prompt listlengths 2 2 | data_source stringclasses 1
value | ability stringclasses 1
value | reward_model dict | extra_info dict | system stringclasses 1
value |
|---|---|---|---|---|---|
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Given eight distinguishable rings, let $n$ be the number of possible five-ring arrangements on the four fin... | contest_math | math | {
"style": "rule",
"ground_truth": "376"
} | {
"index": 0,
"source": "aime",
"d7": 2,
"d32": 1,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "3fad0208df69"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $S$ be the set of all ordered triple of integers $(a_1,a_2,a_3)$ with $1 \\le a_1,a_2,a_3 \\le 10$ . Ea... | contest_math | math | {
"style": "rule",
"ground_truth": "494"
} | {
"index": 1,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "165912a9f994"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 2022 equally spaced points on a circular track $\\gamma$ of circumference 2022. The points are la... | contest_math | math | {
"style": "rule",
"ground_truth": "2 n^{2}-2 n+2"
} | {
"index": 2,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "4afd524d275a"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The L shape made by adjoining three congruent squares can be subdivided into four smaller L shapes. Each of... | contest_math | math | {
"style": "rule",
"ground_truth": "4^{2004}+2^{2004}"
} | {
"index": 3,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "d41876078d03"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "12. (GDR 3) Let $R$ be a set of exactly 6 elements. A set $F$ of subsets of $R$ is called an $S$-family ove... | contest_math | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 4,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "f28455155b08"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The following analog clock has two hands that can move independently of each other.\n\nInitially, both hand... | contest_math | math | {
"style": "rule",
"ground_truth": "608"
} | {
"index": 5,
"source": "amc_aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "9976ec8ebe3c"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "An $11 \\times 11$ grid is labeled with consecutive rows $0,1,2, \\ldots, 10$ and columns $0,1,2, \\ldots, ... | contest_math | math | {
"style": "rule",
"ground_truth": "2^{1100}"
} | {
"index": 6,
"source": "omnimath",
"d7": 15,
"d32": 11,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "717d07d23d85"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Point $P_{}$ is located inside triangle $ABC$ so that angles $PAB, PBC,$ and $PCA$ are all congruent. The ... | contest_math | math | {
"style": "rule",
"ground_truth": "463"
} | {
"index": 7,
"source": "aime",
"d7": 0,
"d32": 0,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "1c694e1d317f"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A teacher was leading a class of four perfectly logical students. The teacher chose a set $S$ of four integ... | contest_math | math | {
"style": "rule",
"ground_truth": "258"
} | {
"index": 8,
"source": "aime",
"d7": 16,
"d32": 14,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "c20d3753399b"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "We call an even positive integer $n$ nice if the set $\\{1, 2, \\dots, n\\}$ can be partitioned into $\\fra... | contest_math | math | {
"style": "rule",
"ground_truth": "2^{2022} - 1"
} | {
"index": 9,
"source": "omnimath",
"d7": 16,
"d32": 15,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "f23c5ffd36bd"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For a real number $a$ , let $\\lfloor a \\rfloor$ denote the greatest integer less than or equal to $a$ . L... | contest_math | math | {
"style": "rule",
"ground_truth": "132"
} | {
"index": 10,
"source": "aime",
"d7": 16,
"d32": 13,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "a5d6bee54bb1"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In quadrilateral $ABCD$ , $\\angle{BAD}\\cong\\angle{ADC}$ and $\\angle{ABD}\\cong\\angle{BCD}$ , $AB = 8$ ... | contest_math | math | {
"style": "rule",
"ground_truth": "69"
} | {
"index": 11,
"source": "aime",
"d7": 16,
"d32": 15,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "98e8c4f47675"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are nonzero integers $a$ , $b$ , $r$ , and $s$ such that the complex number $r+si$ is a zero of the p... | contest_math | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 12,
"source": "aime",
"d7": 10,
"d32": 1,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "86dcbf65552a"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "25. N3 (GBR) Let \\( a_{1}=11^{11}, a_{2}=12^{12}, a_{3}=13^{13} \\), and \n\\[ a_{n}=\\left|a_{n-1}-a_{n-... | contest_math | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 13,
"source": "olympiads_ref",
"d7": 12,
