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
|
|---|---|---|---|---|---|---|---|---|
[
"Camera",
"Laptop",
"Chocolate",
"Car"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 315, 'effective_rotation': -162, 'direction': 'clockwise', 'original_colors': ['lime', 'silver', 'darkorange', 'yellow', 'blanchedalmond', 'orangered'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Camera', 'Laptop', 'Watch', 'Yacht', 'Car', 'Chocolate'], 'rotated_colors': ['yellow', 'blanchedalmond', 'orangered', 'lime', 'silver', 'darkorange'], 'rotated_boundaries': [27.0, 87.0, 147.0, 207.0, 267.0, 327.0], 'rotated_prizes': ['Yacht', 'Car', 'Chocolate', 'Camera', 'Laptop', 'Watch']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 2.55 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,389
| 0.5
|
|
[
"Jewelry",
"Yacht",
"Vacation",
"Pizza"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 225, 'effective_rotation': -165, 'direction': 'clockwise', 'original_colors': ['silver', 'blanchedalmond', 'royalblue', 'darkorange', 'yellow', 'forestgreen'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Pizza', 'Watch', 'Yacht', 'Vacation', 'Jewelry', 'Chocolate'], 'rotated_colors': ['darkorange', 'yellow', 'forestgreen', 'silver', 'blanchedalmond', 'royalblue'], 'rotated_boundaries': [30.0, 90.0, 150.0, 210.0, 270.0, 330.0], 'rotated_prizes': ['Vacation', 'Jewelry', 'Chocolate', 'Pizza', 'Watch', 'Yacht']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 555 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 10,387
| 0.25
|
|
[
"Yacht",
"Laptop",
"Ice Cream",
"Money"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 225, 'effective_rotation': -135, 'direction': 'clockwise', 'original_colors': ['forestgreen', 'orangered', 'royalblue', 'cyan', 'silver', 'blanchedalmond'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Laptop', 'Money', 'Ice Cream', 'Yacht', 'Chocolate', 'Car'], 'rotated_colors': ['cyan', 'silver', 'blanchedalmond', 'forestgreen', 'orangered', 'royalblue'], 'rotated_boundaries': [0.0, 60.0, 120.0, 180.0, 240.0, 300.0], 'rotated_prizes': ['Yacht', 'Chocolate', 'Car', 'Laptop', 'Money', 'Ice Cream']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 945 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,387
| 0.375
|
|
[
"Car",
"Jewelry",
"Ice Cream",
"Vacation"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 315, 'effective_rotation': 54, 'direction': 'counterclockwise', 'original_colors': ['darkorange', 'forestgreen', 'blanchedalmond', 'orangered', 'royalblue', 'lime'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Ice Cream', 'Chocolate', 'Car', 'Vacation', 'Camera', 'Jewelry'], 'rotated_colors': ['lime', 'darkorange', 'forestgreen', 'blanchedalmond', 'orangered', 'royalblue'], 'rotated_boundaries': [39.0, 99.0, 159.0, 219.0, 279.0, 339.0], 'rotated_prizes': ['Jewelry', 'Ice Cream', 'Chocolate', 'Car', 'Vacation', 'Camera']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 2.15 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 10,392
| 0.375
|
|
[
"Chocolate",
"Ice Cream",
"Laptop",
"Vacation"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 45, 'effective_rotation': -165, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'lime', 'royalblue', 'cyan', 'darkorange', 'magenta'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Car', 'Jewelry', 'Chocolate', 'Laptop', 'Vacation', 'Ice Cream'], 'rotated_colors': ['cyan', 'darkorange', 'magenta', 'blanchedalmond', 'lime', 'royalblue'], 'rotated_boundaries': [30.0, 90.0, 150.0, 210.0, 270.0, 330.0], 'rotated_prizes': ['Laptop', 'Vacation', 'Ice Cream', 'Car', 'Jewelry', 'Chocolate']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 915 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,387
| 0.25
|
|
[
"Laptop",
"Jewelry",
"Pizza",
"Money"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 45, 'effective_rotation': -90, 'direction': 'clockwise', 'original_colors': ['yellow', 'magenta', 'blanchedalmond', 'silver', 'forestgreen', 'orangered'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Money', 'Vacation', 'Pizza', 'Watch', 'Jewelry', 'Laptop'], 'rotated_colors': ['forestgreen', 'orangered', 'yellow', 'magenta', 'blanchedalmond', 'silver'], 'rotated_boundaries': [15.0, 75.0, 135.0, 195.0, 255.0, 315.0], 'rotated_prizes': ['Jewelry', 'Laptop', 'Money', 'Vacation', 'Pizza', 'Watch']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 1.75 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 10,389
| 0
|
|
[
"Jewelry",
"Pizza",
"Laptop",
"Car"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 180, 'effective_rotation': -105, 'direction': 'clockwise', 'original_colors': ['silver', 'blanchedalmond', 'yellow', 'cyan', 'darkorange', 'lime'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Laptop', 'Camera', 'Pizza', 'Watch', 'Jewelry', 'Car'], 'rotated_colors': ['darkorange', 'lime', 'silver', 'blanchedalmond', 'yellow', 'cyan'], 'rotated_boundaries': [30.0, 90.0, 150.0, 210.0, 270.0, 330.0], 'rotated_prizes': ['Jewelry', 'Car', 'Laptop', 'Camera', 'Pizza', 'Watch']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1695 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 11,095
| 0.75
|
|
[
"Watch",
"Pizza",
"Vacation",
"Yacht"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 180, 'effective_rotation': 165, 'direction': 'counterclockwise', 'original_colors': ['orangered', 'forestgreen', 'magenta', 'blanchedalmond', 'cyan', 'silver'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Pizza', 'Yacht', 'Money', 'Camera', 'Watch', 'Vacation'], 'rotated_colors': ['blanchedalmond', 'cyan', 'silver', 'orangered', 'forestgreen', 'magenta'], 'rotated_boundaries': [30.0, 90.0, 150.0, 210.0, 270.0, 330.0], 'rotated_prizes': ['Camera', 'Watch', 'Vacation', 'Pizza', 'Yacht', 'Money']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 165 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 11,097
| 0.625
|
|
[
"Yacht",
"Money",
"Jewelry",
"Laptop"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 90, 'effective_rotation': -255, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'silver', 'cyan', 'magenta', 'yellow', 'forestgreen'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Money', 'Ice Cream', 'Yacht', 'Jewelry', 'Laptop', 'Chocolate'], 'rotated_colors': ['silver', 'cyan', 'magenta', 'yellow', 'forestgreen', 'blanchedalmond'], 'rotated_boundaries': [0.0, 60.0, 120.0, 180.0, 240.0, 300.0], 'rotated_prizes': ['Ice Cream', 'Yacht', 'Jewelry', 'Laptop', 'Chocolate', 'Money']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 825 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 11,094
| 0
|
|
[
"Money",
"Laptop",
"Pizza",
"Jewelry"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 45, 'effective_rotation': 252, 'direction': 'counterclockwise', 'original_colors': ['darkorange', 'silver', 'forestgreen', 'magenta', 'royalblue', 'blanchedalmond'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Jewelry', 'Pizza', 'Camera', 'Money', 'Laptop', 'Car'], 'rotated_colors': ['forestgreen', 'magenta', 'royalblue', 'blanchedalmond', 'darkorange', 'silver'], 'rotated_boundaries': [57.0, 117.0, 177.0, 237.0, 297.0, 357.0], 'rotated_prizes': ['Camera', 'Money', 'Laptop', 'Car', 'Jewelry', 'Pizza']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 5.7 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 10,391
| 0.375
|
|
[
"Pizza",
"Money",
"Jewelry",
"Camera"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 225, 'effective_rotation': 234, 'direction': 'counterclockwise', 'original_colors': ['cyan', 'lime', 'darkorange', 'silver', 'royalblue', 'yellow'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Jewelry', 'Camera', 'Watch', 'Pizza', 'Yacht', 'Money'], 'rotated_colors': ['darkorange', 'silver', 'royalblue', 'yellow', 'cyan', 'lime'], 'rotated_boundaries': [39.0, 99.0, 159.0, 219.0, 279.0, 339.0], 'rotated_prizes': ['Watch', 'Pizza', 'Yacht', 'Money', 'Jewelry', 'Camera']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 2.65 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 10,392
| 0
|
|
[
"Laptop",
"Jewelry",
"Money",
"Vacation"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 270, 'effective_rotation': -180, 'direction': 'clockwise', 'original_colors': ['magenta', 'blanchedalmond', 'cyan', 'orangered', 'yellow', 'royalblue'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Vacation', 'Jewelry', 'Money', 'Laptop', 'Watch', 'Pizza'], 'rotated_colors': ['orangered', 'yellow', 'royalblue', 'magenta', 'blanchedalmond', 'cyan'], 'rotated_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'rotated_prizes': ['Laptop', 'Watch', 'Pizza', 'Vacation', 'Jewelry', 'Money']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 3.5 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 11,095
| 0.625
|
|
[
"Watch",
"Ice Cream",
"Pizza",
"Vacation"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 0, 'effective_rotation': -324, 'direction': 'clockwise', 'original_colors': ['darkorange', 'forestgreen', 'cyan', 'silver', 'magenta', 'orangered'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Ice Cream', 'Watch', 'Yacht', 'Jewelry', 'Pizza', 'Vacation'], 'rotated_colors': ['darkorange', 'forestgreen', 'cyan', 'silver', 'magenta', 'orangered'], 'rotated_boundaries': [9.0, 69.0, 129.0, 189.0, 249.0, 309.0], 'rotated_prizes': ['Ice Cream', 'Watch', 'Yacht', 'Jewelry', 'Pizza', 'Vacation']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 4.1 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 11,095
| 0.25
|
|
[
"Chocolate",
"Yacht",
"Pizza",
"Camera"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 90, 'effective_rotation': -144, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'royalblue', 'cyan', 'orangered', 'yellow', 'silver'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Yacht', 'Pizza', 'Vacation', 'Ice Cream', 'Chocolate', 'Camera'], 'rotated_colors': ['orangered', 'yellow', 'silver', 'blanchedalmond', 'royalblue', 'cyan'], 'rotated_boundaries': [9.0, 69.0, 129.0, 189.0, 249.0, 309.0], 'rotated_prizes': ['Ice Cream', 'Chocolate', 'Camera', 'Yacht', 'Pizza', 'Vacation']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 1.6 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chocolate",
"style": "rule"
}
| 11,095
| 0
|
|
[
"Pizza",
"Ice Cream",
"Vacation",
"Watch"
] |
{'angles': [60.0, 60.0, 60.0, 60.0, 60.0, 60.0], 'arrow_at': 90, 'effective_rotation': -252, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'lime', 'yellow', 'royalblue', 'cyan', 'darkorange'], 'original_boundaries': [45.0, 105.0, 165.0, 225.0, 285.0, 345.0], 'original_prizes': ['Pizza', 'Camera', 'Ice Cream', 'Watch', 'Vacation', 'Laptop'], 'rotated_colors': ['yellow', 'royalblue', 'cyan', 'darkorange', 'blanchedalmond', 'lime'], 'rotated_boundaries': [57.0, 117.0, 177.0, 237.0, 297.0, 357.0], 'rotated_prizes': ['Ice Cream', 'Watch', 'Vacation', 'Laptop', 'Pizza', 'Camera']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 5.3 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 11,095
