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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