"d32": 15,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "4be5da757320"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Consider coins with positive real denominations not exceeding 1. Find the smallest $C>0$ such that the foll... | contest_math | math | {
"style": "rule",
"ground_truth": "\\frac{50}{51}"
} | {
"index": 14,
"source": "olympiads_ref",
"d7": 12,
"d32": 12,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "686a3a96ad93"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $F(z)=\\frac{z+i}{z-i}$ for all complex numbers $z\\not= i$ , and let $z_n=F(z_{n-1})$ for all positive... | contest_math | math | {
"style": "rule",
"ground_truth": "275"
} | {
"index": 15,
"source": "aime",
"d7": 4,
"d32": 1,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "feb76c421117"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Given that $x, y,$ and $z$ are real numbers that satisfy:\n\\begin{align*} x &= \\sqrt{y^2-\\frac{1}{16}}+\... | contest_math | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 16,
"source": "amc_aime",
"d7": 6,
"d32": 9,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "7a91357074d4"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "You may assign a color to each of the numbers from 1 to 2014, with exactly half being red and the other hal... | contest_math | math | {
"style": "rule",
"ground_truth": "4023"
} | {
"index": 17,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "c495a478631b"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Circles $\\mathcal{C}_{1}$ and $\\mathcal{C}_{2}$ intersect at two points, one of which is $(9,6)$ , and th... | contest_math | math | {
"style": "rule",
"ground_truth": "282"
} | {
"index": 18,
"source": "aime",
"d7": 6,
"d32": 2,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "504efe647887"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Jacob starts with some complex number $x_{0}$ other than 0 or 1. He repeatedly flips a fair coin. If the $n... | contest_math | math | {
"style": "rule",
"ground_truth": "1, \\frac{2^{2011}+1}{3 \\cdot 2^{2011}}"
} | {
"index": 19,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "83a121a2c54a"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Two players, Blake and Ruby, play the following game on an infinite grid of unit squares, all initially col... | contest_math | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 20,
"source": "olympiads_ref",
"d7": 0,
"d32": 2,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "600e4d19c57d"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In convex quadrilateral $ABCD, \\angle A \\cong \\angle C, AB = CD = 180,$ and $AD \\neq BC.$ The perimeter... | contest_math | math | {
"style": "rule",
"ground_truth": "777"
} | {
"index": 21,
"source": "aime",
"d7": 1,
"d32": 1,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "24a649fb9b26"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $\\Delta ABC$ be an acute triangle with circumcenter $O$ and centroid $G$ . Let $X$ be the intersection... | contest_math | math | {
"style": "rule",
"ground_truth": "592"
} | {
"index": 22,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "a89c53e0bb3a"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "What is the largest positive integer that is not the sum of a positive integral multiple of 42 and a positi... | contest_math | math | {
"style": "rule",
"ground_truth": "215"
} | {
"index": 23,
"source": "aime",
"d7": 7,
"d32": 3,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "c9eee03efb71"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "On a $2023 \\times 2023$ board, some squares contain a beetle, with at most one beetle per square. After on... | contest_math | math | {
"style": "rule",
"ground_truth": "2022^{2}+1"
} | {
"index": 24,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "2bc87ff2e9d2"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a country with $n$ cities, all direct airlines are two-way. There are $r>2014$ routes between pairs of d... | contest_math | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"index": 25,
"source": "olympiads_ref",
"d7": 16,
"d32": 11,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "f862046dca08"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The shortest distances between an interior diagonal of a rectangular parallelepiped , $P$ , and the edges i... | contest_math | math | {
"style": "rule",
"ground_truth": "750"
} | {
"index": 26,
"source": "aime",
"d7": 2,
"d32": 0,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "69a949176eea"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Amy has divided a square up into finitely many white and red rectangles, each with sides parallel to the si... | contest_math | math | {
"style": "rule",
"ground_truth": "2.5"
} | {
"index": 27,
"source": "olympiads_ref",
"d7": 9,
"d32": 5,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "8bad8b4aecae"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Squares $ABCD$ and $EFGH$ have a common center and $\\overline{AB} || \\overline{EF}$ . The area of $ABCD$ ... | contest_math | math | {
"style": "rule",
