Datasets:
options
listlengths 2
4
| solution
stringlengths 72
49.7k
| data_source
stringclasses 1
value | prompt
listlengths 2
2
| images
images listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | tokens
int64 483
13.1k
| avg_reward
float64 0
1
|
|---|---|---|---|---|---|---|---|---|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 7, 'columns': 8, 'removed_positions': [[0, 7], [3, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 28, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 26}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 8 in dimension having a total of 56 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 27 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 27 dominoes in the checkerboard to exactly cover all the remaining 54 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,409
| 1
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 7, 'columns': 6, 'removed_positions': [[2, 4], [5, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 19, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 6 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.75
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 5, 'columns': 7, 'removed_positions': [[4, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 18, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 16}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 7 in dimension having a total of 35 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,869
| 0.375
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 9, 'removed_positions': [[2, 3], [4, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 26, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 26}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 9 in dimension having a total of 54 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 26 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 26 dominoes in the checkerboard to exactly cover all the remaining 52 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,689
| 0.125
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 9, 'removed_positions': [[1, 1], [1, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 17, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 17}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 9 in dimension having a total of 36 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 1,909
| 0.125
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 7, 'removed_positions': [[8, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 32, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 30}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 7 in dimension having a total of 63 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,049
| 0.625
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 7, 'removed_positions': [[1, 1], [4, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 19, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 7 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.75
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 7, 'removed_positions': [[6, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 24, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 24}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 7 in dimension having a total of 49 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 24 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 24 dominoes in the checkerboard to exactly cover all the remaining 48 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.25
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 5, 'columns': 6, 'removed_positions': [[0, 2], [2, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 14, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 14}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 6 in dimension having a total of 30 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 14 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 14 dominoes in the checkerboard to exactly cover all the remaining 28 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,289
| 0.125
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 8, 'columns': 7, 'removed_positions': [[5, 4], [7, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 28, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 26}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 7 in dimension having a total of 56 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 27 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 27 dominoes in the checkerboard to exactly cover all the remaining 54 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,409
| 0.875
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 8, 'removed_positions': [[5, 0], [5, 6]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 24, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 22}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 8 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,989
| 1
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 9, 'removed_positions': [[0, 1], [5, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 26, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 26}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 9 in dimension having a total of 54 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 26 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 26 dominoes in the checkerboard to exactly cover all the remaining 52 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,689
| 0.125
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 8, 'removed_positions': [[2, 1], [3, 7]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 31, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 31}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 8 in dimension having a total of 64 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 9, 'removed_positions': [[0, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 41, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 39}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 9 in dimension having a total of 81 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 40 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 40 dominoes in the checkerboard to exactly cover all the remaining 80 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,829
| 1
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 9, 'removed_positions': [[6, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 31, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 31}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 9 in dimension having a total of 63 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,049
| 0.5
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 5, 'removed_positions': [[1, 1], [1, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 9, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 9}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 5 in dimension having a total of 20 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 9 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 9 dominoes in the checkerboard to exactly cover all the remaining 18 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,167
| 0.125
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 7, 'removed_positions': [[6, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 25, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 23}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 7 in dimension having a total of 49 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 24 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 24 dominoes in the checkerboard to exactly cover all the remaining 48 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,829
| 0.75
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 5, 'columns': 5, 'removed_positions': [[1, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 13, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 11}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 5 in dimension having a total of 25 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 12 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 12 dominoes in the checkerboard to exactly cover all the remaining 24 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,829
| 0.625
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 5, 'removed_positions': [[2, 3], [2, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 9, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 9}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 5 in dimension having a total of 20 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 9 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 9 dominoes in the checkerboard to exactly cover all the remaining 18 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,167
| 0
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 6, 'removed_positions': [[3, 1], [4, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 17, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 17}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 6 in dimension having a total of 36 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.125
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 5, 'columns': 7, 'removed_positions': [[3, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 18, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 16}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 7 in dimension having a total of 35 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,869
| 0.75
