id
string | setting_key
string | difficulty
string | level
int64 | messages
list | ground_truth
string | dataset
string | omega_split
string | __index_level_0__
int64 |
|---|---|---|---|---|---|---|---|---|
math_logic_puzzles_grid_chip_level_5_5_700
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 4) is black, cell (6, 6) is black, cell (0, 0) is black, cell (7, 6) is black, cell (4, 6) is black, cell (3, 1) is black, cell (2, 3) is black, cell (5, 2) is black, cell (3, 5) 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"
}
] |
12
|
math
|
train
| 410,932
|
math_logic_puzzles_grid_chip_level_5_5_701
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 black, cell (5, 4) is black, cell (6, 7) is white, cell (7, 1) is white, cell (4, 3) is white, cell (1, 3) is white, cell (0, 0) is black, cell (3, 5) is white, cell (0, 6) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,933
|
math_logic_puzzles_grid_chip_level_5_5_702
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (7, 1) is black, cell (6, 7) is black, cell (5, 5) is black, cell (2, 4) is black, cell (3, 0) is black, cell (4, 2) is black, cell (0, 3) is white, cell (1, 6) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
math
|
train
| 410,934
|
math_logic_puzzles_grid_chip_level_5_5_703
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 6) is white, cell (1, 3) is white, cell (3, 1) is white, cell (4, 5) is white, cell (4, 4) is white, cell (5, 2) is black, cell (6, 7) is black, cell (2, 7) is black, cell (7, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,935
|
math_logic_puzzles_grid_chip_level_5_5_704
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 0) is white, cell (3, 2) is white, cell (4, 1) is white, cell (3, 3) is white, cell (5, 0) is white, cell (3, 6) is white, cell (3, 5) is white, cell (0, 4) 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"
}
] |
11
|
math
|
train
| 410,936
|
math_logic_puzzles_grid_chip_level_5_5_705
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 4) is white, cell (3, 7) is black, cell (0, 5) is white, cell (4, 2) is black, cell (7, 6) is white, cell (0, 0) is white, cell (2, 2) is black, cell (1, 1) is black, cell (7, 3) is white, cell (6, 1) is black, cell (5, 7) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
math
|
train
| 410,937
|
math_logic_puzzles_grid_chip_level_5_5_706
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 white, cell (3, 4) is black, cell (4, 0) is white, cell (0, 4) is black, cell (2, 5) is black, cell (5, 1) is white, cell (6, 7) is white, cell (7, 2) is white, cell (2, 6) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
math
|
train
| 410,938
|
math_logic_puzzles_grid_chip_level_5_5_707
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (2, 1) is white, cell (4, 6) is black, cell (7, 7) is black, cell (5, 1) is white, cell (0, 1) is white, cell (1, 6) is black, cell (6, 0) is black, cell (6, 5) is black, cell (6, 4) 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"
}
] |
32
|
math
|
train
| 410,939
|
math_logic_puzzles_grid_chip_level_5_5_708
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (7, 2) is white, cell (5, 4) is white, cell (3, 1) is white, cell (0, 3) is white, cell (3, 7) is white, cell (2, 6) 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"
}
] |
14
|
math
|
train
| 410,940
|
math_logic_puzzles_grid_chip_level_5_5_709
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 3) is black, cell (5, 5) is black, cell (5, 5) is black, cell (6, 1) is black, cell (3, 5) is black, cell (1, 6) is black, cell (7, 7) is black, cell (1, 0) is black, cell (1, 4) 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"
}
] |
11
|
math
|
train
| 410,941
|
math_logic_puzzles_grid_chip_level_5_5_710
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 7) is white, cell (1, 6) is white, cell (0, 1) is white, cell (4, 3) is white, cell (5, 3) is white, cell (6, 5) is white, cell (6, 5) is white, cell (1, 4) 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"
}
] |
12
|
math
|
train
| 410,942
|
math_logic_puzzles_grid_chip_level_5_5_711
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 7) is black, cell (0, 1) is black, cell (4, 5) is black, cell (7, 4) is black, cell (4, 5) is black, cell (6, 4) is black, cell (3, 6) 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"