| 0
|
|
[
"Pizza",
"Camera",
"Vacation",
"Ice Cream"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 135, 'effective_rotation': 150, 'direction': 'counterclockwise', 'original_colors': ['lime', 'darkorange', 'orangered', 'forestgreen', 'royalblue', 'cyan', 'magenta', 'blanchedalmond'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Money', 'Car', 'Vacation', 'Yacht', 'Camera', 'Pizza', 'Ice Cream', 'Laptop'], 'rotated_colors': ['royalblue', 'cyan', 'magenta', 'blanchedalmond', 'lime', 'darkorange', 'orangered', 'forestgreen'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Camera', 'Pizza', 'Ice Cream', 'Laptop', 'Money', 'Car', 'Vacation', 'Yacht']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 510 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 10,390
| 0.125
|
|
[
"Pizza",
"Vacation",
"Money",
"Camera"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 0, 'effective_rotation': -18, 'direction': 'clockwise', 'original_colors': ['silver', 'orangered', 'yellow', 'darkorange', 'cyan', 'forestgreen', 'magenta', 'royalblue'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Vacation', 'Pizza', 'Chocolate', 'Watch', 'Jewelry', 'Money', 'Camera', 'Car'], 'rotated_colors': ['royalblue', 'silver', 'orangered', 'yellow', 'darkorange', 'cyan', 'forestgreen', 'magenta'], 'rotated_boundaries': [18.0, 63.0, 108.0, 153.0, 198.0, 243.0, 288.0, 333.0], 'rotated_prizes': ['Car', 'Vacation', 'Pizza', 'Chocolate', 'Watch', 'Jewelry', 'Money', 'Camera']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 3.95 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 11,096
| 0
|
|
[
"Chocolate",
"Car",
"Laptop",
"Ice Cream"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 90, 'effective_rotation': -105, 'direction': 'clockwise', 'original_colors': ['orangered', 'blanchedalmond', 'cyan', 'darkorange', 'silver', 'yellow', 'forestgreen', 'royalblue'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Chocolate', 'Yacht', 'Watch', 'Camera', 'Pizza', 'Car', 'Ice Cream', 'Laptop'], 'rotated_colors': ['yellow', 'forestgreen', 'royalblue', 'orangered', 'blanchedalmond', 'cyan', 'darkorange', 'silver'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Car', 'Ice Cream', 'Laptop', 'Chocolate', 'Yacht', 'Watch', 'Camera', 'Pizza']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 255 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 11,094
| 0
|
|
[
"Pizza",
"Yacht",
"Camera",
"Ice Cream"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 270, 'effective_rotation': 195, 'direction': 'counterclockwise', 'original_colors': ['darkorange', 'cyan', 'royalblue', 'magenta', 'forestgreen', 'yellow', 'blanchedalmond', 'silver'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Yacht', 'Chocolate', 'Car', 'Money', 'Laptop', 'Ice Cream', 'Camera', 'Pizza'], 'rotated_colors': ['magenta', 'forestgreen', 'yellow', 'blanchedalmond', 'silver', 'darkorange', 'cyan', 'royalblue'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Money', 'Laptop', 'Ice Cream', 'Camera', 'Pizza', 'Yacht', 'Chocolate', 'Car']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 555 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 11,097
| 0.125
|
|
[
"Laptop",
"Ice Cream",
"Jewelry",
"Watch"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 0, 'effective_rotation': 342, 'direction': 'counterclockwise', 'original_colors': ['blanchedalmond', 'royalblue', 'forestgreen', 'silver', 'cyan', 'lime', 'orangered', 'darkorange'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Watch', 'Car', 'Yacht', 'Pizza', 'Ice Cream', 'Chocolate', 'Jewelry', 'Laptop'], 'rotated_colors': ['blanchedalmond', 'royalblue', 'forestgreen', 'silver', 'cyan', 'lime', 'orangered', 'darkorange'], 'rotated_boundaries': [27.0, 72.0, 117.0, 162.0, 207.0, 252.0, 297.0, 342.0], 'rotated_prizes': ['Watch', 'Car', 'Yacht', 'Pizza', 'Ice Cream', 'Chocolate', 'Jewelry', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 2.95 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 11,099
| 0.125
|
|
[
"Vacation",
"Money",
"Ice Cream",
"Yacht"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 90, 'effective_rotation': -30, 'direction': 'clockwise', 'original_colors': ['darkorange', 'cyan', 'silver', 'royalblue', 'orangered', 'lime', 'magenta', 'forestgreen'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Yacht', 'Money', 'Watch', 'Chocolate', 'Laptop', 'Vacation', 'Jewelry', 'Ice Cream'], 'rotated_colors': ['forestgreen', 'darkorange', 'cyan', 'silver', 'royalblue', 'orangered', 'lime', 'magenta'], 'rotated_boundaries': [30.0, 75.0, 120.0, 165.0, 210.0, 255.0, 300.0, 345.0], 'rotated_prizes': ['Ice Cream', 'Yacht', 'Money', 'Watch', 'Chocolate', 'Laptop', 'Vacation', 'Jewelry']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1050 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 11,095
| 0
|
|
[
"Ice Cream",
"Jewelry",
"Vacation",
"Yacht"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 45, 'effective_rotation': -150, 'direction': 'clockwise', 'original_colors': ['lime', 'orangered', 'cyan', 'magenta', 'blanchedalmond', 'yellow', 'silver', 'royalblue'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Jewelry', 'Ice Cream', 'Watch', 'Laptop', 'Yacht', 'Car', 'Vacation', 'Camera'], 'rotated_colors': ['blanchedalmond', 'yellow', 'silver', 'royalblue', 'lime', 'orangered', 'cyan', 'magenta'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Yacht', 'Car', 'Vacation', 'Camera', 'Jewelry', 'Ice Cream', 'Watch', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1650 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 10,388
| 0.375
|
|
[
"Yacht",
"Chocolate",
"Money",
"Pizza"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 45, 'effective_rotation': -210, 'direction': 'clockwise', 'original_colors': ['yellow', 'silver', 'magenta', 'cyan', 'blanchedalmond', 'royalblue', 'darkorange', 'orangered'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Pizza', 'Jewelry', 'Yacht', 'Money', 'Vacation', 'Watch', 'Laptop', 'Chocolate'], 'rotated_colors': ['cyan', 'blanchedalmond', 'royalblue', 'darkorange', 'orangered', 'yellow', 'silver', 'magenta'], 'rotated_boundaries': [30.0, 75.0, 120.0, 165.0, 210.0, 255.0, 300.0, 345.0], 'rotated_prizes': ['Money', 'Vacation', 'Watch', 'Laptop', 'Chocolate', 'Pizza', 'Jewelry', 'Yacht']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 510 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 10,387
| 0
|
|
[
"Laptop",
"Car",
"Yacht",
"Camera"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 0, 'effective_rotation': 108, 'direction': 'counterclockwise', 'original_colors': ['magenta', 'orangered', 'yellow', 'royalblue', 'darkorange', 'silver', 'lime', 'blanchedalmond'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Yacht', 'Camera', 'Jewelry', 'Car', 'Laptop', 'Chocolate', 'Pizza', 'Vacation'], 'rotated_colors': ['silver', 'lime', 'blanchedalmond', 'magenta', 'orangered', 'yellow', 'royalblue', 'darkorange'], 'rotated_boundaries': [18.0, 63.0, 108.0, 153.0, 198.0, 243.0, 288.0, 333.0], 'rotated_prizes': ['Chocolate', 'Pizza', 'Vacation', 'Yacht', 'Camera', 'Jewelry', 'Car', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 5.3 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 11,098
| 0.25
|
|
[
"Ice Cream",
"Money",
"Chocolate",
"Jewelry"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 45, 'effective_rotation': 72, 'direction': 'counterclockwise', 'original_colors': ['forestgreen', 'orangered', 'royalblue', 'cyan', 'darkorange', 'silver', 'blanchedalmond', 'lime'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Pizza', 'Chocolate', 'Jewelry', 'Laptop', 'Yacht', 'Money', 'Ice Cream', 'Car'], 'rotated_colors': ['blanchedalmond', 'lime', 'forestgreen', 'orangered', 'royalblue', 'cyan', 'darkorange', 'silver'], 'rotated_boundaries': [27.0, 72.0, 117.0, 162.0, 207.0, 252.0, 297.0, 342.0], 'rotated_prizes': ['Ice Cream', 'Car', 'Pizza', 'Chocolate', 'Jewelry', 'Laptop', 'Yacht', 'Money']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 2.2 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 10,391
| 0.375
|
|
[
"Laptop",
"Camera",
"Money",
"Chocolate"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 270, 'effective_rotation': -165, 'direction': 'clockwise', 'original_colors': ['lime', 'forestgreen', 'royalblue', 'yellow', 'orangered', 'blanchedalmond', 'magenta', 'darkorange'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Laptop', 'Camera', 'Money', 'Vacation', 'Ice Cream', 'Jewelry', 'Yacht', 'Chocolate'], 'rotated_colors': ['orangered', 'blanchedalmond', 'magenta', 'darkorange', 'lime', 'forestgreen', 'royalblue', 'yellow'], 'rotated_boundaries': [30.0, 75.0, 120.0, 165.0, 210.0, 255.0, 300.0, 345.0], 'rotated_prizes': ['Ice Cream', 'Jewelry', 'Yacht', 'Chocolate', 'Laptop', 'Camera', 'Money', 'Vacation']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 555 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 11,094
| 0.125
|
|
[
"Watch",
"Car",
"Ice Cream",
"Yacht"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 180, 'effective_rotation': 144, 'direction': 'counterclockwise', 'original_colors': ['royalblue', 'lime', 'silver', 'darkorange', 'magenta', 'blanchedalmond', 'orangered', 'cyan'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Laptop', 'Ice Cream', 'Money', 'Car', 'Watch', 'Chocolate', 'Pizza', 'Yacht'], 'rotated_colors': ['magenta', 'blanchedalmond', 'orangered', 'cyan', 'royalblue', 'lime', 'silver', 'darkorange'], 'rotated_boundaries': [9.0, 54.0, 99.0, 144.0, 189.0, 234.0, 279.0, 324.0], 'rotated_prizes': ['Watch', 'Chocolate', 'Pizza', 'Yacht', 'Laptop', 'Ice Cream', 'Money', 'Car']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 5.4 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 11,098
| 0
|
|
[
"Ice Cream",
"Vacation",
"Chocolate",
"Car"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 225, 'effective_rotation': -300, 'direction': 'clockwise', 'original_colors': ['magenta', 'orangered', 'blanchedalmond', 'yellow', 'silver', 'lime', 'darkorange', 'cyan'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Laptop', 'Watch', 'Car', 'Ice Cream', 'Yacht', 'Chocolate', 'Vacation', 'Jewelry'], 'rotated_colors': ['orangered', 'blanchedalmond', 'yellow', 'silver', 'lime', 'darkorange', 'cyan', 'magenta'], 'rotated_boundaries': [30.0, 75.0, 120.0, 165.0, 210.0, 255.0, 300.0, 345.0], 'rotated_prizes': ['Watch', 'Car', 'Ice Cream', 'Yacht', 'Chocolate', 'Vacation', 'Jewelry', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 780 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chocolate",
"style": "rule"
}
| 10,387
| 0.5
|
|
[
"Pizza",
"Car",
"Ice Cream",