"ground_truth": "840"
} | {
"index": 28,
"source": "aime",
"d7": 15,
"d32": 14,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "4ab029d02404"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $P(x) = x^2 - 3x - 9$ . A real number $x$ is chosen at random from the interval $5 \\le x \\le 15$ . Th... | contest_math | math | {
"style": "rule",
"ground_truth": "850"
} | {
"index": 29,
"source": "aime",
"d7": 3,
"d32": 3,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "89a6e07245ec"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the smallest number $n$ such that there exist polynomials $f_1, f_2, \\ldots , f_n$ with rational coef... | contest_math | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 30,
"source": "omnimath",
"d7": 10,
"d32": 9,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "fb55262c0ffd"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $a > 1$ and $x > 1$ satisfy $\\log_a(\\log_a(\\log_a 2) + \\log_a 24 - 128) = 128$ and $\\log_a(\\log_a... | contest_math | math | {
"style": "rule",
"ground_truth": "896"
} | {
"index": 31,
"source": "aime",
"d7": 12,
"d32": 12,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "8f61df36d004"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The sequence $(a_n)$ satisfies $a_0=0$ and $a_{n + 1} = \\frac{8}{5}a_n + \\frac{6}{5}\\sqrt{4^n - a_n^2}$ ... | contest_math | math | {
"style": "rule",
"ground_truth": "983"
} | {
"index": 32,
"source": "aime",
"d7": 5,
"d32": 5,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "dd241af51d62"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $\\overline{AB}$ be a chord of a circle $\\omega$ , and let $P$ be a point on the chord $\\overline{AB}... | contest_math | math | {
"style": "rule",
"ground_truth": "65"
} | {
"index": 33,
"source": "aime",
"d7": 16,
"d32": 8,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "b4e9d387eb87"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $n$ be an even positive integer. A sequence of $n$ real numbers is called complete if for every integer... | contest_math | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 34,
"source": "olympiads_ref",
"d7": 14,
"d32": 15,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "029ada18913e"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the least positive integer $n$ for which $2^n + 5^n - n$ is a multiple of $1000$ ."
}
] | contest_math | math | {
"style": "rule",
"ground_truth": "797"
} | {
"index": 35,
"source": "aime",
"d7": 16,
"d32": 8,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "294982b9755b"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Someone observed that $6! = 8 \\cdot 9 \\cdot 10$ . Find the largest positive integer $n^{}_{}$ for which ... | contest_math | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 36,
"source": "aime",
"d7": 13,
"d32": 14,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "393a0effb42c"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $\\overline{MN}$ be a diameter of a circle with diameter $1$ . Let $A$ and $B$ be points on one of the ... | contest_math | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 37,
"source": "aime",
"d7": 13,
"d32": 6,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "c91384b54a8e"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a mathematics competition, 300 participants take part. After the competition, some participants play che... | contest_math | math | {
"style": "rule",
"ground_truth": "200"
} | {
"index": 38,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "18c9d61a2719"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In triangle $ABC$ , $AB=\\sqrt{30}$ , $AC=\\sqrt{6}$ , and $BC=\\sqrt{15}$ . There is a point $D$ for which... | contest_math | math | {
"style": "rule",
"ground_truth": "65"
} | {
"index": 39,
"source": "aime",
"d7": 14,
"d32": 14,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "790250025ff0"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Players $A$ and $B$ play a game on a blackboard that initially contains 2020 copies of the number 1 . In ev... | contest_math | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 40,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "43813ac4d937"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A stack of $2000$ cards is labelled with the integers from $1$ to $2000,$ with different integers on differ... | contest_math | math | {
"style": "rule",
"ground_truth": "927"
} | {
"index": 41,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "982b9e60cbf5"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In an exotic country, the National Bank issues coins that can take any value in the interval $[0,1]$. Find ... | contest_math | math | {
"style": "rule",
"ground_truth": "11-\\frac{11}{1001}"
} | {
"index": 42,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "2a2adaf0714b"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find all solutions to $(m^2+n)(m + n^2)= (m - n)^3$, where m and n are non-zero integers."
