id
stringlengths 31
70
| setting_key
stringclasses 31
values | difficulty
stringclasses 1
value | level
int64 1
1
| messages
listlengths 1
1
| ground_truth
stringlengths 1
19
| dataset
stringclasses 1
value | omega_split
stringclasses 1
value | __index_level_0__
int64 0
160k
|
|---|---|---|---|---|---|---|---|---|
math_logic_puzzles_grid_chip_level_1_1_335
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 1) is black, cell (2, 3) is black, cell (0, 0) is white, cell (1, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,400
|
math_logic_puzzles_grid_chip_level_1_1_336
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 2) is black, cell (2, 2) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,401
|
math_logic_puzzles_grid_chip_level_1_1_337
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is white, cell (0, 3) is black, cell (3, 3) is black, cell (2, 1) is black, cell (1, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,402
|
math_logic_puzzles_grid_chip_level_1_1_338
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (2, 3) is black, cell (3, 1) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,403
|
math_logic_puzzles_grid_chip_level_1_1_339
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 1) is white, cell (1, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,404
|
math_logic_puzzles_grid_chip_level_1_1_340
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 0) is white, cell (3, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
math
|
train
| 159,405
|
math_logic_puzzles_grid_chip_level_1_1_341
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 1) is black, cell (1, 0) is white, cell (0, 0) is white, cell (2, 0) is white, cell (3, 3) is black, cell (3, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,406
|
math_logic_puzzles_grid_chip_level_1_1_342
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 2) is white, cell (3, 1) is black, cell (1, 3) is white, cell (0, 0) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,407
|
math_logic_puzzles_grid_chip_level_1_1_343
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (1, 1) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
math
|
train
| 159,408
|
math_logic_puzzles_grid_chip_level_1_1_344
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 0) is white, cell (0, 3) is white, cell (0, 3) is white, cell (3, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,409
|
math_logic_puzzles_grid_chip_level_1_1_345
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 2) is black, cell (0, 0) is white, cell (3, 1) is black, cell (2, 0) is white, cell (1, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,410
|
math_logic_puzzles_grid_chip_level_1_1_346
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is white, cell (3, 3) is black, cell (3, 0) is black, cell (1, 2) is white, cell (2, 1) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,411
|
math_logic_puzzles_grid_chip_level_1_1_347
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 1) is white, cell (0, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,412
|
math_logic_puzzles_grid_chip_level_1_1_348
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (1, 1) is white, cell (2, 1) is white, cell (3, 0) is white, cell (0, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,413
|
math_logic_puzzles_grid_chip_level_1_1_349
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 1) is white, cell (3, 0) is white, cell (1, 3) is white, cell (2, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,414
|
math_logic_puzzles_grid_chip_level_1_1_350
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 0) is black, cell (0, 3) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,415
|
math_logic_puzzles_grid_chip_level_1_1_351
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 1) is black, cell (0, 1) is black, cell (1, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,416
|
math_logic_puzzles_grid_chip_level_1_1_352
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (1, 1) is black, cell (2, 0) is white, cell (3, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,417
|
math_logic_puzzles_grid_chip_level_1_1_353
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 0) is black, cell (0, 2) is black, cell (1, 2) is black, cell (3, 3) is white, cell (3, 1) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,418
|
math_logic_puzzles_grid_chip_level_1_1_354
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 0) is white, cell (0, 2) is white, cell (3, 0) is white, cell (2, 2) is white, cell (3, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
math
|
train
| 159,419
|
math_logic_puzzles_grid_chip_level_1_1_355
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 1) is black, cell (3, 1) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,420
|
math_logic_puzzles_grid_chip_level_1_1_356
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 3) is black, cell (3, 2) is black, cell (0, 0) is black, cell (1, 1) is black, cell (2, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,421
|
math_logic_puzzles_grid_chip_level_1_1_357
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 3) is white, cell (3, 3) is white, cell (2, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,422
|
math_logic_puzzles_grid_chip_level_1_1_358
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 3) is white, cell (2, 2) is white, cell (0, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,423
|
math_logic_puzzles_grid_chip_level_1_1_359
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 1) is white, cell (0, 0) is white, cell (3, 3) is white, cell (2, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,424
|
math_logic_puzzles_grid_chip_level_1_1_360
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 3) is black, cell (2, 0) is white, cell (0, 3) is black, cell (2, 1) is white, cell (3, 3) is black, cell (2, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,425