"Camera"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 135, 'effective_rotation': 285, 'direction': 'counterclockwise', 'original_colors': ['royalblue', 'lime', 'silver', 'cyan', 'magenta', 'orangered', 'blanchedalmond', 'yellow'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Ice Cream', 'Vacation', 'Car', 'Camera', 'Jewelry', 'Money', 'Pizza', 'Watch'], 'rotated_colors': ['lime', 'silver', 'cyan', 'magenta', 'orangered', 'blanchedalmond', 'yellow', 'royalblue'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Vacation', 'Car', 'Camera', 'Jewelry', 'Money', 'Pizza', 'Watch', 'Ice Cream']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 285 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 10,390
| 0.125
|
|
[
"Vacation",
"Pizza",
"Chocolate",
"Camera"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 180, 'effective_rotation': -150, 'direction': 'clockwise', 'original_colors': ['cyan', 'blanchedalmond', 'forestgreen', 'lime', 'silver', 'yellow', 'darkorange', 'royalblue'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Money', 'Camera', 'Vacation', 'Chocolate', 'Laptop', 'Jewelry', 'Car', 'Pizza'], 'rotated_colors': ['silver', 'yellow', 'darkorange', 'royalblue', 'cyan', 'blanchedalmond', 'forestgreen', 'lime'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Laptop', 'Jewelry', 'Car', 'Pizza', 'Money', 'Camera', 'Vacation', 'Chocolate']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1650 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 11,095
| 0.375
|
|
[
"Money",
"Car",
"Vacation",
"Jewelry"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 315, 'effective_rotation': -198, 'direction': 'clockwise', 'original_colors': ['silver', 'yellow', 'orangered', 'lime', 'cyan', 'darkorange', 'blanchedalmond', 'magenta'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Laptop', 'Money', 'Camera', 'Jewelry', 'Car', 'Watch', 'Vacation', 'Chocolate'], 'rotated_colors': ['lime', 'cyan', 'darkorange', 'blanchedalmond', 'magenta', 'silver', 'yellow', 'orangered'], 'rotated_boundaries': [18.0, 63.0, 108.0, 153.0, 198.0, 243.0, 288.0, 333.0], 'rotated_prizes': ['Jewelry', 'Car', 'Watch', 'Vacation', 'Chocolate', 'Laptop', 'Money', 'Camera']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 2.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 10,389
| 0.375
|
|
[
"Ice Cream",
"Vacation",
"Yacht",
"Laptop"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 225, 'effective_rotation': -60, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'cyan', 'yellow', 'magenta', 'darkorange', 'lime', 'forestgreen', 'royalblue'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Money', 'Ice Cream', 'Laptop', 'Yacht', 'Car', 'Vacation', 'Chocolate', 'Jewelry'], 'rotated_colors': ['forestgreen', 'royalblue', 'blanchedalmond', 'cyan', 'yellow', 'magenta', 'darkorange', 'lime'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Chocolate', 'Jewelry', 'Money', 'Ice Cream', 'Laptop', 'Yacht', 'Car', 'Vacation']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1740 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,388
| 0.625
|
|
[
"Ice Cream",
"Pizza",
"Watch",
"Laptop"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 225, 'effective_rotation': -126, 'direction': 'clockwise', 'original_colors': ['lime', 'darkorange', 'forestgreen', 'royalblue', 'orangered', 'silver', 'yellow', 'cyan'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Chocolate', 'Ice Cream', 'Money', 'Jewelry', 'Pizza', 'Laptop', 'Watch', 'Yacht'], 'rotated_colors': ['silver', 'yellow', 'cyan', 'lime', 'darkorange', 'forestgreen', 'royalblue', 'orangered'], 'rotated_boundaries': [36.0, 81.0, 126.0, 171.0, 216.0, 261.0, 306.0, 351.0], 'rotated_prizes': ['Laptop', 'Watch', 'Yacht', 'Chocolate', 'Ice Cream', 'Money', 'Jewelry', 'Pizza']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 4.65 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 10,389
| 0.125
|
|
[
"Chocolate",
"Pizza",
"Ice Cream",
"Vacation"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 315, 'effective_rotation': -195, 'direction': 'clockwise', 'original_colors': ['yellow', 'lime', 'cyan', 'royalblue', 'blanchedalmond', 'orangered', 'forestgreen', 'magenta'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Vacation', 'Pizza', 'Laptop', 'Jewelry', 'Watch', 'Camera', 'Chocolate', 'Ice Cream'], 'rotated_colors': ['royalblue', 'blanchedalmond', 'orangered', 'forestgreen', 'magenta', 'yellow', 'lime', 'cyan'], 'rotated_boundaries': [15.0, 60.0, 105.0, 150.0, 195.0, 240.0, 285.0, 330.0], 'rotated_prizes': ['Jewelry', 'Watch', 'Camera', 'Chocolate', 'Ice Cream', 'Vacation', 'Pizza', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 525 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 10,387
| 0.125
|
|
[
"Chocolate",
"Camera",
"Ice Cream",
"Laptop"
] |
{'angles': [45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0, 45.0], 'arrow_at': 45, 'effective_rotation': -255, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'lime', 'orangered', 'cyan', 'silver', 'darkorange', 'yellow', 'magenta'], 'original_boundaries': [45.0, 90.0, 135.0, 180.0, 225.0, 270.0, 315.0, 360.0], 'original_prizes': ['Jewelry', 'Laptop', 'Chocolate', 'Watch', 'Camera', 'Car', 'Ice Cream', 'Pizza'], 'rotated_colors': ['orangered', 'cyan', 'silver', 'darkorange', 'yellow', 'magenta', 'blanchedalmond', 'lime'], 'rotated_boundaries': [30.0, 75.0, 120.0, 165.0, 210.0, 255.0, 300.0, 345.0], 'rotated_prizes': ['Chocolate', 'Watch', 'Camera', 'Car', 'Ice Cream', 'Pizza', 'Jewelry', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1185 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chocolate",
"style": "rule"
}
| 10,388
| 0
|
|
[
"Laptop",
"Car",
"Vacation",
"Jewelry"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 225, 'effective_rotation': 54, 'direction': 'counterclockwise', 'original_colors': ['royalblue', 'cyan', 'yellow', 'forestgreen', 'orangered', 'blanchedalmond', 'darkorange', 'silver', 'magenta', 'lime'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Chocolate', 'Camera', 'Jewelry', 'Laptop', 'Pizza', 'Watch', 'Vacation', 'Money', 'Car', 'Yacht'], 'rotated_colors': ['magenta', 'lime', 'royalblue', 'cyan', 'yellow', 'forestgreen', 'orangered', 'blanchedalmond', 'darkorange', 'silver'], 'rotated_boundaries': [27.0, 63.0, 99.0, 135.0, 171.0, 207.0, 243.0, 279.0, 315.0, 351.0], 'rotated_prizes': ['Car', 'Yacht', 'Chocolate', 'Camera', 'Jewelry', 'Laptop', 'Pizza', 'Watch', 'Vacation', 'Money']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 2.15 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,393
| 0
|
|
[
"Ice Cream",
"Yacht",
"Camera",
"Chocolate"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 0, 'effective_rotation': -72, 'direction': 'clockwise', 'original_colors': ['royalblue', 'darkorange', 'cyan', 'magenta', 'yellow', 'blanchedalmond', 'silver', 'orangered', 'lime', 'forestgreen'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Car', 'Ice Cream', 'Jewelry', 'Laptop', 'Money', 'Watch', 'Camera', 'Chocolate', 'Pizza', 'Yacht'], 'rotated_colors': ['orangered', 'lime', 'forestgreen', 'royalblue', 'darkorange', 'cyan', 'magenta', 'yellow', 'blanchedalmond', 'silver'], 'rotated_boundaries': [9.0, 45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0], 'rotated_prizes': ['Chocolate', 'Pizza', 'Yacht', 'Car', 'Ice Cream', 'Jewelry', 'Laptop', 'Money', 'Watch', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 2.8 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 11,096
| 0
|
|
[
"Laptop",
"Ice Cream",
"Watch",
"Vacation"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 45, 'effective_rotation': -198, 'direction': 'clockwise', 'original_colors': ['darkorange', 'magenta', 'forestgreen', 'silver', 'orangered', 'cyan', 'yellow', 'lime', 'blanchedalmond', 'royalblue'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Vacation', 'Ice Cream', 'Money', 'Camera', 'Watch', 'Jewelry', 'Laptop', 'Pizza', 'Car', 'Yacht'], 'rotated_colors': ['orangered', 'cyan', 'yellow', 'lime', 'blanchedalmond', 'royalblue', 'darkorange', 'magenta', 'forestgreen', 'silver'], 'rotated_boundaries': [27.0, 63.0, 99.0, 135.0, 171.0, 207.0, 243.0, 279.0, 315.0, 351.0], 'rotated_prizes': ['Watch', 'Jewelry', 'Laptop', 'Pizza', 'Car', 'Yacht', 'Vacation', 'Ice Cream', 'Money', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 4.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Watch",
"style": "rule"
}
| 10,390
| 0
|
|
[
"Pizza",
"Camera",
"Money",
"Jewelry"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 45, 'effective_rotation': 300, 'direction': 'counterclockwise', 'original_colors': ['silver', 'lime', 'magenta', 'yellow', 'blanchedalmond', 'royalblue', 'darkorange', 'forestgreen', 'cyan', 'orangered'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Watch', 'Camera', 'Pizza', 'Vacation', 'Jewelry', 'Money', 'Laptop', 'Chocolate', 'Car', 'Ice Cream'], 'rotated_colors': ['lime', 'magenta', 'yellow', 'blanchedalmond', 'royalblue', 'darkorange', 'forestgreen', 'cyan', 'orangered', 'silver'], 'rotated_boundaries': [21.0, 57.0, 93.0, 129.0, 165.0, 201.0, 237.0, 273.0, 309.0, 345.0], 'rotated_prizes': ['Camera', 'Pizza', 'Vacation', 'Jewelry', 'Money', 'Laptop', 'Chocolate', 'Car', 'Ice Cream', 'Watch']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 300 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 10,391
| 0.625
|
|
[
"Chocolate",
"Laptop",
"Pizza",
"Car"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 0, 'effective_rotation': 345, 'direction': 'counterclockwise', 'original_colors': ['blanchedalmond', 'darkorange', 'cyan', 'yellow', 'forestgreen', 'silver', 'magenta', 'royalblue', 'lime', 'orangered'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Vacation', 'Pizza', 'Yacht', 'Jewelry', 'Money', 'Ice Cream', 'Laptop', 'Car', 'Camera', 'Chocolate'], 'rotated_colors': ['blanchedalmond', 'darkorange', 'cyan', 'yellow', 'forestgreen', 'silver', 'magenta', 'royalblue', 'lime', 'orangered'], 'rotated_boundaries': [30.0, 66.0, 102.0, 138.0, 174.0, 210.0, 246.0, 282.0, 318.0, 354.0], 'rotated_prizes': ['Vacation', 'Pizza', 'Yacht', 'Jewelry', 'Money', 'Ice Cream', 'Laptop', 'Car', 'Camera', 'Chocolate']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1065 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chocolate",
"style": "rule"
}
| 11,099
| 0.375
|
|
[
"Car",
"Chocolate",
"Yacht",
"Ice Cream"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 315, 'effective_rotation': -150, 'direction': 'clockwise', 'original_colors': ['darkorange', 'lime', 'cyan', 'yellow', 'royalblue', 'forestgreen', 'orangered', 'blanchedalmond', 'magenta', 'silver'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Vacation', 'Watch', 'Laptop', 'Yacht', 'Camera', 'Car', 'Jewelry', 'Ice Cream', 'Chocolate', 'Money'], 'rotated_colors': ['forestgreen', 'orangered', 'blanchedalmond', 'magenta', 'silver', 'darkorange', 'lime', 'cyan', 'yellow', 'royalblue'], 'rotated_boundaries': [15.0, 51.0, 87.0, 123.0, 159.0, 195.0, 231.0, 267.0, 303.0, 339.0], 'rotated_prizes': ['Car', 'Jewelry', 'Ice Cream', 'Chocolate', 'Money', 'Vacation', 'Watch', 'Laptop', 'Yacht', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1290 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 10,389
