problem
stringlengths 20
3.09k
| answer
stringlengths 1
270
| tokenized_prompt
stringlengths 70
3.14k
| responses
listlengths 64
64
| rewards
listlengths 64
64
| mean_reward
float64 0
1
|
|---|---|---|---|---|---|
"[asy]\ndraw((-1,-1)--(1,-1)--(1,1)--(-1,1)--cycle, black+linewidth(.75));\ndraw((0,-1)--(0,1), blac(...TRUNCATED)
|
2\sqrt{3}-2
| "<|im_start|>user\n[asy]\ndraw((-1,-1)--(1,-1)--(1,1)--(-1,1)--cycle, black+linewidth(.75));\ndraw(((...TRUNCATED)
| ["We are given a square clock face, with a dartboard painted using \"hour positions\" as boundaries.(...TRUNCATED)
| [0.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0,0.0,1.0,1.0,0.0,0.0,1.0,1.0,0.0(...TRUNCATED)
| 0.296875
|
"In an equilateral triangle \\(ABC\\) with side length 1, points \\(D\\) and \\(E\\) are taken on si(...TRUNCATED)
|
2\sqrt{3}-3
| "<|im_start|>user\nIn an equilateral triangle \\(ABC\\) with side length 1, points \\(D\\) and \\(E\(...TRUNCATED)
| ["We are given an **equilateral triangle** $ABC$ with side length 1. Points $D$ and $E$ lie on sides(...TRUNCATED)
| [1.0,0.0,1.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,0.0,1.0(...TRUNCATED)
| 0.453125
|
"A cup is filled with a $16 \\%$ salt solution. There are three iron balls: large, medium, and small(...TRUNCATED)
|
10.7
| "<|im_start|>user\nA cup is filled with a $16 \\%$ salt solution. There are three iron balls: large,(...TRUNCATED)
| ["We are given a problem involving a salt solution and three iron balls of different sizes, with a v(...TRUNCATED)
| [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED)
| 0.03125
|
"On the sides \\(AB, BC, CD,\\) and \\(DA\\) of parallelogram \\(ABCD\\), points \\(M, N, K,\\) and (...TRUNCATED)
|
\frac{6}{13}
| "<|im_start|>user\nOn the sides \\(AB, BC, CD,\\) and \\(DA\\) of parallelogram \\(ABCD\\), points \(...TRUNCATED)
| ["We are given a parallelogram $ABCD$ with area 1. Points are taken on the sides as follows:\n\n- On(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED)
| 0.90625
|
"A flea jumps along the number line, where the length of each jump cannot be less than $n$. It start(...TRUNCATED)
|
1006
| "<|im_start|>user\nA flea jumps along the number line, where the length of each jump cannot be less (...TRUNCATED)
| ["We are given a flea that jumps along the number line, starting at 0, and wants to **visit all inte(...TRUNCATED)
| [1.0,1.0,0.0,1.0,0.0,0.0,1.0,0.0,1.0,1.0,0.0,1.0,0.0,1.0,1.0,0.0,1.0,1.0,0.0,1.0,1.0,0.0,0.0,1.0,1.0(...TRUNCATED)
| 0.640625
|
"In a certain kingdom, there were 32 knights. Some of them were vassals to others (a vassal can only(...TRUNCATED)
|
7
| "<|im_start|>user\nIn a certain kingdom, there were 32 knights. Some of them were vassals to others (...TRUNCATED)
| ["We are given a kingdom with **32 knights**, and a hierarchical structure where:\n\n- A **vassal** (...TRUNCATED)
| [1.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,1.0,1.0,0.0,0.0,0.0,1.0,1.0,0.0,1.0,0.0,1.0,0.0,1.0,1.0(...TRUNCATED)
| 0.546875
|
"A diagonal of a regular 2006-gon is called odd if its endpoints divide the boundary into two parts,(...TRUNCATED)
|
1003
| "<|im_start|>user\nA diagonal of a regular 2006-gon is called odd if its endpoints divide the bounda(...TRUNCATED)
| ["We are given a **regular 2006-gon**, and we are to consider **diagonals** that are called **odd** (...TRUNCATED)
| [1.0,1.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED)
| 0.5625
|
"A triangular array of numbers has a first row consisting of the odd integers $1,3,5,\\ldots,99$ in (...TRUNCATED)
|
17
| "<|im_start|>user\nA triangular array of numbers has a first row consisting of the odd integers $1,3(...TRUNCATED)
| ["We are given a triangular array of numbers where:\n\n- The first row consists of the odd integers (...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0(...TRUNCATED)
| 0.875
|
"Sasha and Masha each picked a natural number and communicated them to Vasya. Vasya wrote the sum of(...TRUNCATED)
|
1001
| "<|im_start|>user\nSasha and Masha each picked a natural number and communicated them to Vasya. Vasy(...TRUNCATED)
| ["We are given a logic puzzle involving Sasha and Masha picking natural numbers, and Vasya showing o(...TRUNCATED)
| [1.0,0.0,1.0,1.0,0.0,0.0,1.0,1.0,0.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,0.0(...TRUNCATED)
| 0.75
|
"A square $EFGH$ is inscribed in the region bounded by the parabola $y = x^2 - 6x + 5$ and the $x$-a(...TRUNCATED)
|
24 - 8\sqrt{5}
| "<|im_start|>user\nA square $EFGH$ is inscribed in the region bounded by the parabola $y = x^2 - 6x (...TRUNCATED)
| ["We are given a square $ EFGH $ inscribed in the region bounded by the parabola $ y = x^2 - 6x + 5 (...TRUNCATED)
| [1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED)
| 0.984375
|
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