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 6, 'removed_positions': [[0, 5], [3, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 23, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 23}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 6 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,929
| 0.125
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 5, 'columns': 6, 'removed_positions': [[3, 5], [4, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 13, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 15}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 6 in dimension having a total of 30 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 14 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 14 dominoes in the checkerboard to exactly cover all the remaining 28 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,289
| 0.75
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 6, 'removed_positions': [[0, 3], [3, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 24, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 22}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 6 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,929
| 0.625
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 8, 'removed_positions': [[1, 0], [3, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 23, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 23}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 8 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,989
| 0.25
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 5, 'columns': 9, 'removed_positions': [[0, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 23, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 9 in dimension having a total of 45 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 22 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 22 dominoes in the checkerboard to exactly cover all the remaining 44 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,269
| 0.5
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 6, 'removed_positions': [[0, 4], [3, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 16, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 18}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 6 in dimension having a total of 36 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,829
| 1
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 6, 'removed_positions': [[1, 2], [2, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 24, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 22}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 6 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,929
| 0.875
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 7, 'columns': 6, 'removed_positions': [[4, 4], [5, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 19, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 6 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.75
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 8, 'columns': 5, 'removed_positions': [[4, 1], [6, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 20, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 18}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 5 in dimension having a total of 40 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 19 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 19 dominoes in the checkerboard to exactly cover all the remaining 38 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,509
| 0.625
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 5, 'columns': 9, 'removed_positions': [[3, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 23, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 9 in dimension having a total of 45 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 22 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 22 dominoes in the checkerboard to exactly cover all the remaining 44 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,269
| 0.875
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]]], 'rows': 5, 'columns': 8, 'removed_positions': [[0, 5], [4, 6]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 19, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 19}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 8 in dimension having a total of 40 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 19 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 19 dominoes in the checkerboard to exactly cover all the remaining 38 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,509
| 0.25
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 5, 'removed_positions': [[0, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 17, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 17}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 5 in dimension having a total of 35 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,809
| 0.25
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 8, 'removed_positions': [[1, 2], [2, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 24, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 22}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 8 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,989
| 0.75
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 5, 'removed_positions': [[1, 2], [3, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 10, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 8}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 5 in dimension having a total of 20 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 9 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 9 dominoes in the checkerboard to exactly cover all the remaining 18 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,167
| 0.75
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 6, 'removed_positions': [[0, 4], [6, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 22, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 24}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 6 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,929
| 0.875
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 6, 'removed_positions': [[0, 4], [1, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 16, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 18}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 6 in dimension having a total of 36 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,829
| 1
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 9, 'removed_positions': [[1, 2], [2, 6]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 17, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 17}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 9 in dimension having a total of 36 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 1,909
| 0.125
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 9, 'removed_positions': [[0, 6]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 40, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 40}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 9 in dimension having a total of 81 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 40 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 40 dominoes in the checkerboard to exactly cover all the remaining 80 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.375
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 7, 'removed_positions': [[5, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 24, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 24}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 7 in dimension having a total of 49 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 24 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 24 dominoes in the checkerboard to exactly cover all the remaining 48 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.375
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 5, 'columns': 6, 'removed_positions': [[1, 0], [2, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 14, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 14}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 6 in dimension having a total of 30 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 14 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 14 dominoes in the checkerboard to exactly cover all the remaining 28 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,289
| 0.125
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 7, 'removed_positions': [[4, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 24, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 24}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 7 in dimension having a total of 49 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 24 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 24 dominoes in the checkerboard to exactly cover all the remaining 48 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.5
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 9, 'removed_positions': [[2, 8], [3, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 17, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 17}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 9 in dimension having a total of 36 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 1,909
| 0
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 5, 'removed_positions': [[0, 0], [1, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 8, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 10}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 5 in dimension having a total of 20 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 9 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 9 dominoes in the checkerboard to exactly cover all the remaining 18 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,167
