B calculate an addition problem simultaneously. Person A copied the unit digit of the first addend as $$8$$ and got the answer as $$123$$; person B copied the ten digit of the second addend as $$5$$, and got the answer as $$132$$. What is the correct answer?"}, {"key": "7049", "content": "Using $$96$$ chess pieces to arrange into a three-layer hollow square matrix, (1) consecutive layers differ by chess pieces. (2) The outermost layer has chess pieces."}, {"key": "7050", "content": "The perimeter of the figure below is in decimeters. (Unit: decimeters) question_7050-image_0"}, {"key": "7051", "content": "Set up the division and check the second problem: (1) $$72\\div 4=$$. (2) $$112\\div 9=$$......"}, {"key": "7052", "content": "Eddie and Vi saw that the doctor was working very hard, so they decided to help the doctor with the housework. (1) Eddie is very good at washing dishes; he can wash 42 dishes in 6 minutes. At this rate, he can wash dishes in 8 minutes. (2) Vi is also good at washing dishes; she can wash 25 dishes in 5 minutes. At this rate, to wash 30 dishes, she needs minutes."}, {"key": "7053", "content": "Let's calculate everyone's New Year's money! (1) In 2018, the average New Year's money of three students was $$120$$ yuan. After adding Eddie's New Year's money, the average New Year's money of four students became $$150$$ yuan. Eddie's New Year's money is yuan. (2) In 2019, the average New Year's money of four students was $$160$$ yuan. After removing Vi's New Year's money, the average New Year's money of three students became $$150$$ yuan. Vi's New Year's money is yuan."}, {"key": "7054", "content": "The aquarium prepared $$230$$ kilograms of fish for the $$8$$ walruses in the facility. In the first two days, these $$8$$ walruses together consumed $$80$$ kilograms of fish. Two days later, $$2$$ of the walruses were transported away. If every walrus eats the same amount of fish every day, then the remaining fish can last for the remaining walruses for days."}, {"key": "7055", "content": "Mr. Zhang and Mr. Li ate a total of $$16$$ buns. If Mr. Zhang had eaten $$4$$ more buns and Mr. Li had eaten $$2$$ fewer buns, then the number of buns eaten by Mr. Zhang and Mr. Li would be the same. How many buns did Mr. Zhang originally eat?"}, {"key": "7056", "content": "This year, the combined age of father and daughter is $$52$$ years, the combined age of grandfather and grandmother is $$130$$ years, the father's age in $$14$$ years will be the same as the daughter's age in $$40$$ years, and the grandfather's age $$5$$ years ago was the same as the grandmother's age $$1$$ year ago.$$$$. Please calculate the current ages of the grandfather, grandmother, father, and daughter."}, {"key": "7057", "content": "How many line segments are there in the image? question_7057-image_0"}, {"key": "7058", "content": "The price of each table is $$m$$ yuan, and the price of each chair is $$n$$ yuan. The cost for buying $$50$$ sets of tables and chairs is ___ yuan. (Please write the simplified result)"}, {"key": "7059", "content": "A, B, C three people passing the ball, the ball starts with A, starting to pass from A, counted as the first pass, the ball cannot be passed to oneself, after two passes, how many different ways to pass are there? How many of those return back to A? (Represent with a tree diagram)"}, {"key": "7060", "content": "Eddie and Vi went to pick strawberries, together they picked $$96$$ strawberries in total, Eddie picked $$6$$ more than twice the amount that Vi picked, how many did Eddie and Vi pick respectively? (Draw a line segment diagram to represent this)"}, {"key": "7061", "content": "Calculate using the shortcut method. (1) $$41\\times 236+79\\times 236-20\\times236 $$= (2) $$1360{\\div}8+128{\\div}8-488{\\div}8$$="}, {"key": "7062", "content": "Calculate vertically: $$ (1) 45\\times 32=$$\uff0e$$ (2) 46\\times 35=$$\uff0e$$ (3) 89\\times 64$$=.$$ (4) 132\\times 21=$$"}, {"key": "7063", "content": "Set up vertical calculation: $$\uff081\uff09150\\times 270=$$\uff0e$$\uff082\uff09410\\times 2100=$$\uff0e"}, {"key": "7064", "content": "Perform vertical calculation: $$\uff081\uff09420\\div 5$$ =$$\uff082\uff09540\\div 3$$="}, {"key": "7065", "content": "Eddie bought a storybook. He read 25 pages each day for the first 4 days and 40 pages each day for the next 6 days, just finishing the book. Then, on average, how many pages did he read per day. question_7065-image_0"}, {"key": "7066", "content": "$$25\\times9\\times4=$$."}, {"key": "7067", "content": "The base of a triangle is $$25\\text{dm}$$ and the height is $$4\\text{dm}$$, the area of this triangle is ( )."}, {"key": "7068", "content": "Using a $$120$$ meter long fence to enclose $$5$$ sheep pens of equal area against a wall, as shown in the following diagram. Then, the maximum area of each sheep pen is square meters.\n question_7068-image_0"}, {"key": "7069", "content": "In the multiplication vertical problem below, $$\\triangle =$$.\n question_7069-image_0"}, {"key": "7070", "content": "There is a pile of peaches, the first monkey takes away half and then puts back $$1$$ peach; the second monkey takes away half of the remaining ones and then puts back $$1$$ peach; the third monkey takes away half of the remaining ones and then puts back $$1$$ peach $$\\cdots \\cdots$$ continuing in this manner, the $$2018$$th monkey takes away half of the remaining ones and then puts back one peach, leaving $$2$$ peaches. Originally, there were peaches."}, {"key": "7071", "content": "A little bird pecks at rice. The first time, it ate more than half of the amount of millet by $$10$$ grains. The second time, it ate less than half of the remaining by $$12$$ grains. The third time, it ate $$14$$ grains, and finally, there were $$15$$ grains of millet left.$$.$$ Originally, there were how many grains of millet."}, {"key": "7072", "content": "question_7072-image_0 The correct answer is."}, {"key": "7073", "content": "Calculate the following: (1) Doctor wants to buy a set of books to donate to children. There are a total of $$20$$ books, each costing $$15$$ dollars. The doctor needs to prepare dollars to buy the books. (2) The doctor also wants to buy some milk for the children. Each box of milk costs $$40$$ dollars, buying a total of $$150$$ boxes. The doctor needs to prepare dollars to buy the milk."}, {"key": "7074", "content": "Given a division equation with a quotient of $$22$$, now if we multiply the dividend by $$4$$ and divide the divisor by $$2$$, and then divide the newly obtained dividend by the newly obtained divisor, the quotient is."}, {"key": "7075", "content": "question_7075-image_0 The correct answer is ."}, {"key": "7076", "content": "Class A and Class B went to plant trees together. Class A has $$6$$ groups, and Class B has $$4$$ groups. It is known that on average, each group in Class A planted $$9$$ trees, and the average for both classes together is $$7$$ trees per group. (1) The total number of trees planted by Class A. (2) The total number of trees planted by both classes. (3) The total number of trees planted by Class B. (4) The average number of trees planted by each group in Class B."}, {"key": "7077", "content": "Dakuan and Aidi participated in the Hangzhou Calculation Competition organized by Xueersi. Within the specified time, Dakuan solved 60 more problems than Aidi, and the number of problems solved by Dakuan was 5 times that of Aidi. How many problems did Dakuan and Aidi solve respectively? (Represent with a line segment diagram)"}, {"key": "7078", "content": "(Stage Test) Complete the third-order magic square. question_7078-image_0 The number in the first row and third column, the number in the second row and first column, the number in the third row and third column, the number in the third row and fourth column"}, {"key": "7079", "content": "Carefully observe the line graph and fill in the blanks based on the information from the line graph: question_7079-image_0 (1) The quantity of peaches is the times of apples. (2) Peaches are more than apples by . (3) The total number of both fruits is ."}, {"key": "7080", "content": "Vera has $$3$$ different dresses, $$4$$ different tops, $$3$$ different pants, and $$2$$ different pairs of shoes in her wardrobe. How many different outfits can she put together? question_7080-image_0"}, {"key": "7081", "content": "In the multiplication vertical expression shown in the figure, $$\\triangle$$, $$ \\square$$, $$\\bigcirc$$, $$\\diamondsuit$$ represent different numbers. Question: What is the three-digit number $$\\overline{\\triangle \\square \\bigcirc }$$? question_7081-image_0"}, {"key": "7082", "content": "$$13$$ identical balls are divided into three piles of different quantities, there are a total of ways of dividing."}, {"key": "7083", "content": "Columnar division calculation: (1) $$999\\div 27$$="}, {"key": "7084", "content": "(2) $$3300\\div 55$$="}, {"key": "7085", "content": "Eddie has an $$\"L\"$$ shaped swimming pool, as shown below. He plans to buy some blue tiles to cover the bottom of the swimming pool (not considering the sides). Eddie needs to buy square meters of tiles. question_7085-image_0"}, {"key": "7086", "content": "(2) The total number of squares is."}, {"key": "7087", "content": "Carefully observe the grid in the figure below, answer the following questions: (1) Categorized by size, the figure has a total of classes of squares. question_7087-image_0"}, {"key": "7088", "content": "Xiaoming's age in $$8$$ years will be equal to his mother's age $$20$$ years ago. When Xiaoming was a certain age, his mother's age was exactly $$5$$ times Xiaoming's age."}, {"key": "7089", "content": "In the equation below, insert a pair of parentheses to make the result of the equation the largest. What is the maximum value?\n$$2+3\\times 4+5\\times 4+3\\times 2$$"}, {"key": "7090", "content": "A shepherd has $$10$$ identical sheep and $$3$$ identical sheep pens, and needs to herd the sheep into the pens with no more than $$6$$ sheep in each pen. According to these requirements, there are a total of different arrangements. question_7090-image_0"}, {"key": "7091", "content": "Dividing $$11$$ identical marbles into $$3$$ groups of different quantities, there are a total of different ways of division."}, {"key": "7092", "content": "Calculate the following problems: (1) $$99\\times 4\\times 25$$=\uff0e(2) $$125\\times (119\\times 8)$$=\uff0e(3) $$1248\\times 25$$=\uff0e(4) $$4032\\times 125$$=\uff0e"}, {"key": "7093", "content": "Calculate: (1) $$125\\times 72$$=. (2) $$25\\times 125\\times 16$$=."}, {"key": "7094", "content": "Can you solve the following problems? (1) $$125\\times (80+8)= $$. (2) $$(100-4)\\times 25= $$. (3) $$(200-2)\\times 36 =$$. (4) $$23\\times (300+1)=$$."}, {"key": "7095", "content": "Calculate: (1) $$23\\times 99$$=\uff0e(2) $$25\\times 97$$=\uff0e(3) $$15\\times 101$$=\uff0e(4) $$37\\times 102$$=\uff0e"}, {"key": "7096", "content": "Combining the pattern just discovered, quickly calculate the following expressions: (1) $$(13039+260)\\div 13$$=\uff0e(2) $$(54+81+360)\\div 9$$=\uff0e(3) $$(18000-720)\\div 9$$=\uff0e(4) $$(4800-240+720)\\div 12$$=\uff0e"}, {"key": "7097", "content": "Calculate: (1) $$156\\div 7+194\\div 7+329\\div 7+371\\div 7$$=\uff0e(2) $$31\\div 5+32\\div 5+33\\div 5+34\\div 5+35\\div 5$$=\uff0e(3) $$25\\div 4+25\\div 6+35\\div 4+35\\div 6$$=\uff0e(4) $$120\\div 6+120\\div 4+120\\div 2$$=\uff0e"}, {"key": "7098", "content": "Calculate: (1) $$450\\times 6\\div 54$$ = . (2) $$4200\\div (50\\times 7)$$ = . (3) $$ (54\\times 24)\\div (9\\times 4)$$ = . (4) $$444000\\div 3\\div 25\\div 37\\div 2$$ = ."}, {"key": "7099", "content": "Compute: (1) $$(26\\div 25)\\times (27\\div 17)\\times (25\\div 9)\\times (17\\div 39)$$=\uff0e(2) $$12\\div (3\\div 2)\\times (6\\div 7)\\div (8\\div 7\\div 5\\times 2)\\div (5-2)$$=\uff0e"}, {"key": "7100", "content": "Calculate: (1) $$111\\times 4\\div 9\\times 3\\div 74\\times 2$$=. (2) $$2002\\times 81\\div (7\\times 9\\times 11\\times 13)$$=. (3) $$3\\times 5\\times 7\\times 11\\times 13\\times 17\\div (51\\times 65\\times 77)$$=."}, {"key": "7101", "content": "Calculate: (1) $$1200\\div 25$$=\uff0e(2) $$2000\\div 125$$=\uff0e"}, {"key": "7102", "content": "Calculate: (1) $$215\\div 29+65\\div 29+300\\div 29$$=. (2) $$120\\div 6+120\\div 4+120\\div 2$$="}, {"key": "7103", "content": "Answer the following questions: (1) A rectangle is 12 meters long and 8 meters wide. If its length increases by 2 meters and its width remains unchanged, the area of the rectangle increases by square meters. (2) If the width of a rectangle remains unchanged and its length increases by 8 meters, the area increases by 72 square meters; if the length remains unchanged and the width decreases by 4 meters, the area decreases by 48 square meters, the original area of this rectangle is square meters."}, {"key": "7104", "content": "$$5$$ boxes of apples and $$5$$ boxes of grapes weigh a total of $$75$$ kilograms, with each box of apples being twice the weight of each box of grapes. The weight of each box of apples in kilograms, and the weight of each box of grapes in kilograms."}, {"key": "7105", "content": "The badminton team bought $$360$$ shuttlecocks, which are packed in $$4$$ large boxes and $$4$$ small boxes. If $$2$$ small boxes and $$1$$ large box contain the same number of shuttlecocks, each large box contains , and each small box contains ."}, {"key": "7106", "content": "A strongman can carry $$20$$ books in one hand, while Xiaobai can carry $$10$$ books with both hands. The two of them cooperated to move $$450$$ books from place A to place B, aiming to complete the task in the shortest time. Knowing that the number of times the strongman carries is $$2$$ times that of Xiaobai, then, the strongman carried books, and Xiaobai carried books. (Both the strongman and Xiaobai carry items with both hands)"}, {"key": "7107", "content": "There are $$80$$ apples in the big basket, and there are $$70$$ apples in the small basket. It's necessary to transfer some apples from the big basket to the small basket so that the number of apples in the small basket is exactly $$2$$ times that in the big basket."}, {"key": "7108", "content": "The elder brother has $$25$$ books, and the younger brother has $$20$$ books. After the elder brother gives some books to the younger brother, the total number of books the younger brother has becomes twice that of the elder brother's. So, at this time, the number of books the elder brother and younger brother have are, respectively, $$.$$"}, {"key": "7109", "content": "Four pirates Jack, Jimmy, Tom, and Sanji divide $$560$$ coins among themselves. Jack said: 'I got $$22$$ less coins than Jimmy, $$30$$ more than Tom, and $$40$$ less than Sanji.' So, how many coins did Sanji get?"}, {"key": "7110", "content": "The store had yellow and red balloons for sale, with the red balloons outnumbering the yellow ones by 6. Sisi came and bought 4 yellow balloons. At this point, the number of red balloons was exactly 4 less than double the number of yellow balloons. How many yellow balloons were there originally?"}, {"key": "7111", "content": "Person A and Person B both had some candies. If Person A gives 10 candies to Person B, then they would have the same amount of candies; if Person A and Person B both eat 8 candies, then the remaining candies of Person A would be 3 times the number of Person B's remaining candies. How many candies did they originally have in total?"}, {"key": "7112", "content": "Person A and B both have some reward cards, with A having $$10$$ more than B. If A gives B $$20$$ cards, then A has $$5$$ more than half of B's number of cards. The original number of reward cards A had, and the original number of reward cards B had."}, {"key": "7113", "content": "Person A and person B both have some reward points cards, with A having 10 more than B. If A gives 20 cards to B, then twice the amount of A's cards is 5 more than B's. How many reward points cards did A and B originally have?"}, {"key": "7114", "content": "Answer the following questions: (Fill in the blanks with $$1.2.3.4.5.6.7$$) (1) If today is Wednesday, what day of the week is the $$25$$th day from today? (2) If today is Wednesday, what day of the week is it in $$25$$ days?"}, {"key": "7115", "content": "Answer the questions. (Fill in according to $$1.2.3.4.5.6.7$$) (1) Xiaotong's birthday is on June $$27$$, she was born in a year when June $$1$$ was a Saturday. Xiaotong was born on a weekday. (2) June $$1$$, $$2008$$ was a Sunday, August $$1$$, $$2008$$ was a Friday. (3) October $$10$$, $$2018$$ was a Wednesday. January $$1$$, $$2019$$ was a Tuesday."}, {"key": "7116", "content": "It is known that in a certain month, the number of Tuesdays is more than the number of Wednesdays, and the number of Mondays is more than the number of Sundays. Then, the 5th of this month is a _____, and this month has _____ days. (Fill in the blanks with $$1.2.3.4.5.6.7$$)"}, {"key": "7117", "content": "The midterm task of Graph Theory course is to design a robot with the help of the learned content. Eddie plans to design a garbage cleaning robot. To stand out among many designs, Eddie's robot has optimized its path algorithm, which can automatically calculate and find the shortest path. The following picture shows the street distribution map of a residential area, with the street lengths as shown in the picture (unit: kilometers). Each letter in the picture represents the code of different buildings. A garbage cleaning robot starts from the garbage station (the garbage station is located at place $$P$$ between building $$C$$ and $$D$$) and has to clean all the streets and still return to the garbage station, the shortest route is kilometers. question_7117-image_0"}, {"key": "7118", "content": "There are a total of $$45$$ chickens and rabbits in the same cage with $$100$$ legs in total. Try to calculate how many chickens and how many rabbits are in the cage."