Dataset Viewer
problem
string | answer
string | responses
sequence | 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 | ["To solve the given problem, we begin by analyzing the three equations provided:\n\n1. $\\log_2\\le(...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 | ["To solve this problem, we need to determine the point $ C $ on the segment $ \\overline{AB} $ such(...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 | ["To solve the problem, we need to determine the probability of the grand prize being won given that(...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 | ["To solve the problem, we need to determine the number of positive integers $ n \\leq 2024 $ for wh(...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 | ["To solve the problem, we need to determine the inradius of triangle $ABC$ given that eight circles(...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 | ["To determine the number of intersections of the graphs of the functions\n\n$$\ny = 4 g(f(\\sin(2\\(...TRUNCATED) | [
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"Each vertex of a regular octagon is independently colored either red or blue with equal probability(...TRUNCATED) | 371 | ["To solve this problem, we need to determine the probability that a regular octagon can be rotated (...TRUNCATED) | [
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"Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and \\[a^(...TRUNCATED) | 601 | ["To solve the problem of finding the number of triples of nonnegative integers $(a, b, c)$ satisfyi(...TRUNCATED) | [
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"There exist real numbers $x$ and $y$, both greater than 1, such that $\\log_x\\left(y^x\\right)=\\l(...TRUNCATED) | 25 | ["To solve the problem, we are given two logarithmic equations:\n\n$$\n\\log_x(y^x) = \\log_y(x^{4y}(...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 | ["Okay, let's try to tackle this problem. So, Alice picks a set A of positive integers. Then Bob lis(...TRUNCATED) | [
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