}
] |
16
|
math
|
train
| 410,943
|
math_logic_puzzles_grid_chip_level_5_5_712
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 5) is white, cell (3, 4) 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"
}
] |
22
|
math
|
train
| 410,944
|
math_logic_puzzles_grid_chip_level_5_5_713
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (7, 5) is white, cell (2, 0) is white, cell (1, 1) is white, cell (6, 2) is white, cell (4, 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"
}
] |
19
|
math
|
train
| 410,945
|
math_logic_puzzles_grid_chip_level_5_5_714
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (6, 5) is black, cell (5, 3) is black, cell (3, 4) is white, cell (7, 2) is white, cell (0, 6) is white, cell (2, 7) is black, cell (4, 0) is white, cell (1, 4) is white, cell (5, 1) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,946
|
math_logic_puzzles_grid_chip_level_5_5_715
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 2) is black, cell (2, 1) is white, cell (0, 7) is black, cell (4, 0) is black, cell (1, 5) is black, cell (3, 3) is white, cell (7, 5) is black, cell (5, 6) is white, cell (6, 6) is white, cell (2, 4) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,947
|
math_logic_puzzles_grid_chip_level_5_5_716
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 3) is black, cell (5, 1) is black, cell (4, 5) is black, cell (7, 1) is black, cell (6, 6) is black, cell (0, 1) is black, cell (2, 6) 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"
}
] |
13
|
math
|
train
| 410,948
|
math_logic_puzzles_grid_chip_level_5_5_717
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 5) is black, cell (5, 5) is black, cell (6, 6) is black, cell (5, 5) is black, cell (1, 2) is black, cell (2, 4) is black, cell (3, 7) is black, cell (4, 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"
}
] |
11
|
math
|
train
| 410,949
|
math_logic_puzzles_grid_chip_level_5_5_718
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 black, cell (1, 0) is black, cell (0, 5) is black, cell (6, 7) is black, cell (7, 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"
}
] |
18
|
math
|
train
| 410,950
|
math_logic_puzzles_grid_chip_level_5_5_719
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 1) is black, cell (2, 6) is black, cell (3, 4) is black, cell (6, 5) is black, cell (7, 5) is black, cell (4, 2) is black, cell (1, 7) 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"
}
] |
13
|
math
|
train
| 410,951
|
math_logic_puzzles_grid_chip_level_5_5_720
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 6) is black, cell (2, 1) is black, cell (3, 4) is black, cell (5, 2) is black, cell (4, 0) is black, cell (5, 5) 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"
}
] |
16
|
math
|
train
| 410,952
|
math_logic_puzzles_grid_chip_level_5_5_721
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 2) is white, cell (6, 4) is white, cell (2, 0) is white, cell (3, 4) is white, cell (7, 7) is white, cell (1, 3) is white, cell (3, 4) is white, cell (0, 7) 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"
}
] |
12
|
math
|
train
| 410,953
|
math_logic_puzzles_grid_chip_level_5_5_722
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 3) is white, cell (0, 4) is white, cell (7, 5) 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"
}
] |
19
|
math
|
train
| 410,954
|
math_logic_puzzles_grid_chip_level_5_5_723
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (6, 0) is white, cell (6, 3) is white, cell (1, 5) is black, cell (7, 4) is white, cell (5, 6) is black, cell (3, 7) is black, cell (0, 2) is white, cell (2, 1) is black, cell (4, 5) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,955
|
math_logic_puzzles_grid_chip_level_5_5_724
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 1) is black, cell (1, 5) is black, cell (7, 3) is black, cell (0, 2) is black, cell (6, 7) is black, cell (7, 3) is black, cell (7, 0) is black, cell (4, 6) 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"
}
] |
11
|
math
|
train
| 410,956
|
math_logic_puzzles_grid_chip_level_5_5_725