}, {"key": "7119", "content": "In a parking lot, there are currently $$24$$ vehicles in total, consisting of cars and motorcycles. The cars have $$4$$ wheels each, and the motorcycles have $$3$$ wheels each. Altogether, these vehicles have $$86$$ wheels. How many of the vehicles are motorcycles with three wheels?"}, {"key": "7120", "content": "There are two types of corn launchers: double-barrel corn launchers and triple-barrel corn launchers. The double-barrel corn launcher fires $$2$$ cobs of corn, each capable of eliminating $$17$$ zombies; the triple-barrel corn launcher fires $$3$$ cobs of corn, each capable of eliminating $$16$$ zombies. The corn launcher fires a total of $$10$$ times, launching $$23$$ cobs of corn, and eliminating a total of zombies."}, {"key": "7121", "content": "Ultraman encounters a group of monsters, with the large monsters having $$2$$ heads and $$4$$ legs each, and the small monsters having $$2$$ heads and $$2$$ legs each. Together, they have a total of $$20$$ heads and $$32$$ legs. So, how many large monsters and how many small monsters are there?"}, {"key": "7122", "content": "The kindergarten distributes fruits to the children in the senior and junior classes, with each child in the senior class receiving $$2$$ apples and $$3$$ oranges, and each child in the junior class receiving $$2$$ apples and $$2$$ oranges. It is known that a total of $$48$$ apples and $$55$$ oranges were distributed. Therefore, there are $$17$$ children in the junior class."}, {"key": "7123", "content": "A boy holds $$2$$ red balloons and $$5$$ blue balloons, a girl holds $$3$$ red balloons and $$4$$ blue balloons, there are a total of $$100$$ red balloons and $$166$$ blue balloons. Boys count, girls count."}, {"key": "7124", "content": "The school held a sports event with a \"three-legged race\" and a \"seven-legged race\", both events taking place at the same time with $$200$$ people registered to participate.$$.$$ During the competition, these $$200$$ people had a total of $$232$$ \"legs\" (two legs tied together count as one leg), so there were a total of participating groups."}, {"key": "7125", "content": "There are a total of $$100$$ cards with $$3$$ colors: red, yellow, and green. On the red cards, the numbers $$1$$ and $$2$$ are written on the two sides respectively; on the yellow cards, the numbers $$1$$ and $$3$$ are written on the two sides respectively; and on the green cards, the numbers $$2$$ and $$3$$ are written on the two sides respectively. Now, placing these cards on the table with the side that has the larger number facing up, after calculation, the sum of the numbers displayed on the cards is $$234$$. If all the cards are flipped over, the sum of the numbers displayed then becomes $$123$$. The number of yellow cards is $$11$$."}, {"key": "7126", "content": "The teacher from Xueersi distributed cards to the students in the class, giving each boy 4 constellation credit cards and 2 note master cards, and each girl 6 constellation credit cards and 2 note master cards. It is known that the teacher distributed a total of 88 constellation credit cards and 40 note master cards. The number of girls in this class is."}, {"key": "7127", "content": "The Future Elementary School has entered the 'What You See, What You Learn, What You Hear' theme month, organizing a series of contest activities for the whole school, including poetry contests, carnivals, sports festivals, etc. Among them, the poetry contest consists of two parts, resulting in $$12$$ students scoring full marks. In the first part, $$25$$ students answered correctly, while in the second part, $$19$$ students answered incorrectly, and there were people who answered both parts incorrectly."}, {"key": "7128", "content": "At the fair, $$100$$ students drew lottery tickets with labels ranging from $$1$$ to $$100$$. The rules for awarding prizes based on the ticket numbers are as follows: ($$1$$) If the label number is a multiple of $$2$$, award $$2$$ pencils. ($$2$$) If the label number is a multiple of $$3$$, award $$3$$ pencils. ($$3$$) If the label number is a multiple of both $$2$$ and $$3$$, the prize can be claimed repeatedly. ($$4$$) All other label numbers receive $$1$$ pencil. How many pencils in total should be prepared for this activity at the fair?"}, {"key": "7129", "content": "During the sports festival, $$50$$ honor guard students formed a line facing the teacher. The teacher first had everyone count off from left to right as $$1$$, $$2$$, $$3$$, $$\\cdots$$, $$49$$, $$50$$. Then, those who reported a number that is a multiple of $$4$$ were asked to turn around, followed by those reporting a number that is a multiple of $$6$$. Now, the number of students still facing the teacher is."}, {"key": "7130", "content": "A shepherd herded a flock of sheep across $$10$$ rivers, losing half of the sheep into the river each time they crossed one, but he was able to retrieve $$4$$ each time. In the end, he counted and found he had $$8$$ sheep left. How many sheep were in the flock before crossing the rivers?"}, {"key": "7131", "content": "There are a number of small balls in a box. Teacher Wang took half of the balls from the box for the first time, then added $$1$$ ball back. He repeated the process, taking half of the balls and then adding $$1$$ ball back, $$\\cdots \\cdots$$, doing so a total of $$2020$$ times, and finally, there were two balls left in the box. Thus, before any balls were taken out, there were a number of balls in the box."}, {"key": "7132", "content": "Two oil drums A and B were each filled with $$15$$ kilograms of oil. After selling $$14$$ kilograms of oil, the clerk redistributed the oil between the two drums. He first poured some oil from drum A into drum B, resulting in an increase of $$5$$ kilograms in drum B. Then he poured some oil from drum B back into drum A, doubling the amount of oil in drum A. At this point, the oil in drum A was exactly $$7$$ times that in drum B. Originally, drum A sold __ kilograms of oil, and drum B sold __ kilograms of oil."}, {"key": "7133", "content": "There are two piles of chess pieces, pile A and pile B, with pile A having more pieces than pile B. Now, move the chess pieces as follows: for the first move, take the same number of pieces from pile A and put them into pile B as there are in pile B; for the second move, take out the same number of pieces from pile B and put them into pile A as the remaining in pile A; for the third move, again take out the same number of pieces from pile A and put them into pile B as the remaining in pile B. After three moves, both pile A and pile B exactly have $$32$$ pieces each. Originally, pile A had pieces, and pile B had pieces."}, {"key": "7134", "content": "A, B, and C went fishing together. They put the fish they caught into a basket and lay down to rest on the spot, and all fell asleep. A woke up first, divided the fish in the basket into 3 equal parts, and found there was 1 extra fish, so he threw the extra fish back into the river and took one part of the fish home. B woke up later, divided the remaining fish in the basket into 3 equal parts, found there was 1 extra fish as well, also threw the extra fish back into the river, and took one part of the fish home. Finally, C woke up and also divided the fish in the basket into 3 equal parts, and there was also 1 extra fish. These three people caught at least a number of fish."}, {"key": "7135", "content": "Perform columnar calculations: (1) $$8.94+3.56=$$ (2) $$19.083+12.15=$$ (3) $$40.12-30.57=$$ (4) $$93.37-8.1802=$$"}, {"key": "7136", "content": "Calculate: (1) $$39.2+12.5-2.8-11.9$$=\uff0e(2) $$78.93+21.7-7.68-29.47$$=\uff0e"}, {"key": "7137", "content": "As shown in the diagram, $$\\angle 2$$ is twice $$\\angle 1$$, then $$\\angle 3=$$$$^\\circ $$\uff0e\n question_7137-image_0"}, {"key": "7138", "content": "As shown in the diagram, there is a triangle. question_7138-image_0"}, {"key": "7139", "content": "This year, David and his grandfather have a total age of $$65$$ years. Five years later, the grandfather's age will be $$4$$ times that of David's age. How old is the grandfather this year?"}, {"key": "7140", "content": "The park is planted with many phoenix trees and cedar trees, with the number of phoenix trees being $$m$$, and the number of cedar trees is $$7$$ more than $$3$$ times the number of phoenix trees; the cedar trees were planted; the total number of phoenix trees and cedar trees is\uff0e question_7140-image_0"}, {"key": "7141", "content": "Fill in the $$\\square$$ with an appropriate number so that it is divisible by both $$3$$ and $$5$$. The $$\\square$$ should be filled with $$\\overline{22\\square}$$."}, {"key": "7142", "content": "Using the numbers $$1$$, $$3$$, and $$5$$, different natural numbers without repeated digits can be formed."}, {"key": "7143", "content": "Determine the parity of the result for the following expression:\n$$22\u00d74+33\u00d75+66\u00d78-45\u00d710$$"}, {"key": "7144", "content": "The school bought $$5$$ boxes of colored chalk and $$10$$ boxes of white chalk, each box containing $$20$$ pieces. Total number of chalk pieces. (Calculate using two methods)"}, {"key": "7145", "content": "(2) $$1600\\times15\\div8$$="}, {"key": "7146", "content": "(3) $$400\\div \\left(40\\div25\\right)$$="}, {"key": "7147", "content": "Column removal calculation: (1) $$(144\\div 36)\\times (36\\div 9)\\times (9\\div 3)$$="}, {"key": "7148", "content": "Wei'er plans to study piano, dance, or singing in the next $$4$$ days, learning only one course per day, with different courses on adjacent days. She plans to study piano on the first day and also on the last day. In total, there are various study plans."}, {"key": "7149", "content": "As shown, $$ABCDEF$$ is a regular hexagon, a frog starts at vertex $$A$$, it can jump to either of the two adjacent vertices at each move. If it reaches point $$D$$ within $$4$$ moves, it stops jumping (for example: $$A-B-C-D$$); if it cannot reach point $$D$$ within $$4$$ moves, it also stops after completing $$4$$ moves (for example: $$A-B-C-B-A$$). Then, the total number of different jumping methods possible for the frog from start to stop is. question_7149-image_0"}, {"key": "7150", "content": "Please answer the following questions: (1) The image below is part of a third-order magic square, $$X=$$\uff0e question_7150-image_0"}, {"key": "7151", "content": "(2) The figure below is part of a 3x3 magic square, $$A=$$\uff0e question_7151-image_0"}, {"key": "7152", "content": "(3) The image below is a part of a 3x3 magic square, $$B=$$. question_7152-image_0"}, {"key": "7153", "content": "The number in the third row, third column is:"}, {"key": "7154", "content": "(1) There is a line segment in the diagram. \\\\ question_7154-image_0 \\\\\\\\\\\\(2) There is a triangle in the diagram. question_7154-image_1"}, {"key": "7155", "content": "Fill in the appropriate numbers in the box so that the vertical operation is correct. The correct result is . question_7155-image_0"}, {"key": "7156", "content": "Two line segments, one measuring $$10$$ cm and the other $$8$$ cm in length, are joined end to end. The total length is ( )."}, {"key": "7157", "content": "The perimeter of the figure below is. (Unit: decimeters) question_7157-image_0"}, {"key": "7158", "content": "Set up vertical calculations for the following problems: $$\uff081\uff0954\\times 3= $$$$\uff082\uff097\\times44=$$"}, {"key": "7159", "content": "Perform vertical calculations for the following questions: $$\uff081\uff098\\times112=$$ $$\uff082\uff09304\\times 3=$$"}, {"key": "7160", "content": "Perform vertical calculation: $$\uff081\uff0945\\times 32=$$\uff0e$$\uff082\uff0946\\times 35=$$\uff0e$$\uff083\uff0989\\times 64$$="}, {"key": "7161", "content": "Xiaoming is very good at washing dishes, he can wash $$9$$ dishes in $$7$$ minutes. Based on this speed, Xiaoming can wash $$__$$ dishes in $$14$$ minutes."}, {"key": "7162", "content": "In 2020, three students each had $50 per person per month as pocket money. After Dan joined, the average pocket money of the four people increased by $3. How much pocket money does Dan have each month?"}, {"key": "7163", "content": "There are a total of $$96$$ goats on three mountains. $$4$$ goats ran from Mountain 1 to Mountain 2, and $$8$$ goats ran from Mountain 2 to Mountain 3. At this time, the number of goats on the three mountains is equal. How many goats were there originally on each mountain? Mountain 1: Mountain 2: Mountain 3:"}, {"key": "7164", "content": "Teacher Yang from Xueersi School and three students, Xiao Liu, Xiao Guan, and Xiao Zhang, currently, Teacher Yang's age is exactly the sum of the ages of these three students; $$9$$ years later, Teacher Yang's age will be the sum of the ages of Xiao Liu and Xiao Guan; another $$3$$ years later, Teacher Yang's age will be the sum of the ages of Xiao Liu and Xiao Zhang; another $$3$$ years later, Teacher Yang's age will be the sum of the ages of Xiao Guan and Xiao Zhang. Calculate the current ages: Xiao Guan is $$12$$ years old, Xiao Liu is $$15$$ years old, Xiao Zhang is $$9$$ years old, and Teacher Yang is $$36$$ years old."}, {"key": "7165", "content": "Complete the following questions: (1) Numbers $$1$$, $$2$$, $$3$$ can form different two-digit numbers without repeated digits. (2) Numbers $$1$$, $$3$$, $$6$$ can form different three-digit numbers without repeated digits."}, {"key": "7166", "content": "Eddie went to the children's restaurant to buy a special meal for $$15$$, he has several $$1$$ dollar, $$2$$ dollar, and $$5$$ dollar bills, but the condition for purchasing the special meal is that you must figure out a total of different payment methods (requiring every denomination of bill to be used), the discount period is about to end, can you help Eddie successfully buy the discounted meal?"}, {"key": "7167", "content": "Perform vertical multiplication calculations. (1) $$56\\times 9=$$ (2) $$314\\times 2=$$ (3) $$732\\times 4=$$ (4) $$284\\times 6=$$ (5) $$1234\\times 7=$$"}, {"key": "7168", "content": "Calculate using columnar method. (1) $$60\\times 34=$$ (2) $$55\\times 29=$$ (3) $$18\\times 63=$$ (4) $$123\\times 45=$$ (5) $$721\\times 28=$$"}, {"key": "7169", "content": "Calculate the following expressions: (1) $$41\\times 30=$$\uff0e(2) $$60\\times 2300=$$\uff0e(3) $$520\\times 40=$$\uff0e(4) $$250\\times 40=$$\uff0e"}, {"key": "7170", "content": "Eddie goes to the stationery store to buy stationery for the teacher, with the unit prices as follows: the automatic pencil is $$4$$ yuan each, the stationery box is $$26$$ yuan each, the fountain pen is $$45$$ yuan each, the backpack is $$128$$ yuan each. Eddie needs to buy $$32$$ pencils, $$24$$ stationery boxes, $$65$$ fountain pens, $$9$$ backpacks, costing Eddie yuan."}, {"key": "7171", "content": "Set up and calculate the division, then check your answer: (1) $$217\\div 7=$$\uff0e(2) $$692\\div 9=$$$$\\cdots \\cdots $$\uff0e(3) $$609\\div 3=$$\uff0e(4) $$524\\div 5=$$$$\\cdots \\cdots $$\uff0e(5) $$600\\div 5=$$\uff0e(6) $$243\\div 6=$$$$\\cdots \\cdots $$\uff0e"}, {"key": "7172", "content": "Set up vertical calculations and verify: (1) $$8104\\div 4=$$\uff0e (2) $$2009\\div 2=$$$$\\cdots \\cdots $$\uff0e (3) $$2340\\div 9=$$\uff0e (4) $$4802\\div 4=$$$$\\cdots \\cdots $$\uff0e"}, {"key": "7173", "content": "Based on the rule of change of the quotient, directly from $$48\\div 6=8$$, quickly calculate the following problems: (1)$$96\\div 12=$$. (2)$$144\\div18=$$. (3)$$192\\div 6=$$. (4)$$48\\div3=$$."}, {"key": "7174", "content": "Complete the following questions: (1) Eddie completes $$24$$ questions in $$6$$ hours, at this rate, how many questions can he complete in $$8$$ hours. (2) Vi completes $$45$$ questions in $$5$$ hours, at this rate, how many hours does she need to complete $$81$$ questions."}, {"key": "7175", "content": "It is known that $$5$$ monkeys picked $$35$$ peaches in $$1$$ hour. question_7175-image_0 (1) Based on this calculation, $$6$$ monkeys can pick peaches in $$1$$ hour. (2) Based on this calculation, $$8$$ monkeys can pick peaches in $$4$$ hours."}, {"key": "7176", "content": "$$3$$ workers process $$90$$ parts in $$5$$ hours. If each worker processes the same amount per hour, $$10$$ workers will process parts in $$10$$ hours."}, {"key": "7177", "content": "$$2$$ monkeys eat $$2$$ bunches of bananas in $$2$$ days, at this rate, $$4$$ monkeys will eat bunches of bananas in $$4$$ days, $$6$$ monkeys need to eat $$6$$ bunches of bananas, it takes days."}, {"key": "7178", "content": "$$7$$ vehicles of \"Flying Legs\" brand trucks transport $$6$$ trips can carry away $$336$$ tons of sand. Based on this calculation: (1) If another $$8$$ trucks are added, $$4$$ trips can carry away tons. (2) There are currently $$840$$ tons of sand, it requires $$5$$ trips to transport completely, in total needing vehicles."}, {"key": "7179", "content": "Mo Mo and Kaliya went to the stationery store together to buy things. Together, they brought $$22$$ yuan. Kaliya used her money to buy $$8$$ composition books, and Mo Mo used his money to buy $$6$$ single-line notebooks, and they both spent all their money. It is known that the money for $$1$$ composition book can buy $$2$$ single-line notebooks. Mo Mo brought yuan, Kaliya brought yuan. If Kaliya changed to buying single-line notebooks and Mo Mo changed to buying composition books, then together they could buy a total of notebooks."}, {"key": "7180", "content": "Convert the following fractions to mixed numbers: $$\\frac{4}{3}=$$; $$\\frac{7}{5}=$$; $$\\frac{15}{7}=$$."}, {"key": "7181", "content": "Convert the following fractions into improper fractions: $$1\\frac{2}{3}=$$; $$2\\frac{3}{5}=$$; $$1\\frac{4}{7}=$$."