}
] | contest_math | math | {
"style": "rule",
"ground_truth": "(-1,-1),(8,-10),(9,-6),(9,-21)"
} | {
"index": 43,
"source": "amc_aime",
"d7": 11,
"d32": 4,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "e7f75f88ef2c"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The numbers 1, 2, 3, 4, 5, 6, 7, and 8 are randomly written on the faces of a regular octahedron so that ea... | contest_math | math | {
"style": "rule",
"ground_truth": "85"
} | {
"index": 44,
"source": "aime",
"d7": 15,
"d32": 14,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "8f8dfc0a37ab"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For positive integers $N$ and $k$ , define $N$ to be $k$ -nice if there exists a positive integer $a$ such ... | contest_math | math | {
"style": "rule",
"ground_truth": "749"
} | {
"index": 45,
"source": "aime",
"d7": 9,
"d32": 4,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "ccd29aa66af4"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In $\\triangle ABC$ let $I$ be the center of the inscribed circle, and let the bisector of $\\angle ACB$ in... | contest_math | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 46,
"source": "aime",
"d7": 11,
"d32": 8,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "62fed3af36fd"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "100 couples are invited to a traditional Moldovan dance. The 200 people stand in a line, and then in a step... | contest_math | math | {
"style": "rule",
"ground_truth": "N-1"
} | {
"index": 47,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "d9291802c25f"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find all triples $(x,y,z)$ of positive integers such that $x \\leq y \\leq z$ and \n\\[x^3(y^3+z^3)=2012(xy... | contest_math | math | {
"style": "rule",
"ground_truth": "(2, 251, 252)"
} | {
"index": 48,
"source": "omnimath",
"d7": 6,
"d32": 7,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "97bd4c5a9ea8"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 2018 frogs in a pool and there is 1 frog on the shore. In each time-step thereafter, one random f... | contest_math | math | {
"style": "rule",
"ground_truth": "2^{2018}-1"
} | {
"index": 49,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "1e2d301fdf45"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Equilateral $\\triangle ABC$ has side length $\\sqrt{111}$ . There are four distinct triangles $AD_1E_1$ , ... | contest_math | math | {
"style": "rule",
"ground_truth": "677"
} | {
"index": 50,
"source": "aime",
"d7": 12,
"d32": 8,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "8bb865258430"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $n > 1$ be a given integer. An $n \\times n \\times n$ cube is composed of $n^3$ unit cubes. Each unit ... | contest_math | math | {
"style": "rule",
"ground_truth": "{\\frac{n(n+1)(2n+1)}{6}}"
} | {
"index": 51,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "44500d62dfd9"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $S$ be the sum of the base $10$ logarithms of all the proper divisors of $1000000$ . What is the intege... | contest_math | math | {
"style": "rule",
"ground_truth": "141"
} | {
"index": 52,
"source": "aime",
"d7": 0,
"d32": 0,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "32484dc05ee9"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the number of permutations $x_1, x_2, x_3, x_4, x_5$ of numbers $1, 2, 3, 4, 5$ such that the sum of f... | contest_math | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 53,
"source": "aime",
"d7": 11,
"d32": 0,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "49c2c9746b8e"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For positive real numbers $s$ , let $\\tau(s)$ denote the set of all obtuse triangles that have area $s$ an... | contest_math | math | {
"style": "rule",
"ground_truth": "736"
} | {
"index": 54,
"source": "aime",
"d7": 10,
"d32": 0,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "d7bb62ecd87e"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Three speed skaters have a friendly race on a skating oval. They all start from the same point and skate in... | contest_math | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 55,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "fd96e16440f3"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "8. II 2 (NET 3) ${ }^{\\mathrm{IMO} 5}$ If $a, b, c, d$ are arbitrary positive real numbers, find all possi... | contest_math | math | {
"style": "rule",
"ground_truth": "(1,2)"
} | {
"index": 56,
"source": "olympiads_ref",
"d7": 5,
"d32": 1,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "b11631c0b33e"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Square $ABCD$ is inscribed in a circle. Square $EFGH$ has vertices $E$ and $F$ on $\\overline{CD}$ and vert... | contest_math | math | {
"style": "rule",
"ground_truth": "251"
} | {
"index": 57,
"source": "aime",
"d7": 4,
