source_hf stringclasses 3 values | in_source_id stringlengths 5 38 | fine_source stringclasses 31 values | messages listlengths 3 3 |
|---|---|---|---|
openr1_math | 1d57f4b3-c516-5522-91cc-a60dd91f6f66_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed,... |
openr1_math | 1d57f4b3-c516-5522-91cc-a60dd91f6f66_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed,... |
openr1_math | ea24dff6-9e4d-5c55-9ec0-c4d55424997a_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll ... |
openr1_math | ea24dff6-9e4d-5c55-9ec0-c4d55424997a_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll ... |
openr1_math | a583d65c-9b4c-56ce-8263-47edbc22baa3_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$. Provide your final response in... |
openr1_math | a583d65c-9b4c-56ce-8263-47edbc22baa3_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$. Provide your final response in... |
openr1_math | 79e837be-2801-5a6a-bc7a-0acee3cdd5fd_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "A right-angled triangle has side lengths that are integers. What could be the last digit of the area's measure, if the length of t... |
openr1_math | 79e837be-2801-5a6a-bc7a-0acee3cdd5fd_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "A right-angled triangle has side lengths that are integers. What could be the last digit of the area's measure, if the length of t... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_2 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a... |
openr1_math | 167ecbbb-4270-534f-afa5-75d01d968ab5_3 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a... |
openr1_math | 84f224e8-719b-5b42-a410-27816014bdd3_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a, b, c$ respectively, and $\\sqrt{3} b \\co... |
openr1_math | 84f224e8-719b-5b42-a410-27816014bdd3_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a, b, c$ respectively, and $\\sqrt{3} b \\co... |
openr1_math | 96c9bf5f-cffe-505b-80c0-e679e10d2cf9_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 6 The rules of a \"level-up game\" stipulate: On the $n$-th level, a die must be rolled $n$ times. If the sum of the point... |
openr1_math | 96c9bf5f-cffe-505b-80c0-e679e10d2cf9_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 6 The rules of a \"level-up game\" stipulate: On the $n$-th level, a die must be rolled $n$ times. If the sum of the point... |
openr1_math | 39a6c760-dfa3-5201-aa87-105127951e16_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. (9th Canadian Mathematical Competition) $N$ is an integer, its representation in base $b$ is 777. Find the smallest positive in... |
openr1_math | 39a6c760-dfa3-5201-aa87-105127951e16_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. (9th Canadian Mathematical Competition) $N$ is an integer, its representation in base $b$ is 777. Find the smallest positive in... |
openr1_math | bdcc2598-b04d-5cb8-8634-d35d03fc6bf2_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 6. (8 points) In the plane, there is a non-closed, non-self-intersecting broken line consisting of 31 segments (adjacent s... |
openr1_math | bdcc2598-b04d-5cb8-8634-d35d03fc6bf2_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 6. (8 points) In the plane, there is a non-closed, non-self-intersecting broken line consisting of 31 segments (adjacent s... |
openr1_math | 09902996-6e6f-5507-94c7-f8b8045a702b_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "7.1. Solve the equation $\\frac{n!}{2}=k!+l!$ in natural numbers, where $n!=1 \\cdot 2 \\cdot \\ldots n$. If there are no solution... |
openr1_math | 09902996-6e6f-5507-94c7-f8b8045a702b_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "7.1. Solve the equation $\\frac{n!}{2}=k!+l!$ in natural numbers, where $n!=1 \\cdot 2 \\cdot \\ldots n$. If there are no solution... |