| 0.25
|
|
[
"Watch",
"Laptop",
"Money",
"Jewelry"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 45, 'effective_rotation': -330, 'direction': 'clockwise', 'original_colors': ['royalblue', 'magenta', 'forestgreen', 'cyan', 'orangered', 'blanchedalmond', 'yellow', 'silver', 'darkorange', 'lime'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Laptop', 'Vacation', 'Watch', 'Jewelry', 'Camera', 'Chocolate', 'Ice Cream', 'Yacht', 'Money', 'Car'], 'rotated_colors': ['royalblue', 'magenta', 'forestgreen', 'cyan', 'orangered', 'blanchedalmond', 'yellow', 'silver', 'darkorange', 'lime'], 'rotated_boundaries': [15.0, 51.0, 87.0, 123.0, 159.0, 195.0, 231.0, 267.0, 303.0, 339.0], 'rotated_prizes': ['Laptop', 'Vacation', 'Watch', 'Jewelry', 'Camera', 'Chocolate', 'Ice Cream', 'Yacht', 'Money', 'Car']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1110 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,389
| 0.125
|
|
[
"Vacation",
"Chocolate",
"Yacht",
"Money"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 0, 'effective_rotation': -90, 'direction': 'clockwise', 'original_colors': ['silver', 'lime', 'cyan', 'forestgreen', 'yellow', 'orangered', 'magenta', 'blanchedalmond', 'royalblue', 'darkorange'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Pizza', 'Laptop', 'Chocolate', 'Ice Cream', 'Vacation', 'Yacht', 'Money', 'Watch', 'Car', 'Camera'], 'rotated_colors': ['blanchedalmond', 'royalblue', 'darkorange', 'silver', 'lime', 'cyan', 'forestgreen', 'yellow', 'orangered', 'magenta'], 'rotated_boundaries': [27.0, 63.0, 99.0, 135.0, 171.0, 207.0, 243.0, 279.0, 315.0, 351.0], 'rotated_prizes': ['Watch', 'Car', 'Camera', 'Pizza', 'Laptop', 'Chocolate', 'Ice Cream', 'Vacation', 'Yacht', 'Money']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 270 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 11,095
| 0
|
|
[
"Watch",
"Vacation",
"Jewelry",
"Yacht"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 45, 'effective_rotation': 285, 'direction': 'counterclockwise', 'original_colors': ['royalblue', 'cyan', 'orangered', 'blanchedalmond', 'magenta', 'darkorange', 'yellow', 'silver', 'forestgreen', 'lime'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Pizza', 'Car', 'Jewelry', 'Money', 'Laptop', 'Chocolate', 'Watch', 'Vacation', 'Camera', 'Yacht'], 'rotated_colors': ['cyan', 'orangered', 'blanchedalmond', 'magenta', 'darkorange', 'yellow', 'silver', 'forestgreen', 'lime', 'royalblue'], 'rotated_boundaries': [6.0, 42.0, 78.0, 114.0, 150.0, 186.0, 222.0, 258.0, 294.0, 330.0], 'rotated_prizes': ['Car', 'Jewelry', 'Money', 'Laptop', 'Chocolate', 'Watch', 'Vacation', 'Camera', 'Yacht', 'Pizza']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 645 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 10,391
| 0.25
|
|
[
"Laptop",
"Camera",
"Jewelry",
"Money"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 45, 'effective_rotation': 198, 'direction': 'counterclockwise', 'original_colors': ['yellow', 'lime', 'blanchedalmond', 'silver', 'cyan', 'magenta', 'orangered', 'royalblue', 'forestgreen', 'darkorange'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Money', 'Laptop', 'Camera', 'Car', 'Jewelry', 'Vacation', 'Watch', 'Pizza', 'Yacht', 'Chocolate'], 'rotated_colors': ['cyan', 'magenta', 'orangered', 'royalblue', 'forestgreen', 'darkorange', 'yellow', 'lime', 'blanchedalmond', 'silver'], 'rotated_boundaries': [27.0, 63.0, 99.0, 135.0, 171.0, 207.0, 243.0, 279.0, 315.0, 351.0], 'rotated_prizes': ['Jewelry', 'Vacation', 'Watch', 'Pizza', 'Yacht', 'Chocolate', 'Money', 'Laptop', 'Camera', 'Car']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 4.55 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 10,393
| 0.25
|
|
[
"Jewelry",
"Watch",
"Yacht",
"Ice Cream"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 90, 'effective_rotation': 285, 'direction': 'counterclockwise', 'original_colors': ['yellow', 'silver', 'blanchedalmond', 'royalblue', 'lime', 'darkorange', 'orangered', 'cyan', 'magenta', 'forestgreen'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Vacation', 'Jewelry', 'Laptop', 'Watch', 'Money', 'Pizza', 'Yacht', 'Ice Cream', 'Car', 'Camera'], 'rotated_colors': ['silver', 'blanchedalmond', 'royalblue', 'lime', 'darkorange', 'orangered', 'cyan', 'magenta', 'forestgreen', 'yellow'], 'rotated_boundaries': [6.0, 42.0, 78.0, 114.0, 150.0, 186.0, 222.0, 258.0, 294.0, 330.0], 'rotated_prizes': ['Jewelry', 'Laptop', 'Watch', 'Money', 'Pizza', 'Yacht', 'Ice Cream', 'Car', 'Camera', 'Vacation']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1365 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Watch",
"style": "rule"
}
| 11,099
| 0.375
|
|
[
"Car",
"Chocolate",
"Money",
"Watch"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 45, 'effective_rotation': 198, 'direction': 'counterclockwise', 'original_colors': ['blanchedalmond', 'yellow', 'cyan', 'royalblue', 'silver', 'darkorange', 'orangered', 'magenta', 'forestgreen', 'lime'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Yacht', 'Ice Cream', 'Money', 'Camera', 'Car', 'Watch', 'Jewelry', 'Vacation', 'Laptop', 'Chocolate'], 'rotated_colors': ['silver', 'darkorange', 'orangered', 'magenta', 'forestgreen', 'lime', 'blanchedalmond', 'yellow', 'cyan', 'royalblue'], 'rotated_boundaries': [27.0, 63.0, 99.0, 135.0, 171.0, 207.0, 243.0, 279.0, 315.0, 351.0], 'rotated_prizes': ['Car', 'Watch', 'Jewelry', 'Vacation', 'Laptop', 'Chocolate', 'Yacht', 'Ice Cream', 'Money', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 4.55 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Car",
"style": "rule"
}
| 10,393
| 0.625
|
|
[
"Vacation",
"Jewelry",
"Camera",
"Car"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 45, 'effective_rotation': -270, 'direction': 'clockwise', 'original_colors': ['lime', 'silver', 'orangered', 'forestgreen', 'blanchedalmond', 'magenta', 'darkorange', 'yellow', 'cyan', 'royalblue'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Laptop', 'Jewelry', 'Camera', 'Pizza', 'Ice Cream', 'Watch', 'Car', 'Chocolate', 'Vacation', 'Money'], 'rotated_colors': ['orangered', 'forestgreen', 'blanchedalmond', 'magenta', 'darkorange', 'yellow', 'cyan', 'royalblue', 'lime', 'silver'], 'rotated_boundaries': [27.0, 63.0, 99.0, 135.0, 171.0, 207.0, 243.0, 279.0, 315.0, 351.0], 'rotated_prizes': ['Camera', 'Pizza', 'Ice Cream', 'Watch', 'Car', 'Chocolate', 'Vacation', 'Money', 'Laptop', 'Jewelry']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 4.25 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 10,390
| 0
|
|
[
"Camera",
"Laptop",
"Money",
"Yacht"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 135, 'effective_rotation': 300, 'direction': 'counterclockwise', 'original_colors': ['lime', 'forestgreen', 'royalblue', 'yellow', 'blanchedalmond', 'magenta', 'cyan', 'darkorange', 'silver', 'orangered'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Chocolate', 'Laptop', 'Money', 'Pizza', 'Camera', 'Car', 'Vacation', 'Watch', 'Ice Cream', 'Yacht'], 'rotated_colors': ['forestgreen', 'royalblue', 'yellow', 'blanchedalmond', 'magenta', 'cyan', 'darkorange', 'silver', 'orangered', 'lime'], 'rotated_boundaries': [21.0, 57.0, 93.0, 129.0, 165.0, 201.0, 237.0, 273.0, 309.0, 345.0], 'rotated_prizes': ['Laptop', 'Money', 'Pizza', 'Camera', 'Car', 'Vacation', 'Watch', 'Ice Cream', 'Yacht', 'Chocolate']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 300 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 10,391
| 0.25
|
|
[
"Vacation",
"Jewelry",
"Money",
"Laptop"
] |
{'angles': [36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0, 36.0], 'arrow_at': 225, 'effective_rotation': -45, 'direction': 'clockwise', 'original_colors': ['darkorange', 'cyan', 'forestgreen', 'lime', 'silver', 'magenta', 'blanchedalmond', 'orangered', 'yellow', 'royalblue'], 'original_boundaries': [45.0, 81.0, 117.0, 153.0, 189.0, 225.0, 261.0, 297.0, 333.0, 369.0], 'original_prizes': ['Car', 'Laptop', 'Pizza', 'Vacation', 'Watch', 'Money', 'Chocolate', 'Camera', 'Ice Cream', 'Jewelry'], 'rotated_colors': ['yellow', 'royalblue', 'darkorange', 'cyan', 'forestgreen', 'lime', 'silver', 'magenta', 'blanchedalmond', 'orangered'], 'rotated_boundaries': [18.0, 54.0, 90.0, 126.0, 162.0, 198.0, 234.0, 270.0, 306.0, 342.0], 'rotated_prizes': ['Ice Cream', 'Jewelry', 'Car', 'Laptop', 'Pizza', 'Vacation', 'Watch', 'Money', 'Chocolate', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1755 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 10,389
| 0.5
|
|
[
"Laptop",
"Vacation",
"Camera",
"Ice Cream"
] |
{'angles': [30, 60, 90, 75, 60, 45], 'arrow_at': 315, 'effective_rotation': 144, 'direction': 'counterclockwise', 'original_colors': ['blanchedalmond', 'darkorange', 'magenta', 'cyan', 'orangered', 'yellow'], 'original_boundaries': [45.0, 75.0, 135.0, 225.0, 300.0, 360.0], 'original_prizes': ['Camera', 'Yacht', 'Laptop', 'Car', 'Vacation', 'Ice Cream'], 'rotated_colors': ['cyan', 'orangered', 'yellow', 'blanchedalmond', 'darkorange', 'magenta'], 'rotated_boundaries': [9.0, 84.0, 144.0, 189.0, 219.0, 279.0], 'rotated_prizes': ['Car', 'Vacation', 'Ice Cream', 'Camera', 'Yacht', 'Laptop']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 4.4 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,391
| 0.375
|
|
[
"Money",
"Pizza",
"Vacation",
"Jewelry"
] |
{'angles': [30, 30, 60, 90, 90, 60], 'arrow_at': 270, 'effective_rotation': 342, 'direction': 'counterclockwise', 'original_colors': ['orangered', 'silver', 'royalblue', 'yellow', 'darkorange', 'cyan'], 'original_boundaries': [45.0, 75.0, 105.0, 165.0, 255.0, 345.0], 'original_prizes': ['Pizza', 'Jewelry', 'Vacation', 'Camera', 'Money', 'Chocolate'], 'rotated_colors': ['orangered', 'silver', 'royalblue', 'yellow', 'darkorange', 'cyan'], 'rotated_boundaries': [27.0, 57.0, 87.0, 147.0, 237.0, 327.0], 'rotated_prizes': ['Pizza', 'Jewelry', 'Vacation', 'Camera', 'Money', 'Chocolate']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 1.95 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 11,099
| 0.625
|
|
[
"Chocolate",
"Laptop",
"Money",
"Camera"
] |
{'angles': [60, 75, 75, 60, 45, 45], 'arrow_at': 225, 'effective_rotation': 198, 'direction': 'counterclockwise', 'original_colors': ['lime', 'cyan', 'silver', 'blanchedalmond', 'forestgreen', 'yellow'], 'original_boundaries': [45.0, 105.0, 180.0, 255.0, 315.0, 360.0], 'original_prizes': ['Laptop', 'Chocolate', 'Camera', 'Yacht', 'Ice Cream', 'Money'], 'rotated_colors': ['silver', 'blanchedalmond', 'forestgreen', 'yellow', 'lime', 'cyan'], 'rotated_boundaries': [18.0, 93.0, 153.0, 198.0, 243.0, 303.0], 'rotated_prizes': ['Camera', 'Yacht', 'Ice Cream', 'Money', 'Laptop', 'Chocolate']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 5.55 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 10,392