"d32": 0,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "af897f45a8a6"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A right rectangular prism $P_{}$ (i.e., a rectangular parallelepiped) has sides of integral length $a, b, c... | contest_math | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 58,
"source": "aime",
"d7": 9,
"d32": 1,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "538ced5a080e"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Evaluate the sum \\begin{gather*} \\sum_{k=0}^\\infty \\left( 3 \\cdot \\frac{\\ln(4k+2)}{4k+2} - \\frac{\\... | contest_math | math | {
"style": "rule",
"ground_truth": "$(\\log 2)^2$"
} | {
"index": 59,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "baebad0a2795"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A set $S$ of natural numbers is called good, if for each element $x \\in S, x$ does not divide the sum of t... | contest_math | math | {
"style": "rule",
"ground_truth": "61"
} | {
"index": 60,
"source": "olympiads_ref",
"d7": 14,
"d32": 16,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "6c4bde948e90"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Starting with the number 0, Casey performs an infinite sequence of moves as follows: he chooses a number fr... | contest_math | math | {
"style": "rule",
"ground_truth": "\\frac{11}{2^{20}"
} | {
"index": 61,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "34e3486d1bda"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "David found four sticks of different lengths that can be used to form three non-congruent convex cyclic qua... | contest_math | math | {
"style": "rule",
"ground_truth": "59"
} | {
"index": 62,
"source": "aime",
"d7": 16,
"d32": 13,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "1acd127eec8a"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Consider the paper triangle whose vertices are $(0,0), (34,0),$ and $(16,24).$ The vertices of its midpoint... | contest_math | math | {
"style": "rule",
"ground_truth": "408"
} | {
"index": 63,
"source": "aime",
"d7": 6,
"d32": 2,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "a700ad92f328"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $O_{1}, O_{2}$ be two convex octahedron whose faces are all triangles, and $O_{1}$ is inside $O_{2}$. L... | contest_math | math | {
"style": "rule",
"ground_truth": "(A), (B), (C), (D)"
} | {
"index": 64,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "895df2b2374f"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $A,B,C$ be angles of an acute triangle with \\begin{align*} \\cos^2 A + \\cos^2 B + 2 \\sin A \\sin B \... | contest_math | math | {
"style": "rule",
"ground_truth": "222"
} | {
"index": 65,
"source": "aime",
"d7": 12,
"d32": 10,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "893afba1f9db"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let \\[P(x) = 24x^{24} + \\sum_{j = 1}^{23}(24 - j)(x^{24 - j} + x^{24 + j}).\\] Let $z_{1},z_{2},\\ldots,z... | contest_math | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 66,
"source": "amc_aime",
"d7": 15,
"d32": 12,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "f61fa270ed68"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Consider the region $A^{}_{}$ in the complex plane that consists of all points $z^{}_{}$ such that both $\\... | contest_math | math | {
"style": "rule",
"ground_truth": "572"
} | {
"index": 67,
"source": "aime",
"d7": 6,
"d32": 4,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "5948b3499f90"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $SP_1P_2P_3EP_4P_5$ be a heptagon. A frog starts jumping at vertex $S$ . From any vertex of the heptago... | contest_math | math | {
"style": "rule",
"ground_truth": "351"
} | {
"index": 68,
"source": "aime",
"d7": 14,
"d32": 2,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "7ee6812a7956"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For integers $a$ and $b$ consider the complex number \\[\\frac{\\sqrt{ab+2016}}{ab+100}-\\left(\\frac{\\sqr... | contest_math | math | {
"style": "rule",
"ground_truth": "103"
} | {
"index": 69,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "ad92f7afa2d1"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the largest possible integer $k$, such that the following statement is true: \nLet $2009$ arbitrary n... | contest_math | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 70,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "44114cfe3aeb"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For an integer $n$, let $f(n)$ denote the number of pairs $(x, y)$ of integers such that $x^{2}+x y+y^{2}=n... | contest_math | math | {
"style": "rule",
"ground_truth": "1.813759629294 \\cdot 10^{12}"
} | {
"index": 71,
"source": "omnimath",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "2b5dc5bed5b3"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Four lighthouses are located at points $A$ , $B$ , $C$ , and $D$ . The lighthouse at $A$ is $5$ kilometers ... | contest_math | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 72,
"source": "aime",
"d7": 2,