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 0) is black, cell (7, 4) is black, cell (6, 7) is black, cell (0, 2) is black, cell (5, 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"
}
] |
17
|
math
|
train
| 410,957
|
math_logic_puzzles_grid_chip_level_5_5_726
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 3) is black, cell (2, 6) is black, cell (5, 6) is black, cell (5, 6) is black, cell (3, 7) is black, cell (0, 6) is black, cell (1, 6) 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"
}
] |
16
|
math
|
train
| 410,958
|
math_logic_puzzles_grid_chip_level_5_5_727
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 4) is white, cell (3, 7) is white, cell (4, 0) is white, cell (1, 2) is white, cell (5, 1) is white, cell (2, 0) is white, cell (1, 6) 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"
}
] |
15
|
math
|
train
| 410,959
|
math_logic_puzzles_grid_chip_level_5_5_728
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 1) is black, cell (3, 3) is black, cell (1, 5) is black, cell (3, 3) is black, cell (1, 7) is black, cell (7, 6) 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"
}
] |
18
|
math
|
train
| 410,960
|
math_logic_puzzles_grid_chip_level_5_5_729
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (3, 1) is white, cell (4, 5) is white, cell (7, 7) is black, cell (5, 4) is black, cell (6, 0) is white, cell (0, 2) is black, cell (2, 2) is black, cell (1, 6) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,961
|
math_logic_puzzles_grid_chip_level_5_5_730
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 6) is black, cell (4, 7) is white, cell (5, 3) is white, cell (6, 7) is white, cell (7, 0) is black, cell (1, 5) is white, cell (3, 2) is black, cell (0, 1) is black, cell (2, 4) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,962
|
math_logic_puzzles_grid_chip_level_5_5_731
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 7) is black, cell (0, 6) is white, cell (6, 3) is black, cell (3, 4) is white, cell (5, 6) is white, cell (3, 2) is white, cell (2, 1) is white, cell (1, 5) is white, cell (7, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
math
|
train
| 410,963
|
math_logic_puzzles_grid_chip_level_5_5_732
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 4) is black, cell (7, 5) is black, cell (2, 6) is black, cell (6, 7) is black, cell (1, 2) is black, cell (0, 0) is black, cell (3, 1) is black, cell (7, 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"
}
] |
11
|
math
|
train
| 410,964
|
math_logic_puzzles_grid_chip_level_5_5_733
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (7, 2) is white, cell (2, 1) is white, cell (6, 5) is white, cell (4, 3) is white, cell (3, 0) is white, cell (1, 7) 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"
}
] |
14
|
math
|
train
| 410,965
|
math_logic_puzzles_grid_chip_level_5_5_734
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 7) is black, cell (6, 4) is white, cell (2, 2) is black, cell (7, 0) is black, cell (4, 1) is white, cell (0, 3) is black, cell (3, 3) is black, cell (6, 5) is white, cell (5, 0) is black, cell (4, 6) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,966
|
math_logic_puzzles_grid_chip_level_5_5_735
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 4) is black, cell (4, 6) is black, cell (3, 3) is black, cell (1, 5) is black, cell (5, 7) is black, cell (2, 0) is black, cell (7, 4) 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"
}
] |
12
|
math
|
train
| 410,967
|
math_logic_puzzles_grid_chip_level_5_5_736
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 2) is black, cell (2, 6) is black, cell (4, 2) is black, cell (6, 1) is black, cell (7, 7) 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"
}
] |
15
|
math
|
train
| 410,968
|
math_logic_puzzles_grid_chip_level_5_5_737
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 5) is white, cell (3, 3) is white, cell (1, 6) is black, cell (3, 1) is white, cell (3, 4) is white, cell (4, 7) is black, cell (6, 0) is black, cell (5, 7) is black, cell (2, 0) is black, cell (0, 7) is black, cell (7, 6) 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"
}
] |
26
|
math
|
train
| 410,969
|
math_logic_puzzles_grid_chip_level_5_5_738