|
math_logic_puzzles_grid_chip_level_1_1_361
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 1) is black, cell (2, 3) is black, cell (3, 0) is black, cell (3, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,426
|
math_logic_puzzles_grid_chip_level_1_1_362
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 1) is white, cell (2, 2) is white, cell (3, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,427
|
math_logic_puzzles_grid_chip_level_1_1_363
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 1) is black, cell (3, 3) is white, cell (3, 0) is white, cell (0, 2) is black, cell (1, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,428
|
math_logic_puzzles_grid_chip_level_1_1_364
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 3) is black, cell (2, 1) is white, cell (0, 2) is black, cell (3, 0) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,429
|
math_logic_puzzles_grid_chip_level_1_1_365
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 1) is white, cell (3, 0) is black, cell (3, 3) is black, cell (0, 1) is white, cell (2, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,430
|
math_logic_puzzles_grid_chip_level_1_1_366
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 3) is black, cell (2, 2) is black, cell (3, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,431
|
math_logic_puzzles_grid_chip_level_1_1_367
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 2) is white, cell (2, 2) is white, cell (1, 0) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,432
|
math_logic_puzzles_grid_chip_level_1_1_368
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is white, cell (2, 0) is black, cell (3, 3) is white, cell (1, 1) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,433
|
math_logic_puzzles_grid_chip_level_1_1_369
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 3) is black, cell (3, 2) is black, cell (1, 1) is white, cell (2, 0) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,434
|
math_logic_puzzles_grid_chip_level_1_1_370
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 1) is black, cell (2, 2) is black, cell (3, 0) is black, cell (0, 3) is white, cell (1, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,435
|
math_logic_puzzles_grid_chip_level_1_1_371
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 0) is white, cell (3, 1) is white, cell (2, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,436
|
math_logic_puzzles_grid_chip_level_1_1_372
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is black, cell (1, 0) is black, cell (3, 3) is black, cell (0, 1) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,437
|
math_logic_puzzles_grid_chip_level_1_1_373
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 2) is white, cell (0, 2) is white, cell (1, 3) is white, cell (2, 0) is white, cell (3, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,438
|
math_logic_puzzles_grid_chip_level_1_1_374
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is white, cell (3, 3) is black, cell (0, 1) is black, cell (2, 3) is black, cell (1, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,439
|
math_logic_puzzles_grid_chip_level_1_1_375
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 1) is black, cell (1, 3) is black, cell (0, 1) is black, cell (0, 2) is black, cell (3, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,440
|
math_logic_puzzles_grid_chip_level_1_1_376
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is white, cell (1, 0) is black, cell (2, 3) is white, cell (2, 1) is white, cell (3, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,441
|
math_logic_puzzles_grid_chip_level_1_1_377
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is white, cell (1, 0) is white, cell (0, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,442
|
math_logic_puzzles_grid_chip_level_1_1_378
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 3) is white, cell (0, 3) is white, cell (1, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,443
|
math_logic_puzzles_grid_chip_level_1_1_379
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 1) is black, cell (0, 0) is black, cell (3, 2) is black, cell (1, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,444
|
math_logic_puzzles_grid_chip_level_1_1_380
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 3) is white, cell (0, 0) is black, cell (1, 2) is white, cell (2, 3) is white, cell (0, 1) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,445
|
math_logic_puzzles_grid_chip_level_1_1_381
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 3) is white, cell (2, 1) is black, cell (0, 0) is white, cell (1, 1) is black, cell (3, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,446
|
math_logic_puzzles_grid_chip_level_1_1_382
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 0) is white, cell (2, 3) is white, cell (0, 2) is white, cell (2, 3) is white, cell (2, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,447
|
math_logic_puzzles_grid_chip_level_1_1_383
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 2) is black, cell (2, 2) is black, cell (3, 3) is black, cell (2, 2) is black, cell (0, 1) is black, cell (2, 2) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,448
|
math_logic_puzzles_grid_chip_level_1_1_384
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 1) is black, cell (3, 0) is white, cell (2, 3) is black, cell (0, 0) is white, cell (2, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,449
|
math_logic_puzzles_grid_chip_level_1_1_385
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 2) is white, cell (0, 0) is black, cell (2, 1) is black, cell (2, 3) is black, cell (3, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,450
|
math_logic_puzzles_grid_chip_level_1_1_386