| 0.25
|
|
[
"Watch",
"Car",
"Chocolate",
"Vacation"
] |
{'angles': [45, 45, 75, 45, 75, 75], 'arrow_at': 315, 'effective_rotation': 240, 'direction': 'counterclockwise', 'original_colors': ['darkorange', 'lime', 'silver', 'forestgreen', 'yellow', 'blanchedalmond'], 'original_boundaries': [45.0, 90.0, 135.0, 210.0, 255.0, 330.0], 'original_prizes': ['Chocolate', 'Vacation', 'Pizza', 'Watch', 'Car', 'Yacht'], 'rotated_colors': ['silver', 'forestgreen', 'yellow', 'blanchedalmond', 'darkorange', 'lime'], 'rotated_boundaries': [15.0, 90.0, 135.0, 210.0, 285.0, 330.0], 'rotated_prizes': ['Pizza', 'Watch', 'Car', 'Yacht', 'Chocolate', 'Vacation']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1320 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chocolate",
"style": "rule"
}
| 10,391
| 0.25
|
|
[
"Vacation",
"Pizza",
"Money",
"Ice Cream"
] |
{'angles': [45, 60, 75, 60, 30, 90], 'arrow_at': 180, 'effective_rotation': -18, 'direction': 'clockwise', 'original_colors': ['royalblue', 'forestgreen', 'yellow', 'magenta', 'orangered', 'blanchedalmond'], 'original_boundaries': [45.0, 90.0, 150.0, 225.0, 285.0, 315.0], 'original_prizes': ['Vacation', 'Ice Cream', 'Pizza', 'Car', 'Money', 'Chocolate'], 'rotated_colors': ['royalblue', 'forestgreen', 'yellow', 'magenta', 'orangered', 'blanchedalmond'], 'rotated_boundaries': [63.0, 108.0, 168.0, 243.0, 303.0, 333.0], 'rotated_prizes': ['Vacation', 'Ice Cream', 'Pizza', 'Car', 'Money', 'Chocolate']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 3.95 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 11,096
| 0
|
|
[
"Yacht",
"Chocolate",
"Watch",
"Vacation"
] |
{'angles': [60, 90, 60, 60, 45, 45], 'arrow_at': 180, 'effective_rotation': 0, 'direction': 'clockwise', 'original_colors': ['magenta', 'royalblue', 'darkorange', 'lime', 'forestgreen', 'blanchedalmond'], 'original_boundaries': [45.0, 105.0, 195.0, 255.0, 315.0, 360.0], 'original_prizes': ['Chocolate', 'Watch', 'Yacht', 'Vacation', 'Laptop', 'Pizza'], 'rotated_colors': ['blanchedalmond', 'magenta', 'royalblue', 'darkorange', 'lime', 'forestgreen'], 'rotated_boundaries': [0.0, 45.0, 105.0, 195.0, 255.0, 315.0], 'rotated_prizes': ['Pizza', 'Chocolate', 'Watch', 'Yacht', 'Vacation', 'Laptop']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 360 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Watch",
"style": "rule"
}
| 11,094
| 1
|
|
[
"Ice Cream",
"Watch",
"Vacation",
"Car"
] |
{'angles': [30, 60, 75, 45, 90, 60], 'arrow_at': 45, 'effective_rotation': -210, 'direction': 'clockwise', 'original_colors': ['royalblue', 'yellow', 'blanchedalmond', 'darkorange', 'orangered', 'cyan'], 'original_boundaries': [45.0, 75.0, 135.0, 210.0, 255.0, 345.0], 'original_prizes': ['Watch', 'Vacation', 'Ice Cream', 'Jewelry', 'Chocolate', 'Car'], 'rotated_colors': ['darkorange', 'orangered', 'cyan', 'royalblue', 'yellow', 'blanchedalmond'], 'rotated_boundaries': [60.0, 105.0, 195.0, 255.0, 285.0, 345.0], 'rotated_prizes': ['Jewelry', 'Chocolate', 'Car', 'Watch', 'Vacation', 'Ice Cream']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1590 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 10,388
| 0.5
|
|
[
"Jewelry",
"Ice Cream",
"Vacation",
"Watch"
] |
{'angles': [75, 60, 60, 45, 45, 75], 'arrow_at': 180, 'effective_rotation': 75, 'direction': 'counterclockwise', 'original_colors': ['cyan', 'forestgreen', 'darkorange', 'royalblue', 'orangered', 'blanchedalmond'], 'original_boundaries': [45.0, 120.0, 180.0, 240.0, 285.0, 330.0], 'original_prizes': ['Ice Cream', 'Vacation', 'Watch', 'Yacht', 'Camera', 'Jewelry'], 'rotated_colors': ['orangered', 'blanchedalmond', 'cyan', 'forestgreen', 'darkorange', 'royalblue'], 'rotated_boundaries': [0.0, 45.0, 120.0, 195.0, 255.0, 315.0], 'rotated_prizes': ['Camera', 'Jewelry', 'Ice Cream', 'Vacation', 'Watch', 'Yacht']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 795 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 11,097
| 0.25
|
|
[
"Ice Cream",
"Watch",
"Vacation",
"Car"
] |
{'angles': [90, 30, 90, 75, 45, 30], 'arrow_at': 180, 'effective_rotation': 90, 'direction': 'counterclockwise', 'original_colors': ['lime', 'yellow', 'blanchedalmond', 'forestgreen', 'magenta', 'cyan'], 'original_boundaries': [45.0, 135.0, 165.0, 255.0, 330.0, 375.0], 'original_prizes': ['Ice Cream', 'Car', 'Vacation', 'Money', 'Yacht', 'Watch'], 'rotated_colors': ['magenta', 'cyan', 'lime', 'yellow', 'blanchedalmond', 'forestgreen'], 'rotated_boundaries': [60.0, 105.0, 135.0, 225.0, 255.0, 345.0], 'rotated_prizes': ['Yacht', 'Watch', 'Ice Cream', 'Car', 'Vacation', 'Money']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1530 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 11,098
| 0.375
|
|
[
"Money",
"Laptop",
"Watch",
"Yacht"
] |
{'angles': [75, 45, 45, 75, 45, 75], 'arrow_at': 0, 'effective_rotation': 162, 'direction': 'counterclockwise', 'original_colors': ['lime', 'blanchedalmond', 'royalblue', 'yellow', 'forestgreen', 'orangered'], 'original_boundaries': [45.0, 120.0, 165.0, 210.0, 285.0, 330.0], 'original_prizes': ['Vacation', 'Camera', 'Watch', 'Money', 'Laptop', 'Yacht'], 'rotated_colors': ['yellow', 'forestgreen', 'orangered', 'lime', 'blanchedalmond', 'royalblue'], 'rotated_boundaries': [12.0, 87.0, 132.0, 207.0, 282.0, 327.0], 'rotated_prizes': ['Money', 'Laptop', 'Yacht', 'Vacation', 'Camera', 'Watch']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 3.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Watch",
"style": "rule"
}
| 11,099
| 0.25
|
|
[
"Vacation",
"Pizza",
"Laptop",
"Car"
] |
{'angles': [90, 60, 30, 75, 30, 75], 'arrow_at': 315, 'effective_rotation': -45, 'direction': 'clockwise', 'original_colors': ['magenta', 'lime', 'yellow', 'darkorange', 'orangered', 'forestgreen'], 'original_boundaries': [45.0, 135.0, 195.0, 225.0, 300.0, 330.0], 'original_prizes': ['Vacation', 'Laptop', 'Ice Cream', 'Pizza', 'Watch', 'Car'], 'rotated_colors': ['forestgreen', 'magenta', 'lime', 'yellow', 'darkorange', 'orangered'], 'rotated_boundaries': [15.0, 90.0, 180.0, 240.0, 270.0, 345.0], 'rotated_prizes': ['Car', 'Vacation', 'Laptop', 'Ice Cream', 'Pizza', 'Watch']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1035 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 10,388
| 0.25
|
|
[
"Camera",
"Jewelry",
"Vacation",
"Pizza"
] |
{'angles': [90, 60, 45, 60, 30, 75], 'arrow_at': 90, 'effective_rotation': -162, 'direction': 'clockwise', 'original_colors': ['orangered', 'cyan', 'darkorange', 'blanchedalmond', 'royalblue', 'forestgreen'], 'original_boundaries': [45.0, 135.0, 195.0, 240.0, 300.0, 330.0], 'original_prizes': ['Pizza', 'Camera', 'Ice Cream', 'Jewelry', 'Vacation', 'Money'], 'rotated_colors': ['blanchedalmond', 'royalblue', 'forestgreen', 'orangered', 'cyan', 'darkorange'], 'rotated_boundaries': [42.0, 102.0, 132.0, 207.0, 297.0, 357.0], 'rotated_prizes': ['Jewelry', 'Vacation', 'Money', 'Pizza', 'Camera', 'Ice Cream']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 3.55 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 11,096
| 0.5
|
|
[
"Chocolate",
"Jewelry",
"Money",
"Ice Cream"
] |
{'angles': [30, 75, 45, 90, 30, 90], 'arrow_at': 315, 'effective_rotation': -54, 'direction': 'clockwise', 'original_colors': ['yellow', 'orangered', 'royalblue', 'magenta', 'cyan', 'silver'], 'original_boundaries': [45.0, 75.0, 150.0, 195.0, 285.0, 315.0], 'original_prizes': ['Chocolate', 'Laptop', 'Money', 'Jewelry', 'Watch', 'Ice Cream'], 'rotated_colors': ['silver', 'yellow', 'orangered', 'royalblue', 'magenta', 'cyan'], 'rotated_boundaries': [9.0, 99.0, 129.0, 204.0, 249.0, 339.0], 'rotated_prizes': ['Ice Cream', 'Chocolate', 'Laptop', 'Money', 'Jewelry', 'Watch']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 3.85 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 10,389
| 0.5
|
|
[
"Chocolate",
"Watch",
"Laptop",
"Camera"
] |
{'angles': [45, 60, 75, 75, 60, 45], 'arrow_at': 270, 'effective_rotation': -54, 'direction': 'clockwise', 'original_colors': ['lime', 'silver', 'orangered', 'forestgreen', 'magenta', 'blanchedalmond'], 'original_boundaries': [45.0, 90.0, 150.0, 225.0, 300.0, 360.0], 'original_prizes': ['Laptop', 'Vacation', 'Chocolate', 'Watch', 'Car', 'Camera'], 'rotated_colors': ['blanchedalmond', 'lime', 'silver', 'orangered', 'forestgreen', 'magenta'], 'rotated_boundaries': [54.0, 99.0, 144.0, 204.0, 279.0, 354.0], 'rotated_prizes': ['Camera', 'Laptop', 'Vacation', 'Chocolate', 'Watch', 'Car']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 3.85 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chocolate",
"style": "rule"
}
| 11,096
| 0.75
|
|
[
"Yacht",
"Car",
"Pizza",
"Vacation"
] |
{'angles': [60, 75, 75, 30, 30, 90], 'arrow_at': 315, 'effective_rotation': -234, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'magenta', 'forestgreen', 'royalblue', 'darkorange', 'lime'], 'original_boundaries': [45.0, 105.0, 180.0, 255.0, 285.0, 315.0], 'original_prizes': ['Yacht', 'Watch', 'Ice Cream', 'Vacation', 'Pizza', 'Car'], 'rotated_colors': ['forestgreen', 'royalblue', 'darkorange', 'lime', 'blanchedalmond', 'magenta'], 'rotated_boundaries': [54.0, 129.0, 159.0, 189.0, 279.0, 339.0], 'rotated_prizes': ['Ice Cream', 'Vacation', 'Pizza', 'Car', 'Yacht', 'Watch']}
|
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>A fortune wheel has 6 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 3.35 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 10,389
| 0
|
|
[
"Car",
"Laptop",
"Chocolate",
"Camera"
] |
{'angles': [60, 45, 30, 45, 30, 90, 30, 30], 'arrow_at': 90, 'effective_rotation': -15, 'direction': 'clockwise', 'original_colors': ['royalblue', 'forestgreen', 'blanchedalmond', 'darkorange', 'magenta', 'yellow', 'orangered', 'cyan'], 'original_boundaries': [45.0, 105.0, 150.0, 180.0, 225.0, 255.0, 345.0, 375.0], 'original_prizes': ['Camera', 'Watch', 'Yacht', 'Pizza', 'Ice Cream', 'Chocolate', 'Car', 'Laptop'], 'rotated_colors': ['orangered', 'cyan', 'royalblue', 'forestgreen', 'blanchedalmond', 'darkorange', 'magenta', 'yellow'], 'rotated_boundaries': [0.0, 30.0, 60.0, 120.0, 165.0, 195.0, 240.0, 270.0], 'rotated_prizes': ['Car', 'Laptop', 'Camera', 'Watch', 'Yacht', 'Pizza', 'Ice Cream', 'Chocolate']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1785 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 11,095
| 0.125
|
|
[
"Yacht",
"Laptop",
"Chocolate",
"Car"
] |