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 4) is white, cell (7, 3) is white, cell (3, 2) is black, cell (5, 2) is black, cell (6, 2) is black, cell (2, 0) is white, cell (1, 5) is black, cell (2, 6) is white, cell (2, 1) is white, cell (0, 7) is white, cell (4, 5) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
math
|
train
| 410,970
|
math_logic_puzzles_grid_chip_level_5_5_739
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 1) is black, cell (5, 7) is black, cell (6, 2) is black, cell (4, 0) is black, cell (1, 1) is black, cell (6, 4) is black, cell (6, 6) is black, cell (2, 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"
}
] |
12
|
math
|
train
| 410,971
|
math_logic_puzzles_grid_chip_level_5_5_740
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 6) is white, cell (7, 7) is white, cell (1, 2) is white, cell (2, 5) is white, cell (0, 5) is white, cell (5, 7) 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"
}
] |
16
|
math
|
train
| 410,972
|
math_logic_puzzles_grid_chip_level_5_5_741
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (7, 7) is white, cell (2, 0) is black, cell (0, 4) is white, cell (4, 0) is black, cell (6, 1) is white, cell (5, 0) is black, cell (1, 3) is white, cell (0, 5) is white, cell (6, 6) is white, 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"
}
] |
32
|
math
|
train
| 410,973
|
math_logic_puzzles_grid_chip_level_5_5_742
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 black, cell (7, 3) is black, cell (1, 0) is white, cell (4, 0) is white, cell (3, 1) is white, cell (0, 6) is black, cell (2, 4) is black, cell (6, 5) is white, cell (2, 7) is black, cell (5, 1) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 410,974
|
math_logic_puzzles_grid_chip_level_5_5_743
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 6) is white, cell (2, 0) is black, cell (3, 6) is white, cell (7, 1) is white, cell (2, 3) is black, cell (5, 5) is white, cell (2, 7) is black, cell (6, 4) is black, cell (4, 4) 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"
}
] |
32
|
math
|
train
| 410,975
|
math_logic_puzzles_grid_chip_level_5_5_744
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 5) is black, cell (2, 0) is black, cell (1, 6) is white, cell (5, 7) is black, cell (6, 2) is white, cell (4, 3) is white, cell (7, 0) is black, cell (0, 1) is white, cell (1, 4) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,976
|
math_logic_puzzles_grid_chip_level_5_5_745
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (5, 4) is white, cell (3, 7) is black, cell (6, 4) is white, cell (4, 3) is black, cell (7, 0) is white, cell (2, 3) is black, cell (1, 1) is black, cell (7, 2) is white, cell (1, 5) is black, cell (0, 6) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
math
|
train
| 410,977
|
math_logic_puzzles_grid_chip_level_5_5_746
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 6) is white, cell (0, 2) is white, cell (3, 4) is white, cell (4, 3) is white, cell (2, 0) 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"
}
] |
12
|
math
|
train
| 410,978
|
math_logic_puzzles_grid_chip_level_5_5_747
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 1) is black, cell (2, 3) is white, cell (7, 0) is white, cell (3, 4) is white, cell (7, 6) is white, cell (5, 3) is white, cell (6, 7) is black, cell (1, 5) is black, cell (0, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,979
|
math_logic_puzzles_grid_chip_level_5_5_748
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 7) is white, cell (3, 3) is white, cell (5, 2) is white, cell (7, 3) is white, cell (4, 0) is white, cell (6, 5) 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"
}
] |
16
|
math
|
train
| 410,980
|
math_logic_puzzles_grid_chip_level_5_5_749
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (7, 5) is black, cell (7, 7) is black, cell (5, 1) is black, cell (2, 6) is white, cell (6, 0) is white, cell (3, 3) is white, cell (1, 6) is white, cell (3, 4) is white, cell (4, 6) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,981
|
math_logic_puzzles_grid_chip_level_5_5_750
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 5) is black, cell (6, 6) is black, cell (7, 3) is white, cell (1, 4) is white, cell (6, 7) is black, cell (0, 0) is black, cell (4, 1) is white, cell (2, 5) is black, cell (5, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