}, {"key": "7182", "content": "Calculate: (1) $$\\frac{1}{53}+\\frac{2}{53}=$$\uff0e(2) $$\\frac{5}{79}-\\frac{1}{79}=$$\uff0e(3) $$\\frac{7}{117}+\\frac{8}{117}-\\frac{5}{117}+\\frac{1}{117}=$$\uff0e(4) $$\\frac{7}{92}-\\left( \\frac{5}{89}+\\frac{7}{92} \\right)+\\frac{6}{89}=$$\uff0e"}, {"key": "7183", "content": "This year, Dad's age is $$\\frac{1}{2}$$ of Grandpa's, so we can divide Grandpa's age into two parts, with Dad's age being one of them. It is also known that Xiao Ming's age is $$\\frac{2}{7}$$ of Dad's age, so similarly, we can divide Dad's age evenly into $$7$$ parts, with Xiao Ming's age being $$2$$ parts. It is also known that Grandpa is $$84$$ years old this year, and Xiao Ming is years old this year."}, {"key": "7184", "content": "A rope $$16$$ meters long, the first time cut it by $$\\frac{1}{2}$$, the second time cut the remaining $$\\frac{1}{2}$$, the third time cut the remaining $$\\frac{1}{2}$$, then there are meters left."}, {"key": "7185", "content": "On one side of a road with a total length of $$2700$$ meters, a pine tree is planted every $$10$$ meters, and between every two adjacent pine trees, a willow tree is planted every $$2$$ meters. The number of willow trees planted is."}, {"key": "7186", "content": "On both sides of a 120 meter long road, a plane tree is planted every 20 meters (including both ends). Between every two adjacent plane trees, another camphor tree is planted. Thus, a total number of trees planted on both sides of the road is. (The width of the trees is negligible)"}, {"key": "7187", "content": "Please answer the following questions: (1) In a military parade, a convoy of decorated vehicles being reviewed has a total of $$30$$ vehicles, each vehicle is $$4$$ meters long, and there is a $$5$$ meter space between each vehicle. The total length of this convoy is meters. (2) The total length of a train is $$532$$ meters, including a $$12$$ meter long locomotive, each of the remaining carriages is $$25$$ meters long, and it is known that the distance between every two carriages (including the locomotive) is $$1$$ meter, how many carriages are there in total in this train. (Including the locomotive)"}, {"key": "7188", "content": "Cinderella attended the prince's ball, and the clock on the wall struck three times at $$3$$ o'clock, completing in $$6$$ seconds (ignoring the time it takes to strike). Thus, if it takes twelve strikes at $$12$$ o'clock, and Cinderella must leave the banquet before the twelve strikes are completed, then Cinderella has seconds to escape starting from the first strike at $$12$$ o'clock."}, {"key": "7189", "content": "Eddie and the Doctor were racing up the stairs, starting from floor $$1$$. When Eddie reached floor $$4$$, the Doctor was at floor $$3$$. By that calculation, when Eddie reached floor $$16$$, the Doctor reached floor $$.$$"}, {"key": "7190", "content": "Xiao Ming plants trees around the playground, initially planting one every $$3$$ meters. After planting the $$17$$th tree, he found that there were not enough saplings, so he decided to replant, changing to one every $$4$$ meters. When replanting, there was a tree that did not need to be removed."}, {"key": "7191", "content": "This year, Ning is $$9$$ years old, mom is $$34$$ years old, when mom is $$52$$ years old, Ning will be years old."}, {"key": "7192", "content": "The older brother and younger brother had an age difference of $$5$$ years last year, and this year the sum of their ages is $$15$$ years. So, this year the older brother is __ years old, and the younger brother is __ years old. question_7192-image_0"}, {"key": "7193", "content": "There is a rectangular piece of paper, whose length is $$10$$ cm and width is $$5$$ cm. (1) Cut horizontally with scissors once (as shown in the figure), adding centimeters; if cut vertically once, it will add centimeters. question_7193-image_0 (2) If cutting horizontally and vertically with scissors twice each, then the sum of the perimeters of all the small rectangles formed is centimeters."}, {"key": "7194", "content": "Calculate: $$\uff081\uff0968+66-37-51+72-29+34$$=$$\uff082\uff0982-16+37-24+58-17+66-26$$="}, {"key": "7195", "content": "Calculate: $$\uff081\uff0930-29+28-27+26-25+24-23+22-21+20-19+18-17$$=$$\uff082\uff0920+21-22+23-24+25-26+27-28+29-30+31-32+33$$="}, {"key": "7196", "content": "Calculate: $$\uff081\uff0960-59-58+57+56-55-54+53+52-51-50+49+48-47-46+45$$=$$\uff082\uff09100+10-11-12+13+14-15-16+17+18-19-20+21+22-23-24+25$$="}, {"key": "7197", "content": "As shown in the diagram, an electronic flea can jump from one circle to an adjacent one with every leap. Now, a red flea jumps 123 steps clockwise from the circle marked with the number $$0$$, and lands in a circle. A black flea also starts from the circle marked with $$0$$ but it jumps 320 steps counter-clockwise, and lands in another circle. Question: What is the product of the numbers in these two circles. question_7197-image_0"}, {"key": "7198", "content": "The school organized a picking activity, with a total of $$55$$ people participating. There were $$30$$ people picking strawberries and $$30$$ people picking grapes. There were $$7$$ people who picked neither, and there were people who picked both types of fruit."}, {"key": "7199", "content": "There is a rectangular piece of paper with a length of $$10$$ cm and a width of $$5$$ cm. (1) Cut horizontally with scissors once (as shown in the diagram), increasing the length in centimeters; cut vertically once, increasing the width in centimeters. question_7199-image_0 (2) Cut horizontally and vertically with scissors five times each, then the sum of the perimeters of all the small rectangles divided is in centimeters."}, {"key": "7200", "content": "The last item of the outdoor expansion is first aid knowledge training. The school prepared some first aid kits. If they are all distributed to the third grade, with $$10$$ per class, then $$8$$ are left; if they are all distributed to the fourth grade, with $$12$$ per class, then $$22$$ are missing. It is known that there are $$2$$ fewer classes in the third grade than in the fourth grade. (1) The fourth grade has two more classes than the third grade, and these two classes were given first aid kits. (2) The third and fourth grades have and classes respectively, and there are a total of first aid kits. (Fill in the order)"}, {"key": "7201", "content": "List and calculate vertically: (1) The age of an ancient tree is $$504$$ years, Xiao Ming's age is $$9$$ years, the age of this ancient tree is times the age of Xiao Ming. (2) At the National Day parade, a rectangular marching troop has $$658$$ people. If there are $$7$$ people per row, there are total rows."}, {"key": "7202", "content": "In order to restore the ecology of the magic forest, Eddie planted $$28$$ trees on one side of a road, planting one tree every three meters. (1) If Eddie planted trees from one end of the road to the other, the length of this road in meters is. (2) If trees are not planted at one end, the length of this road in meters is. (3) If trees are not planted at both ends, the length of this road in meters is."}, {"key": "7203", "content": "The little monkeys in the Flower Fruit Mountain are eating peaches. If $$6$$ monkeys can eat $$180$$ peaches in $$3$$ days, based on this calculation: (1) One monkey can eat $$400$$ peaches in $$5$$ days. (2) It takes $$10$$ monkeys $$200$$ peaches to eat for days."}, {"key": "7204", "content": "It takes $$10$$ people $$15$$ days to finish a road. Based on this calculation, if only $$3$$ people are working on it, then the number of days needed to finish this road will increase by ."}, {"key": "7205", "content": "$$1+2+3+\\cdots +22+23+24=$$\uff0e"}, {"key": "7206", "content": "There is a triangle in the right figure.\n question_7206-image_0"}, {"key": "7207", "content": "Among the students in the class, there are $$15$$ people who can swim, $$19$$ people who can play basketball. There are $$7$$ people who can do both. The class has a total of people."}, {"key": "7208", "content": "A survey of the whole class found that $$16$$ people can swim, $$21$$ people can play basketball, $$10$$ people can do both, and $$8$$ people can do neither. There are a total of people in this class."}, {"key": "7209", "content": "Weier numbered her diary from page $$1$$ to page $$32$$, totaling how many numbers were written."}, {"key": "7210", "content": "If a book has a total of $$150$$ pages, the numbers of digits used in pages $$1\\sim 150$$ altogether are."}, {"key": "7211", "content": "Eddie read a comic book, he read from page $$1$$ to page $$66$$ on the first day, a total of pages; the second day from page $$67$$ to page $$135$$, a total of pages."}, {"key": "7212", "content": "Expanding $$81.376$$ to $$10$$ times its original size is; reducing $$156.2$$ to $$\\frac{1}{100}$$ of its original size is."}, {"key": "7213", "content": "As shown in the figure, it is known that $$\\angle 1=60{}^\\circ $$, find what degree $$\\angle 2$$ is. question_7213-image_0"}, {"key": "7214", "content": "As shown in the figure, it is known that $$\\angle 1=72{}^\\circ $$, find the degree of $$\\angle 2$$. question_7214-image_0"}, {"key": "7215", "content": "Last year, the age difference between the elder brother and the younger brother was 5 years, and this year the sum of their ages is 15 years. How old are the elder brother and the younger brother this year? Elder brother: years, Younger brother: years"}, {"key": "7216", "content": "Xiaoming is $$8$$ years old this year, and his mother is $$44$$ years old. When Xiaoming was at a certain age, his mother's age was exactly $$4$$ times Xiaoming's age."}, {"key": "7217", "content": "Dongdong is $$10$$ years old this year, the sum of his parents' ages is $$80$$ years old, then the total age of the three of them next year would be $$120$$ years."}, {"key": "7218", "content": "The sum of five consecutive natural numbers is $$100$$, the largest of these natural numbers is."}, {"key": "7219", "content": "Calculate: $$6.33+12.25-9.377=$$."}, {"key": "7220", "content": "Xiaoqing's age 2 years ago is equal to Xiaojing's age 1 year from now, and the sum of Xiaoqing's age 3 years ago and Xiaojing's age 2 years from now is 20 years old. So, Xiaoqing is years old this year, and Xiaojing is years old this year."}, {"key": "7221", "content": "If the sum of $$\\angle A$$ and $$\\angle B$$ is $$160{}^\\circ$$, and $$\\angle A$$ is three times $$\\angle B$$, then $$\\angle B=$$${}^\\circ$$ ."}, {"key": "7222", "content": "There are a total of several triangles in the image.\n question_7222-image_0"}, {"key": "7223", "content": "During the military training, the students formed a three-layer hollow square formation consisting of $$204$$ people. How many people are there on each side of the outermost layer?"}, {"key": "7224", "content": "The doctor allocates his monthly salary in the following manner: half of the monthly salary is deposited into the bank, half of the remaining amount minus $$300$$ is used to pay the mortgage, then half of the leftover amount plus $$300$$ is used for meal expenses, leaving $$800$$ remaining. The doctor's monthly salary is __ yuan."}, {"key": "7225", "content": "There is a team of students arranged in a hollow square formation, with the outermost layer having a total of $$52$$ people, and the innermost layer having a total of $$28$$ people. This team has a total of people."}, {"key": "7226", "content": "Eddie is $$9$$ years old this year, his mom is $$37$$ years old this year, in $$6$$ more years, how many years older will the mom be compared to Eddie? ( )"}, {"key": "7227", "content": "A basketball player participated in $$10$$ games, and he scored $$23$$, $$14$$, $$11$$, and $$20$$ points in the $$6$$th, $$7$$th, $$8$$th, and $$9$$th games, respectively. His average score in the first $$9$$ games was higher than in the first $$5$$ games. If his average score in the $$10$$ games exceeded $$18$$ points, then the minimum score he must have had in the $$10$$th game is."}, {"key": "7228", "content": "$$35$$ numbers arranged in $$5$$ rows and $$7$$ columns. The average of the $$7$$ columns are $$39$$, $$41$$, $$40$$, $$45$$, $$42$$, $$39$$, $$41$$ respectively, and the averages of the first $$4$$ rows are $$42$$, $$39$$, $$44$$, $$41$$ respectively. Then, the average of the last row is."}, {"key": "7229", "content": "The average age of male teachers at a certain school is $$27$$ years old, the average age of female teachers is $$32$$ years old, and the average age of all teachers is $$30$$ years old. If there are $$13$$ fewer male teachers than female teachers, then the school has a total of teachers."}, {"key": "7230", "content": "Mixing milk candy and fruit candy together makes mixed candy, with an average price per kilogram of $$9.13$$. Knowing there are $$35$$ kilograms of milk candy priced at $$10.3$$ per kilogram, and fruit candy priced at $$8.5$$ per kilogram, then how many kilograms of fruit candy are there?"}, {"key": "7231", "content": "Given that the average of seven numbers $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, $$F$$, $$G$$ is $$15$$, where the average of the first $$5$$ numbers is $$14$$ and the average of the last $$5$$ numbers is $$16$$, then the average of $$C$$, $$D$$, and $$E$$ is."}, {"key": "7232", "content": "In a kindergarten, there are senior, middle, and junior classes totaling 420 students. During an exam, it is known that the senior class has an average score of 88, the middle class has an average score of 84, and the junior class has an average score of 83. If the average score of all the students in the kindergarten is 85, and the number of students in the senior class is twice that of the junior class, then, the number of students in the middle class is."}, {"key": "7233", "content": "Guan Yin Bodhisattva awarded some ginseng fruits to Tang Seng and his three disciples, and on average, the four of them owned $$20$$ ginseng fruits. Tang Seng and Sun Wukong on average owned $$24$$, and Sun Wukong, Zhu Bajie, and Sha Seng on average had $$16$$. Then, the number of ginseng fruits Sun Wukong had is\uff0e"}, {"key": "7234", "content": "The fruit store mixes 5 kilograms of crisp sugar at $$4$$ dollars per kilogram, 2 kilograms of fruit sugar at $$6$$ dollars per kilogram, and 5 kilograms of milk sugar at $$8$$ dollars per kilogram, to make mixed candy, whose price per kilogram is dollars."}, {"key": "7235", "content": "Class 1 of grade 4 has $$6$$ female students, their average height is $$140$$ cm. If one of them leaves, the average height of the remaining $$5$$ persons becomes $$135$$ cm. What is the height of the girl who left in cm."}, {"key": "7236", "content": "As shown in the figure, it is known that $$\\angle ACE=4\\angle ECB$$. The degree measure of $$\\angle DCE$$ is degrees. question_7236-image_0"}, {"key": "7237", "content": "In the police station, $$5$$ theft suspects are being interrogated by the police. Among them, only one is the real thief. Within the statements of these $$5$$ people, only $$3$$ statements are true. Who is the thief? A says: D is the thief; B says: I am not the thief; C says: I am very sure that E is not the thief; D says: A is lying; E says: What B said is true."}, {"key": "7238", "content": "Given a sequence of numbers $$3$$, $$7$$, $$11$$, $$15$$, $$19$$, $$\\cdots $$, $$43$$, then the total number of terms in this sequence is."}, {"key": "7239", "content": "Complete the following questions: Today is Thursday. Counting from today, the $$25$$th day falls on a."}, {"key": "7240", "content": "Today is Tuesday, in $$22$$ days it will be a week of."}, {"key": "7241", "content": "Complete the following questions: Every year on March 12 is Arbor Day. It is known that Arbor Day in a certain year is on a Monday. What day of the week is March 28 of that year?"}, {"key": "7242", "content": "One year on Children's Day, June 1, is Monday. The August 5 of that year falls on a ."}, {"key": "7243", "content": "February 8, 2008 was a Friday, February 8, 2009 was a Sunday."}, {"key": "7244", "content": "$$2015$$ year $$1$$ January $$1$$ is Thursday, $$2017$$ year $$2$$ February $$5$$ is Sunday."}, {"key": "7245", "content": "As shown in the diagram are two parts of toy blocks' plan (unit: centimeters), kids, please use your brain to calculate the perimeter. (1) question_7245-image_0 question_7245-image_8 \u200b\u200b\u200b\u200b\u200b\u200b\u200bThe perimeter is in centimeters (2)\u200b\u200b\u200b The perimeter is in centimeters"}, {"key": "7246", "content": "The numbers indicated in the image below represent the length of each side, in centimeters. Its perimeter is in centimeters. question_7246-image_0"}, {"key": "7247", "content": "In the diagram, two adjacent sides are perpendicular to each other, the perimeter of this shape is centimeters. (Unit: centimeters) question_7247-image_0"}, {"key": "7248", "content": "A shipping company needs to transport $$864$$ boxes of goods with a total of $$6$$ trucks. If each truck carries the same amount of cargo, then each truck needs to carry boxes of goods."}, {"key": "7249", "content": "The professor distributed $$137$$ reward cards evenly among $$8$$ students, and there was $$1$$ card left undistributed in the end. How many reward cards did each student receive?"