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is black, cell (1, 2) is black, cell (1, 1) is black, cell (2, 3) is white, cell (0, 3) is white, cell (3, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,451
|
math_logic_puzzles_grid_chip_level_1_1_387
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 1) is black, cell (3, 2) is black, cell (0, 0) is white, cell (2, 1) is black, cell (0, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,452
|
math_logic_puzzles_grid_chip_level_1_1_388
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 0) is black, cell (1, 1) is black, cell (1, 3) is black, cell (2, 0) is black, cell (1, 2) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
math
|
train
| 159,453
|
math_logic_puzzles_grid_chip_level_1_1_389
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 1) is white, cell (3, 3) is white, cell (0, 0) is white, cell (1, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,454
|
math_logic_puzzles_grid_chip_level_1_1_390
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 2) is black, cell (1, 3) is black, cell (0, 3) is black, cell (3, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,455
|
math_logic_puzzles_grid_chip_level_1_1_391
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (3, 0) is white, cell (1, 3) is white, cell (2, 3) is white, cell (0, 1) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,456
|
math_logic_puzzles_grid_chip_level_1_1_392
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 0) is white, cell (3, 1) is black, cell (2, 3) is black, cell (1, 1) is black, cell (0, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,457
|
math_logic_puzzles_grid_chip_level_1_1_393
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 3) is black, cell (1, 0) is white, cell (0, 1) is black, cell (3, 3) is black, cell (1, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,458
|
math_logic_puzzles_grid_chip_level_1_1_394
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (1, 0) is black, cell (2, 3) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
math
|
train
| 159,459
|
math_logic_puzzles_grid_chip_level_1_1_395
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (3, 0) is black, cell (3, 0) is black, cell (1, 3) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,460
|
math_logic_puzzles_grid_chip_level_1_1_396
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 2) is white, cell (3, 0) is white, cell (2, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,461
|
math_logic_puzzles_grid_chip_level_1_1_397
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 3) is black, cell (2, 0) is white, cell (0, 1) is white, cell (1, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,462
|
math_logic_puzzles_grid_chip_level_1_1_398
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 0) is white, cell (1, 1) is white, cell (3, 1) is white, cell (0, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,463
|
math_logic_puzzles_grid_chip_level_1_1_399
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 1) is black, cell (0, 3) is black, cell (2, 3) is black, cell (1, 2) is white, cell (1, 0) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,464
|
math_logic_puzzles_grid_chip_level_1_1_400
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 0) is white, cell (1, 3) is white, cell (1, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,465
|
math_logic_puzzles_grid_chip_level_1_1_401
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 3) is white, cell (2, 2) is white, cell (2, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,466
|
math_logic_puzzles_grid_chip_level_1_1_402
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 3) is white, cell (2, 0) is white, cell (2, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,467
|
math_logic_puzzles_grid_chip_level_1_1_403
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 2) is white, cell (1, 1) is white, cell (1, 1) is white, cell (0, 1) is white, cell (0, 1) is white, cell (3, 1) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,468
|
math_logic_puzzles_grid_chip_level_1_1_404
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 0) is black, cell (3, 2) is black, cell (1, 1) is white, cell (0, 1) is white, cell (3, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,469
|
math_logic_puzzles_grid_chip_level_1_1_405
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 3) is white, cell (1, 0) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,470
|
math_logic_puzzles_grid_chip_level_1_1_406
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 2) is white, cell (1, 0) is white, cell (3, 3) is black, cell (1, 1) is white, cell (0, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,471
|
math_logic_puzzles_grid_chip_level_1_1_407
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 1) is white, cell (3, 3) is black, cell (0, 2) is black, cell (2, 2) is black, cell (1, 0) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,472
|
math_logic_puzzles_grid_chip_level_1_1_408
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is black, cell (1, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,473
|
math_logic_puzzles_grid_chip_level_1_1_409
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 0) is black, cell (3, 1) is white, cell (0, 0) is black, cell (3, 3) is white, cell (3, 2) is white, cell (1, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,474
|
math_logic_puzzles_grid_chip_level_1_1_410
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 3) is black, cell (0, 2) is white, cell (1, 0) is white, cell (1, 1) is white, cell (2, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,475
|
math_logic_puzzles_grid_chip_level_1_1_411
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 3) is white, cell (3, 2) is white, cell (2, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,476
|
math_logic_puzzles_grid_chip_level_1_1_412