openr1_math | fe9fef53-41be-5c76-bbcf-bbc81ece2080_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. If the set\n$$\nA=\\{1,2, \\cdots, 10\\}, B=\\{1,2,3,4\\},\n$$\n$C$ is a subset of $A$, and $C \\cap B \\neq \\varnothing$, the... |
openr1_math | fe9fef53-41be-5c76-bbcf-bbc81ece2080_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. If the set\n$$\nA=\\{1,2, \\cdots, 10\\}, B=\\{1,2,3,4\\},\n$$\n$C$ is a subset of $A$, and $C \\cap B \\neq \\varnothing$, the... |
openr1_math | d0246a87-5e79-5337-904b-c098b279a7bd_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "12.180. A side of the triangle is equal to 15, the sum of the other two sides is 27. Find the cosine of the angle opposite the giv... |
openr1_math | d0246a87-5e79-5337-904b-c098b279a7bd_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "12.180. A side of the triangle is equal to 15, the sum of the other two sides is 27. Find the cosine of the angle opposite the giv... |
openr1_math | 5b87c250-7b32-5287-8810-f83a8c6a5b3c_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "83. Fill in the following squares with $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ respectively, so that the sum of the two five-digit numbers ... |
openr1_math | 5b87c250-7b32-5287-8810-f83a8c6a5b3c_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "83. Fill in the following squares with $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ respectively, so that the sum of the two five-digit numbers ... |
openr1_math | 26ac9e7a-f8f3-5ef9-b051-f84dfb5129ce_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "On a board, the numbers from 1 to 2009 are written. A couple of them are erased and instead of them, on the board is written the r... |
openr1_math | 26ac9e7a-f8f3-5ef9-b051-f84dfb5129ce_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "On a board, the numbers from 1 to 2009 are written. A couple of them are erased and instead of them, on the board is written the r... |
openr1_math | 8cb60360-b6a8-5af7-bf94-bb5348b2b5d3_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. The number of real solutions to the equation $\\left|x^{2}-3 x+2\\right|+\\left|x^{2}+2 x-3\\right|=11$ is ( ).\n(A) 0\n(B) 1\n... |
openr1_math | 8cb60360-b6a8-5af7-bf94-bb5348b2b5d3_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. The number of real solutions to the equation $\\left|x^{2}-3 x+2\\right|+\\left|x^{2}+2 x-3\\right|=11$ is ( ).\n(A) 0\n(B) 1\n... |
openr1_math | 59b0b709-19a9-5073-aedc-14576d104c24_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Problem Statement\n\nCalculate the limit of the numerical sequence:\n\n$\\lim _{n \\rightarrow \\infty} \\frac{(n+1)^{4}-(n-1)^... |
openr1_math | 59b0b709-19a9-5073-aedc-14576d104c24_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Problem Statement\n\nCalculate the limit of the numerical sequence:\n\n$\\lim _{n \\rightarrow \\infty} \\frac{(n+1)^{4}-(n-1)^... |
openr1_math | df4f8552-e64a-5168-a68f-2561adbeabef_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Condition of the problem\n\nFind the derivative.\n\n$$\ny=\\frac{1}{24}\\left(x^{2}+8\\right) \\sqrt{x^{2}-4}+\\frac{x^{2}}{16} \\... |
openr1_math | df4f8552-e64a-5168-a68f-2561adbeabef_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Condition of the problem\n\nFind the derivative.\n\n$$\ny=\\frac{1}{24}\\left(x^{2}+8\\right) \\sqrt{x^{2}-4}+\\frac{x^{2}}{16} \\... |
openr1_math | 98326df5-29ae-59b9-8286-d2ddeb417dd3_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "6. Let $[x]$ denote the greatest integer not exceeding the real number $x$,\n$$\n\\begin{array}{c}\nS=\\left[\\frac{1}{1}\\right]+... |