{'angles': [30, 45, 30, 30, 75, 60, 60, 30], 'arrow_at': 90, 'effective_rotation': 0, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'magenta', 'cyan', 'darkorange', 'silver', 'yellow', 'lime', 'forestgreen'], 'original_boundaries': [45.0, 75.0, 120.0, 150.0, 180.0, 255.0, 315.0, 375.0], 'original_prizes': ['Ice Cream', 'Yacht', 'Jewelry', 'Car', 'Camera', 'Laptop', 'Chocolate', 'Pizza'], 'rotated_colors': ['forestgreen', 'blanchedalmond', 'magenta', 'cyan', 'darkorange', 'silver', 'yellow', 'lime'], 'rotated_boundaries': [15.0, 45.0, 75.0, 120.0, 150.0, 180.0, 255.0, 315.0], 'rotated_prizes': ['Pizza', 'Ice Cream', 'Yacht', 'Jewelry', 'Car', 'Camera', 'Laptop', 'Chocolate']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 360 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 11,094
| 1
|
|
[
"Ice Cream",
"Laptop",
"Yacht",
"Money"
] |
{'angles': [30, 30, 30, 30, 90, 90, 30, 30], 'arrow_at': 135, 'effective_rotation': 345, 'direction': 'counterclockwise', 'original_colors': ['royalblue', 'blanchedalmond', 'forestgreen', 'orangered', 'silver', 'lime', 'magenta', 'cyan'], 'original_boundaries': [45.0, 75.0, 105.0, 135.0, 165.0, 255.0, 345.0, 375.0], 'original_prizes': ['Ice Cream', 'Car', 'Camera', 'Laptop', 'Vacation', 'Chocolate', 'Yacht', 'Money'], 'rotated_colors': ['cyan', 'royalblue', 'blanchedalmond', 'forestgreen', 'orangered', 'silver', 'lime', 'magenta'], 'rotated_boundaries': [0.0, 30.0, 60.0, 90.0, 120.0, 150.0, 240.0, 330.0], 'rotated_prizes': ['Money', 'Ice Cream', 'Car', 'Camera', 'Laptop', 'Vacation', 'Chocolate', 'Yacht']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 345 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,390
| 0.25
|
|
[
"Yacht",
"Money",
"Car",
"Laptop"
] |
{'angles': [30, 45, 90, 45, 60, 30, 30, 30], 'arrow_at': 0, 'effective_rotation': -300, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'darkorange', 'magenta', 'lime', 'cyan', 'royalblue', 'forestgreen', 'silver'], 'original_boundaries': [45.0, 75.0, 120.0, 210.0, 255.0, 315.0, 345.0, 375.0], 'original_prizes': ['Car', 'Laptop', 'Camera', 'Yacht', 'Money', 'Chocolate', 'Pizza', 'Jewelry'], 'rotated_colors': ['darkorange', 'magenta', 'lime', 'cyan', 'royalblue', 'forestgreen', 'silver', 'blanchedalmond'], 'rotated_boundaries': [15.0, 60.0, 150.0, 195.0, 255.0, 285.0, 315.0, 345.0], 'rotated_prizes': ['Laptop', 'Camera', 'Yacht', 'Money', 'Chocolate', 'Pizza', 'Jewelry', 'Car']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 780 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Car",
"style": "rule"
}
| 11,094
| 0
|
|
[
"Money",
"Pizza",
"Watch",
"Camera"
] |
{'angles': [30, 30, 30, 75, 60, 30, 60, 45], 'arrow_at': 135, 'effective_rotation': 45, 'direction': 'counterclockwise', 'original_colors': ['forestgreen', 'cyan', 'magenta', 'lime', 'orangered', 'yellow', 'darkorange', 'blanchedalmond'], 'original_boundaries': [45.0, 75.0, 105.0, 135.0, 210.0, 270.0, 300.0, 360.0], 'original_prizes': ['Camera', 'Pizza', 'Money', 'Vacation', 'Yacht', 'Jewelry', 'Watch', 'Laptop'], 'rotated_colors': ['blanchedalmond', 'forestgreen', 'cyan', 'magenta', 'lime', 'orangered', 'yellow', 'darkorange'], 'rotated_boundaries': [45.0, 90.0, 120.0, 150.0, 180.0, 255.0, 315.0, 345.0], 'rotated_prizes': ['Laptop', 'Camera', 'Pizza', 'Money', 'Vacation', 'Yacht', 'Jewelry', 'Watch']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1125 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 10,391
| 0.25
|
|
[
"Ice Cream",
"Yacht",
"Money",
"Vacation"
] |
{'angles': [30, 30, 30, 30, 30, 45, 75, 90], 'arrow_at': 225, 'effective_rotation': 342, 'direction': 'counterclockwise', 'original_colors': ['magenta', 'silver', 'forestgreen', 'blanchedalmond', 'royalblue', 'cyan', 'yellow', 'lime'], 'original_boundaries': [45.0, 75.0, 105.0, 135.0, 165.0, 195.0, 240.0, 315.0], 'original_prizes': ['Money', 'Chocolate', 'Laptop', 'Ice Cream', 'Car', 'Vacation', 'Yacht', 'Watch'], 'rotated_colors': ['magenta', 'silver', 'forestgreen', 'blanchedalmond', 'royalblue', 'cyan', 'yellow', 'lime'], 'rotated_boundaries': [27.0, 57.0, 87.0, 117.0, 147.0, 177.0, 222.0, 297.0], 'rotated_prizes': ['Money', 'Chocolate', 'Laptop', 'Ice Cream', 'Car', 'Vacation', 'Yacht', 'Watch']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 5.95 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 10,392
| 0.125
|
|
[
"Car",
"Chocolate",
"Watch",
"Jewelry"
] |
{'angles': [60, 30, 30, 90, 30, 30, 30, 60], 'arrow_at': 45, 'effective_rotation': -198, 'direction': 'clockwise', 'original_colors': ['forestgreen', 'magenta', 'orangered', 'yellow', 'silver', 'lime', 'darkorange', 'royalblue'], 'original_boundaries': [45.0, 105.0, 135.0, 165.0, 255.0, 285.0, 315.0, 345.0], 'original_prizes': ['Camera', 'Vacation', 'Watch', 'Jewelry', 'Chocolate', 'Ice Cream', 'Pizza', 'Car'], 'rotated_colors': ['yellow', 'silver', 'lime', 'darkorange', 'royalblue', 'forestgreen', 'magenta', 'orangered'], 'rotated_boundaries': [3.0, 93.0, 123.0, 153.0, 183.0, 243.0, 303.0, 333.0], 'rotated_prizes': ['Jewelry', 'Chocolate', 'Ice Cream', 'Pizza', 'Car', 'Camera', 'Vacation', 'Watch']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 2.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 10,389
| 0
|
|
[
"Car",
"Laptop",
"Money",
"Ice Cream"
] |
{'angles': [30, 60, 30, 30, 30, 30, 75, 75], 'arrow_at': 180, 'effective_rotation': 75, 'direction': 'counterclockwise', 'original_colors': ['yellow', 'royalblue', 'silver', 'darkorange', 'lime', 'forestgreen', 'blanchedalmond', 'orangered'], 'original_boundaries': [45.0, 75.0, 135.0, 165.0, 195.0, 225.0, 255.0, 330.0], 'original_prizes': ['Ice Cream', 'Car', 'Vacation', 'Pizza', 'Laptop', 'Yacht', 'Money', 'Chocolate'], 'rotated_colors': ['orangered', 'yellow', 'royalblue', 'silver', 'darkorange', 'lime', 'forestgreen', 'blanchedalmond'], 'rotated_boundaries': [45.0, 120.0, 150.0, 210.0, 240.0, 270.0, 300.0, 330.0], 'rotated_prizes': ['Chocolate', 'Ice Cream', 'Car', 'Vacation', 'Pizza', 'Laptop', 'Yacht', 'Money']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1155 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Car",
"style": "rule"
}
| 11,098
| 0
|
|
[
"Laptop",
"Pizza",
"Chocolate",
"Yacht"
] |
{'angles': [45, 30, 75, 90, 30, 30, 30, 30], 'arrow_at': 225, 'effective_rotation': 255, 'direction': 'counterclockwise', 'original_colors': ['forestgreen', 'orangered', 'cyan', 'silver', 'royalblue', 'blanchedalmond', 'yellow', 'magenta'], 'original_boundaries': [45.0, 90.0, 120.0, 195.0, 285.0, 315.0, 345.0, 375.0], 'original_prizes': ['Jewelry', 'Laptop', 'Camera', 'Car', 'Pizza', 'Yacht', 'Watch', 'Chocolate'], 'rotated_colors': ['cyan', 'silver', 'royalblue', 'blanchedalmond', 'yellow', 'magenta', 'forestgreen', 'orangered'], 'rotated_boundaries': [15.0, 90.0, 180.0, 210.0, 240.0, 270.0, 300.0, 345.0], 'rotated_prizes': ['Camera', 'Car', 'Pizza', 'Yacht', 'Watch', 'Chocolate', 'Jewelry', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1335 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 10,391
| 0
|
|
[
"Vacation",
"Watch",
"Jewelry",
"Money"
] |
{'angles': [60, 60, 30, 30, 30, 90, 30, 30], 'arrow_at': 0, 'effective_rotation': -126, 'direction': 'clockwise', 'original_colors': ['yellow', 'silver', 'royalblue', 'darkorange', 'magenta', 'cyan', 'blanchedalmond', 'orangered'], 'original_boundaries': [45.0, 105.0, 165.0, 195.0, 225.0, 255.0, 345.0, 375.0], 'original_prizes': ['Watch', 'Ice Cream', 'Car', 'Vacation', 'Money', 'Pizza', 'Yacht', 'Jewelry'], 'rotated_colors': ['cyan', 'blanchedalmond', 'orangered', 'yellow', 'silver', 'royalblue', 'darkorange', 'magenta'], 'rotated_boundaries': [21.0, 111.0, 141.0, 171.0, 231.0, 291.0, 321.0, 351.0], 'rotated_prizes': ['Pizza', 'Yacht', 'Jewelry', 'Watch', 'Ice Cream', 'Car', 'Vacation', 'Money']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 1.65 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 11,096
| 0.125
|
|
[
"Money",
"Yacht",
"Pizza",
"Laptop"
] |
{'angles': [30, 45, 75, 45, 30, 30, 30, 75], 'arrow_at': 0, 'effective_rotation': -198, 'direction': 'clockwise', 'original_colors': ['lime', 'forestgreen', 'darkorange', 'magenta', 'royalblue', 'orangered', 'silver', 'cyan'], 'original_boundaries': [45.0, 75.0, 120.0, 195.0, 240.0, 270.0, 300.0, 330.0], 'original_prizes': ['Pizza', 'Jewelry', 'Laptop', 'Chocolate', 'Car', 'Money', 'Yacht', 'Ice Cream'], 'rotated_colors': ['magenta', 'royalblue', 'orangered', 'silver', 'cyan', 'lime', 'forestgreen', 'darkorange'], 'rotated_boundaries': [33.0, 78.0, 108.0, 138.0, 168.0, 243.0, 273.0, 318.0], 'rotated_prizes': ['Chocolate', 'Car', 'Money', 'Yacht', 'Ice Cream', 'Pizza', 'Jewelry', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 5.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 11,096
| 0
|
|
[
"Pizza",
"Ice Cream",
"Vacation",
"Money"
] |
{'angles': [30, 30, 75, 30, 30, 90, 30, 45], 'arrow_at': 135, 'effective_rotation': 45, 'direction': 'counterclockwise', 'original_colors': ['cyan', 'orangered', 'blanchedalmond', 'darkorange', 'silver', 'lime', 'yellow', 'magenta'], 'original_boundaries': [45.0, 75.0, 105.0, 180.0, 210.0, 240.0, 330.0, 360.0], 'original_prizes': ['Money', 'Vacation', 'Camera', 'Yacht', 'Jewelry', 'Watch', 'Ice Cream', 'Pizza'], 'rotated_colors': ['yellow', 'magenta', 'cyan', 'orangered', 'blanchedalmond', 'darkorange', 'silver', 'lime'], 'rotated_boundaries': [15.0, 45.0, 90.0, 120.0, 150.0, 225.0, 255.0, 285.0], 'rotated_prizes': ['Ice Cream', 'Pizza', 'Money', 'Vacation', 'Camera', 'Yacht', 'Jewelry', 'Watch']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 405 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 10,390
| 0.875
|
|
[
"Jewelry",
"Money",
"Chocolate",
"Car"
] |
{'angles': [30, 90, 30, 60, 30, 30, 30, 60], 'arrow_at': 315, 'effective_rotation': 255, 'direction': 'counterclockwise', 'original_colors': ['darkorange', 'yellow', 'silver', 'lime', 'cyan', 'blanchedalmond', 'magenta', 'forestgreen'], 'original_boundaries': [45.0, 75.0, 165.0, 195.0, 255.0, 285.0, 315.0, 345.0], 'original_prizes': ['Money', 'Ice Cream', 'Car', 'Chocolate', 'Jewelry', 'Yacht', 'Vacation', 'Pizza'], 'rotated_colors': ['silver', 'lime', 'cyan', 'blanchedalmond', 'magenta', 'forestgreen', 'darkorange', 'yellow'], 'rotated_boundaries': [60.0, 90.0, 150.0, 180.0, 210.0, 240.0, 300.0, 330.0], 'rotated_prizes': ['Car', 'Chocolate', 'Jewelry', 'Yacht', 'Vacation', 'Pizza', 'Money', 'Ice Cream']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 615 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 10,390
| 0
|
|
[
"Chocolate",
"Laptop",
"Ice Cream",
"Money"
] |
{'angles': [30, 60, 30, 30, 30, 75, 30, 75], 'arrow_at': 225, 'effective_rotation': -270, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'silver', 'lime', 'cyan', 'forestgreen', 'magenta', 'orangered', 'royalblue'], 'original_boundaries': [45.0, 75.0, 135.0, 165.0, 195.0, 225.0, 300.0, 330.0], 'original_prizes': ['Chocolate', 'Jewelry', 'Laptop', 'Money', 'Camera', 'Car', 'Ice Cream', 'Pizza'], 'rotated_colors': ['lime', 'cyan', 'forestgreen', 'magenta', 'orangered', 'royalblue', 'blanchedalmond', 'silver'], 'rotated_boundaries': [45.0, 75.0, 105.0, 135.0, 210.0, 240.0, 315.0, 345.0], 'rotated_prizes': ['Laptop', 'Money', 'Camera', 'Car', 'Ice Cream', 'Pizza', 'Chocolate', 'Jewelry']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 1.25 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 10,389