| 0.625
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 8, 'removed_positions': [[0, 7], [1, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 23, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 23}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 8 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,989
| 0
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 9, 'columns': 6, 'removed_positions': [[2, 1], [5, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 27, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 25}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 6 in dimension having a total of 54 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 26 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 26 dominoes in the checkerboard to exactly cover all the remaining 52 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,689
| 0.75
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 4, 'columns': 6, 'removed_positions': [[2, 0], [2, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 11, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 11}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 6 in dimension having a total of 24 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 11 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 11 dominoes in the checkerboard to exactly cover all the remaining 22 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,689
| 0.125
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 9, 'removed_positions': [[4, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 31, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 31}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 9 in dimension having a total of 63 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,049
| 0.375
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 7, 'columns': 6, 'removed_positions': [[0, 4], [2, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 20, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 20}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 6 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,349
| 0.125
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 7, 'removed_positions': [[4, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 25, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 23}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 7 in dimension having a total of 49 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 24 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 24 dominoes in the checkerboard to exactly cover all the remaining 48 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,829
| 0.75
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 7, 'columns': 5, 'removed_positions': [[3, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 17, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 17}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 5 in dimension having a total of 35 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,809
| 0.625
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 5, 'removed_positions': [[1, 1], [2, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 9, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 9}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 5 in dimension having a total of 20 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 9 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 9 dominoes in the checkerboard to exactly cover all the remaining 18 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,167
| 0
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 8, 'columns': 7, 'removed_positions': [[6, 3], [7, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 27, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 27}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 7 in dimension having a total of 56 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 27 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 27 dominoes in the checkerboard to exactly cover all the remaining 54 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,409
| 0.125
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 7, 'removed_positions': [[1, 2], [5, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 21, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 19}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 7 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.625
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 7, 'removed_positions': [[0, 0], [1, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 19, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 7 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.75
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 7, 'columns': 6, 'removed_positions': [[0, 5], [3, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 21, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 19}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 6 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.875
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 7, 'columns': 6, 'removed_positions': [[0, 1], [0, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 21, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 19}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 7 * 6 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.875
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 5, 'removed_positions': [[1, 3], [5, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 14, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 14}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 5 in dimension having a total of 30 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 14 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 14 dominoes in the checkerboard to exactly cover all the remaining 28 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,229
| 0.25
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 6, 'columns': 6, 'removed_positions': [[3, 2], [4, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 17, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 17}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 6 in dimension having a total of 36 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 17 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 17 dominoes in the checkerboard to exactly cover all the remaining 34 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.25
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 4, 'columns': 7, 'removed_positions': [[2, 1], [3, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 14, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 12}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 7 in dimension having a total of 28 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 13 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 13 dominoes in the checkerboard to exactly cover all the remaining 26 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,329
| 0.875
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 7, 'removed_positions': [[4, 0], [4, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 19, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 7 in dimension having a total of 42 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 20 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 20 dominoes in the checkerboard to exactly cover all the remaining 40 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,349
| 0.875
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 9, 'columns': 6, 'removed_positions': [[1, 1], [6, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 26, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 26}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 6 in dimension having a total of 54 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 26 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 26 dominoes in the checkerboard to exactly cover all the remaining 52 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,689
| 0.125
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 9, 'removed_positions': [[5, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 40, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 40}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 9 in dimension having a total of 81 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 40 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 40 dominoes in the checkerboard to exactly cover all the remaining 80 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.375
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 6, 'columns': 5, 'removed_positions': [[2, 2], [3, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 13, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 15}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 6 * 5 in dimension having a total of 30 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 14 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 14 dominoes in the checkerboard to exactly cover all the remaining 28 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,229
| 0.875
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 7, 'removed_positions': [[4, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 32, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 30}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 7 in dimension having a total of 63 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,049
| 0.625