"d32": 1,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "9bb59cce0705"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the number of functions $f$ from $\\{0, 1, 2, 3, 4, 5, 6\\}$ to the integers such that $f(0) = 0$, $f(... | contest_math | math | {
"style": "rule",
"ground_truth": "185"
} | {
"index": 73,
"source": "amc_aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "80e05ac6b17d"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The Planar National Park is an undirected 3-regular planar graph (i.e., all vertices have degree 3). A visi... | contest_math | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 74,
"source": "olympiads_ref",
"d7": 12,
"d32": 7,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "0735b5e47036"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The real root of the equation $8x^3-3x^2-3x-1=0$ can be written in the form $\\frac{\\sqrt[3]{a}+\\sqrt[3]{... | contest_math | math | {
"style": "rule",
"ground_truth": "98"
} | {
"index": 75,
"source": "aime",
"d7": 1,
"d32": 0,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "b76b1cbb64be"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $\\mathcal{A}$ denote the set of all polynomials in three variables $x, y, z$ with integer coefficients... | contest_math | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 76,
"source": "omnimath",
"d7": 8,
"d32": 3,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "7afd645fabb0"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In $\\triangle ABC, AB = 3, BC = 4,$ and $CA = 5$ . Circle $\\omega$ intersects $\\overline{AB}$ at $E$ and... | contest_math | math | {
"style": "rule",
"ground_truth": "41"
} | {
"index": 77,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "7e28702b178f"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A frog is placed at the origin on the number line , and moves according to the following rule: in a given m... | contest_math | math | {
"style": "rule",
"ground_truth": "169"
} | {
"index": 78,
"source": "aime",
"d7": 13,
"d32": 10,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "042cbf910390"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Consider the points $A(0,12), B(10,9), C(8,0),$ and $D(-4,7).$ There is a unique square $S$ such that each ... | contest_math | math | {
"style": "rule",
"ground_truth": "936"
} | {
"index": 79,
"source": "aime",
"d7": 9,
"d32": 7,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "7f62b299b812"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A hexagon is inscribed in a circle. Five of the sides have length 81 and the sixth, denoted by $\\overline{... | contest_math | math | {
"style": "rule",
"ground_truth": "384"
} | {
"index": 80,
"source": "aime",
"d7": 10,
"d32": 4,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "b3bb4722d12a"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "几个世纪前，海盗船长黑板在 $M \\times N(2 \\leq M, N)$ 网格结构的岛屿上的一个单元格中埋藏了一大笔宝藏。你和你的船员已经到达了岛屿，并带来了特殊的宝藏探测器来找到藏有宝藏的单元格。对于每... | contest_math | math | {
"style": "rule",
"ground_truth": "m+n"
} | {
"index": 81,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "e40b607d70d6"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The Annual Interplanetary Mathematics Examination (AIME) is written by a committee of five Martians, five V... | contest_math | math | {
"style": "rule",
"ground_truth": "346"
} | {
"index": 82,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "3a4590b9da23"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "(Luxembourg). Let $n$ be a positive integer. Dominoes are placed on a $2 n \\times 2 n$ board in such a way... | contest_math | math | {
"style": "rule",
"ground_truth": "\\frac{n(n+1)}{2}"
} | {
"index": 83,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "2374980b75c4"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For real number $x$ let $\\lfloor x\\rfloor$ be the greatest integer less than or equal to $x$ , and define... | contest_math | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 84,
"source": "aime",
"d7": 14,
"d32": 10,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "df5c7e628250"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find all triples $(x, y, z)$ of real numbers that satisfy the system\n\n$$\n\\left\\{\\begin{array}{l}\nx+y... | contest_math | math | {
"style": "rule",
"ground_truth": "(2008,4016,-4016)"
} | {
"index": 85,
"source": "olympiads_ref",
"d7": 1,
"d32": 2,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "beaf4a71a30e"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the number of four-element subsets of $\\{1,2,3,4,\\dots, 20\\}$ with the property that two distinct e... | contest_math | math | {
"style": "rule",
"ground_truth": "210"
} | {
"index": 86,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "138a9b3e2b0b"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Ten chairs are arranged in a circle. Find the number of subsets of this set of chairs that contain at least... | contest_math | math | {
"style": "rule",
"ground_truth": "581"
} | {
"index": 87,
"source": "aime",
"d7": 16,