}, {"key": "7250", "content": "Fill in the blanks with appropriate numbers to make the subtraction vertical method correct. From top to bottom, these three numbers are , , . question_7250-image_0"}, {"key": "7251", "content": "In the equation below, the same letters represent the same digits, and different letters represent different digits. Then, the number represented by \u201c$$\\overline{EDCAD}$$\u201d is. question_7251-image_0"}, {"key": "7252", "content": "Fill in each blank with an appropriate number so that the equation holds true. From top to bottom, these three numbers are respectively question_7252-image_0"}, {"key": "7253", "content": "In the following arithmetic figure, $$\\square $$, $$\\bigcirc $$, and $$\\triangle $$ each represent different numbers, where $$\\square $$ stands for, $$\\bigcirc $$ stands for, $$\\triangle $$ stands for. question_7253-image_0"}, {"key": "7254", "content": "Fill in the blanks with appropriate numbers to make the addition vertical problem below correct. From top to bottom, these three numbers are ,,. question_7254-image_0"}, {"key": "7255", "content": "Please calculate the numeric representation in the equation, where '\u5b66' represents, and '\u597d' represents. question_7255-image_0"}, {"key": "7256", "content": "As shown in the diagram, $$\\square $$, $$\\bigcirc $$, and $$\\triangle $$ each represent different numbers. $$\\square $$ represents , $$\\bigcirc $$ represents , $$\\triangle $$ represents. question_7256-image_0"}, {"key": "7257", "content": "Using the numbers $$1\\sim5$$, fill in the blanks in the vertical equation below. (Each number can only be used once.) From top to bottom, the two numbers are respectively. question_7257-image_0"}, {"key": "7258", "content": "One side of the road needs to be paved with tiles, with a total length of $$80$$ meters. If $$4$$ workers work at the same time, it can be completed in $$10$$ days, with each person having the same workload every day. If it is required to be completed in $$8$$ days, then additional workers are needed."}, {"key": "7259", "content": "A super spacecraft requires $$120$$ liters of gasoline to travel $$30$$ kilometers. If each super spacecraft consumes the same amount of gasoline per kilometer, and now $$5$$ super spacecrafts are transporting goods to a place $$80$$ kilometers away together, the amount of gasoline needed in liters is."}, {"key": "7260", "content": "$$5$$ individuals can type $$300$$ characters in $$3$$ minutes. Based on the current speed, $$8$$ individuals can finish typing a manuscript in $$20$$ minutes, which has characters."}, {"key": "7261", "content": "5 boxes of bees can produce $$50$$ kg of honey in a year. Based on this calculation, to produce $$90$$ kg of honey in a year, the number of bee boxes needs to be increased."}, {"key": "7262", "content": "Answer the question as required: (1) When we divide $$3$$ pizzas equally among $$3$$ people, $$3\\div 3=1$$ (piece), we can say each person gets $$1$$ pizza. Then, if we want to divide $$1$$ pizza equally between $$2$$ people, $$1\\div 2=\\frac{1}{2}$$ (piece), we can say each person gets $$\\frac{1}{2}$$ of a pizza. So how would you represent the following image with numbers? Please write down what fraction of the whole (considering each pizza as a whole) is taken out with a fork. question_7262-image_0 \u200b\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\\\\ \\\\"}, {"key": "7263", "content": "(2) Based on the answer from the score wall, divide the unit \"1\" into $$10$$ equal parts, take $$7$$ parts of them, represented as a fraction. The numerator of this fraction is, the denominator is, its fractional unit is, and there are units of the fractional unit; question_7263-image_0 question_7263-image_2 \u200b\u200b"}, {"key": "7264", "content": " question_7264-image_1 (3) Based on the fraction wall, the meaning of $$\\frac{5}{8}$$ is to divide the unit \"1\" evenly into parts, taking among them parts, its fraction unit is $$\\frac{1}{8}$$, and there are  parts in total. question_7264-image_3"}, {"key": "7265", "content": "Please write out the fractions indicated by the shaded area or the curly brackets in the image. From left to right, from bottom to top, these $$4$$ blanks are respectively ,,,. question_7265-image_0"}, {"key": "7266", "content": "There is a circular flower bed in the square. The circumference of the flower bed is $$80$$ meters. Now, a pot of flowers is to be placed every $$8$$ meters around the edge of the flower bed. A total number of pots that can be placed is ."}, {"key": "7267", "content": "A stick of $$20$$ meters long is cut into $$5$$ equal parts, each part is meters."}, {"key": "7268", "content": "Calculate: $$168-(136+111)+143-(254-211)+(132+137)$$="}, {"key": "7269", "content": "Da Ming, Er Ming, San Ming, and Si Ming went to buy fruits. They each had their own tasks: one bought watermelons, one bought apples, one bought bananas, and one bought dragon fruit. Based on the four conditions below, please analyze the distribution of their tasks. ($$1$$) Da Ming does not buy watermelons or dragon fruit; ($$2$$) Si Ming does not buy bananas or watermelons; ($$3$$) Er Ming does not buy watermelons or bananas; ($$4$$) If Si Ming does not buy dragon fruit, then San Ming will not buy watermelons. Da Ming buys, Er Ming buys, San Ming buys, Si Ming buys."}, {"key": "7270", "content": "Perform vertical multiplication calculations: (1) $$45\\times 32=$$\uff0e(2) $$46\\times 35=$$\uff0e(3) $$89\\times 64$$="}, {"key": "7271", "content": "(1) The school organized a charity sale, and Wei'er was in charge of sales. Wei'er sold $$25$$ boxes of apples, each box containing $$36$$ apples, and each apple was sold for $$4$$ yuan. How much money did Wei'er make in total? question_7271-image_0 4$$\\times$$(2) Please simplify the following expression $25\\times6\\times4$=$8\\times9\\times125$="}, {"key": "7272", "content": "$$2020$$ year $$10$$ month $$1$$ day is Thursday. Starting from this day, the $$25$$th day falls on a ."}, {"key": "7273", "content": "The 10th of August in that year falls on a week."}, {"key": "7274", "content": "When Lili was doing addition, she misread one of the digits in the unit place of an addend as $$9$$, which resulted in a result that was $$3$$ less than the correct answer. What did Lili mistakenly read $$9$$ as?"}, {"key": "7275", "content": "A deck of playing cards contains $$54$$ cards, among which there are $$2$$ joker cards, and $$13$$ cards each of the four suits: spades, hearts, clubs, and diamonds. (3) At least how many cards must be drawn to ensure drawing three $$A$$s."}, {"key": "7276", "content": "As shown in the figure, there is a vertical addition equation, where $$\\triangle $$, $$\\square $$, and $$\\Diamond$$ represent three different numbers, respectively. Then, $$\\triangle +\\square -\\Diamond$$ is equal to _. question_7276-image_0"}, {"key": "7277", "content": "The total age of father, mother, and daughter this year is $$88$$ years, the mother's age is $$3$$ times the daughter's age, and the father's age is $$8$$ years less than $$4$$ times the daughter's age, so the daughter's age this year is."}, {"key": "7278", "content": "Wei'er and her mother have a combined age of $$40$$ years this year. In $$3$$ more years, what will be their combined age? ( )"}, {"key": "7279", "content": "20 people originally planned to produce 2000 parts in 10 days, but actually found 5 more helpers before starting work, and each person makes 6 more parts per day than originally planned. Then, in reality, all parts can be completed in just a few days."}, {"key": "7280", "content": "When Xiaoming was $$9$$ years old, his father was $$37$$ years old. The age of Xiaoming's father was exactly $$3$$ times Xiaoming's age."}, {"key": "7281", "content": "Arithmetic sequence: $$4$$, $$7$$, $$10$$, $$13$$, \u2026\u2026, $$40$$, this sequence has a total number of elements."}, {"key": "7282", "content": "The elder brother has $$95$$ books, and the younger brother has $$155$$ books. After the elder brother gave the younger brother some books, the total number of books the younger brother has exactly became $$4$$ times that of the elder brother. (1) After the elder brother gave the younger brother some books, how many books do the elder brother and the younger brother have in total. (2) How many books did the elder brother give to the younger brother? question_7282-image_0"}, {"key": "7283", "content": "There are east and west stations in a certain town. The east station has $$84$$ buses, and the west station has $$56$$ buses. To make the number of buses at the east station $$4$$ times that of the west station, how many buses need to be transferred from the west station to the east station? question_7283-image_0"}, {"key": "7284", "content": "Originally, Class B had $$6$$ times more books than Class D. Now, after giving $$20$$ books to Class D, Class B has $$5$$ fewer books than Class D. How many books did Class B and Class D originally have?"}, {"key": "7285", "content": "Using the numbers $$1$$, $$2$$, $$3$$ to form odd numbers with no repeating digits."}, {"key": "7286", "content": "In a certain place, there are four different denominations of coins as shown in the figure. Assuming you have exactly one of each of these four coins. How many different amounts of money can you make? question_7286-image_0 question_7286-image_1 question_7286-image_2 question_7286-image_3"}, {"key": "7287", "content": "In a certain place, there are three types of coins with different denominations, as shown in the picture. Assuming you have the following four coins, how many different amounts of money can be formed. question_7287-image_0"}, {"key": "7288", "content": "Perform vertical calculation: $$(1) 132\\times 21=$$ $$(2) 124\\times 23=$$"}, {"key": "7289", "content": "There is a series of numbers arranged in the order of 141592614159261415926$\\cdots\\cdots$, the $$100$$th number is . In these $$100$$ numbers, the digit \u201c1\u201d appears a total of times."}, {"key": "7290", "content": "(Stage Test) Calculate using the simplest method: $32\\times(100+3)=$"}, {"key": "7291", "content": "(Stage Test) Complete a third-order magic square, with the magic sum equal to. question_7291-image_0"}, {"key": "7292", "content": "The perimeter of a rectangle is $$30$$ cm, and its length is $$11$$ cm, then the width of this rectangle is, and the area is."}, {"key": "7293", "content": "Briar Bear and Bramble Bear originally collected the same amount of honey jars. After one week, Briar Bear collected an additional 12 honey jars, while Bramble Bear not only did not collect any new honey jars but also consumed 18 of them. At this point, the number of honey jars Briar Bear had was 3 times that of Bramble Bear. So, how many honey jars did Bramble Bear originally have?"}, {"key": "7294", "content": "Viola went to the aquarium for fun and counted a total of $$176$$ sea apples, sea anemones, and starfish. The number of sea anemones is $$2$$ times the number of sea apples, and the number of starfish is $$4$$ times the number of sea apples plus $$1$$. Do you know how many sea apples, sea anemones, and starfish there are? (Represented with a line segment diagram)"}, {"key": "7295", "content": "Calculate using a simple method: $768\\div8+232\\div8=$"}, {"key": "7296", "content": "A, B, and C are passing a ball, starting with A holding the ball. The first pass from A is considered the first time the ball is passed. The ball cannot be passed back to oneself. After three passes, how many different passing methods are there? Among them, how many methods return the ball to A's hands? (Represent with a tree diagram)"}, {"key": "7297", "content": "A little ant starts from point $$A$$ and reaches point $$B$$ along the lines in the diagram, it can only move up or to the right, and it cannot pass through point $$C$$. There are a total of different routes. question_7297-image_0"}, {"key": "7298", "content": "There is a three-layer hollow square matrix on the square, with a total of $$252$$ people, with people on each side of the outer layer."}, {"key": "7299", "content": "$$330.08-135.8+6.8=$$\uff0e"}, {"key": "7300", "content": "Eddie is $$8$$ years old this year. He asked the doctor how old he is this year, and the doctor said: \"When you reach my age, I will already be $$86$$ years old.\" So, how old is the doctor this year."}, {"key": "7301", "content": "Given an arithmetic sequence $$5$$, $$8$$, $$11$$, $$14$$... The $$10$$th number is, and the sum of these $$10$$ numbers is."}, {"key": "7302", "content": "Fill in \"$$+$$\" in the appropriate places to make the equation valid (two adjacent numbers can form one number). $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7=99$$ The correct way to fill in is ( )."}, {"key": "7303", "content": "As shown in the figure, $$\\angle 1=\\angle 2=30{}^\\circ $$, $$\\angle 3=\\angle 4=\\angle 5=$$ degrees. question_7303-image_0"}, {"key": "7304", "content": "The third grade class one participates in a summer camp outing. If each tent houses $$4$$ people, then there are $$10$$ people without a tent. If each tent houses $$6$$ people, then there is one extra tent with no one living in it. There are people in the third grade class one."}, {"key": "7305", "content": "Split $$6$$ into the sum of $$3$$ natural numbers, there are a total of different methods."}, {"key": "7306", "content": "Count the number of triangles in the image. question_7306-image_0"}, {"key": "7307", "content": "A store held a lottery event, placing 100 red, blue, and yellow balls each in a box. Exchanging 50 balls of the same color for a stuffed toy, 80 balls of the same color for a snack pack, and 85 balls of the same color for a model. Each ball can only be exchanged for a prize once. Xiao Ming participates in the lottery, where he can only draw one ball from the box without putting it back each time. He needs to draw several times to guarantee that he can exchange for each type of prize at least once."}, {"key": "7308", "content": "(1) The length of the rectangle is $$2a$$, and the width is $$b$$. The perimeter of the rectangle is, and the area is.\n(2) Chickens and rabbits have a total of $$120$$ legs, with $$y$$ rabbits. Thus, there are legs for rabbits, legs for chickens, and chickens."}, {"key": "7309", "content": "It is known that a certain school has 16 classes in the fifth grade, each with 36 students; and 13 classes in the sixth grade, each with 38 students. Therefore, the total number of students in the fifth and sixth grades of this school is ."}, {"key": "7310", "content": "The blank part in the picture is the safe area, and the shaded part contains $$3$$ mines. Please mark them with \u201c$$\\rm X$$\u201d. There is a mine in the $$3$$rd row and a mine in the $$5$$th column. question_7310-image_0"}, {"key": "7311", "content": "In the shaded area of the chart, which squares are mines, mark with \u201c$$X$$\u201d; which squares are safe zones, mark with \u201c$$O$$\u201d\uff0e question_7311-image_0 There are a total of mines in the three diagrams."}, {"key": "7312", "content": "In the squares shaded with shadows, which ones are mines, mark \u201c$$X$$\u201d on the squares, and which ones are safe zones, mark \u201c$$O$$\u201d on the squares. There are a total of mines. question_7312-image_0"}, {"key": "7313", "content": "On Sunday, the Young Pioneers helped to clean the windows at the nursing home, Xiao Hua cleaned $$7$$ windows, Xiao Hong and Xiao Gang worked together to clean $$13$$ windows, and Xiao Fang cleaned $$4$$ windows. On average, each person cleaned windows."}, {"key": "7314", "content": "In a basketball team of six people, the average height of everyone is $$150$$ cm. Among them, the average height of $$4$$ team members is $$2$$ cm lower than the average height of the whole team, and the average height of the other $$2$$ team members is cm."}, {"key": "7315", "content": "In the future, in Class 5 of Grade 3 of elementary school, Group 1 has $$3$$ boys and $$5$$ girls. It is known that in a skipping rope competition, the girls' average score is $$98$$ points, and the boys' average score is $$90$$ points. Then, the average score of this group of students is points."}, {"key": "7316", "content": "Class A, B, and C have $$45$$, $$57$$, and $$54$$ students respectively. It is known that the average score of Class A is $$92$$ points, the average score of Class B is $$90$$ points, and the total average score of the three classes is $$93$$ points. The average score of Class C is points."}, {"key": "7317", "content": "Xiao Ming participated in a shooting competition. He fired a total of $$10$$ shots, each shot hit the target, as shown by the \u201c$$\\times$$\u201d in the diagram below. The numbers in the diagram indicate the scores that can be obtained by hitting different parts of the target. Please calculate Xiao Ming's average score per shot. question_7317-image_0"}, {"key": "7318", "content": "Complete the following questions. (1) The different two-digit numbers that can be formed using the digits $$1$$, $$2$$, $$3$$. (2) The different three-digit numbers that can be formed using the digits $$1$$, $$3$$, $$6$$."}, {"key": "7319", "content": "The circus bought some red, yellow, and blue balloons to decorate the circular stage. A red balloon was tied up at regular intervals, exactly using up the $$40$$ red balloons that were purchased. Next, a yellow balloon was tied in the exact middle position between every two adjacent red balloons, resulting in a shortage of $$3$$ yellow balloons. Finally, a blue balloon was tied between each pair of adjacent balloons, exactly using up all the blue balloons. So, the number of yellow and blue balloons bought by the circus was."}, {"key": "7320", "content": "A Ph.D. wants to make a wooden stool, he first saws a piece of wood into $$4$$ pieces, taking $$12$$ minutes. To saw another piece of wood into $$8$$ pieces, it would take minutes. (Assuming the time taken for each sawing by the Ph.D. is the same)"}, {"key": "7321", "content": "Two ropes, the first one is $$31$$ meters long, the second one is $$19$$ meters long. After cutting off the same length from both, the remaining length of the first rope is $$3$$ times the length of the second rope. The remaining length of the first rope is meters, the second rope's remaining length is meters."}, {"key": "7322", "content": "100 teachers and students participate in greening the campus, with each teacher planting 3 trees and every two students planting 1 tree, for a total of 100 trees planted. How many trees did the students plant in total."