openr1_math | 98326df5-29ae-59b9-8286-d2ddeb417dd3_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "6. Let $[x]$ denote the greatest integer not exceeding the real number $x$,\n$$\n\\begin{array}{c}\nS=\\left[\\frac{1}{1}\\right]+... |
openr1_math | 457619ca-a880-58ea-a675-80512f47920f_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "19. Given $m \\in\\{11,13,15,17,19\\}$, $n \\in\\{1999,2000, \\cdots, 2018\\}$.\nThen the probability that the unit digit of $m^{n... |
openr1_math | 457619ca-a880-58ea-a675-80512f47920f_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "19. Given $m \\in\\{11,13,15,17,19\\}$, $n \\in\\{1999,2000, \\cdots, 2018\\}$.\nThen the probability that the unit digit of $m^{n... |
openr1_math | 46eb6c3b-bc5d-5fc0-8913-2c4a06359b71_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. (6 points) Today is January 31, 2015, welcome to the 2015 \"Spring Cup\" Final. The calculation result of the expression $\\fra... |
openr1_math | 46eb6c3b-bc5d-5fc0-8913-2c4a06359b71_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. (6 points) Today is January 31, 2015, welcome to the 2015 \"Spring Cup\" Final. The calculation result of the expression $\\fra... |
openr1_math | cb62d969-8b55-5c63-882f-199860473630_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Consider a regular hexagon with an incircle. What is the ratio of the area inside the incircle to the area of the hexagon?\n Provi... |
openr1_math | cb62d969-8b55-5c63-882f-199860473630_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Consider a regular hexagon with an incircle. What is the ratio of the area inside the incircle to the area of the hexagon?\n Provi... |
openr1_math | 0b423c8a-0e77-586e-adf3-9a3b1d065c24_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with centroid $G$. Determine, with proof, the position of the point $P$ in the plane of $ABC$ such that $A... |
openr1_math | 0b423c8a-0e77-586e-adf3-9a3b1d065c24_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with centroid $G$. Determine, with proof, the position of the point $P$ in the plane of $ABC$ such that $A... |
openr1_math | 577a5162-4356-5db9-9c92-511f854949b4_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The function $f$ maps the set of positive integers into itself, and satisfies the equation\n\n$$\nf(f(n))+f(n)=2 n+6\n$$\n\nWhat c... |
openr1_math | 577a5162-4356-5db9-9c92-511f854949b4_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The function $f$ maps the set of positive integers into itself, and satisfies the equation\n\n$$\nf(f(n))+f(n)=2 n+6\n$$\n\nWhat c... |
openr1_math | 12b14f92-3f01-5f14-9fb9-abf68de16852_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "30. Find the remainder when the 2018-digit number $\\underbrace{\\overline{55 \\cdots}}_{2018 \\text { 555 }}$ is divided by 13. P... |
openr1_math | 12b14f92-3f01-5f14-9fb9-abf68de16852_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "30. Find the remainder when the 2018-digit number $\\underbrace{\\overline{55 \\cdots}}_{2018 \\text { 555 }}$ is divided by 13. P... |
openr1_math | a963b473-4719-5873-a189-0c6e08b203b9_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. A line $l$ intersects a hyperbola $c$, then the maximum number of intersection points is ( ).\nA. 1\nB. 2\nC. 3\nD. 4 Provide y... |
openr1_math | a963b473-4719-5873-a189-0c6e08b203b9_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. A line $l$ intersects a hyperbola $c$, then the maximum number of intersection points is ( ).\nA. 1\nB. 2\nC. 3\nD. 4 Provide y... |
openr1_math | 6c66cda2-e28f-5dba-8960-e80de252eda9_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. Let the universal set be the set of real numbers. If $A=\\{x \\mid \\sqrt{x-2} \\leqslant 0\\}, B=\\left\\{x \\mid 10^{x^{2}-2}... |