"d32": 15,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "94ecdfcb4c86"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For each integer $n\\geq3$ , let $f(n)$ be the number of $3$ -element subsets of the vertices of a regular ... | contest_math | math | {
"style": "rule",
"ground_truth": "245"
} | {
"index": 88,
"source": "aime",
"d7": 13,
"d32": 8,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "8a57b5129116"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The probability that a set of three distinct vertices chosen at random from among the vertices of a regular... | contest_math | math | {
"style": "rule",
"ground_truth": "503"
} | {
"index": 89,
"source": "aime",
"d7": 13,
"d32": 12,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "87d5f2b48b9d"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $S$ be the set of positive integers $k$ such that the two parabolas \\[y=x^2-k~~\\text{and}~~x=2(y-20)^... | contest_math | math | {
"style": "rule",
"ground_truth": "285"
} | {
"index": 90,
"source": "aime",
"d7": 15,
"d32": 13,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "40f924a1561b"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "2. (BRA 3) A polyhedron has 12 faces and is such that: (i) all faces are isosceles triangles, (ii) all edge... | contest_math | math | {
"style": "rule",
"ground_truth": "\\frac{5}{3}"
} | {
"index": 91,
"source": "olympiads_ref",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "6ca08b5b4423"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "12. B6 (FIN 3) Four distinct circles \\( C, C_{1}, C_{2}, C_{3} \\) and a line \\( L \\) are given in the p... | contest_math | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 92,
"source": "olympiads_ref",
"d7": 13,
"d32": 6,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "7519d55c0b07"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The graph of the equation $9x+223y=2007$ is drawn on graph paper with each square representing one unit in ... | contest_math | math | {
"style": "rule",
"ground_truth": "888"
} | {
"index": 93,
"source": "aime",
"d7": 12,
"d32": 9,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "2a0d0cd120f4"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A square has sides of length 2. Set $S$ is the set of all line segments that have length 2 and whose endpoi... | contest_math | math | {
"style": "rule",
"ground_truth": "86"
} | {
"index": 94,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "713abad651ea"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A standard six-sided fair die is rolled four times. The probability that the product of all four numbers ro... | contest_math | math | {
"style": "rule",
"ground_truth": "187"
} | {
"index": 95,
"source": "aime",
"d7": 11,
"d32": 0,
"pass_rate": 0.25,
"n_samples": 4,
"split": "train",
"qid": "fa4a53d448b4"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $m$ and $n$ be odd integers greater than $1.$ An $m\\times n$ rectangle is made up of unit squares wher... | contest_math | math | {
"style": "rule",
"ground_truth": "248"
} | {
"index": 96,
"source": "aime",
"d7": 16,
"d32": 16,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "f83a5669fbe4"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the least positive integer $n$ for which there exists a set $\\{s_1, s_2, \\ldots , s_n\\}$ consisting... | contest_math | math | {
"style": "rule",
"ground_truth": "39"
} | {
"index": 97,
"source": "omnimath",
"d7": 11,
"d32": 8,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "203af0dba2a6"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For any integer $k\\geq 1$ , let $p(k)$ be the smallest prime which does not divide $k$ . Define the intege... | contest_math | math | {
"style": "rule",
"ground_truth": "149"
} | {
"index": 98,
"source": "aime",
"d7": 16,
"d32": 6,
"pass_rate": 0.5,
"n_samples": 4,
"split": "train",
"qid": "d2c4d355c9c1"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In each square of a garden shaped like a $2022 \\times 2022$ board, there is initially a tree of height $0$... | contest_math | math | {
"style": "rule",
"ground_truth": "2271380"
} | {
"index": 99,
"source": "omnimath",
"d7": 16,
"d32": 13,
"pass_rate": 0,
"n_samples": 4,
"split": "train",
"qid": "812446f0c637"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
End of preview. Expand in Data Studio
kushasareen/contest-math-hard
Competition mathematics problems with short closed-form answers, drawn from the contest-grade sources of
Skywork-OR1-RL-Data (AIME 1983-2023, Omni-MATH, AoPS olympiad references, AMC/AIME), filtered for problems that
can be checked automatically (no figures, no proofs, no multiple choice, no two-part questions, no yes/no answers)
and deduplicated. Columns: prompt (system + user turn), data_source, ability, reward_model (ground_truth),
extra_info (source, pass_rate: the fraction of 4 samples a 4B reference model solved at 16k tokens, n_samples).
277 train / 64 test rows; mean reference pass rate 0.22.
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