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 2) is white, cell (0, 0) is white, cell (3, 1) is black, cell (2, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 159,477
|
math_logic_puzzles_grid_chip_level_1_1_413
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 1) is black, cell (2, 0) is white, cell (3, 3) is black, cell (1, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,478
|
math_logic_puzzles_grid_chip_level_1_1_414
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 3) is white, cell (3, 2) is white, cell (3, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
math
|
train
| 159,479
|
math_logic_puzzles_grid_chip_level_1_1_415
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is white, cell (3, 2) is white, cell (2, 3) is white, cell (2, 3) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,480
|
math_logic_puzzles_grid_chip_level_1_1_416
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 2) is black, cell (1, 3) is white, cell (2, 0) is black, cell (2, 1) is black, cell (0, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,481
|
math_logic_puzzles_grid_chip_level_1_1_417
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 2) is white, cell (0, 3) is black, cell (1, 2) is white, cell (0, 1) is black, cell (0, 0) is black, cell (3, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,482
|
math_logic_puzzles_grid_chip_level_1_1_418
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 0) is black, cell (1, 1) is black, cell (0, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,483
|
math_logic_puzzles_grid_chip_level_1_1_419
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 0) is black, cell (0, 2) is black, cell (0, 2) is black, cell (2, 0) is black, cell (1, 1) is black, cell (2, 3) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,484
|
math_logic_puzzles_grid_chip_level_1_1_420
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 2) is black, cell (1, 3) is black, cell (0, 1) is black, cell (3, 0) is black, cell (3, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
train
| 159,485
|
math_logic_puzzles_grid_chip_level_1_1_421
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is black, cell (2, 2) is white, cell (0, 1) is black, cell (3, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,486
|
math_logic_puzzles_grid_chip_level_1_1_422
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 3) is white, cell (0, 1) is black, cell (2, 3) is white, cell (0, 2) is black, cell (0, 0) is black, cell (1, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,487
|
math_logic_puzzles_grid_chip_level_1_1_423
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 0) is white, cell (2, 2) is black, cell (3, 3) is black, cell (0, 1) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,488
|
math_logic_puzzles_grid_chip_level_1_1_424
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 3) is white, cell (2, 0) is white, cell (2, 1) is white, cell (3, 3) is white, cell (3, 2) is white. What is the maximum number of black chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,489
|
math_logic_puzzles_grid_chip_level_1_1_425
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 2) is black, cell (1, 3) is white, cell (3, 1) is white, cell (2, 3) is white, cell (0, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,490
|
math_logic_puzzles_grid_chip_level_1_1_426
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 2) is black, cell (0, 0) is black, cell (3, 3) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
math
|
train
| 159,491
|
math_logic_puzzles_grid_chip_level_1_1_427
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 0) is black, cell (1, 1) is black, cell (1, 3) is black, cell (2, 2) is white, cell (0, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,492
|
math_logic_puzzles_grid_chip_level_1_1_428
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 3) is black, cell (2, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,493
|
math_logic_puzzles_grid_chip_level_1_1_429
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 1) is white, cell (2, 1) is white, cell (0, 3) is black, cell (1, 0) is black, cell (1, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,494
|
math_logic_puzzles_grid_chip_level_1_1_430
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (0, 1) is black, cell (2, 2) is white, cell (3, 3) is white, cell (1, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,495
|
math_logic_puzzles_grid_chip_level_1_1_431
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 2) is black, cell (3, 1) is black, cell (2, 0) is black, cell (0, 3) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,496
|
math_logic_puzzles_grid_chip_level_1_1_432
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour, c) any additional chip placed on the grid would violate one or more of the previous two conditions. Furthermore, we have the following constraints (with the cells 0-indexed): cell (1, 1) is black, cell (2, 1) is black, cell (0, 2) is white, cell (0, 0) is white, cell (3, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,497
|
math_logic_puzzles_grid_chip_level_1_1_433
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (2, 0) is black, cell (2, 2) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
train
| 159,498
|
math_logic_puzzles_grid_chip_level_1_1_434
|
logic_puzzles_grid_chip1
|
easy (level 1)
| 1
|
[
{
"content": "Chips, colored either black or white, are placed in a 4x4 grid such that: a) each cell contains at most one chip, b) all chips in the same row and all chips in the same column have the same colour. Furthermore, we have the following constraints (with the cells 0-indexed): cell (3, 2) is black, cell (1, 2) is black, cell (2, 0) is black. What is the maximum number of white chips that can be placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
math
|
train
| 159,499
|
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