prompt_idx int64 | prompts string | correct_format int64 | student_responses string |
|---|---|---|---|
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
The operation \(\otimes\) is defined for all nonzero numbers by \(a \otimes b = \frac{a^2}{b}\). We need to determine \([(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]\).
First, compute \((1 \otimes 2)\):
\[
1 \otimes 2 = \frac{1^2}{2} = \frac{1}{2}
\]
Next, use this result to... |
1 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
Doug constructs a square window using 8 panes of glass, each with a height-to-width ratio of 5:2, and borders that are 2 inches wide. To determine the side length of the square window, we need to consider the arrangement of the panes and the contributions of the borders.
1. **Pane Di... |
1 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
Doug constructs a square window using 8 panes of glass, each with a height-to-width ratio of 5:2, and borders that are 2 inches wide. To determine the side length of the square window, we need to consider the arrangement of the panes and the contributions of the borders.
1. **Pane Di... |
1 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
Doug constructs a square window using 8 panes of glass, each with a height-to-width ratio of 5:2, and borders that are 2 inches wide. To determine the side length of the square window, we need to consider the arrangement of the panes and the contributions of the borders.
1. **Pane Di... |
1 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
Doug constructs a square window using 8 panes of glass, each with a height-to-width ratio of 5:2, and borders that are 2 inches wide. To determine the side length of the square window, we need to consider the arrangement of the panes and the contributions of the borders.
1. **Pane Di... |
1 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
Doug constructs a square window using 8 panes of glass, each with a height-to-width ratio of 5:2, and borders that are 2 inches wide. To determine the side length of the square window, we need to consider the arrangement of the panes and the contributions of the borders.
1. **Pane Di... |
1 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | 1 | _thought|>
<|begin_of_solution|>
Doug constructs a square window using 8 panes of glass, each with a height-to-width ratio of 5:2, and borders that are 2 inches wide. To determine the side length of the square window, we need to consider the arrangement of the panes and the contributions of the borders.
1. **Pane Di... |
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