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 9, 'removed_positions': [[8, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 40, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 40}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 9 in dimension having a total of 81 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 40 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 40 dominoes in the checkerboard to exactly cover all the remaining 80 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.625
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 5, 'removed_positions': [[5, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 23, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 21}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 5 in dimension having a total of 45 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 22 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 22 dominoes in the checkerboard to exactly cover all the remaining 44 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,269
| 0.5
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 4, 'columns': 6, 'removed_positions': [[0, 3], [3, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 11, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 11}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 4 * 6 in dimension having a total of 24 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 11 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 11 dominoes in the checkerboard to exactly cover all the remaining 22 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,689
| 0.25
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 7, 'removed_positions': [[5, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 32, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 30}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 7 in dimension having a total of 63 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 3,049
| 0.75
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 9, 'removed_positions': [[8, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 40, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 40}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 9 in dimension having a total of 81 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 40 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 40 dominoes in the checkerboard to exactly cover all the remaining 80 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,829
| 0.5
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 8, 'columns': 5, 'removed_positions': [[6, 1], [6, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 20, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 18}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 5 in dimension having a total of 40 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 19 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 19 dominoes in the checkerboard to exactly cover all the remaining 38 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,509
| 0.875
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 5, 'columns': 9, 'removed_positions': [[1, 3]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 22, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 22}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 9 in dimension having a total of 45 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 22 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 22 dominoes in the checkerboard to exactly cover all the remaining 44 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,269
| 0.375
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 6, 'removed_positions': [[1, 1], [4, 0]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 22, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 24}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 6 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,929
| 0.875
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 1.0, 1.0], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]]], 'rows': 8, 'columns': 9, 'removed_positions': [[1, 0], [7, 1]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 35, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 35}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 9 in dimension having a total of 72 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 35 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 35 dominoes in the checkerboard to exactly cover all the remaining 70 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,469
| 0
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 9, 'columns': 7, 'removed_positions': [[8, 2]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 31, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 31}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 9 * 7 in dimension having a total of 63 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 31 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 31 dominoes in the checkerboard to exactly cover all the remaining 62 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 3,049
| 0.25
|
|
[
"Yes",
"No"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 8, 'columns': 6, 'removed_positions': [[0, 2], [2, 4]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 22, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 24}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 8 * 6 in dimension having a total of 48 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. Two of the squares have been removed from the board in the position of the white coloured cells, as shown in the image. You have 23 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 23 dominoes in the checkerboard to exactly cover all the remaining 46 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "No",
"style": "rule"
}
| 2,929
| 1
|
|
[
"No",
"Yes"
] |
{'board': [[[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 1.0, 1.0], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]], [[1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702]], [[1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235], [1.0, 0.902, 0.702], [1.0, 0.7647, 0.2235]]], 'rows': 5, 'columns': 9, 'removed_positions': [[1, 5]], 'color1': [1.0, 0.7647, 0.2235], 'squares_of_color1': 22, 'color2': [1.0, 0.902, 0.702], 'squares_of_color2': 22}
|
algopuzzle
|
[
{
"content": "You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.",
"role": "system"
},
{
"content": "<image>The checkerboard shown in the image was originally of 5 * 9 in dimension having a total of 45 squares. It uses two colours of squares, one light yellow and one dark yellow, in a chequered pattern. One of the squares have been removed from the board in the position of the white coloured cell, as shown in the image. You have 22 dominoes of size 2 * 1. You can use them as is or you can rotate them to use as a 1 * 2 domino. Is it possible to place all the 22 dominoes in the checkerboard to exactly cover all the remaining 44 squares? Answer Yes or No.",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yes",
"style": "rule"
}
| 2,269
| 0.375
|
OpenMMReasoner: Pushing the Frontiers for Multimodal Reasoning with an Open and General Recipe
Overview
Recent advancements in large reasoning models have fueled growing interest in extending such capabilities to multimodal domains. However, despite notable progress in visual reasoning, the lack of transparent and reproducible data curation and training strategies remains a major barrier to scalable research. In this work, we introduce OpenMMReasoner, a fully transparent two-stage recipe for multimodal reasoning spanning supervised fine-tuning (SFT) and reinforcement learning (RL). In the SFT stage, we construct an 874K-sample cold-start dataset with rigorous step-by-step validation, providing a strong foundation for reasoning capabilities. The subsequent RL stage leverages a 74K-sample dataset across diverse domains to further sharpen and stabilize these abilities, resulting in a more robust and efficient learning process. Extensive evaluations demonstrate that our training recipe not only surpasses strong baselines but also highlights the critical role of data quality and training design in shaping multimodal reasoning performance. Notably, our method achieves a 11.6% improvement over the Qwen2.5-VL-7B-Instruct baseline across nine multimodal reasoning benchmarks, establishing a solid empirical foundation for future large-scale multimodal reasoning research.
Here are the RL Data used to train OpenMMReasoner-RL. We use verl as the training framework.
To use this dataset, first snapshot-download the entire repository to your local machine. After that, you can load the dataset using the example script provided in our GitHub repository by pointing it to your local data folder and the parquet file.
An example configuration file would be:
DATA_FOLDER=/path/to/your/data
ray job submit --address="http://127.0.0.1:8265" \
--runtime-env=verl/trainer/runtime_env.yaml \
-- \
bash -c "cd /path/to/your/verl/ && \
python3 -m verl.trainer.main_ppo \
algorithm.adv_estimator=${adv_estimator} \
actor_rollout_ref.actor.policy_loss.loss_mode=${loss_mode} \
data.train_files=[$DATA_FOLDER/algopuzzle_train.parquet,$DATA_FOLDER/mmk12_train.parquet,$DATA_FOLDER/puzzlevqa_train.parquet,$DATA_FOLDER/thinklite_vl_hard_train.parquet,$DATA_FOLDER/tqa_train.parquet,$DATA_FOLDER/virl39k_train.parquet,$DATA_FOLDER/wemath_standard.parquet,$DATA_FOLDER/wemath_pro.parquet] \
data.val_files=${DATA_FOLDER}/val.parquet \
... rest of the command args ...
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