math
|
train
| 410,982
|
math_logic_puzzles_grid_chip_level_5_5_751
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (6, 6) is black, cell (2, 3) is white, cell (1, 5) is white, cell (4, 0) is white, cell (5, 3) is white, cell (7, 1) is white, cell (0, 7) is white, cell (3, 4) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
math
|
train
| 410,983
|
math_logic_puzzles_grid_chip_level_5_5_752
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (5, 1) is white, cell (6, 5) is black, cell (2, 2) is white, cell (0, 1) is white, cell (4, 6) is white, cell (6, 7) is black, cell (6, 3) is black, cell (3, 4) is black, cell (1, 0) is black, cell (7, 6) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 410,984
|
math_logic_puzzles_grid_chip_level_5_5_753
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (6, 1) is black, cell (5, 6) is black, cell (3, 0) is black, cell (0, 2) is black, cell (1, 6) is black, cell (4, 0) is black, cell (7, 4) 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"
}
] |
12
|
math
|
train
| 410,985
|
math_logic_puzzles_grid_chip_level_5_5_754
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 7) is black, cell (5, 0) is black, cell (3, 1) is white, cell (2, 6) is white, cell (1, 7) is black, cell (4, 3) is white, cell (7, 5) is white, cell (4, 2) is white, cell (3, 4) is white, cell (6, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,986
|
math_logic_puzzles_grid_chip_level_5_5_755
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (5, 3) is white, cell (0, 5) is white, cell (2, 6) is white, cell (6, 4) is white, cell (4, 0) is black, cell (3, 5) is white, cell (1, 2) is black, cell (7, 1) is black, cell (7, 7) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,987
|
math_logic_puzzles_grid_chip_level_5_5_756
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 6) is black, cell (7, 5) is white, cell (1, 7) is white, cell (2, 0) is white, cell (4, 4) is white, cell (7, 3) is white, cell (6, 2) is black, cell (5, 1) is white, cell (3, 6) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
math
|
train
| 410,988
|
math_logic_puzzles_grid_chip_level_5_5_757
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (6, 1) is black, cell (4, 3) is black, cell (2, 1) is black, cell (5, 7) is black, cell (0, 6) 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"
}
] |
15
|
math
|
train
| 410,989
|
math_logic_puzzles_grid_chip_level_5_5_758
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 6) is black, cell (0, 1) is white, cell (6, 2) is white, cell (5, 3) is white, cell (4, 5) is black, cell (0, 7) is white, cell (2, 2) is white, cell (7, 0) is white, cell (7, 4) is white, cell (1, 5) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
math
|
train
| 410,990
|
math_logic_puzzles_grid_chip_level_5_5_759
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 6) is white, cell (2, 2) is white, cell (0, 5) is white, cell (2, 4) is white, cell (6, 7) is white, cell (6, 7) is white, cell (1, 3) is white, cell (0, 5) 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"
}
] |
13
|
math
|
train
| 410,991
|
math_logic_puzzles_grid_chip_level_5_5_760
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (2, 7) is black, cell (2, 1) is black, cell (4, 2) is white, cell (2, 6) is black, cell (6, 4) is white, cell (7, 5) is white, cell (0, 2) is white, cell (5, 3) is black, cell (3, 2) is white, cell (1, 4) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
math
|
train
| 410,992
|
math_logic_puzzles_grid_chip_level_5_5_761
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 6) is black, cell (2, 2) is black, cell (5, 1) is black, cell (6, 0) is black, cell (3, 5) 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"
}
] |
18
|
math
|
train
| 410,993
|
math_logic_puzzles_grid_chip_level_5_5_762
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 3) is black, cell (1, 2) is white, cell (3, 2) is white, cell (5, 4) is white, cell (4, 7) is black, cell (7, 2) is white, cell (0, 0) is white, cell (4, 6) is black, cell (2, 5) is white, cell (6, 1) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,994
