data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "a^{-2}+b^{-2}",
"style": "rule"
} | {
"index": 1082,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"index": 7907,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Find the value of \\( \\cos \\frac{\\pi}{11} + \\cos \\frac{3\\pi}{11} + \\cos \\frac{5\\pi}{11} + \\cos \\frac{7\\pi}{11} + \\cos \\frac{9\\pi}{11} \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 1900,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "A $37$-gon $Q_1$ is drawn in the Cartesian plane, and the sum of the $x$-coordinates of its $37$ vertices equals $185$. The midpoints of the sides of $Q_1$ form a second $37$-gon, $Q_2$. Then, the midpoints of the sides of $Q_2$ form a third $37$-gon, $Q_3$. Find the sum of the $x$-coordinates of ... | math | {
"ground_truth": "185",
"style": "rule"
} | {
"index": 6027,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{5}{12}",
"style": "rule"
} | {
"index": 4164,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "For real numbers $x$, let \\[f(x) = \\left\\{\n\\begin{array}{cl}\nx+2 &\\text{ if }x>3, \\\\\n2x+a &\\text{ if }x\\le 3.\n\\end{array}\n\\right.\\]What must the value of $a$ be to make the piecewise function continuous (which means that its graph can be drawn without lifting your pencil from the ... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"index": 9134,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "28077",
"style": "rule"
} | {
"index": 1508,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1626",
"style": "rule"
} | {
"index": 1473,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "On the Island of Misfortune, there are knights, who always tell the truth, and liars, who always lie. One day, $n$ islanders gathered in a room.\n\nThe first person said: \"Exactly 1 percent of the people present in this room are liars.\"\n\nThe second person said: \"Exactly 2 percent of the peopl... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"index": 1601,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "4571",
"style": "rule"
} | {
"index": 5987,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"index": 4371,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 3187,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1089",
"style": "rule"
} | {
"index": 833,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "168",
"style": "rule"
} | {
"index": 5821,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"index": 2391,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "12\\pi",
"style": "rule"
} | {
"index": 359,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{8}{5}",
"style": "rule"
} | {
"index": 1902,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 3713,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 290,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"index": 12254,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"index": 10787,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "For positive integers $n,$ let $\\tau (n)$ denote the number of positive integer divisors of $n,$ including 1 and $n.$ Define $S(n)$ by $S(n)=\\tau(1)+ \\tau(2) + \\cdots + \\tau(n).$ Let $a$ denote the number of positive integers $n \\leq 3000$ with $S(n)$ odd, and let $b$ denote the number of po... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"index": 655,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 1522,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "128",
"style": "rule"
} | {
"index": 78,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"index": 1378,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "When someone tries to withdraw money from an ATM with a forgotten last digit of the password, calculate the probability that they will press the correct digit in no more than 2 attempts.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{1}{5}",
"style": "rule"
} | {
"index": 1814,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "500",
"style": "rule"
} | {
"index": 75,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Find $n$ such that $2^6 \\cdot 3^3 \\cdot n = 10!$.",
"role": "user"
}
] | math | {
"ground_truth": "2100",
"style": "rule"
} | {
"index": 11524,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"index": 1550,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "3\\sqrt{5} - 5",
"style": "rule"
} | {
"index": 4709,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1641",
"style": "rule"
} | {
"index": 901,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "52",
"style": "rule"
} | {
"index": 12769,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "83\\%",
"style": "rule"
} | {
"index": 2621,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 1881,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "What is the slope of the line passing through $(-3,5)$ and $(2,-5)$?",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"index": 3640,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "The sum of the first 1000 terms of a geometric sequence is 300. The sum of the first 2000 terms is 570. Find the sum of the first 3000 terms.",
"role": "user"
}
] | math | {
"ground_truth": "813",
"style": "rule"
} | {
"index": 2423,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "-\\frac{8}{3}",
"style": "rule"
} | {
"index": 7135,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"index": 594,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{8}{3}",
"style": "rule"
} | {
"index": 10407,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "If the sum of the coefficients of each term in the expansion of $(x- \\frac {4}{x})^{n}$ is $81$, then the constant term in the expansion is ________.",
"role": "user"
}
] | math | {
"ground_truth": "96",
"style": "rule"
} | {
"index": 11549,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "The length of edge PQ of a tetrahedron PQRS measures 51 units, and the lengths of the other edges are 12, 19, 24, 33, and 42 units. Determine the length of edge RS.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"index": 2332,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 1068,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "555",
"style": "rule"
} | {
"index": 1998,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "84",
"style": "rule"
} | {
"index": 4538,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 737,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "148",
"style": "rule"
} | {
"index": 1141,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "The café has enough chairs to seat $312_8$ people. If $3$ people are supposed to sit at one table, how many tables does the café have?",
"role": "user"
}
] | math | {
"ground_truth": "67",
"style": "rule"
} | {
"index": 1166,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": 1699,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "38",
"style": "rule"
} | {
"index": 954,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"index": 4386,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1/2",
"style": "rule"
} | {