openr1_math | 6c66cda2-e28f-5dba-8960-e80de252eda9_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. Let the universal set be the set of real numbers. If $A=\\{x \\mid \\sqrt{x-2} \\leqslant 0\\}, B=\\left\\{x \\mid 10^{x^{2}-2}... |
openr1_math | ea501978-91dd-5cdd-8010-5c6ba822b1c1_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. As shown in Figure 1, in the right triangular prism $A B C-A_{1} B_{1} C_{1}$, $A A_{1}=A B=A C$, and $M$ and $Q$ are the midpo... |
openr1_math | ea501978-91dd-5cdd-8010-5c6ba822b1c1_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. As shown in Figure 1, in the right triangular prism $A B C-A_{1} B_{1} C_{1}$, $A A_{1}=A B=A C$, and $M$ and $Q$ are the midpo... |
openr1_math | 2bfb42a5-11c9-5aee-b6df-edb9b8efee0e_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "7.242. $\\left(16 \\cdot 5^{2 x-1}-2 \\cdot 5^{x-1}-0.048\\right) \\lg \\left(x^{3}+2 x+1\\right)=0$. Provide your final response ... |
openr1_math | 2bfb42a5-11c9-5aee-b6df-edb9b8efee0e_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "7.242. $\\left(16 \\cdot 5^{2 x-1}-2 \\cdot 5^{x-1}-0.048\\right) \\lg \\left(x^{3}+2 x+1\\right)=0$. Provide your final response ... |
openr1_math | 80c5345a-b5f8-5bef-8c9f-f624dc51008a_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 1 In $\\triangle ABC$, it is known that $x \\sin A + y \\sin B + z \\sin C = 0$. Find the value of $(y + z \\cos A)(z + x ... |
openr1_math | 80c5345a-b5f8-5bef-8c9f-f624dc51008a_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 1 In $\\triangle ABC$, it is known that $x \\sin A + y \\sin B + z \\sin C = 0$. Find the value of $(y + z \\cos A)(z + x ... |
openr1_math | 9f1b8d76-1de2-5183-93e5-acebd8955df9_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "11.005. The plane angle at the vertex of a regular triangular pyramid is $90^{\\circ}$. Find the ratio of the lateral surface area... |
openr1_math | 9f1b8d76-1de2-5183-93e5-acebd8955df9_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "11.005. The plane angle at the vertex of a regular triangular pyramid is $90^{\\circ}$. Find the ratio of the lateral surface area... |
openr1_math | 16dbe1c7-62c1-5abf-88b4-a4d83a5c8276_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "A father wants to divide his property among his children: first, he gives 1000 yuan and one-tenth of the remaining property to the... |
openr1_math | 16dbe1c7-62c1-5abf-88b4-a4d83a5c8276_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "A father wants to divide his property among his children: first, he gives 1000 yuan and one-tenth of the remaining property to the... |
openr1_math | 6bb59c32-e03b-53f3-9abf-a23cdeb0c3a1_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "9. Given is a regular tetrahedron of volume 1 . We obtain a second regular tetrahedron by reflecting the given one through its cen... |
openr1_math | 6bb59c32-e03b-53f3-9abf-a23cdeb0c3a1_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "9. Given is a regular tetrahedron of volume 1 . We obtain a second regular tetrahedron by reflecting the given one through its cen... |
openr1_math | 95bcc8e7-a809-533d-8cbd-45e190531b31_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Zadatak B-1.2.\n\nNa slici su prikazani pravilni peterokut. $A B C D E$ i kvadrat $A B F G$. Odredite mjeru kuta $F A D$.\n\n![... |
openr1_math | 95bcc8e7-a809-533d-8cbd-45e190531b31_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Zadatak B-1.2.\n\nNa slici su prikazani pravilni peterokut. $A B C D E$ i kvadrat $A B F G$. Odredite mjeru kuta $F A D$.\n\n![... |
openr1_math | b325fc9f-7ff8-5556-976b-f72348f99405_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The equation of line $\\ell_1$ is $24x-7y = 319$ and the equation of line $\\ell_2$ is $12x-5y = 125$. Let $a$ be the number of po... |