}, {"key": "7323", "content": "The father is $$34$$ years old this year, and the son is $$9$$ years old. $$x$$ years ago, the father's age was $$6$$ times that of the son."}, {"key": "7324", "content": "6 years ago, the mother's age was 5 times that of her son, 6 years later, the combined age of the mother and son will be 78 years old. Question: How old is the mother this year ()?"}, {"key": "7325", "content": "As shown in the figure, it is known that $$\\angle 1=72{}^\\circ $$, $$\\angle 2$$ is in degrees. question_7325-image_0"}, {"key": "7326", "content": "As shown in the figure, it is known that $$\\angle 1=72{}^\\circ $$, find $$\\angle 2$$ in degrees. question_7326-image_0"}, {"key": "7327", "content": "Perform vertical calculation: $$\uff081\uff09408\\div 4$$=$$\uff082\uff091216\\div 4$$="}, {"key": "7328", "content": "This year, Ningning is $$9$$ years old, mom is $$34$$ years old. When mom is $$52$$ years old, Ningning will be $$.$$ years old."}, {"key": "7329", "content": "In 2020, three classmates had an average of $50 per person per month for pocket money. After Dan joined, the average pocket money for the four of them increased by $3. Dan has $ per month for pocket money."}, {"key": "7330", "content": "As shown in the figure, it is known that $$\\angle AOB=32{}^\\circ $$, find the degree of $$\\angle BOC$$. question_7330-image_0"}, {"key": "7331", "content": "There are four people A, B, C, and D working as a gardener, florist, designer, and music conductor respectively. It is known that: A is allergic to pollen; Only B likes classical music; C, the music conductor, and the gardener do not know each other: What is Ding's profession?"}, {"key": "7332", "content": "Put all the $$7$$ identical lollipops into two different boxes, with no box left empty. Then, there are a total of different methods. question_7332-image_0"}, {"key": "7333", "content": "Count the rectangles below. question_7333-image_0"}, {"key": "7334", "content": "Given $$1000\\div a=b$$, $$500=c\\times d$$, $$e+f=800$$, find the value of $$(a\\times e\\div 2)\\times b+c\\times d\\times f$$. "}, {"key": "7335", "content": "If $$2{{x}^{2}}-{{y}^{3}}-4=0$$, then the value of $$10{{x}^{2}}-5{{y}^{3}}+5$$ is."}, {"key": "7336", "content": "Arithmetic sequence summation (Gauss summation): 1+2+3+4+5+6+\u2026\u2026+98+99+100=."}, {"key": "7337", "content": "Count the number of squares in the figure. question_7337-image_0"}, {"key": "7338", "content": "Count, how many line segments are there in total in the figure below? question_7338-image_0"}, {"key": "7339", "content": "Count, how many triangles are there in total in the figure. question_7339-image_0"}, {"key": "7340", "content": "The doctor took Eddie and Vi to the tropical fish museum. In one of the aquariums, there were a total of $$36$$ fish living together, in three different colors. Eddie found that the quantity of red fish was twice that of blue fish, and the quantity of green fish was three times that of red fish. So, how many fish are there of each color? Blue: fish Red: fish Green: fish"}, {"key": "7341", "content": "As shown in the figure, please fill in the appropriate numbers in the blanks in the diagram to make the multiplication vertical method valid. The result of this multiplication formula is 0 \u00d7 9 5 1 8"}, {"key": "7342", "content": "Calculate: $$80\\times 75-150+75\\times 22=$$."}, {"key": "7343", "content": "Calculate: $$24\\times 47+24\\times 54-24$$ =."}, {"key": "7344", "content": "At a point $$A$$ on a regular hexagon, there is a frog. If each side is considered as $$1$$ square, and the frog jumps clockwise with the number of squares jumped in the sequence of $$1$$, $$3$$, $$5$$, $$7$$, $$9\\ldots \\ldots $$, then on the $$45$$th jump, the frog lands on the point. question_7344-image_0"}, {"key": "7345", "content": "$$900\\div 25=$$\uff0e"}, {"key": "7346", "content": "January 4, 2016 is Monday, then March 11, 2016 is Friday."}, {"key": "7347", "content": "Xue Er Si altogether has $$956$$ students, the number of male students is $$2$$ times less than female students by $$4$$ people. Then, the number of male students is ____."}, {"key": "7348", "content": "The sum of three numbers A, B, and C is $$120$$. The number A is twice the number B, and the number C is $$20$$ more than the number B. The number C is."}, {"key": "7349", "content": "Schools A, B, and C have a total of 2999 students. It is known that twice the number of students in School A, minus 3 students in School B, plus 4 students in School C are equal. Hence, School A has, School B has, and School C has students."}, {"key": "7350", "content": "Calculate: $$68\\times 94+32\\times 96$$=."}, {"key": "7351", "content": "Calculate: $$25\\div 7+24\\div 7=$$."}, {"key": "7352", "content": "In the nine squares of the diagram, four numbers have already been filled in. Please fill in five more natural numbers so that the product of any three numbers in any row or column is equal. Then, the sum of all the numbers you filled in is. question_7352-image_0"}, {"key": "7353", "content": "In the natural number sequence $$1\\sim 500$$, the number of natural numbers that can be divided by $$3$$ or $$4$$ or $$5$$ is ."}, {"key": "7354", "content": "Xiaobai and Xiaohua saw a magical insect that doubles in size every hour. It can grow to 20 cm in 1 day. How many hours does it take for the insect to grow to 5 cm?"}, {"key": "7355", "content": "A and B each have a certain number of candies. A has fewer candies than B. In each operation, the person with more candies gives some to the person with less, making the number of candies of the latter increase by 1 times. After 2017 such operations, A has 10 candies, and B has 8 candies. A originally had candies, and B originally had candies."}, {"key": "7356", "content": "In a fourth-grade class of $$20$$ students, on a hot summer day, a few children went to a cold drink shop, each wanting at least one cold drink. Among them, $$6$$ children had popsicles, $$7$$ had sodas, $$4$$ had Sprite. There were $$3$$ children who had both popsicles and soda, $$1$$ who had both popsicles and Sprite, and $$1$$ who had both soda and Sprite; there was $$1$$ who had all three. Then, there were a number of children who did not go to the cold drink shop."}, {"key": "7357", "content": "Teacher Zhang said: \"If you add $$4$$ to my age, divide by $$4$$, then subtract $$4$$, and finally multiply by $$25$$, it happens to be $$100$$ years old.\" Teacher Zhang is $$ years old this year."}, {"key": "7358", "content": "Companies $$A$$, $$B$$, and $$C$$ often borrow trucks from each other for transport. On the first day, $$A$$ lends out a number of trucks equal to their own original number to companies $$B$$ and $$C$$. On the second day, $$B$$ lends out a number of trucks equal to their current number to companies $$A$$ and $$C$$. On the third day, $$C$$ lends out the same number of trucks as they currently have to companies $$A$$ and $$B$$. At this point, each company has $$48$$ trucks. Therefore, initially, the number of trucks company $$A$$ had, the number of trucks company $$B$$ had, and the number of trucks company $$C$$ had."}, {"key": "7359", "content": "The 15th number in the arithmetic sequence $$3$$, $$13$$, $$23$$, $$33$$, $$\\cdots$$ is."}, {"key": "7360", "content": "Calculate: $$\uff081\uff0968+66-37-51+72-29+34$$=$$\uff082\uff0982-16+37-24+58-17+66-26$$="}, {"key": "7361", "content": "Fang Fang and Yuan Yuan have a total of $$70$$ books. If Fang Fang gives Yuan Yuan $$5$$ books, then Yuan Yuan will have $$4$$ more books than Fang Fang. Question: How many books does Fang Fang have, and how many books does Yuan Yuan have?"}, {"key": "7362", "content": "Xiaoming is $$8$$ years old this year, and his mother is $$44$$ years old. When Xiaoming was a certain age, his mother's age was exactly $$4$$ times Xiaoming's age."}, {"key": "7363", "content": "Student Xiaoyang's final exam scores in three subjects are: $$88$$, $$93$$, $$89$$, respectively. The average score of these three subjects is ."}, {"key": "7364", "content": "Convert the following decimals to fractions: (1) $$0.83$$ = (2) $$0.009$$ = (3) $$0.5$$ = (4) $$0.23$$ ="}, {"key": "7365", "content": "Convert the following fractions into decimals. $$\\frac{7}{10}=$$; $$\\frac{7}{100}=$$; $$\\frac{7}{1000}=$$; $$\\frac{19}{100}=$$; $$\\frac{17}{1000}=$$; $$\\frac{409}{1000}=$$."}, {"key": "7366", "content": "First write down the fraction based on the picture, then write down the decimal: question_7366-image_0 From left to right are sequentially:,,,,,,,"}, {"key": "7367", "content": "Compare the sizes: $$18.9$$$$19.8$$; $$12.02$$$$12.2$$; $$56.310$$$$56.31$$."}, {"key": "7368", "content": "To expand $$6.103$$ by $$100$$ times is; to reduce $$320.7$$ to $$\\frac{1}{100}$$ of its original size is."}, {"key": "7369", "content": "The kind-hearted princess was chased by the wicked witch into the depths of the magical forest, where she came upon a fork in the road with three paths, each bearing a message.\nThe first path: 'This path leads to your castle.'\nThe second path: 'The first path does not lead to your castle.'\nThe third path: 'This path does not lead to your castle.'\nThe witch was closing in, and among the three statements, only one was true, and only one path could take the princess back to her castle. The princess should choose the path number. (Fill in the number)"}, {"key": "7370", "content": "$$ABC$$ three classmates chose different professions after graduation, one of them became a journalist. Once someone asked them about their professions, $$A$$ said: 'I am a journalist.' $$B$$ said: 'I am not a journalist.' $$C$$ said: '$$A$$ is lying.' If only one of their statements is true, then who is the journalist (fill in $$A$$ or $$B$$ or $$C$$)."}, {"key": "7371", "content": "4, 7, 10, 13, \u2026 the 10th number in this sequence is."}, {"key": "7372", "content": "Arithmetic sequence summation: $$12+16+20+24+28+32+36+40=$$"}, {"key": "7373", "content": "The birthday of the PhD is October 23rd. Knowing that September 1st, 2018, was a Saturday, then the PhD's birthday in 2019 falls on a weekday (fill in the number)."}, {"key": "7374", "content": "$$2017$$ year $$2$$ month $$1$$ day is Wednesday. $$2018$$ year $$2$$ month $$1$$ day is a week. (Fill in the number)"}, {"key": "7375", "content": "September 10, 2018 (Teacher's Day) is a Monday, the same year's September 29 is ( )."}, {"key": "7376", "content": "Fit two squares with side lengths of $$5$$ cm each into a rectangle. The perimeter of the formed rectangle is in cm."}, {"key": "7377", "content": "Xiaoming and his dad both had some marbles, after Xiaoming gave his dad $$5$$ marbles, Xiaoming had $$2$$ fewer marbles than his dad. How many more marbles did Xiaoming originally have than his dad?"}, {"key": "7378", "content": "The number of people in Class B is exactly $$5$$ times the number of people in Class A. If $$40$$ people are transferred from Class B to Class A, then the two classes will have the same number of people. The original number of people in Class B is people."}, {"key": "7379", "content": "Sisters have a total of $$42$$ notebooks, after the elder sister bought another $$6$$ notebooks, her total number of notebooks is $$3$$ times that of the younger sister, how many notebooks did the elder sister originally have."}, {"key": "7380", "content": "The number of apples in basket A is $$9$$ times that in basket B. If $$24$$ apples are taken from basket A and put into basket B, then the two baskets will have the same number of apples. Basket B originally had $$x$$ apples."}, {"key": "7381", "content": "If a number is divided by $$12$$, the quotient is $$30$$, with a remainder, then the largest possible dividend is."}, {"key": "7382", "content": "In a division equation, if the quotient is $$4$$ and the remainder is $$8$$, then the smallest possible dividend is."}, {"key": "7383", "content": "Calculate: $$5.6+5.96=$$\uff0e$$15.4-5.16=$$\uff0e"}, {"key": "7384", "content": "In solving a subtraction problem, due to a careless mistake, the subtrahend $$58$$ was mistaken for $$73$$, and the result was a difference of $$26$$. Therefore, the correct answer should be."}, {"key": "7385", "content": "When Xiao Ming was doing an addition problem, he mistook a digit in the units place for $$7$$ as $$2$$, and another digit in the tens place for $$9$$ as $$6$$, resulting in a sum of $$123$$. What should the correct sum be?"}, {"key": "7386", "content": "While working on a subtraction problem, due to carelessness, the minuend $$128$$ was mistaken for $$182$$, and the result obtained was $$102$$. Therefore, the correct answer should be."}, {"key": "7387", "content": "When Xiao Shuai was paying at the supermarket, the cashier carelessly mistook the 'amount due' $$69$$ for $$96$$, and as a result, gave Xiao Shuai $$4$$ back, the cashier should have given Xiao Shuai $$31$$."}, {"key": "7388", "content": "When Xiao Dong was doing a subtraction problem, he mistook the minuend $$75$$ for $$90$$, resulting in a difference of $$55$$. Then, the correct result is ()."}, {"key": "7389", "content": "When George was doing addition, he accidentally wrote a ten's digit $$7$$ as $$1$$ and a unit's digit $$6$$ as $$9$$. Then, the result will be ( )."}, {"key": "7390", "content": "The solid square formation of Class 1, Grade 5, has a total of $$36$$ people on the outermost layer, and there are people on each side of the outermost layer of this square formation."}, {"key": "7391", "content": "There are four small islands below, and the number on each island indicates the number of bridges connected to that island. Please connect all these small islands together. Note: (1) The direction of the bridges can only be horizontal or vertical; (2) At most two bridges can be built between any two islands. Then, two \"3\" should have bridges built between them. question_7391-image_0"}, {"key": "7392", "content": "There are four small islands below, and the number on each island indicates the number of bridges connected to the island. Please connect all these islands together. Note: ($$1$$) Bridges can only be in horizontal or vertical directions; ($$2$$) There can be at most two bridges between any two islands. So, can a bridge be built between two \"1\"s? question_7392-image_0"}, {"key": "7393", "content": "(1) The school organized a charity sale, and Wei Er was in charge of selling goods. Wei Er sold $$25$$ boxes of apples, with each box containing $$36$$ apples and each apple costing $$4$$ yuan. Calculate the total amount of money Wei Er made. question_7393-image_0 (2) Please simplify the following expressions $25\\times6\\times4$=$8\\times9\\times125$="}, {"key": "7394", "content": "Calculate (1) $$26\\times 99$$= (2) $$123\\times 999 $$= (3) $$37\\times 103$$="}, {"key": "7395", "content": "Columnar subtraction calculations: (1) $$330\\div 15$$=\uff0e(2) $$888\\div 24$$=\uff0e"}, {"key": "7396", "content": "Unit conversion: (1) $$5{{\\text{m}}^{2}}=$$ $$\\text{d}{{\\text{m}}^{2}}$$; $$3\\text{d}{{\\text{m}}^{2}}=$$ $$\\text{c}{{\\text{m}}^{2}}$$. (2) $$1200$$ $$\\text{c}{{\\text{m}}^{2}}$$= $$\\text{d}{{\\text{m}}^{2}}$$; $$3800$$ $$\\text{d}{{\\text{m}}^{2}}$$= $${{\\text{m}}^{2}}$$. "}, {"key": "7397", "content": "Fill in the blanks. (1) The perimeter of a square is $$36$$ meters, the side length of this square is meters, and the area of this square is square meters; (2) The area of a rectangle is $$40$$ square meters, the length is $$8$$ meters, the width is meters, and the perimeter of this rectangle is meters."}, {"key": "7398", "content": "Complete the following questions: (Fill in according to $$1.2.3.4.5.6.7$$) (1) March 12th is Arbor Day every year, it is known that Arbor Day was a Monday in a certain year, what day of the week was March 28th that year? (2) If Children's Day (June 1st) was a Monday in a certain year, what day of the week was August 5th that year?"}, {"key": "7399", "content": "A rhombus has a perimeter of $$52\\text{cm}$$, and one of its diagonals is $$10\\text{cm}$$ long, then its area is square centimeters."}, {"key": "7400", "content": "Using the numbers $$1$$, $$2$$, $$3$$, you can form different natural numbers."}, {"key": "7401", "content": "Two ropes of the same length, the first one is cut by $$31$$ meters, and the second one is cut by $$19$$ meters, the remaining length of the second rope is $$4$$ times that of the first one, the original length of each rope in meters."}, {"key": "7402", "content": "Fill in the appropriate numbers in the $$16$$ squares as shown (some numbers have been provided) so that the sum of the four numbers in each row, column, and diagonal is equal. Then, $$B\\times C-A\\times D=$$.\n question_7402-image_0"}, {"key": "7403", "content": "The 'Mastering Thinking Skills' series published by the Xueersi Exceptional Teaching and Research Department consists of two volumes, with the first volume having $$168$$ pages and the second volume having $$133$$ pages. Question: How many digits are used in total to number the pages of this set of books."}, {"key": "7404", "content": "\"How Steel Was Tempered\" is a novel written by the Soviet author Nikolai Ostrovsky, completed in $$1933$$. The novel tells the story of Pavel Korchagin's path to growth, explaining to people that one can only achieve miracles and grow into a steel warrior by overcoming both the enemy and oneself amidst the hardships of revolution, and by linking one's own aspirations with the interests of the motherland and its people. The book has a total of $$334$$ pages. How many times does the number \u201c0\u201d appear in all the page numbers of this book?"}, {"key": "7405", "content": "To number a encyclopedia requires $$6945$$ digits. So, how many pages does this book have in total."