|
math_logic_puzzles_grid_chip_level_5_5_763
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 6) is black, cell (4, 5) is black, cell (5, 1) is black, cell (5, 7) 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"
}
] |
25
|
math
|
train
| 410,995
|
math_logic_puzzles_grid_chip_level_5_5_764
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 5) is black, cell (5, 6) is white, cell (3, 1) is white, cell (4, 2) is white, cell (6, 0) is black, cell (0, 6) is white, cell (7, 4) is black, cell (4, 7) 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"
}
] |
32
|
math
|
train
| 410,996
|
math_logic_puzzles_grid_chip_level_5_5_765
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (5, 7) is black, cell (0, 0) is white, cell (4, 6) is black, cell (3, 2) is black, cell (1, 1) is white, cell (2, 5) is black, cell (7, 3) is white, cell (6, 2) is black, cell (4, 4) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
math
|
train
| 410,997
|
math_logic_puzzles_grid_chip_level_5_5_766
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (6, 6) is black, cell (7, 1) is black, cell (4, 0) is white, cell (4, 7) is white, cell (0, 6) is black, cell (2, 4) is white, cell (5, 3) is white, cell (4, 5) is white, cell (3, 2) is white, cell (1, 6) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 410,998
|
math_logic_puzzles_grid_chip_level_5_5_767
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (7, 4) is white, cell (7, 0) is white, cell (5, 6) is white, cell (4, 7) 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"
}
] |
19
|
math
|
train
| 410,999
|
math_logic_puzzles_grid_chip_level_5_5_768
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 5) is black, cell (1, 4) is black, cell (6, 0) is black, cell (1, 2) is black, cell (3, 7) is black, cell (5, 3) is black, cell (0, 6) is black, cell (4, 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"
}
] |
11
|
math
|
train
| 411,000
|
math_logic_puzzles_grid_chip_level_5_5_769
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 4) is white, cell (4, 0) is white, cell (6, 6) is white, cell (3, 6) 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"
}
] |
15
|
math
|
train
| 411,001
|
math_logic_puzzles_grid_chip_level_5_5_770
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 4) is white, cell (7, 1) is black, cell (4, 2) is white, cell (5, 5) is black, cell (3, 3) is black, cell (6, 5) is black, cell (3, 6) is black, cell (1, 0) is black, cell (0, 1) is black, cell (4, 7) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
math
|
train
| 411,002
|
math_logic_puzzles_grid_chip_level_5_5_771
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 black, cell (2, 6) is black, cell (2, 3) is black, cell (0, 4) is black, cell (7, 2) is black, cell (4, 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"
}
] |
13
|
math
|
train
| 411,003
|
math_logic_puzzles_grid_chip_level_5_5_772
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (0, 3) is black, cell (6, 1) is white, cell (3, 4) is white, cell (3, 7) is white, cell (1, 3) is black, cell (7, 0) is white, cell (3, 5) is white, cell (7, 6) is white, cell (5, 2) is white, cell (4, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 411,004
|
math_logic_puzzles_grid_chip_level_5_5_773
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (6, 1) is white, cell (7, 3) is white, cell (0, 6) is black, cell (3, 2) is white, cell (5, 4) is white, cell (2, 0) is black, cell (4, 7) is black, cell (1, 6) is black, cell (2, 5) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 411,005
|
math_logic_puzzles_grid_chip_level_5_5_774
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 0) is white, cell (2, 1) is white, cell (2, 6) is white, cell (5, 7) 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"
}
] |
22
|
math
|
train
| 411,006
|
math_logic_puzzles_grid_chip_level_5_5_775
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 7) is black, cell (2, 4) is white, cell (7, 3) is white, cell (0, 0) is white, cell (4, 5) is black, cell (5, 6) is white, cell (6, 1) is black, cell (4, 2) 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"
}
] |
32
|
math
|
train
| 411,007
|
math_logic_puzzles_grid_chip_level_5_5_776