openr1_math | b325fc9f-7ff8-5556-976b-f72348f99405_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The equation of line $\\ell_1$ is $24x-7y = 319$ and the equation of line $\\ell_2$ is $12x-5y = 125$. Let $a$ be the number of po... |
openr1_math | 04a9ffed-3e45-56b4-a5aa-88bbb91a6050_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 1 The range of the function $y=-x^{2}-2 x+3(-5 \\leqslant x \\leqslant 0)$ is $(\\quad)$.\n(A) $(-\\infty, 4]$\n(B) $[3,12... |
openr1_math | 04a9ffed-3e45-56b4-a5aa-88bbb91a6050_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 1 The range of the function $y=-x^{2}-2 x+3(-5 \\leqslant x \\leqslant 0)$ is $(\\quad)$.\n(A) $(-\\infty, 4]$\n(B) $[3,12... |
openr1_math | e93a8cbd-336b-5aa7-9e39-b81d5037510d_0 | inequalities | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4.206 There are two forces $f_{1}$ and $f_{2}$ acting on the origin $O$ of the coordinate axis,\n$$\\begin{array}{l}\n\\vec{f}_{1}... |
openr1_math | e93a8cbd-336b-5aa7-9e39-b81d5037510d_1 | inequalities | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4.206 There are two forces $f_{1}$ and $f_{2}$ acting on the origin $O$ of the coordinate axis,\n$$\\begin{array}{l}\n\\vec{f}_{1}... |
openr1_math | 9941a501-7cbb-5f6c-9005-e629b9d55555_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1B. If for the non-zero real numbers $a, b$ and $c$ the equalities $a^{2}+a=b^{2}, b^{2}+b=c^{2}$ and $c^{2}+c=a^{2}$ hold, determ... |
openr1_math | 9941a501-7cbb-5f6c-9005-e629b9d55555_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1B. If for the non-zero real numbers $a, b$ and $c$ the equalities $a^{2}+a=b^{2}, b^{2}+b=c^{2}$ and $c^{2}+c=a^{2}$ hold, determ... |
openr1_math | 5fe89991-5e64-5f7e-952e-97e28e99c211_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. As shown in Figure 1, the side length of rhombus $A B C D$ is $a$, and $O$ is a point on the diagonal $A C$, with $O A=a, O B=$... |
openr1_math | 5fe89991-5e64-5f7e-952e-97e28e99c211_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. As shown in Figure 1, the side length of rhombus $A B C D$ is $a$, and $O$ is a point on the diagonal $A C$, with $O A=a, O B=$... |
openr1_math | c8a6178c-e74a-5a3d-a899-590ea913cc0e_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. Given $a, b>0, a \\neq 1$, and $a^{b}=\\log _{a} b$, then the value of $a^{a^{b}}-\\log _{a} \\log _{a} b^{a}$ is Provide your ... |
openr1_math | c8a6178c-e74a-5a3d-a899-590ea913cc0e_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. Given $a, b>0, a \\neq 1$, and $a^{b}=\\log _{a} b$, then the value of $a^{a^{b}}-\\log _{a} \\log _{a} b^{a}$ is Provide your ... |
openr1_math | 05c6feba-c571-5253-9e7a-a43d0032fefc_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In a stairwell, there are 10 mailboxes. One distributor drops a flyer into 5 mailboxes. Later, another distributor also drops a fl... |
openr1_math | 05c6feba-c571-5253-9e7a-a43d0032fefc_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In a stairwell, there are 10 mailboxes. One distributor drops a flyer into 5 mailboxes. Later, another distributor also drops a fl... |
openr1_math | e32aa5a1-3bc5-5982-9571-0440038ed832_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "18. (3 points) Li Shuang rides a bike at a speed of 320 meters per minute from location $A$ to location $B$. On the way, due to a ... |
openr1_math | e32aa5a1-3bc5-5982-9571-0440038ed832_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "18. (3 points) Li Shuang rides a bike at a speed of 320 meters per minute from location $A$ to location $B$. On the way, due to a ... |
openr1_math | 9981f4e1-f944-5276-b5c5-9399972a55c5_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "53. How many four-digit numbers contain at least one even digit? Provide your final response in \\boxed{}",
