prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "The number line between 0 and 2 is divided into 8 equal parts. The numbers 1 and S are marked on the line. Find the value of S. Express your answer as a decimal number rounded to 2 decimal places.",
"role": "user"
}
] | {
"ground_truth": "1.25",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Six chairs are evenly spaced around a circular table. One person is seated in each chair. Each person gets up and sits down in a chair that is not the same and is not adjacent to the chair he or she originally occupied, so that again one person is seated in each chair. In how many ways can this be... | {
"ground_truth": "20",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\underline{\\text { Cepreев } \\text { I.n. }}$.\n\nFor given natural numbers $k_{0}<k_{1}<k_{2}$, determine the smallest number of roots on the interval $[0 ; 2 \\pi)$ that the equation of the form\n\n$$\n\\sin \\left(k_{0} x\\right)+A_{1} \\cdot \\sin \\left(k_{1} x\\right)+A_{2} \\cdot \\sin ... | {
"ground_truth": "2k_{0}",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Regular hexagon $ABCDEF$ and regular square $AFGH$ are drawn on opposite sides of line segment $AF$ such that they are coplanar. What is the degree measure of exterior angle $GFD$?",
"role": "user"
}
] | {
"ground_truth": "150^\\circ",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. In the sequence $\\left\\{a_{n}\\right\\}_{n=1}^{+\\infty}$, $x_{1}=1$, if for any positive integer $n$ there is $x_{n+1}=x_{n}+\\left[\\sqrt{x_{n}}\\right]$, where the symbol $[x]$ denotes the greatest integer not exceeding $x$, then the smallest positive integer $n$ such that $x_{n} \\geqslan... | {
"ground_truth": "95",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "49. As shown in the figure, $\\angle A+\\angle B+\\angle C+\\angle D+\\angle E+\\angle F+\\angle G=n \\cdot 90^{\\circ}$, then $n=$",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Abby has 7 pieces of candy and Ben has 15. They decide to give some candy to their little brother Carl, with Ben giving 2 more pieces than Abby. Compute the number of positive divisors of the total number of ways they can give candy to Carl.",
"role": "user"
}
] | {
"ground_truth": "96",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a train travel aficionado who is planning a railway circumnavigation trip around the world. He plans to visit 5 continents, spending an equal number of days on each continent. The total duration of his trip is 60 days. During his travels, Alex will use 10 different trains, with each train ... | {
"ground_truth": "40",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A vertical wooden pillar has a rope tied to its top. The part of the rope hanging down from the top of the pillar to the ground measures 4 feet. When pulling the rope, it runs out when 8 feet away from the base of the pillar. Calculate the total length of the rope. Express your answer in feet.",
... | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. As shown in Figure 3(a), the eight vertices of a cube are assigned values $a, b, c, d, e, f, g, h$, respectively. Then, the arithmetic mean of the values of the three adjacent vertices of each vertex, denoted as $\\bar{a}, \\bar{b}, \\bar{c}, \\bar{d}, \\bar{e}, \\bar{f}, \\bar{g}, \\bar{h}$, ... | {
"ground_truth": "20",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 11.4. (12 points)\n\nEmployees of the company are divided into hard workers and slackers. In 2016, the average salary of hard workers was twice the average salary of slackers. After improving their qualifications, hard workers in 2017 began to earn $50 \\%$ more, while the salary of slackers ... | {
"ground_truth": "16",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( w, x, y, \\) and \\( z \\) be positive real numbers such that\n\\[\n\\begin{aligned}\n0 & \\neq \\cos w \\cos x \\cos y \\cos z \\\\\n2 \\pi & = w + x + y + z \\\\\n3 \\tan w & = k(1 + \\sec w) \\\\\n4 \\tan x & = k(1 + \\sec x) \\\\\n5 \\tan y & = k(1 + \\sec y) \\\\\n6 \\tan z & = k(1 + ... | {
"ground_truth": "\\sqrt{19}",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Each principal of Lincoln High School serves exactly one $3$-year term. What is the maximum number of principals this school could have during an $8$-year period?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Quadrilateral $ABCD$ satisfies $AB = 8, BC = 5, CD = 17, DA = 10$. Let $E$ be the intersection of $AC$ and $BD$. Suppose $BE : ED = 1 : 2$. Find the area of $ABCD$.",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 1. What day of the week was October 1, 1949?",
"role": "user"
}
] | {
"ground_truth": "Saturday",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let the ordered triples $(x,y,z)$ of complex numbers that satisfy\n\\begin{align*}\nx + yz &= 9, \\\\\ny + xz &= 13, \\\\\nz + xy &= 12.\n\\end{align*}\nbe $(x_1,y_1,z_1),$ $(x_2,y_2,z_2),$ $\\dots,$ $(x_n,y_n,z_n).$ Find $x_1 + x_2 + \\dots + x_n.$",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7th Putnam 1947 Problem B3 Let O be the origin (0, 0) and C the line segment { (x, y) : x ∈ [1, 3], y = 1 }. Let K be the curve { P : for some Q ∈ C, P lies on OQ and PQ = 0.01 }. Let k be the length of the curve K. Is k greater or less than 2? Solution",
"role": "user"
}
] | {