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 7) is white, cell (6, 4) is white, cell (1, 0) is black, cell (7, 3) is black, cell (5, 0) is black, cell (0, 5) is white, cell (4, 3) is black, cell (3, 2) is white, cell (0, 6) is white, cell (6, 1) is white, cell (2, 0) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
math
|
train
| 411,008
|
math_logic_puzzles_grid_chip_level_5_5_777
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 4) is white, cell (3, 6) is black, cell (5, 7) is white, cell (4, 1) is black, cell (0, 5) is black, cell (0, 2) is black, cell (7, 0) is black, cell (1, 3) is white, cell (6, 3) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 411,009
|
math_logic_puzzles_grid_chip_level_5_5_778
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 1) is white, cell (1, 5) is white, cell (3, 2) is white, cell (0, 3) is white, cell (5, 0) is white, cell (3, 7) 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"
}
] |
17
|
math
|
train
| 411,010
|
math_logic_puzzles_grid_chip_level_5_5_779
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 4) is black, cell (2, 2) is white, cell (3, 0) is white, cell (6, 3) is black, cell (5, 5) is white, cell (2, 7) is white, cell (1, 6) is white, cell (7, 3) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 411,011
|
math_logic_puzzles_grid_chip_level_5_5_780
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (6, 3) is white, cell (7, 3) is white, cell (0, 2) is white, cell (1, 4) is white, cell (3, 5) is white, cell (4, 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"
}
] |
16
|
math
|
train
| 411,012
|
math_logic_puzzles_grid_chip_level_5_5_781
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 3) is white, cell (3, 0) is white, cell (4, 5) is white, cell (7, 1) is black, cell (5, 1) is black, cell (4, 6) is white, cell (1, 4) is black, cell (6, 1) is black, cell (3, 7) is white, cell (3, 2) 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"
}
] |
24
|
math
|
train
| 411,013
|
math_logic_puzzles_grid_chip_level_5_5_782
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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, 7) is white, cell (4, 7) is white, cell (6, 5) is black, cell (5, 1) is white, cell (7, 0) is black, cell (7, 3) is black, cell (6, 6) is black, cell (7, 2) is black, cell (3, 1) is white, cell (0, 7) is white, cell (1, 1) is white, cell (6, 4) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
math
|
train
| 411,014
|
math_logic_puzzles_grid_chip_level_5_5_783
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 4) is white, cell (6, 0) is black, cell (0, 5) is white, cell (0, 7) is white, cell (5, 6) is white, cell (2, 1) is black, cell (7, 0) is black, 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"
}
] |
32
|
math
|
train
| 411,015
|
math_logic_puzzles_grid_chip_level_5_5_784
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 3) is white, cell (7, 1) is white, cell (7, 2) is white, cell (4, 3) is white, cell (2, 7) is white, cell (6, 5) 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"
}
] |
19
|
math
|
train
| 411,016
|
math_logic_puzzles_grid_chip_level_5_5_785
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (6, 6) is white, cell (0, 5) is white, cell (3, 2) is black, cell (0, 7) is white, cell (4, 1) is white, cell (7, 2) is black, cell (1, 3) is black, cell (2, 2) is black, cell (5, 4) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 411,017
|
math_logic_puzzles_grid_chip_level_5_5_786
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 5) is white, cell (7, 7) is white, cell (6, 0) is black, cell (4, 4) is white, cell (3, 2) is black, cell (1, 3) is black, cell (2, 1) is black, cell (0, 2) is black, cell (5, 0) is black, cell (4, 6) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 411,018
|
math_logic_puzzles_grid_chip_level_5_5_787
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 5) is white, cell (1, 0) is white, cell (2, 2) is white, cell (6, 5) is white, cell (5, 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"
}
] |
21
|
math
|
train
| 411,019
|
math_logic_puzzles_grid_chip_level_5_5_788