"role": "user"
}... |
openr1_math | 9981f4e1-f944-5276-b5c5-9399972a55c5_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "53. How many four-digit numbers contain at least one even digit? Provide your final response in \\boxed{}",
"role": "user"
}... |
openr1_math | c893b886-f879-5c5e-8d98-225848b20901_0 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. The range of the function $f(x)=\\sin x+\\cos x+\\tan x+$ $\\arcsin x+\\arccos x+\\arctan x$ is $\\qquad$ . Provide your final ... |
openr1_math | c893b886-f879-5c5e-8d98-225848b20901_1 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. The range of the function $f(x)=\\sin x+\\cos x+\\tan x+$ $\\arcsin x+\\arccos x+\\arctan x$ is $\\qquad$ . Provide your final ... |
openr1_math | c893b886-f879-5c5e-8d98-225848b20901_2 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. The range of the function $f(x)=\\sin x+\\cos x+\\tan x+$ $\\arcsin x+\\arccos x+\\arctan x$ is $\\qquad$ . Provide your final ... |
openr1_math | c893b886-f879-5c5e-8d98-225848b20901_3 | cn_contest | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. The range of the function $f(x)=\\sin x+\\cos x+\\tan x+$ $\\arcsin x+\\arccos x+\\arctan x$ is $\\qquad$ . Provide your final ... |
openr1_math | 06740483-7ea9-51a8-9c93-ac3eb5552512_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_1,a_2,\\ldots,a_n$ be a permutation of the numbers $1,2,\\ldots,n$, with $n\\geq 2$. Determine the largest possible value o... |
openr1_math | 06740483-7ea9-51a8-9c93-ac3eb5552512_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_1,a_2,\\ldots,a_n$ be a permutation of the numbers $1,2,\\ldots,n$, with $n\\geq 2$. Determine the largest possible value o... |
openr1_math | ec38bd78-c486-5455-a4c4-6780cc81372f_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "10.319. The diagonals of an isosceles trapezoid are perpendicular to each other, and its area is $a^{2}$. Determine the height of ... |
openr1_math | ec38bd78-c486-5455-a4c4-6780cc81372f_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "10.319. The diagonals of an isosceles trapezoid are perpendicular to each other, and its area is $a^{2}$. Determine the height of ... |
openr1_math | 079495cf-64e8-565d-ab82-523255814ae6_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_1, a_2, a_3, a_4$ be integers with distinct absolute values. In the coordinate plane, let $A_1=(a_1,a_1^2)$, $A_2=(a_2,a_2^... |
openr1_math | 079495cf-64e8-565d-ab82-523255814ae6_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $a_1, a_2, a_3, a_4$ be integers with distinct absolute values. In the coordinate plane, let $A_1=(a_1,a_1^2)$, $A_2=(a_2,a_2^... |
openr1_math | 06140285-54b0-55d4-9ff6-0c1a0effe8ca_0 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. Find all integer solutions of the inequality\n\n$$\nx^{2} y^{2}+y^{2} z^{2}+x^{2}+z^{2}-38(x y+z)-40(y z+x)+4 x y z+761 \\leq 0... |
openr1_math | 06140285-54b0-55d4-9ff6-0c1a0effe8ca_1 | olympiads | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. Find all integer solutions of the inequality\n\n$$\nx^{2} y^{2}+y^{2} z^{2}+x^{2}+z^{2}-38(x y+z)-40(y z+x)+4 x y z+761 \\leq 0... |
openr1_math | f09e4bd6-0c9c-5d39-b5cf-316ecd9d323c_0 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Find all triples $(m,p,q)$ where $ m $ is a positive integer and $ p , q $ are primes.\n\\[ 2^m p^2 + 1 = q^5 \\] Provide your fin... |
openr1_math | f09e4bd6-0c9c-5d39-b5cf-316ecd9d323c_1 | aops_forum | [
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Find all triples $(m,p,q)$ where $ m $ is a positive integer and $ p , q $ are primes.\n\\[ 2^m p^2 + 1 = q^5 \\] Provide your fin... |
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