"index": 922,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 150,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Let $ABC$ be a triangle with area $5$ and $BC = 10.$ Let $E$ and $F$ be the midpoints of sides $AC$ and $AB$ respectively, and let $BE$ and $CF$ intersect at $G.$ Suppose that quadrilateral $AEGF$ can be inscribed in a circle. Determine the value of $AB^2+AC^2.$ *Proposed by... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"index": 2164,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"index": 12824,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 254,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "An equilateral triangle is inscribed in a circle. A smaller equilateral triangle has one vertex coinciding with a vertex of the larger triangle and another vertex on the midpoint of a side of the larger triangle. What percent of the area of the larger triangle is the area of the smaller triangle?"... | math | {
"ground_truth": "25\\%",
"style": "rule"
} | {
"index": 239,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 8269,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{6007}{2}",
"style": "rule"
} | {
"index": 787,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"index": 1682,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{25}{32}",
"style": "rule"
} | {
"index": 1052,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "192",
"style": "rule"
} | {
"index": 7326,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "A palindrome between $1000$ and $10000$ is chosen at random. What is the probability that it is divisible by $7$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{5}",
"style": "rule"
} | {
"index": 11247,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "- \\frac {2}{3}",
"style": "rule"
} | {
"index": 11216,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 3980,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 11948,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "a = 2",
"style": "rule"
} | {
"index": 530,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "How many positive whole numbers have cube roots that are less than $8$?",
"role": "user"
}
] | math | {
"ground_truth": "511",
"style": "rule"
} | {
"index": 1344,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "108",
"style": "rule"
} | {
"index": 3600,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "231",
"style": "rule"
} | {
"index": 333,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"index": 1608,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "9\\sqrt{3}",
"style": "rule"
} | {
"index": 682,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "How many numbers should there be in a lottery for the probability of getting an ambo to be $\\frac{5}{473}$, when drawing five numbers?",
"role": "user"
}
] | math | {
"ground_truth": "44",
"style": "rule"
} | {
"index": 449,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1000",
"style": "rule"
} | {
"index": 1060,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 1496,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Let $S = \\{1, 22, 333, \\dots , 999999999\\}$ . For how many pairs of integers $(a, b)$ where $a, b \\in S$ and $a < b$ is it the case that $a$ divides $b$ ?",
"role": "user"
}
] | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 2281,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"index": 803,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "881",
"style": "rule"
} | {
"index": 1013,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Consider an isosceles triangle $T$ with base 10 and height 12. Define a sequence $\\omega_{1}, \\omega_{2}, \\ldots$ of circles such that $\\omega_{1}$ is the incircle of $T$ and $\\omega_{i+1}$ is tangent to $\\omega_{i}$ and both legs of the isosceles triangle for $i>1$. Find the total area cont... | math | {
"ground_truth": "\\frac{180 \\pi}{13}",
"style": "rule"
} | {
"index": 2489,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "Given the function $f\\left( x \\right)=\\frac{{{x}^{2}}}{1+{{x}^{2}}}$.\n\n(1) Find the values of $f\\left( 2 \\right)+f\\left( \\frac{1}{2} \\right),f\\left( 3 \\right)+f\\left( \\frac{1}{3} \\right),f\\left( 4 \\right)+f\\left( \\frac{1}{4} \\right)$ and conjecture a general conclusion (proof i... | math | {
"ground_truth": "4032",
"style": "rule"
} | {
"index": 7704,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "x^6-5832",
"style": "rule"
} | {
"index": 8273,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "0.488",
"style": "rule"
} | {
"index": 1605,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 44,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "8+4i",
"style": "rule"
} | {
"index": 11592,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "In an isosceles trapezoid \\(ABCD\\) (\\(BC \\parallel AD\\)), the angles \\(ABD\\) and \\(DBC\\) are \\(135^{\\circ}\\) and \\(15^{\\circ}\\) respectively, and \\(BD = \\sqrt{6}\\). Find the perimeter of the trapezoid.",
"role": "user"
}
] | math | {
"ground_truth": "9 - \\sqrt{3}",
"style": "rule"
} | {
"index": 734,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "2019!",
"style": "rule"
} | {
"index": 1791,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"index": 2484,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "91",
"style": "rule"
} | {
"index": 4025,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"index": 641,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "-\\frac{1}{4}",
"style": "rule"
} | {
"index": 2383,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "4:5",
"style": "rule"
} | {
"index": 1189,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"index": 1716,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Apartment rentals in Fairview run $\\$$0.90 per square foot. Jillian has determined that she can afford $\\$$630 per month for rent. What is the largest apartment, in square feet, she should consider at the given rate?",
"role": "user"
}
] | math | {
"ground_truth": "700",
"style": "rule"
} | {
"index": 2253,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 1139,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"index": 586,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "17\\frac{7}{9}",
"style": "rule"
} | {
"index": 1990,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "14k",
"style": "rule"
} | {
"index": 6861,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "What is the value of $\\sqrt{3! \\cdot 3!}$ expressed as a positive integer?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 7425,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\dfrac13",
"style": "rule"
} | {
"index": 6550,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Regular polygons $I C A O, V E N T I$, and $A L B E D O$ lie on a plane. Given that $I N=1$, compute the number of possible values of $O N$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 427,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "41.25",
"style": "rule"
} | {
"index": 928,
"no_hint_prompt": false,
"split": "train"
} |
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