| 0.25
|
|
[
"Car",
"Camera",
"Jewelry",
"Chocolate"
] |
{'angles': [75, 30, 30, 30, 30, 30, 90, 45], 'arrow_at': 270, 'effective_rotation': -330, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'silver', 'cyan', 'magenta', 'orangered', 'darkorange', 'forestgreen', 'yellow'], 'original_boundaries': [45.0, 120.0, 150.0, 180.0, 210.0, 240.0, 270.0, 360.0], 'original_prizes': ['Chocolate', 'Yacht', 'Laptop', 'Pizza', 'Camera', 'Jewelry', 'Car', 'Money'], 'rotated_colors': ['blanchedalmond', 'silver', 'cyan', 'magenta', 'orangered', 'darkorange', 'forestgreen', 'yellow'], 'rotated_boundaries': [15.0, 90.0, 120.0, 150.0, 180.0, 210.0, 240.0, 330.0], 'rotated_prizes': ['Chocolate', 'Yacht', 'Laptop', 'Pizza', 'Camera', 'Jewelry', 'Car', 'Money']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1110 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Car",
"style": "rule"
}
| 11,095
| 0.375
|
|
[
"Jewelry",
"Chocolate",
"Yacht",
"Pizza"
] |
{'angles': [30, 30, 75, 60, 30, 60, 30, 45], 'arrow_at': 0, 'effective_rotation': -234, 'direction': 'clockwise', 'original_colors': ['cyan', 'silver', 'blanchedalmond', 'darkorange', 'lime', 'yellow', 'forestgreen', 'magenta'], 'original_boundaries': [45.0, 75.0, 105.0, 180.0, 240.0, 270.0, 330.0, 360.0], 'original_prizes': ['Money', 'Chocolate', 'Jewelry', 'Car', 'Pizza', 'Yacht', 'Laptop', 'Vacation'], 'rotated_colors': ['darkorange', 'lime', 'yellow', 'forestgreen', 'magenta', 'cyan', 'silver', 'blanchedalmond'], 'rotated_boundaries': [54.0, 114.0, 144.0, 204.0, 234.0, 279.0, 309.0, 339.0], 'rotated_prizes': ['Car', 'Pizza', 'Yacht', 'Laptop', 'Vacation', 'Money', 'Chocolate', 'Jewelry']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 5.35 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 11,096
| 0
|
|
[
"Vacation",
"Camera",
"Ice Cream",
"Laptop"
] |
{'angles': [75, 30, 30, 30, 90, 45, 30, 30], 'arrow_at': 45, 'effective_rotation': 54, 'direction': 'counterclockwise', 'original_colors': ['cyan', 'yellow', 'royalblue', 'forestgreen', 'lime', 'magenta', 'silver', 'darkorange'], 'original_boundaries': [45.0, 120.0, 150.0, 180.0, 210.0, 300.0, 345.0, 375.0], 'original_prizes': ['Ice Cream', 'Watch', 'Car', 'Camera', 'Pizza', 'Chocolate', 'Laptop', 'Vacation'], 'rotated_colors': ['silver', 'darkorange', 'cyan', 'yellow', 'royalblue', 'forestgreen', 'lime', 'magenta'], 'rotated_boundaries': [39.0, 69.0, 99.0, 174.0, 204.0, 234.0, 264.0, 354.0], 'rotated_prizes': ['Laptop', 'Vacation', 'Ice Cream', 'Watch', 'Car', 'Camera', 'Pizza', 'Chocolate']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 2.15 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,392
| 0.625
|
|
[
"Laptop",
"Chocolate",
"Ice Cream",
"Watch"
] |
{'angles': [30, 30, 30, 45, 75, 90, 30, 30], 'arrow_at': 135, 'effective_rotation': 195, 'direction': 'counterclockwise', 'original_colors': ['magenta', 'forestgreen', 'darkorange', 'cyan', 'blanchedalmond', 'silver', 'yellow', 'royalblue'], 'original_boundaries': [45.0, 75.0, 105.0, 135.0, 180.0, 255.0, 345.0, 375.0], 'original_prizes': ['Camera', 'Yacht', 'Jewelry', 'Laptop', 'Vacation', 'Watch', 'Chocolate', 'Ice Cream'], 'rotated_colors': ['blanchedalmond', 'silver', 'yellow', 'royalblue', 'magenta', 'forestgreen', 'darkorange', 'cyan'], 'rotated_boundaries': [15.0, 90.0, 180.0, 210.0, 240.0, 270.0, 300.0, 330.0], 'rotated_prizes': ['Vacation', 'Watch', 'Chocolate', 'Ice Cream', 'Camera', 'Yacht', 'Jewelry', 'Laptop']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1635 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Watch",
"style": "rule"
}
| 10,391
| 0
|
|
[
"Camera",
"Laptop",
"Car",
"Vacation"
] |
{'angles': [75, 30, 60, 45, 30, 30, 30, 60], 'arrow_at': 315, 'effective_rotation': -285, 'direction': 'clockwise', 'original_colors': ['magenta', 'blanchedalmond', 'forestgreen', 'lime', 'orangered', 'yellow', 'darkorange', 'royalblue'], 'original_boundaries': [45.0, 120.0, 150.0, 210.0, 255.0, 285.0, 315.0, 345.0], 'original_prizes': ['Camera', 'Ice Cream', 'Laptop', 'Jewelry', 'Chocolate', 'Money', 'Vacation', 'Car'], 'rotated_colors': ['blanchedalmond', 'forestgreen', 'lime', 'orangered', 'yellow', 'darkorange', 'royalblue', 'magenta'], 'rotated_boundaries': [45.0, 75.0, 135.0, 180.0, 210.0, 240.0, 270.0, 330.0], 'rotated_prizes': ['Ice Cream', 'Laptop', 'Jewelry', 'Chocolate', 'Money', 'Vacation', 'Car', 'Camera']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1515 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Car",
"style": "rule"
}
| 10,388
| 0
|
|
[
"Vacation",
"Jewelry",
"Laptop",
"Yacht"
] |
{'angles': [45, 30, 30, 30, 45, 45, 60, 75], 'arrow_at': 180, 'effective_rotation': 240, 'direction': 'counterclockwise', 'original_colors': ['lime', 'cyan', 'magenta', 'royalblue', 'silver', 'forestgreen', 'darkorange', 'yellow'], 'original_boundaries': [45.0, 90.0, 120.0, 150.0, 180.0, 225.0, 270.0, 330.0], 'original_prizes': ['Yacht', 'Vacation', 'Laptop', 'Camera', 'Chocolate', 'Money', 'Jewelry', 'Car'], 'rotated_colors': ['magenta', 'royalblue', 'silver', 'forestgreen', 'darkorange', 'yellow', 'lime', 'cyan'], 'rotated_boundaries': [0.0, 30.0, 60.0, 105.0, 150.0, 210.0, 285.0, 330.0], 'rotated_prizes': ['Laptop', 'Camera', 'Chocolate', 'Money', 'Jewelry', 'Car', 'Yacht', 'Vacation']}
|
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>A fortune wheel has 8 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1680 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 11,098
| 0.25
|
|
[
"Watch",
"Jewelry",
"Chocolate",
"Pizza"
] |
{'angles': [20, 20, 45, 45, 20, 45, 20, 25, 60, 60], 'arrow_at': 180, 'effective_rotation': 90, 'direction': 'counterclockwise', 'original_colors': ['darkorange', 'royalblue', 'orangered', 'forestgreen', 'yellow', 'silver', 'blanchedalmond', 'lime', 'magenta', 'cyan'], 'original_boundaries': [45.0, 65.0, 85.0, 130.0, 175.0, 195.0, 240.0, 260.0, 285.0, 345.0], 'original_prizes': ['Pizza', 'Jewelry', 'Chocolate', 'Ice Cream', 'Watch', 'Yacht', 'Car', 'Vacation', 'Laptop', 'Money'], 'rotated_colors': ['magenta', 'cyan', 'darkorange', 'royalblue', 'orangered', 'forestgreen', 'yellow', 'silver', 'blanchedalmond', 'lime'], 'rotated_boundaries': [15.0, 75.0, 135.0, 155.0, 175.0, 220.0, 265.0, 285.0, 330.0, 350.0], 'rotated_prizes': ['Laptop', 'Money', 'Pizza', 'Jewelry', 'Chocolate', 'Ice Cream', 'Watch', 'Yacht', 'Car', 'Vacation']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 90 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chocolate",
"style": "rule"
}
| 11,097
| 0.125
|
|
[
"Pizza",
"Ice Cream",
"Jewelry",
"Camera"
] |
{'angles': [20, 20, 30, 45, 30, 30, 20, 60, 45, 60], 'arrow_at': 45, 'effective_rotation': -288, 'direction': 'clockwise', 'original_colors': ['darkorange', 'blanchedalmond', 'cyan', 'orangered', 'royalblue', 'silver', 'lime', 'magenta', 'yellow', 'forestgreen'], 'original_boundaries': [45.0, 65.0, 85.0, 115.0, 160.0, 190.0, 220.0, 240.0, 300.0, 345.0], 'original_prizes': ['Pizza', 'Vacation', 'Yacht', 'Camera', 'Chocolate', 'Jewelry', 'Ice Cream', 'Car', 'Money', 'Watch'], 'rotated_colors': ['cyan', 'orangered', 'royalblue', 'silver', 'lime', 'magenta', 'yellow', 'forestgreen', 'darkorange', 'blanchedalmond'], 'rotated_boundaries': [13.0, 43.0, 88.0, 118.0, 148.0, 168.0, 228.0, 273.0, 333.0, 353.0], 'rotated_prizes': ['Yacht', 'Camera', 'Chocolate', 'Jewelry', 'Ice Cream', 'Car', 'Money', 'Watch', 'Pizza', 'Vacation']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 5.2 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Camera",
"style": "rule"
}
| 10,389
| 0
|
|
[
"Chocolate",
"Camera",
"Jewelry",
"Watch"
] |
{'angles': [30, 20, 20, 20, 75, 20, 20, 20, 60, 75], 'arrow_at': 315, 'effective_rotation': 120, 'direction': 'counterclockwise', 'original_colors': ['royalblue', 'cyan', 'lime', 'yellow', 'silver', 'forestgreen', 'orangered', 'darkorange', 'blanchedalmond', 'magenta'], 'original_boundaries': [45.0, 75.0, 95.0, 115.0, 135.0, 210.0, 230.0, 250.0, 270.0, 330.0], 'original_prizes': ['Yacht', 'Camera', 'Chocolate', 'Laptop', 'Jewelry', 'Car', 'Ice Cream', 'Vacation', 'Watch', 'Pizza'], 'rotated_colors': ['darkorange', 'blanchedalmond', 'magenta', 'royalblue', 'cyan', 'lime', 'yellow', 'silver', 'forestgreen', 'orangered'], 'rotated_boundaries': [10.0, 30.0, 90.0, 165.0, 195.0, 215.0, 235.0, 255.0, 330.0, 350.0], 'rotated_prizes': ['Vacation', 'Watch', 'Pizza', 'Yacht', 'Camera', 'Chocolate', 'Laptop', 'Jewelry', 'Car', 'Ice Cream']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1560 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 10,392
| 0
|
|
[
"Money",
"Pizza",
"Laptop",
"Watch"
] |
{'angles': [75, 20, 20, 45, 20, 60, 20, 60, 20, 20], 'arrow_at': 225, 'effective_rotation': -198, 'direction': 'clockwise', 'original_colors': ['yellow', 'silver', 'forestgreen', 'blanchedalmond', 'magenta', 'orangered', 'royalblue', 'lime', 'cyan', 'darkorange'], 'original_boundaries': [45.0, 120.0, 140.0, 160.0, 205.0, 225.0, 285.0, 305.0, 365.0, 385.0], 'original_prizes': ['Chocolate', 'Ice Cream', 'Car', 'Money', 'Camera', 'Watch', 'Yacht', 'Jewelry', 'Pizza', 'Laptop'], 'rotated_colors': ['magenta', 'orangered', 'royalblue', 'lime', 'cyan', 'darkorange', 'yellow', 'silver', 'forestgreen', 'blanchedalmond'], 'rotated_boundaries': [43.0, 63.0, 123.0, 143.0, 203.0, 223.0, 243.0, 318.0, 338.0, 358.0], 'rotated_prizes': ['Camera', 'Watch', 'Yacht', 'Jewelry', 'Pizza', 'Laptop', 'Chocolate', 'Ice Cream', 'Car', 'Money']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 1.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,390
| 0.25
|
|
[
"Money",
"Ice Cream",
"Camera",
"Vacation"
] |
{'angles': [20, 75, 30, 20, 30, 30, 40, 20, 75, 20], 'arrow_at': 45, 'effective_rotation': -330, 'direction': 'clockwise', 'original_colors': ['silver', 'yellow', 'darkorange', 'cyan', 'blanchedalmond', 'royalblue', 'orangered', 'forestgreen', 'lime', 'magenta'], 'original_boundaries': [45.0, 65.0, 140.0, 170.0, 190.0, 220.0, 250.0, 290.0, 310.0, 385.0], 'original_prizes': ['Chocolate', 'Vacation', 'Ice Cream', 'Pizza', 'Yacht', 'Money', 'Laptop', 'Jewelry', 'Watch', 'Camera'], 'rotated_colors': ['silver', 'yellow', 'darkorange', 'cyan', 'blanchedalmond', 'royalblue', 'orangered', 'forestgreen', 'lime', 'magenta'], 'rotated_boundaries': [15.0, 35.0, 110.0, 140.0, 160.0, 190.0, 220.0, 260.0, 280.0, 355.0], 'rotated_prizes': ['Chocolate', 'Vacation', 'Ice Cream', 'Pizza', 'Yacht', 'Money', 'Laptop', 'Jewelry', 'Watch', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 390 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 10,388
| 0
|
|
[
"Watch",
"Vacation",
"Pizza",