}, {"key": "7406", "content": "Answer the following question. December 31, 2018, is Monday, December 31, 2019, is what day of the week."}, {"key": "7407", "content": "Using a rectangle with a length of $$9$$ cm and a width of $$3$$ cm to form the shape shown below, the perimeter of the obtained shape is cm. question_7407-image_0"}, {"key": "7408", "content": "In the figure below, adjacent sides are perpendicular to each other. The perimeter of this shape is centimeters. (Unit: centimeters) question_7408-image_0"}, {"key": "7409", "content": "Perform the following calculations by setting up vertical calculations$$ (1) 136\\times 123=$$ $$ (2) 155\\times301=$$"}, {"key": "7410", "content": "To make $$450$$ divided by \u25a1 (where \u25a1 is a single digit), resulting in a quotient with a $$0$$ at the end, \u25a1 can be filled with."}, {"key": "7411", "content": "A professor evenly distributed $$137$$ reward cards among $$8$$ students, but in the end, there was $$1$$ card left undistributed. How many reward cards did each student receive?"}, {"key": "7412", "content": "Let's calculate everyone's New Year's money! (1) In 2020, the average amount of New Year's money for three classmates was $$120$$, and after adding Eddie's New Year's money, the average amount for four classmates became $$150$$, Eddie's New Year's money was $$.$$ (2) In 2020, the average amount of New Year's money for four classmates was $$160$$, and after removing Vi's New Year's money, the average amount for three classmates became $$150$$, Vi's New Year's money was $$.$$"}, {"key": "7413", "content": "The sum of two numbers, A and B, is $$620$$. If a third number, C, is added, the average of the three numbers is $$9$$ more than the average of the two numbers, A and B. Find the number C."}, {"key": "7414", "content": "The average height of four players in a basketball team is $$182$$ cm, and another player is $$8$$ cm shorter than the average height of these five players, the height of this player is."}, {"key": "7415", "content": "The image below is an incomplete order-4 magic square. Therefore, the values in the blanks A=, B=\uff0e question_7415-image_0"}, {"key": "7416", "content": "Uncle Zhou has a circular fish pond with a circumference of $$140$$ meters. He wants to plant a willow tree every $$5$$ meters along the pond, and he needs to plant willow trees."}, {"key": "7417", "content": "There is a triangular piece of land with sides measuring $$40$$ meters, $$50$$ meters, and $$70$$ meters, respectively. If one tree is planted every $$10$$ meters, and at each of the three corners, how many trees are there in total along the three sides. (The width of the trees is considered negligible)"}, {"key": "7418", "content": "An old grandfather walks at a steady pace. It takes him $$11$$ minutes to walk from his house to the $$11$$th tree, with each pair of adjacent trees being equally distant. If the grandfather walks for $$24$$ minutes, he should reach the $$nth$$ tree."}, {"key": "7419", "content": "The school has a pathway that is $$60$$ meters long and plans to plant trees on one side of the pathway. A tree is planted every $$10$$ meters (including at both ends), for a total of trees needed. (The width of the trees is negligible)"}, {"key": "7420", "content": "On one side of a $$100$$ meters long road, a poplar tree is planted every $$10$$ meters, including at both ends. Between two adjacent poplar trees, a willow tree is planted every $$2$$ meters. How many poplar trees and willow trees are there in total?"}, {"key": "7421", "content": "In front of the 'Youth Activity Center', there is a straight road. Trees are planted on one side of the road (with no trees planted at the end near the door), totaling $$30$$ trees, with each tree spaced $$5$$ meters apart. Question: How long is this road. (The width of the trees is negligible)"}, {"key": "7422", "content": "The distance between two buildings is $$40$$ meters. A cedar tree is planted every $$4$$ meters, for a total of cedar trees. (The width of the tree is negligible)"}, {"key": "7423", "content": "Xiao Qian rides past a road, and on one side of the road, there is a pine tree planted every $$6$$ meters. As Xiao Qian rides, she counts the pine trees she passes, counting the first tree as $$1$$, skipping the second tree, the third tree as $$2$$, skipping the fourth tree, and so on. Please calculate how many meters she has ridden when she has counted up to $$21$$."}, {"key": "7424", "content": "Trees are planted on one side of a road that is $$110$$ meters long, leaving both ends vacant, with a total of $$10$$ trees planted. The distance between each pair of neighboring trees is equal, and a tree is planted every some number of meters. (The width of the trees is considered negligible)"}, {"key": "7425", "content": "Doctor, Eddie, and Vi pass the ball to each other, starting with Doctor and after $$4$$ passes$.$, if the ball returns to Doctor's hands, there are several different ways of passing."}, {"key": "7426", "content": "Please direct Mr. Bear to bypass the obstacle and successfully put the tail on the pony. First go east, then northeast, then southeast, then east again, and finally northeast to reach the pony. question_7426-image_0"}, {"key": "7427", "content": "In Tianjin, the most frequent wind throughout the year is the northwest wind, so whenever this kind of wind blows, the national flag on the flagpole will flutter towards the ( ) direction."}, {"key": "7428", "content": "An average of ( ) branches per vase, with ( ) branches remaining. question_7428-image_0"}, {"key": "7429", "content": "This box of buttons can be used to fasten ( ) pieces of clothing at most. question_7429-image_0"}, {"key": "7430", "content": "The quotient of $$732\\div 8$$ is a digit number, and the quotient of $$948\\div 6$$ is a digit number."}, {"key": "7431", "content": "Who runs faster? question_7431-image_0"}, {"key": "7432", "content": "The flower shop is planning to sell bouquets made of $$3$$ carnations and $$4$$ lilies each. The table shows that these flowers can be combined into a maximum number of bouquets. Flower types and quantity: Carnations: $$345$$ stems, Lilies: $$396$$ stems"}, {"key": "7433", "content": "The product of the largest two-digit number and the largest single-digit number is."}, {"key": "7434", "content": "The expression that is closest to $$900$$ is ( )."}, {"key": "7435", "content": "Eddie can dribble a basketball $$46$$ times per minute. If he maintains this speed constantly, Eddie can dribble ( ) times in $$3$$ minutes."}, {"key": "7436", "content": "Eddie earns an average of $$68$$ points per class, so for $$21$$ classes, Eddie can approximately earn ( ) points."}, {"key": "7437", "content": "The weekend has arrived, and the doctor took $$36$$ students to the aquarium. The student ticket for the aquarium costs $$46$$ yuan each, and the adult ticket costs $$50$$ yuan each, then everyone together will need yuan."}, {"key": "7438", "content": "Ping An Hope Primary School is going on a spring outing, are these vehicles enough? question_7438-image_0"}, {"key": "7439", "content": "Find the pattern, what comes next? question_7439-image_0"}, {"key": "7440", "content": "Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, Pig$$12$$ kinds of animals represent the zodiac of each year in order. It is known that the year $$2021$$ is the year of the Ox, then the year $$2019$$ is the year of the."}, {"key": "7441", "content": "The teacher asked everyone to count in the order of $$1$$, $$2$$, $$3$$, $$4$$, $$1$$, $$2$$, $$3$$, $$4$$, $$\\cdots \\cdots $$. The number that the $$15$$th student should report is ( )."}, {"key": "7442", "content": "A sequence of numbers is arranged in the order $$1$$, $$4$$, $$2$$, $$8$$, $$5$$, $$1$$, $$4$$, $$2$$, $$8$$, $$5$$, $$\\cdots \\cdots$$. What is the 52nd number, how many times does \"$$1$$\" appear among these 52 numbers, and what is the sum of these 52 numbers."}, {"key": "7443", "content": "There's a bunch of Go pieces. Wei'er placed two black pieces first, then followed by a sequence of three black pieces and two white pieces, totaling $$35$$ pieces. What color is the $$35$$th piece?"}, {"key": "7444", "content": "$$\\triangle $$\u2606$$\\bigcirc \\triangle $$\u2606$$\\bigcirc \\triangle $$\u2606$$\\bigcirc \\triangle $$\u2026\u2026The 18th figure is ( )."}, {"key": "7445", "content": "With the digits $$0$$, $$1$$, $$2$$, $$3$$, the number of different three-digit numbers without repeated digits can be formed."}, {"key": "7446", "content": "Eddie lives on the first floor, and Vi lives on the tenth floor. Eddie wants to visit Vi at her home. How many flights of stairs must he climb from the first floor to the tenth floor?"}, {"key": "7447", "content": "Xiao Ning reads a 390-page storybook. If it takes 5 days to finish, on average each day they need to read ( ) pages."}, {"key": "7448", "content": "A three-digit number divided by the largest one-digit number, the quotient is ( )."}, {"key": "7449", "content": "There are a bunch of chess pieces. Wei'er arranges them on the table in a pattern of \"four black and five white\", as seen in the figure below. A total of $$72$$ pieces were arranged. (3) How many identical groups can the $$72$$ chess pieces be divided into? How many white chess pieces are there in total? question_7449-image_0"}, {"key": "7450", "content": "The maintenance station of Sunshine Electric Car Company has $$7$$ electric cars that need to be repaired. If using one worker to repair these $$7$$ electric cars, the repair times respectively are $$12$$, $$17$$, $$8$$, $$18$$, $$23$$, $$30$$, $$14$$ minutes. The loss for each electric car being idle for $$1$$ minute is $$11$$ yuan. Now, with $$3$$ maintenance workers, each working separately and with the same efficiency: (2) Arrange rationally, to make the duration from the start of the repair to the end of the repair as short as possible in minutes."}, {"key": "7451", "content": "If you happen to have four coins ($$1$$, $$5$$, $$5$$, $$8$$), how many different amounts of money can be made."}, {"key": "7452", "content": "The teacher gave three cards to Wei'er, with the numbers $$6$$, $$6$$, $$9$$ written on them respectively. Wei'er can use these cards to display different numbers. (The cards can be rotated)"}, {"key": "7453", "content": "The teacher brought three wooden boards, each marked with the numbers $$1$$, $$3$$, $$9$$. Wei'er can use these boards to display different numbers. (Note that the boards can be rotated)"}, {"key": "7454", "content": "There are $$2$$ five-yuan notes, $$4$$ two-yuan notes, $$8$$ one-yuan notes. There are different ways to take out $$11$$ yuan."}, {"key": "7455", "content": "Eddie received three different denominations of coins, as shown in the picture. Assuming you have exactly the following four coins, how many different amounts of money can you make? question_7455-image_0 question_7455-image_1 question_7455-image_2 question_7455-image_3"}, {"key": "7456", "content": "A certain junior high school has a total of $$1422$$ students. Each grade has the same number of students in each class. It is known that the first and second grades together have $$20$$ classes, with $$48$$ students per class; the third grade has $$11$$ classes. Then, each class in the third grade has people."}, {"key": "7457", "content": "In the problem below, each Chinese character represents a number. Different characters represent different numbers, and the same characters represent the same numbers. If the equation is correct, then the six-digit number represented by \"$$\\overline{\u529b\u4e89\u529e\u5965\u8fd0\u4f1a}$$\" is. question_7457-image_0 \u200b"}, {"key": "7458", "content": "Based on the given calculation, \u2606 represents, $$ \\triangle$$ represents. $$\\begin{matrix}& 5 & \u2606 \\\\ -&\u2606 & \\triangle \\\\ \\hline &1 & 8 \\end{matrix}$$"}, {"key": "7459", "content": "Fill in the blanks with appropriate numbers to make the equations valid. From top to bottom, these four numbers are respectively: question_7459-image_0"}, {"key": "7460", "content": "In the equation below, each square represents a number. The question asks for the sum of the numbers in all the squares of each equation. question_7460-image_0"}, {"key": "7461", "content": "A basket of peaches can feed $$10$$ monkeys for $$5$$ days. After $$2$$ days, $$4$$ monkeys leave. How many days can the remaining peaches feed the remaining monkeys? (Assuming each monkey eats the same amount of peaches every day)"}, {"key": "7462", "content": "A grain processing plant needs to grind $$21000$$ kilograms of flour. Using $$4$$ grinding machines, $$6000$$ kilograms of flour were ground in $$3$$ hours, with each grinding machine having the same efficiency. If one more grinding machine is added, the number of hours needed to grind the remaining flour is."}, {"key": "7463", "content": "The aquarium prepared $$140$$ kilograms of fish for the $$8$$ walruses in the museum. In the first $$2$$ days, these $$8$$ walruses ate a total of $$80$$ kilograms of fish. Two days later, $$2$$ of the walruses were taken away. If each walrus eats the same amount of fish every day, then the remaining fish can last for how many more days for the remaining walruses."}, {"key": "7464", "content": "A grain processing factory grinds flour, using $$3$$ flour mills for $$2$$ hours to grind $$300$$ kilograms. Based on this calculation, if one more flour mill is added, it can grind kilograms of flour in $$7$$ hours."}, {"key": "7465", "content": "Filling in the form: The original number is enlarged to $$10$$ times, to $$100$$ times, to $$1000$$ times $$7.74$$$$2.003$$ The original number is reduced to $$\\frac{1}{10}$$, reduced to $$\\frac{1}{100}$$, reduced to $$\\frac{1}{1000}$$$$345.61$$$$60.8$$"}, {"key": "7466", "content": "In the figure below, how many line segments are there in total? Total:.\n question_7466-image_0"}, {"key": "7467", "content": "What are the angles (less than or equal to $$180$$ degrees) formed by the hour hand and the minute hand in the clocks below in order? question_7467-image_0 question_7467-image_1 question_7467-image_2 From left to right, the angles are \u00b0, \u00b0, \u00b0, \u00b0."}, {"key": "7468", "content": "Fill in the underline below with \"$$+$$\" and \"$$-$$\" to make the equation valid: 1197531=0"}, {"key": "7469", "content": "Fill in the appropriate places with \"$$+$$\" or \"$$-$$\" (you can leave spaces between the two numbers) in the equation below, to make the equation correct. $$7$$$$8$$$$9$$$$1$$$$2$$$$1$$$$3$$$$1$$$$4 = 48$$ Can you do it?"}, {"key": "7470", "content": "Using the numbers $$2$$, $$3$$, $$5$$, $$6$$, fill in between them with $$+$$, $$-$$, $$\\times $$, $$\\div $$, or ( ) to make the result equal to $$24$$ (each number can only be used once)."}, {"key": "7471", "content": "Fill in the appropriate operators and parentheses in the equation below to make the equation true: $$1$$ $$2$$ $$3$$ $$4$$ $$5$$$$=$$$$20$$. The correct answer(s) is(are) ( )."}, {"key": "7472", "content": "Calculate using the simpler method: $25\\times(40+4)=$"}, {"key": "7473", "content": "In all the pages of a math book, the number $$3$$ appears a total of $$310$$ times. So, how many pages does this math book have?"}, {"key": "7474", "content": "Four students in the class held a checkers competition, where each pair of students played against each other once. The winner of each game received $$2$$ points, a draw awarded $$1$$ point to each, and the loser received $$0$$ points. At the end of the competition, students A, B, and C scored $$3$$, $$4$$, and $$4$$ points respectively, with student C having no draws and student A having won some games, and student B having some draws. The questions are:\n1) How many points did student D score?\n2) What was the result of the game between student A and student D?"}, {"key": "7475", "content": "Six teams participate in the competition, and every two teams have to play a match. The competition rules are that the winner gets $$3$$ points, the loser gets $$0$$ points, and a draw results in both getting $$1$$ point each. The total points in the end are $$42$$ points, so there are draws in the matches."}, {"key": "7476", "content": "Six people, $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, and $$F$$, play chess in a round-robin tournament. Currently, it is known that $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ have played $$5$$, $$4$$, $$3$$, $$2$$, and $$1$$ games, respectively. At this point, $$F$$ has already played some games."}, {"key": "7477", "content": "The correct answer to question_7477-image_0 is."}, {"key": "7478", "content": "Observe the pattern of the following sequence of numbers: $$1$$, $$1$$, $$2$$, $$4$$, $$7$$, $$13$$, $$24$$\u2026, what is the remainder when the $$2000$$th number is divided by $$4$$?"}, {"key": "7479", "content": "There is a bamboo in its vigorous growth period, its length was measured as $$14$$ centimeters for the $$1$$st time, and each subsequent measurement was $$3$$ centimeters more than the last. question_7479-image_0 (1) At the $$5$$th measurement, the length of the bamboo was centimeters. (2) At the $$31$$st measurement, the length of the bamboo was centimeters."}, {"key": "7480", "content": "The National Day is coming soon, and the Young Pioneers of the Xueersi School are going to arrange flower pots. If each person arranges $$6$$ pots, there are $$3$$ pots left without anyone to arrange them; if among them $$2$$ people each arrange $$5$$ pots, and the rest each arrange $$7$$ pots, then these flower pots are just enough. Ask how many Young Pioneers participated in the flower pot arranging activity, and how many flower pots were arranged in total."