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 white, cell (7, 1) is white, cell (1, 4) is black, cell (2, 6) is black, cell (6, 7) is white, cell (0, 5) is black, cell (2, 0) is black, cell (2, 3) is black, cell (5, 7) is white, cell (4, 2) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 411,020
|
math_logic_puzzles_grid_chip_level_5_5_789
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (4, 5) is black, cell (6, 5) is black, cell (7, 5) is black, cell (1, 6) is white, cell (1, 1) is white, cell (0, 2) is black, cell (2, 2) is black, cell (5, 2) is black, cell (1, 3) is white, cell (3, 4) is black, cell (1, 7) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
math
|
train
| 411,021
|
math_logic_puzzles_grid_chip_level_5_5_790
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (5, 7) is white, cell (7, 0) is black, cell (6, 1) is black, cell (0, 1) is black, cell (3, 4) is white, cell (7, 6) is black, cell (2, 1) is black, cell (3, 2) is white, cell (1, 3) is white, cell (5, 5) is white, cell (4, 1) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 411,022
|
math_logic_puzzles_grid_chip_level_5_5_791
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (5, 4) is black, cell (3, 5) is black, cell (1, 3) is black, cell (4, 0) is black, cell (7, 6) is black, cell (6, 5) 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"
}
] |
9
|
math
|
train
| 411,023
|
math_logic_puzzles_grid_chip_level_5_5_792
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 1) is white, cell (1, 6) is white, cell (7, 4) is white, cell (0, 5) is white, cell (4, 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"
}
] |
15
|
math
|
train
| 411,024
|
math_logic_puzzles_grid_chip_level_5_5_793
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (7, 0) is black, cell (3, 1) is white, cell (2, 7) is white, cell (1, 4) is black, cell (2, 6) is white, cell (4, 1) is white, cell (5, 3) is white, cell (2, 5) is white, cell (6, 2) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
math
|
train
| 411,025
|
math_logic_puzzles_grid_chip_level_5_5_794
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (7, 5) is black, cell (0, 0) is black, cell (1, 1) is black, cell (1, 6) is black, cell (3, 4) is black, cell (5, 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"
}
] |
14
|
math
|
train
| 411,026
|
math_logic_puzzles_grid_chip_level_5_5_795
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (4, 2) is white, cell (0, 0) is white, cell (0, 4) is white, cell (3, 1) is white, cell (4, 3) is white, cell (7, 5) 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"
}
] |
18
|
math
|
train
| 411,027
|
math_logic_puzzles_grid_chip_level_5_5_796
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (7, 2) is black, cell (5, 4) is white, cell (3, 2) is black, cell (0, 1) is black, cell (4, 3) is black, cell (6, 2) is black, cell (2, 5) is black, cell (1, 7) is black, cell (5, 0) is white, cell (5, 6) is white. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
math
|
train
| 411,028
|
math_logic_puzzles_grid_chip_level_5_5_797
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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 (7, 0) is black, cell (6, 2) is black, cell (1, 4) is black, cell (0, 5) is black, cell (2, 3) is black, cell (2, 6) 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"
}
] |
15
|
math
|
train
| 411,029
|
math_logic_puzzles_grid_chip_level_5_5_798
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in a 8x8 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, 4) is white, cell (7, 7) is white, cell (6, 6) is white, cell (6, 0) is white, cell (5, 4) 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"
}
] |
22
|
math
|
train
| 411,030
|
math_logic_puzzles_grid_chip_level_5_5_799
|
logic_puzzles_grid_chip5
|
hard (level 4,5)
| 5
|
[
{
"content": "Chips, colored either black or white, are placed in the cells of a 8x8 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 (5, 0) is black, cell (6, 4) is white, cell (1, 6) is white, cell (4, 7) is black, cell (2, 6) is white, cell (0, 1) is white, cell (3, 3) is white, cell (5, 2) is black, cell (7, 5) is black. How many chips are placed on the grid?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
math
|
train
| 411,031
|
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