"Laptop"
] |
{'angles': [20, 60, 30, 55, 30, 30, 20, 75, 20, 20], 'arrow_at': 315, 'effective_rotation': -60, 'direction': 'clockwise', 'original_colors': ['blanchedalmond', 'magenta', 'yellow', 'orangered', 'royalblue', 'darkorange', 'cyan', 'silver', 'forestgreen', 'lime'], 'original_boundaries': [45.0, 65.0, 125.0, 155.0, 210.0, 240.0, 270.0, 290.0, 365.0, 385.0], 'original_prizes': ['Jewelry', 'Camera', 'Vacation', 'Watch', 'Money', 'Laptop', 'Chocolate', 'Yacht', 'Car', 'Pizza'], 'rotated_colors': ['forestgreen', 'lime', 'blanchedalmond', 'magenta', 'yellow', 'orangered', 'royalblue', 'darkorange', 'cyan', 'silver'], 'rotated_boundaries': [65.0, 85.0, 105.0, 125.0, 185.0, 215.0, 270.0, 300.0, 330.0, 350.0], 'rotated_prizes': ['Car', 'Pizza', 'Jewelry', 'Camera', 'Vacation', 'Watch', 'Money', 'Laptop', 'Chocolate', 'Yacht']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1020 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Laptop",
"style": "rule"
}
| 10,389
| 0.875
|
|
[
"Pizza",
"Yacht",
"Money",
"Watch"
] |
{'angles': [60, 20, 20, 20, 45, 20, 75, 20, 60, 20], 'arrow_at': 90, 'effective_rotation': 225, 'direction': 'counterclockwise', 'original_colors': ['orangered', 'royalblue', 'forestgreen', 'blanchedalmond', 'lime', 'cyan', 'silver', 'darkorange', 'magenta', 'yellow'], 'original_boundaries': [45.0, 105.0, 125.0, 145.0, 165.0, 210.0, 230.0, 305.0, 325.0, 385.0], 'original_prizes': ['Chocolate', 'Car', 'Camera', 'Vacation', 'Ice Cream', 'Yacht', 'Pizza', 'Watch', 'Laptop', 'Money'], 'rotated_colors': ['blanchedalmond', 'lime', 'cyan', 'silver', 'darkorange', 'magenta', 'yellow', 'orangered', 'royalblue', 'forestgreen'], 'rotated_boundaries': [10.0, 30.0, 75.0, 95.0, 170.0, 190.0, 250.0, 270.0, 330.0, 350.0], 'rotated_prizes': ['Vacation', 'Ice Cream', 'Yacht', 'Pizza', 'Watch', 'Laptop', 'Money', 'Chocolate', 'Car', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 945 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Yacht",
"style": "rule"
}
| 11,098
| 0.125
|
|
[
"Jewelry",
"Camera",
"Yacht",
"Watch"
] |
{'angles': [20, 35, 75, 75, 30, 20, 20, 45, 20, 20], 'arrow_at': 180, 'effective_rotation': -252, 'direction': 'clockwise', 'original_colors': ['lime', 'blanchedalmond', 'orangered', 'royalblue', 'magenta', 'silver', 'darkorange', 'yellow', 'forestgreen', 'cyan'], 'original_boundaries': [45.0, 65.0, 100.0, 175.0, 250.0, 280.0, 300.0, 320.0, 365.0, 385.0], 'original_prizes': ['Vacation', 'Watch', 'Money', 'Laptop', 'Ice Cream', 'Jewelry', 'Pizza', 'Car', 'Yacht', 'Camera'], 'rotated_colors': ['royalblue', 'magenta', 'silver', 'darkorange', 'yellow', 'forestgreen', 'cyan', 'lime', 'blanchedalmond', 'orangered'], 'rotated_boundaries': [67.0, 142.0, 172.0, 192.0, 212.0, 257.0, 277.0, 297.0, 317.0, 352.0], 'rotated_prizes': ['Laptop', 'Ice Cream', 'Jewelry', 'Pizza', 'Car', 'Yacht', 'Camera', 'Vacation', 'Watch', 'Money']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 4.3 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Jewelry",
"style": "rule"
}
| 11,096
| 0.375
|
|
[
"Pizza",
"Chocolate",
"Ice Cream",
"Car"
] |
{'angles': [60, 20, 20, 20, 20, 45, 20, 60, 60, 35], 'arrow_at': 45, 'effective_rotation': -252, 'direction': 'clockwise', 'original_colors': ['yellow', 'forestgreen', 'royalblue', 'darkorange', 'blanchedalmond', 'lime', 'silver', 'orangered', 'cyan', 'magenta'], 'original_boundaries': [45.0, 105.0, 125.0, 145.0, 165.0, 185.0, 230.0, 250.0, 310.0, 370.0], 'original_prizes': ['Jewelry', 'Vacation', 'Yacht', 'Ice Cream', 'Laptop', 'Car', 'Pizza', 'Chocolate', 'Watch', 'Money'], 'rotated_colors': ['royalblue', 'darkorange', 'blanchedalmond', 'lime', 'silver', 'orangered', 'cyan', 'magenta', 'yellow', 'forestgreen'], 'rotated_boundaries': [17.0, 37.0, 57.0, 77.0, 122.0, 142.0, 202.0, 262.0, 297.0, 357.0], 'rotated_prizes': ['Yacht', 'Ice Cream', 'Laptop', 'Car', 'Pizza', 'Chocolate', 'Watch', 'Money', 'Jewelry', 'Vacation']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 4.3 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Ice Cream",
"style": "rule"
}
| 10,389
| 0
|
|
[
"Pizza",
"Laptop",
"Yacht",
"Vacation"
] |
{'angles': [60, 20, 60, 20, 20, 45, 75, 20, 20, 20], 'arrow_at': 90, 'effective_rotation': 30, 'direction': 'counterclockwise', 'original_colors': ['cyan', 'blanchedalmond', 'darkorange', 'lime', 'silver', 'orangered', 'magenta', 'royalblue', 'yellow', 'forestgreen'], 'original_boundaries': [45.0, 105.0, 125.0, 185.0, 205.0, 225.0, 270.0, 345.0, 365.0, 385.0], 'original_prizes': ['Pizza', 'Yacht', 'Chocolate', 'Money', 'Vacation', 'Jewelry', 'Laptop', 'Camera', 'Car', 'Watch'], 'rotated_colors': ['royalblue', 'yellow', 'forestgreen', 'cyan', 'blanchedalmond', 'darkorange', 'lime', 'silver', 'orangered', 'magenta'], 'rotated_boundaries': [15.0, 35.0, 55.0, 75.0, 135.0, 155.0, 215.0, 235.0, 255.0, 300.0], 'rotated_prizes': ['Camera', 'Car', 'Watch', 'Pizza', 'Yacht', 'Chocolate', 'Money', 'Vacation', 'Jewelry', 'Laptop']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 1470 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 11,099
| 0.25
|
|
[
"Chocolate",
"Watch",
"Car",
"Money"
] |
{'angles': [20, 20, 20, 20, 20, 75, 20, 60, 45, 60], 'arrow_at': 135, 'effective_rotation': 345, 'direction': 'counterclockwise', 'original_colors': ['blanchedalmond', 'darkorange', 'forestgreen', 'cyan', 'lime', 'silver', 'magenta', 'yellow', 'orangered', 'royalblue'], 'original_boundaries': [45.0, 65.0, 85.0, 105.0, 125.0, 145.0, 220.0, 240.0, 300.0, 345.0], 'original_prizes': ['Jewelry', 'Pizza', 'Chocolate', 'Watch', 'Ice Cream', 'Money', 'Vacation', 'Laptop', 'Car', 'Camera'], 'rotated_colors': ['blanchedalmond', 'darkorange', 'forestgreen', 'cyan', 'lime', 'silver', 'magenta', 'yellow', 'orangered', 'royalblue'], 'rotated_boundaries': [30.0, 50.0, 70.0, 90.0, 110.0, 130.0, 205.0, 225.0, 285.0, 330.0], 'rotated_prizes': ['Jewelry', 'Pizza', 'Chocolate', 'Watch', 'Ice Cream', 'Money', 'Vacation', 'Laptop', 'Car', 'Camera']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it rotates 345 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 10,391
| 0.25
|
|
[
"Watch",
"Chocolate",
"Vacation",
"Camera"
] |
{'angles': [20, 20, 45, 30, 30, 75, 20, 60, 30, 30], 'arrow_at': 270, 'effective_rotation': -162, 'direction': 'clockwise', 'original_colors': ['lime', 'silver', 'forestgreen', 'magenta', 'orangered', 'darkorange', 'royalblue', 'cyan', 'yellow', 'blanchedalmond'], 'original_boundaries': [45.0, 65.0, 85.0, 130.0, 160.0, 190.0, 265.0, 285.0, 345.0, 375.0], 'original_prizes': ['Chocolate', 'Camera', 'Vacation', 'Jewelry', 'Pizza', 'Watch', 'Ice Cream', 'Car', 'Laptop', 'Yacht'], 'rotated_colors': ['royalblue', 'cyan', 'yellow', 'blanchedalmond', 'lime', 'silver', 'forestgreen', 'magenta', 'orangered', 'darkorange'], 'rotated_boundaries': [67.0, 87.0, 147.0, 177.0, 207.0, 227.0, 247.0, 292.0, 322.0, 352.0], 'rotated_prizes': ['Ice Cream', 'Car', 'Laptop', 'Yacht', 'Chocolate', 'Camera', 'Vacation', 'Jewelry', 'Pizza', 'Watch']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 5.55 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Vacation",
"style": "rule"
}
| 11,097
| 0.25
|
|
[
"Pizza",
"Vacation",
"Car",
"Chocolate"
] |
{'angles': [20, 60, 20, 50, 60, 20, 30, 20, 20, 60], 'arrow_at': 45, 'effective_rotation': -120, 'direction': 'clockwise', 'original_colors': ['royalblue', 'blanchedalmond', 'darkorange', 'orangered', 'silver', 'forestgreen', 'yellow', 'lime', 'cyan', 'magenta'], 'original_boundaries': [45.0, 65.0, 125.0, 145.0, 195.0, 255.0, 275.0, 305.0, 325.0, 345.0], 'original_prizes': ['Camera', 'Ice Cream', 'Vacation', 'Chocolate', 'Laptop', 'Money', 'Car', 'Pizza', 'Jewelry', 'Yacht'], 'rotated_colors': ['forestgreen', 'yellow', 'lime', 'cyan', 'magenta', 'royalblue', 'blanchedalmond', 'darkorange', 'orangered', 'silver'], 'rotated_boundaries': [15.0, 35.0, 65.0, 85.0, 105.0, 165.0, 185.0, 245.0, 265.0, 315.0], 'rotated_prizes': ['Money', 'Car', 'Pizza', 'Jewelry', 'Yacht', 'Camera', 'Ice Cream', 'Vacation', 'Chocolate', 'Laptop']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it rotates 1680 degrees before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Car",
"style": "rule"
}
| 10,389
| 0
|
|
[
"Pizza",
"Camera",
"Car",
"Ice Cream"
] |
{'angles': [20, 20, 75, 75, 20, 20, 60, 30, 20, 20], 'arrow_at': 315, 'effective_rotation': -198, 'direction': 'clockwise', 'original_colors': ['royalblue', 'blanchedalmond', 'yellow', 'orangered', 'magenta', 'lime', 'silver', 'darkorange', 'forestgreen', 'cyan'], 'original_boundaries': [45.0, 65.0, 85.0, 160.0, 235.0, 255.0, 275.0, 335.0, 365.0, 385.0], 'original_prizes': ['Money', 'Yacht', 'Pizza', 'Ice Cream', 'Watch', 'Chocolate', 'Laptop', 'Jewelry', 'Camera', 'Car'], 'rotated_colors': ['magenta', 'lime', 'silver', 'darkorange', 'forestgreen', 'cyan', 'royalblue', 'blanchedalmond', 'yellow', 'orangered'], 'rotated_boundaries': [73.0, 93.0, 113.0, 173.0, 203.0, 223.0, 243.0, 263.0, 283.0, 358.0], 'rotated_prizes': ['Watch', 'Chocolate', 'Laptop', 'Jewelry', 'Camera', 'Car', 'Money', 'Yacht', 'Pizza', 'Ice Cream']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel clockwise and it makes 2.45 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Pizza",
"style": "rule"
}
| 10,390
| 0.125
|
|
[
"Money",
"Jewelry",
"Pizza",
"Camera"
] |
{'angles': [30, 20, 20, 35, 60, 20, 75, 20, 20, 60], 'arrow_at': 45, 'effective_rotation': 324, 'direction': 'counterclockwise', 'original_colors': ['cyan', 'magenta', 'royalblue', 'silver', 'forestgreen', 'orangered', 'yellow', 'blanchedalmond', 'darkorange', 'lime'], 'original_boundaries': [45.0, 75.0, 95.0, 115.0, 150.0, 210.0, 230.0, 305.0, 325.0, 345.0], 'original_prizes': ['Jewelry', 'Money', 'Yacht', 'Vacation', 'Camera', 'Pizza', 'Laptop', 'Watch', 'Ice Cream', 'Chocolate'], 'rotated_colors': ['cyan', 'magenta', 'royalblue', 'silver', 'forestgreen', 'orangered', 'yellow', 'blanchedalmond', 'darkorange', 'lime'], 'rotated_boundaries': [9.0, 39.0, 59.0, 79.0, 114.0, 174.0, 194.0, 269.0, 289.0, 309.0], 'rotated_prizes': ['Jewelry', 'Money', 'Yacht', 'Vacation', 'Camera', 'Pizza', 'Laptop', 'Watch', 'Ice Cream', 'Chocolate']}
|
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>A fortune wheel has 10 segments of different colour. The initial position of the wheel is shown in the figure. Each segment is associated with a prize as shown in the embedded text within the segment. The axis of rotation of the wheel passes through its center and is perpendicular to the surface of the wheel. You spin the wheel counterclockwise and it makes 4.9 full rotations before stopping. You are going to win the prize for the segment that now falls in front of the brown arrow. What is your prize?",
"role": "user"
}
] |
math
|
{
"ground_truth": "Money",
"style": "rule"
}
| 10,392
| 0.75
|
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