}, {"key": "7481", "content": "A tourist group comes to Xi'an for sightseeing and needs to divide into rooms. If each room is occupied by one person, there are still $$50$$ people without a place to stay. If each room is occupied by three people, there are $$50$$ rooms left. Therefore, there are rooms, and there are many tourists."}, {"key": "7482", "content": "The Monkey King distributes peaches to the little monkeys. If each little monkey gets 10 peaches, there are 100 peaches left; if the total number of little monkeys doubles, and each little monkey still gets 10 peaches, there would be 200 peaches short. How many peaches did the Monkey King prepare in total?"}, {"key": "7483", "content": "How many four-digit even numbers can be formed with no repeated digits using $$0,1,3,4,7,8$$?"}, {"key": "7484", "content": "Paint areas labeled $$A$$, $$B$$, $$C$$, $$D$$ with $$6$$ colors such that no two adjacent areas share the same color, there are a total of different methods.\n question_7484-image_0"}, {"key": "7485", "content": "As shown in the diagram, there are $$2$$ routes from point A to point B, $$4$$ routes from point B to point C, $$3$$ routes from point A to point D, and also $$3$$ routes from point D to point C. How many different ways are there to get from point A to point C? ( )\n question_7485-image_0"}, {"key": "7486", "content": "Calculate:\n(1) $$124\\div 4+76\\div 4=$$\n(2) $$95\\div 8+96\\div 8+97\\div 8=$$\n(3) $$1440\\div 6+1440\\div 18+1440\\div 16=$$"}, {"key": "7487", "content": "Given: $$a\\Delta b=3a+2b\uff0ca\\nabla b=4a-3b$$\uff0cfind $$3\\Delta (4\\nabla 5)=$$\uff0e"}, {"key": "7488", "content": "It is known that the 6th and 10th terms of an arithmetic sequence are 38 and 62, respectively, and the common difference is."}, {"key": "7489", "content": "On a highway, there is a warehouse every $$10$$ kilometers, for a total of $$4$$ warehouses (as shown in the figure). The numbers in the diagram represent the weight of the goods in stock at each warehouse. Now, if all the goods are to be concentrated in one warehouse, and the transport cost for every ton of goods per kilometer is $$0.5$$ yuan, then the minimum cost of concentrating the goods in one warehouse is yuan.\n question_7489-image_0"}, {"key": "7490", "content": "$$6$$ drawers, no matter how you put them, there is always at least one drawer that contains at least $$4$$ balls, with a minimum total of balls."}, {"key": "7491", "content": "If $$16$$ backpacks are placed into $$5$$ drawers, then at least one drawer will contain $$$4$$$ or more backpacks."}, {"key": "7492", "content": "There are $$3$$ apples and $$3$$ oranges on the table. How many fruits must you take to ensure that you have $$3$$ of the same kind of fruit?"}, {"key": "7493", "content": "Groups A, B, and C have a total of $$42$$ students. First, $$5$$ students are transferred from group A to group B, then the same number of students as in group C are transferred from group B to group C. Then, $$4$$ students are transferred from group C to group A. In this way, the number of people in groups A, B, and C are equal. Originally, group A had fewer people than group B."}, {"key": "7494", "content": "\"Journey to the West\" has a total of $$60$$ episodes, with $$2$$ episodes aired every day, starting on Friday. What day of the week will the airing end? (Represent the answer with numbers $$1\\sim 7$$)"}, {"key": "7495", "content": "$$2012$$ year $$1$$ month $$4$$ day is Wednesday, then $$2013$$ year $$1$$ month $$4$$ day is what day of the week. (Fill in the number)"}, {"key": "7496", "content": "Five students form a circle playing a passing game, as shown in the diagram, starting with student number 1, the ball is passed clockwise 23 times, the ball should be with student number.\n question_7496-image_0"}, {"key": "7497", "content": "Last year, the grandfather was $$48$$ years older than his grandson. This year, the grandfather's age is $$3$$ times the grandson's age. (1) The grandfather is older than the grandson by ____ years. (2) This year, the grandfather's age is ____ years. question_7497-image_0"}, {"key": "7498", "content": "Xiaoming's age, 8 years from now, will be equal to his mother's age 20 years ago. When Xiaoming was a certain age, his mother's age was exactly 5 times Xiaoming's age."}, {"key": "7499", "content": "The figure below contains a total of triangles. question_7499-image_0"}, {"key": "7500", "content": "For a number, we call the process of 'first adding $$4$$, then multiplying by $$4$$, subtracting $$4$$, and then dividing by $$4$$' as one operation. There is a number, after $$100$$ operations, the result is $$2014$$. What was the original number?"}, {"key": "7501", "content": "While doing subtraction, Fang Fang mistakenly wrote the units digit of the minuend as $$8$$ instead of $$0$$, and the tens digit as $$2$$ instead of $$6$$. This resulted in an answer of $$513$$. The correct difference should be."}, {"key": "7502", "content": "There are $$4$$ numbers, their average is $$32$$. The average of the first $$3$$ numbers is $$29$$, and the average of the last $$2$$ numbers is $$35$$. Then, the third number is\uff0e"}, {"key": "7503", "content": "Natural numbers $$12$$, $$456$$, $$1256$$ share a common feature where each digit is lesser than the one following it. We call these 'ascending numbers'. Using the four numbers $$3$$, $$6$$, $$7$$, $$9$$ (not necessarily all of them), you can form a certain number of 'ascending numbers'."}, {"key": "7504", "content": "Dividing $$10$$ identical balls into $$3$$ piles, with each pile having a different number of balls, how many ways are there to do it?"}, {"key": "7505", "content": "Divide $$15$$ chili peppers into $$5$$ equal parts, each part has\uff0e question_7505-image_0"}, {"key": "7506", "content": "In the orchard, there are peach trees, pear trees, and apple trees totaling $$392$$ trees. The number of peach trees is $$12$$ more than twice the number of pear trees, and the number of apple trees is $$20$$ less than the number of pear trees. Therefore, there are peach trees, pear trees, and apple trees."}, {"key": "7507", "content": "In the park, there are a total of $$350$$ people including the elderly, youth, and children. The number of youths is $$2$$ times that of the elderly, and the number of children is $$2$$ times that of the youths. There are elderly people, youth people, and children people."}, {"key": "7508", "content": "Three pieces of cloth have a total length of $$90$$ meters, the total length of the first and the third piece is $$8$$ times that of the second piece, and the first piece is $$14$$ meters longer than the third piece. What is the length of the third piece of cloth?"}, {"key": "7509", "content": "Mao Mao likes to eat three kinds of snacks: chocolate, lollipops, and potato chips. She will not eat the same kind on two consecutive days. If she eats chocolate on the first day and also on the fourth day, then there are different arrangements for her diet over these four days."}, {"key": "7510", "content": "Calculate: $$57\\div 3=$$"}, {"key": "7511", "content": "Calculate: $$630\\div 6=$$.$$896\\div 8= $$."}, {"key": "7512", "content": "Calculate: $$86421\\div 3= $$."}, {"key": "7513", "content": "The image below is a $$5\\times 5$$ area with $$5$$ trees planted. Now, it is required to set up tents on the vacant land where no trees are planted, and tents must be set up next to a tree. No two tents can occupy squares that share a corner point, and the number of tents in each row is shown on the far left, while the number of tents in each column is shown at the top. Is there a tent in the place marked with a question mark? ( ) question_7513-image_0"}, {"key": "7514", "content": "The figure below shows a $$6\\times 6$$ area with $$7$$ trees planted. Now it's required to set up tents on the tree-free land, with the condition that the tents must be set up beside a tree, any two tents do not share a common point, and the number of tents in each row is as shown on the very left. Does the $$6$$th row and $$1$$st column have a tent? ( ) question_7514-image_0"}, {"key": "7515", "content": "$$5$$ students line up for a photo, where student A cannot stand in the very middle, there are a total of methods for queuing."}, {"key": "7516", "content": "Count separately, how many squares are there in each of the two pictures? (1) question_7516-image_0 question_7516-image_2 (2)"}, {"key": "7517", "content": "The elder brother and younger brother had an age difference of 5 years last year. This year, their combined age is 15 years old. So, this year, the elder brother is __ years old, and the younger brother is __ years old. question_7517-image_0"}, {"key": "7518", "content": "Grandpa is $$74$$ years old this year. When Grandpa was as old as Dad is now, Dad was only $$18$$ years old. So, how old is Dad this year? question_7518-image_0"}, {"key": "7519", "content": "Starting from $$2$$, the continuous even numbers $$2$$, $$4$$, $$6$$, $$8$$, $$10\\cdots \\cdots $$, then $$36$$ is the nth number in this sequence."}, {"key": "7520", "content": "A movie theater has a total of $$11$$ rows of seats, with each subsequent row having $$2$$ more seats than the previous row. The first row has $$10$$ seats. question_7520-image_0 (1) The last row has seats. (2) This theater has a total of seats."}, {"key": "7521", "content": "Second grade choir formation, with a total of $$81$$ people. If one more row and one more column are added, how many more people are needed? question_7521-image_0"}, {"key": "7522", "content": "The solid square formation of Class 3, Grade 3, has a total of $$56$$ people on the outermost layer. The number of people on each side of the outermost layer is, and the total number of people in this square formation is."}, {"key": "7523", "content": "The elder brother has $$15$$ building blocks, and the younger brother has $$5$$ more building blocks than the elder brother; the correct statement is ( )."}, {"key": "7524", "content": "Estimate, there are a total of $$28$$ cardboard boxes, is it enough? question_7524-image_0"}, {"key": "7525", "content": "Below is a statistical table of the number of mineral water bottles collected by three environmental protection teams in the third grade. question_7525-image_0"}, {"key": "7526", "content": "Teacher Cheng and Teacher Zhang are taking $$36$$ children to go boating. Each boat can hold up to $$4$$ people at most, a minimum number of boats need to be rented."}, {"key": "7527", "content": "Teacher Li has $$325$$ yuan, what is the maximum number of Rubik's cubes that can be purchased? How much money is left? ( ) question_7527-image_0"}, {"key": "7528", "content": "In a division equation with a remainder, the remainder is $$7$$, the smallest possible divisor is ( )."}, {"key": "7529", "content": "A number divided by $$9$$ has a remainder, the largest possible remainder is ( )."}, {"key": "7530", "content": "$$\\triangle \\div 4=25\\ldots \\ldots$$\u2606, the maximum \u2606 is, at this time $$\\triangle $$ is."}, {"key": "7531", "content": "Fill in the blanks with the appropriate numbers. ( ) $$\\div 8=60\\cdots \\cdots 7$$$$75\\div $$ ( ) $$=9\\cdots \\cdots 3$$$$31\\div $$ ( ) $$=7\\cdots \\cdots 3$$"}, {"key": "7532", "content": "Dividing two numbers, with the divisor being $$6$$ and the quotient being $$115$$, the largest possible dividend is."}, {"key": "7533", "content": "Teacher Wang brought 400 yuan and bought 9 identical toys, what could she have bought?"}, {"key": "7534", "content": "$$28\\times 35=$$\uff08 \uff09."}, {"key": "7535", "content": "$$34\\times 11=$$$$55\\times 11=$$$$56\\times 11=$$$$37\\times 11=$$$$72\\times 11=$$$$86\\times 11=$$"}, {"key": "7536", "content": "Hope community has $$38$$ residential buildings, each building has $$23$$ floors, each floor has $$6$$ households. If the Hope community is fully occupied, then the community has households."}, {"key": "7537", "content": "When Xiao Jun was doing a calculation of multiplying a two-digit number by another two-digit number, he mistook the ones digit $$1$$ of the second multiplicand for $$7$$, leading to a result that was $$72$$ more than the correct product. The correct product should be."}, {"key": "7538", "content": "Define the operation \"\u25bd\" as: $$a$$\u25bd$$b=(a+2)\\times (b-2)$$, please calculate:\n(1) $$8$$\u25bd$$10=$$\uff0e\n(2) $$10$$\u25bd$$8=$$\uff0e"}, {"key": "7539", "content": "Define a new operation $$a\\Lambda b=a+3\\times b$$, then $$7\\Lambda 5=$$."}, {"key": "7540", "content": "Define a new operator \"$$\\Delta $$\" with the following calculation rule, $$a\\Delta b=a\\times 2+b\\times 3$$. Please calculate $$(5\\Delta 7)\\Delta 3=$$."}, {"key": "7541", "content": "Define a new operation: $$A$$\u203b$$B=3\\times A+4\\times B$$, then $$9$$\u203b$$10=$$."}, {"key": "7542", "content": "Define the symbol \"$$\\Sigma $$\", where $$a\\Sigma b=\\left( a+b \\right)\\div 2$$. For example, $$2\\Sigma 4=\\left( 2+4 \\right)\\div 2=3$$. Calculate $$5\\Sigma 1=$$."}, {"key": "7543", "content": "Hashi: Connect all the islands with bridges to form a region where they can all access each other. The bridges can only go up, down, left, or right, and cannot cross one another. A maximum of two bridges can be built between any two islands. The number on each island indicates the number of bridges connected to that island. How many bridges are there between the islands enclosed in the rectangle in the picture.\n question_7543-image_0"}, {"key": "7544", "content": "(3) square meters $$=$$$$600$$ square decimeters $$=$$ square centimeters."}, {"key": "7545", "content": "Unit conversion. (1) $$100$$ centimeters $$=$$ decimeters $$=$$ meters;"}, {"key": "7546", "content": "(2) $$3$$ square meters $$=$$ square decimeters; $$4$$ square decimeters $$=$$ square centimeters;"}, {"key": "7547", "content": "The young pioneers of Grade 3, Class 1, participated in brick-moving labor at the school. If each person moves $4$ bricks, there will be $17$ bricks left; if each person moves $5$ bricks, then there will be $9$ bricks left. There are people in this class of young pioneers. The total number of bricks to be moved is ."}, {"key": "7548", "content": "A teacher distributes some pencils among children. If each child gets 5 pencils, there are 5 pencils short; if each child gets 8 pencils, there are 23 pencils short. How many children are there in total, and how many pencils are there in total?"}, {"key": "7549", "content": "A batch of exercise books is distributed to students. If each student gets 5 books, there are 70 books left over. If each student gets 7 books, there are 10 books short. How many students are in the class, and how many exercise books are there in total?"}, {"key": "7550", "content": "A kindergarten teacher distributes fruits to the children, giving $$3$$ per child, and has $$10$$ left over; giving $$5$$ per child, and has $$2$$ left over; thus, there are children and fruits."}, {"key": "7551", "content": "The library purchased a new batch of books. If $$15$$ books are distributed to each class, there are $$20$$ books left over; if $$20$$ books are distributed to each class, there are $$100$$ books short. How many classes are there and how many books in total?"}, {"key": "7552", "content": "Class 3 ($$1$$) has $$46$$ people, among them $$29$$ people joined the sports group, $$25$$ people joined the art group, there are $$15$$ people who joined both groups, then there are people who didn't join any group."}, {"key": "7553", "content": "In a certain school's third grade class 2, there are $$14$$ students who joined the math interest group, $$16$$ students who joined the English interest group, and $$8$$ students who joined both interest groups. Thus, a total of people joined the interest groups."}, {"key": "7554", "content": "Given $$A=a+b$$, $$B=a-b$$, $$C=ab$$, $$D=b^2$$: (1) When $$a=5$$, $$b=1$$, calculate $$A+B$$=, $$A-C$$=;"}, {"key": "7555", "content": "(2) When $$a=4$$, $$b=3$$, calculate $$AB+D$$=, $$A^2-2C$$=."}, {"key": "7556", "content": "In an exam, the scores of the three students in the first group happened to form an arithmetic progression. Eddie found that his score was undercounted and, after having it corrected by the teacher, his score was increased by $$6$$ points. At this point, their scores still formed an arithmetic progression, and the total score of the three after the correction was $$270$$ points. Please find the possible scores Eddie could have had before the correction, in ascending order."}, {"key": "7557", "content": "Fourth-grade students formed a solid square formation for a Taekwondo performance, with $$10$$ people on each side of the outermost layer. (1) Counting from the outside in, the second layer has people on each side, and the second layer has a total of people;"}, {"key": "7558", "content": "(4) Total number of students."}, {"key": "7559", "content": "A said to B: \"My current age is twice your age at the time when I was your current age; when you reach my current age, our combined ages will be 81 years old.\", A is currently __ years old, B is currently __ years old."}, {"key": "7560", "content": "One chicken has two legs, $$n$$ chickens have how many legs."}, {"key": "7561", "content": "The forest planted phoenix trees $$x$$ rows, cedars $$y$$ rows. It is known that there are $$12$$ phoenix trees per row, $$14$$ cedars per row. Thus, there are a total of phoenix trees and cedars; if $$y$$ is $$3$$ times that of $$x$$, then the total of phoenix trees and cedars is (expressed in a formula containing only the letter $$x$$), at this time, if $$x=20$$, then there are a total of phoenix trees and cedars."}, {"key": "7562", "content": "Eddy and Vi read the same storybook. Eddy reads $$50$$ pages on the first day, then $$15$$ pages each following day; Vi reads $$22$$ pages every day, and eventually, they both finish on the same day. Assuming both read for $$x$$ days, please list the equation relationship contained in the question based on the given conditions."