problem string | answer string | responses sequence | tokenized_prompt string | rewards sequence | mean_reward float64 |
|---|---|---|---|---|---|
"Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations: \n\\[\\l(...TRUNCATED) | 33 | ["<description>\nUse the change‐of‐base formula to rewrite logarithms with different bases in te(...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Let $O(0,0), A(\\tfrac{1}{2}, 0),$ and $B(0, \\tfrac{\\sqrt{3}}{2})$ be points in the coordinate pl(...TRUNCATED) | 23 | ["<description>\nThe locus of points equidistant from two fixed points (the perpendicular bisector) (...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers(...TRUNCATED) | 116 | ["<description>\nUse the hypergeometric distribution to compute probabilities of drawing a specific (...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take tur(...TRUNCATED) | 809 | ["<description>\nModel the game as a finite state machine where each state corresponds to the curren(...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ a(...TRUNCATED) | 197 | ["<description>\nWhen multiple congruent circles are tangent to a straight line, the distance from t(...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$. Find the number of intersection(...TRUNCATED) | 385 | ["<description>\nWhen a function is defined as the absolute value of an expression, it splits into p(...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Each vertex of a regular octagon is independently colored either red or blue with equal probability(...TRUNCATED) | 371 | ["<description>\nModel a random coloring of vertices as a product of independent Bernoulli trials, w(...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and \\[a^(...TRUNCATED) | 601 | ["<description>\nWhen the sum of variables is fixed, any symmetric sum of their pairwise products ca(...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"There exist real numbers $x$ and $y$, both greater than 1, such that $\\log_x\\left(y^x\\right)=\\l(...TRUNCATED) | 25 | ["<description>\nWhen an equation involves logarithms of the same base, apply the inverse relationsh(...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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"Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positi(...TRUNCATED) | 55 | ["<description>\nWhen a problem involves a finite list of sets and a “maximal” condition, count (...TRUNCATED) | "<|im_start|>user\nYou are an expert problem-solving assistant tasked with analyzing and solving a g(...TRUNCATED) | [
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] | 0 |
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