}, {"key": "7563", "content": "One side of the rectangle is equal to $$2a+b$$, and the other side is $$a-b$$ smaller than it, so the perimeter of this rectangle is."}, {"key": "7564", "content": "Eddie and Will are planning to visit Grandma Li at the nursing home, as shown in the following figure: Starting from the school and passing through the downtown, there are a total of several shortest routes to the nursing home. question_7564-image_0"}, {"key": "7565", "content": "If there are a total of routes for them to reach the nursing home without going through the city center. question_7565-image_0"}, {"key": "7566", "content": "In the evening, a heavy rain fell near the city center, making the nearby roads impassable. How many shortest routes are there to the nursing home in total? question_7566-image_0"}, {"key": "7567", "content": "In the right figure, connect adjacent letters using horizontal or vertical lines. When walking along these lines, the number of paths that exactly spell out 'APPLE' is . question_7567-image_0"}, {"key": "7568", "content": "Is the result of the expression $$123+325-462\\times 101+233\\times 722$$ odd or even ( )?"}, {"key": "7569", "content": "Please express the following diagram in an equation: ( ).\n question_7569-image_0"}, {"key": "7570", "content": "The little bee goes through the beehive rooms, where it can only enter a room with a bigger number from a room with a smaller number. (1) Room number $$3$$ can be entered from room numbers , Room number $$4$$ can be entered from room numbers .(Fill in the sequence from small to large) (2) There are methods for the little bee to reach room $$7$$ from room $$1$$. question_7570-image_0"}, {"key": "7571", "content": "To divide $$8$$ watermelons of the same size into $$3$$ piles, there are several different ways. question_7571-image_0 \u200b\u200b\u200b"}, {"key": "7572", "content": "4 years ago, Uncle Wang's age was $$5$$ times that of Xiao Ming's; $$8$$ years later, Uncle Wang's age will be $$3$$ times that of Xiao Ming's, Xiao Ming's age this year is"}, {"key": "7573", "content": "$$6$$ students form a circle to play the pass-the-handkerchief game. As shown in the figure, starting from student number $$1$$, pass clockwise $$20$$ times, then counterclockwise $$3$$ times, the handkerchief ends up with student number. question_7573-image_0"}, {"key": "7574", "content": "Fill in the appropriate number in the squares in the image so that the sum of the three numbers in each row, each column, and each diagonal is equal. question_7574-image_0 The first number in the third row is:"}, {"key": "7575", "content": "Try one by one, among these figures below which can be drawn in one stroke (without lifting the pen off the paper and without repeating lines, allowing intersections between lines). question_7575-image_0"}, {"key": "7576", "content": "The number of people in classes A, B, and C are respectively $$45$$, $$57$$, $$54$$. It is known that the average score of class A is $$92$$ points, the average score of class B is $$90$$ points, and the total average score of the three classes is $$93$$ points, the average score of class C is points."}, {"key": "7577", "content": "Fourth-grade students formed a three-layer hollow square formation to perform magic, with 18 people on each side of the outermost layer, (1) number of people in the outermost layer; (2) total number of people in the second layer; (3) total number of people in the square formation;"}, {"key": "7578", "content": "Using $$64$$ pots of flowers, you can form a two-layer hollow square matrix. (1) The outermost layer has pots. (2) If you want to add another layer outside, you need to add pots of flowers."}, {"key": "7579", "content": "Trees are planted on both sides of a $$120$$ meters long road, without planting at both ends, a total of $$10$$ trees were planted, the distance between every two neighboring trees is equal, with one tree planted every few meters. (The width of the trees is negligible)"}, {"key": "7580", "content": "On the green belt in the middle of the highway, workers planted a pine tree every $$3$$ meters, for a total of $$50$$ pine trees. They plan to plant a willow tree every $$1$$ meter between every two adjacent pine trees, then the number of willow trees needed is."}, {"key": "7581", "content": "Scientists conduct an experiment, making a record every $$5$$ hours. When making the $$12$$th record, the hour hand of the clock exactly points to $$9$$. Question: At the first record, where does the hour hand point to."}, {"key": "7582", "content": "There are three keys made of gold, silver, and copper that can speak. One of them can open the treasure chest. The gold key says: I can open the treasure chest; the silver key says: I can open the treasure chest; the copper key says: The gold key can open the treasure chest. Only one of the keys is lying. So, among the gold, silver, and copper keys, who can open the treasure chest?"}, {"key": "7583", "content": "Arithmetic sequence sum: $$4+8+12+\\cdot \\cdot \\cdot +28+32+36=$$."}, {"key": "7584", "content": "Somewhere is on fire, and the fire brigade needs to reach the fire spot by the fastest method. It is known that passage through question_7584-image_0 is not possible, so there are routes for the shortest path from the fire brigade to the fire spot. question_7584-image_1"}, {"key": "7585", "content": "As shown in the figure, there are paths for the shortest route from $$A$$ to $$B$$. question_7585-image_0"}, {"key": "7586", "content": "The cage contains two types of animals, spiders and dragonflies. Each spider has $$1$$ head and $$8$$ legs, each dragonfly has $$1$$ head and $$6$$ legs. Currently, there are a total of $$15$$ heads and $$100$$ legs. The number of spiders and dragonflies are respectively."}, {"key": "7587", "content": "There are a total of $$10$$ bicycles and tricycles, with $$23$$ wheels in total. The number of tricycles is ."}, {"key": "7588", "content": "Divide $$9$$ identical marbles into $$3$$ piles, there are different ways of doing so."}, {"key": "7589", "content": "$$100$$ monks and $$160$$ buns, each big monk gets $$3$$ buns, each small monk gets $$1$$ bun. Question: how many big monks and how many small monks are there?"}, {"key": "7590", "content": "The teacher bought $$7$$ balloons to share among Xiaoyun, Xiaojuan, and Xiaohong - three people (each person must get at least one, otherwise, there will be tears!), there is a method of distribution."}, {"key": "7591", "content": "Divide $$10$$ apples into $$3$$ piles of different amounts, in total there are different methods."}, {"key": "7592", "content": "Divide $$9$$ identical marbles into $$3$$ piles, there are different ways to do it."}, {"key": "7593", "content": "$$22\\times 84+42\\times 156=$$"}, {"key": "7594", "content": "The figure below is a rectangle composed of $$6$$ squares. Given that the perimeter of the square is $$8$$ cm, the perimeter of the rectangle is in cm question_7594-image_0"}, {"key": "7595", "content": "A rectangle with a length of $$25$$ cm and a width of $$8$$ cm is cut horizontally into two smaller rectangles (as shown in the diagram), the sum of the perimeters of these two rectangles is how many centimeters more than the perimeter of the original rectangle. question_7595-image_0"}, {"key": "7596", "content": "There are two shelves of books, totaling $$200$$ books. After taking away $$20$$ books from the second shelf, the books on the second shelf are twice as many as those on the first shelf. Then, the first shelf has books."}, {"key": "7597", "content": "The number of people in Class B is exactly $$4$$ times the number of people in Class A. If $$30$$ people are transferred from Class B to Class A, then the two classes will have the same number of people. How many people were there originally in Class A and Class B?"}, {"key": "7598", "content": "The number of apples in basket A is 4 times that of basket B. If 24 apples are taken from basket A and put into basket B, then basket A will have 3 less than basket B. How many apples were originally in basket B."}, {"key": "7599", "content": "The number of hairpins owned by the older sister is $$4$$ times that of the younger sister. After giving $$6$$ hairpins to the younger sister, she has $$3$$ more than the younger sister. How many hairpins did the younger sister originally have?"}, {"key": "7600", "content": "The small animals are lining up, with the calf needing to be on the very left. There are in total several ways to line up. question_7600-image_0"}, {"key": "7601", "content": "Xiaoming has $$6$$ different shirts, $$5$$ different pairs of pants, $$2$$ different pairs of shoes, and he must choose one shirt, one pair of pants, and one pair of shoes, so he has a number of different ways to dress."}, {"key": "7602", "content": "$$\\square \\div 10=19\\ldots \\ldots 7 $$, the dividend is."}, {"key": "7603", "content": "$$3.8-2.3+6.2-3.7=$$."}, {"key": "7604", "content": "When Jianjian was doing a subtraction problem, due to carelessness, the unit digit of the subtrahend was seen as $$8$$ instead of $$3$$, and the tens digit was seen as $$5$$ instead of $$7$$, resulting in a difference of $$26$$. Then, the correct answer should be."}, {"key": "7605", "content": "As shown in the figure, it is known that $$\\angle 1=60{}^\\circ $$, $$\\angle 2$$=\u00b0. question_7605-image_0"}, {"key": "7606", "content": "Xiao Ming, Xiao Hua, and Xiao Li are from Beijing, Shanghai, and Guangzhou respectively. It is known that: Xiao Ming does not know the child from Guangzhou, Xiao Hua is from Beijing, so Xiao Li is from ( )."}, {"key": "7607", "content": "God's wedding ring was lost, so a prophet, a witch, and a fool were called to face each other on the spot. The fool said: it was the prophet who stole it. The prophet said: the fool is lying. The witch said: I agree with the prophet. If only one of the three tells the truth, the one telling the truth, the one who stole the ring is. (Fill in the letter) A. Fool B. Witch C. Prophet"}, {"key": "7608", "content": "This year, uncle is $$20$$ years older than Xiao Lin. Next year, uncle's age will be $$3$$ times that of Xiao Lin. Xiao Lin's age this year is."}, {"key": "7609", "content": "This year, the father is 4 times as old as his son. The combined age of father and son 2 years from now will be 49 years. Therefore, the father's age this year is ____ years old."}, {"key": "7610", "content": "Xiaoma is $$12$$ years old this year, and his mother said to him: 'When you are as old as me, I will be $$66$$ years old.' Mom\u2019s age this year is ."}, {"key": "7611", "content": "Fill in the appropriate number in the \"$$\\square $$\" in the vertical multiplication below so that the equation is valid, and the product is. 6 9 \u00d7 2 9"}, {"key": "7612", "content": "The figure below is a multiplication number puzzle, the product should be. question_7612-image_0"}, {"key": "7613", "content": "September 10, 2018 (Teacher's Day) is Monday. After another 23 days, it is Wednesday. (Fill in the number)"}, {"key": "7614", "content": "Insert \"$$+$$\" or \"$$-$$\" between every two numbers below to make the equation true. $$1\\bigcirc 2\\bigcirc 3\\bigcirc 4\\bigcirc 5\\bigcirc 6\\bigcirc 7=2$$ Can you do it?"}, {"key": "7615", "content": "When dividing two numbers, the quotient is $$4$$ with a remainder of $$3$$. If both the dividend and divisor are increased to $$10$$ times their original size, the new quotient and remainder are."}, {"key": "7616", "content": "When dividing two numbers, the quotient is $$5$$ with no remainder. The sum of the dividend and the divisor is $$72$$. Find the dividend."}, {"key": "7617", "content": "$$0.7+0.97+0.997+0.9997=$$."}, {"key": "7618", "content": "The distance between two buildings is $$40$$ meters. A cedar tree is planted every $$4$$ meters, a total of how many cedar trees can be planted. (The width of the tree is negligible)"}, {"key": "7619", "content": "Using the digits $$0$$, $$1$$, $$2$$, $$3$$, how many different three-digit numbers can be formed without repeating digits."}, {"key": "7620", "content": "The teacher brought three wooden blocks, which were respectively labeled with the numbers $$1$$, $$3$$, $$9$$. WeiEr can use these wooden blocks to display different numbers. (Note that the wooden blocks can be rotated)"}, {"key": "7621", "content": "Eddie received three different denominations of coins, as shown in the figure. Assuming you have exactly the following four coins, how many different amounts of money can be formed. question_7621-image_0 question_7621-image_1 question_7621-image_2 question_7621-image_3"}, {"key": "7622", "content": "The image is a partial vertical multiplication and division operation, the product in this equation is.\n question_7622-image_0"}, {"key": "7623", "content": "There is an arithmetic sequence: $$2$$, $$9$$, $$16$$, $$\\cdots \\cdots$$, $$86$$, this sequence has a total number of terms."}, {"key": "7624", "content": "If $$x=-2$$ is a root of the quadratic equation $${{x}^{2}}+\\frac{3}{2}ax-{{a}^{2}}=0$$ about $$x$$, then the value of $$a$$ is ( )."}, {"key": "7625", "content": "The exploration of literacy $$1$$ involves a quadratic equation."}, {"key": "7626", "content": "If $$( m-1 ){{x}^{2}}+\\sqrt{m}x=1$$ is a quadratic equation in terms of $$x$$, then the range of values for $$m$$ is ( )."}, {"key": "7627", "content": "Xiaofei needs to get to the 8th floor of a building. It took him 60 seconds to walk from the 1st floor to the 4th floor, how many more seconds will it take to continue at the same speed to the 8th floor."}, {"key": "7628", "content": "Grandpa is $$72$$ years old this year, and the granddaughter is $$12$$ years old this year. When the granddaughter's age is considered, grandpa's age was $$4$$ times the granddaughter's age."}, {"key": "7629", "content": "Having $$2$$ five-yuan notes, $$4$$ two-yuan notes, and $$8$$ one-yuan notes. There are several different ways to take out $$11$$ yuan."}, {"key": "7630", "content": "Xiaomei has a box of black and white beads. She arranges the beads as follows: ($$1$$) The 18th bead should be this color; ($$2$$) There are a total of white beads in the first 20 beads. question_7630-image_0"}, {"key": "7631", "content": "$$A$$, $$B$$, and $$C$$ three children pass the ball to each other, starting with $$A$$ to serve. After $$2$$ passes, there are a total of different ways to pass the ball."}, {"key": "7632", "content": "Somewhere is on fire, and the fire department needs to reach the fire scene by the fastest method. It is known that question_7632-image_0 is impassable, so the shortest route from the fire department to the fire scene has several routes. question_7632-image_1"}, {"key": "7633", "content": "Susan walks from $$A$$ to $$Z$$, always heading east or south, as shown in the diagram. There are different routes Susan can take from $$A$$ to $$Z$$.\n question_7633-image_0"}, {"key": "7634", "content": "As shown in the figure, starting from point $$A$$ and walking along the line segment to point $$B$$, there is a shortest path.\n question_7634-image_0"}, {"key": "7635", "content": "Xiao Zhang has a total of $$10$$ banknotes, consisting of $$2$$ yuan and $$5$$ yuan denominations, with a total value of $$32$$ yuan. How many $$2$$ yuan and $$5$$ yuan banknotes does he have?"}, {"key": "7636", "content": "There are a total of $10$ tigers and chickens, with a total of $26$ legs between them. How many tigers are there?."}, {"key": "7637", "content": "Chenchen is $$18$$ years old this year, and Xingxing is $$14$$ years old this year. When their combined ages amount to $$70$$ years, Xingxing will be $$--$$ years old."}, {"key": "7638", "content": "The teacher bought $$7$$ balloons, which were to be divided among two people (it's possible for someone to get none), and they were exactly all given out. There are several ways to divide them."}, {"key": "7639", "content": "Calculate: $$97\\times 22+97\\times 78=$$."}, {"key": "7640", "content": "Calculate: $$117-81+83-19=$$"}, {"key": "7641", "content": "Calculate: $$43\\times 77+43\\times 14+43\\times9=$$."}, {"key": "7642", "content": "$$275+29+(25+41)$$=\uff0e"}, {"key": "7643", "content": "The perimeter of the figure below is in centimeters. question_7643-image_0"}, {"key": "7644", "content": "The perimeter of the left image is in centimeters, and the perimeter of the right image is in meters. question_7644-image_0"}, {"key": "7645", "content": "Please choose the shape that does not have a perimeter ( )."}, {"key": "7646", "content": "$$\\frac{12}{23}+\\left( \\frac{5}{23}+\\frac{7}{16} \\right)-\\frac{17}{23}$$=\uff0e$$\\frac{7}{92}-\\left( \\frac{5}{89}+\\frac{7}{92} \\right)+\\frac{6}{89}=$$\uff0e"}, {"key": "7647", "content": "Calculate: $$38\\times 32+37\\times 33+36\\times 34=$$"}, {"key": "7648", "content": "$$12\\times 92+22\\times 82+32\\times 72$$="}, {"key": "7649", "content": "Eddie went to the stationery store to buy stationery for the teacher, with the following prices per item: mechanical pencils $$4$$ yuan each, stationery boxes $$26$$ yuan each, fountain pens $$45$$ yuan each, backpacks $$128$$ yuan each. Eddie needs to buy $$32$$ pencils, $$24$$ stationery boxes, $$65$$ fountain pens, and $$9$$ backpacks. How much money does Eddie need to spend in total?"}, {"key": "7650", "content": "On Sunday, the Young Pioneers helped to clean the windows at the nursing home, Xiao Hua cleaned $$7$$ windows, Xiao Hong and Xiao Gang together cleaned $$13$$ windows, Xiao Fang cleaned $$4$$ windows. On average, each person cleaned windows."}, {"key": "7651", "content": "In the future, in Grade 3 Class 5, Group 1, there are $$3$$ boys and $$5$$ girls. It is known that in a skipping rope competition, the average score of the girls was $$98$$ points, and the average score of the boys was $$90$$ points. Therefore, the average score of this group of students is points."}]