"ground_truth": "k<2",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14. Some of the 20 metal cubes, identical in size and appearance, are aluminum, the rest are duralumin (heavier). How can you determine the number of duralumin cubes using no more than 11 weighings on a balance scale without weights?\n\nNote. The problem assumes that all cubes can be aluminum, but... | {
"ground_truth": "11",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The graph below shows the number of home runs in April for the top hitters in the league. What is the mean (average) number of home runs hit by these players?\n\n[asy]\ndraw((0,0)--(0,7)--(24,7)--(24,0)--cycle);\nlabel(\"KEY:\",(3,5));\nfill((3,2.5)..(3.5,2)..(3,1.5)..(2.5,2)..cycle);\nlabel(\"- o... | {
"ground_truth": "7",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task A-2.7.\n\nIn a basketball tournament, each team plays exactly twice against each of the other teams. A win brings 2 points, a loss 0 points, and there are no draws. Determine all natural numbers $n$ for which there exists a basketball tournament with $n$ teams where one team, the tournamen... | {
"ground_truth": "12",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Simplify $\\left(\\dfrac{-1+i\\sqrt{3}}{2}\\right)^8+\\left(\\dfrac{-1-i\\sqrt{3}}{2}\\right)^8.$",
"role": "user"
}
] | {
"ground_truth": "-1.",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $k \\geq 1$ be an integer.\n\nWe consider $4 k$ chips, $2 k$ of which are red and $2 k$ of which are blue. A sequence of those $4 k$ chips can be transformed into another sequence by a so-called move, consisting of interchanging a number (possibly one) of consecutive red chips with an equal nu... | {
"ground_truth": "k",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Anička received a rectangular cake for her birthday. She cut the cake with two straight cuts. The first cut was made such that it intersected both longer sides of the rectangle at one-third of their length. The second cut was made such that it intersected both shorter sides of the rectangle at one... | {
"ground_truth": "2/15",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1500 products are packed into 15 boxes for shipment. After sealing the boxes, it is discovered that one product was not packed into any box. Due to strict sealing requirements, boxes cannot be reopened for inspection. Someone suggests using a scale to weigh the boxes to find which box is missing a... | {
"ground_truth": "4",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two people play a math game. Player A selects a group of single-digit integers \\( x_{1}, x_{2}, \\cdots, x_{n} \\) as the secret numbers, which can be positive or negative. Player B can ask questions about the sum \\( a_{1} x_{1} + a_{2} x_{2} + \\cdots + a_{n} x_{n} \\), where \\( a_{1}, a_{2}, ... | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $ m,n\\in \\mathbb{N}^*$ . Find the least $ n$ for which exists $ m$ , such that rectangle $ (3m \\plus{} 2)\\times(4m \\plus{} 3)$ can be covered with $ \\dfrac{n(n \\plus{} 1)}{2}$ squares, among which exist $ n$ squares of length $ 1$ , $ n \\minus{} 1$ of length $ 2$ , $ ...... | {
"ground_truth": " n = 8 ",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Arjun and Beth play a game in which they take turns removing one brick or two adjacent bricks from one \"wall\" among a set of several walls of bricks, with gaps possibly creating new walls. The walls are one brick tall. The player who removes the last brick wins. Determine the starting configurat... | {
"ground_truth": "(6, 2, 1)",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A $6 \\times 6$ board is given such that each unit square is either red or green. It is known that there are no $4$ adjacent unit squares of the same color in a horizontal, vertical, or diagonal line. A $2 \\times 2$ subsquare of the board is [i]chesslike[/i] if it has one red and one green diagon... | {
"ground_truth": "25",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let the sequence $(a_n)$ be defined as $a_1 = \\\\frac{1}{3}$ and $a_{n+1} = \\\\frac{a_n}{\\\\sqrt{1 + 13a_n^2}}$ for every $n \\\\geq 1$. Find the largest value of $k$ such that $a_k < \\\\frac{1}{50}$. Express your answer as a single integer value for $k$.",
"role": "user"
}
] | {
"ground_truth": "193",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Isosceles, Inscribed, and Circumscribed Trapezoids ]\n\n[Properties and characteristics of isosceles triangles. ]\n\nLet $M$ be the point of intersection of the diagonals of a convex quadrilateral $ABCD$, in which sides $AB$, $AD$, and $BC$ are equal to each other.\n\nFind the angle $CMD$, given... | {
"ground_truth": "120",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest \\( n \\) such that the sum of the fourth powers of any \\( n \\) prime numbers greater than 10 is divisible by \\( n \\).",
"role": "user"
}
] | {
"ground_truth": "240",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Let $1<b<\\frac{5}{4}$, the number of distinct real roots of the equation $\\left|x^{2}-1\\right|=x+b$ is\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly. \n\n---\n\n9. Let $1<b<\\frac{5}{4}$, the numbe... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If a cash flow of $100 has a discount rate of 5% and to be received in 5 years, what is the present value of the cash flow?",
"role": "user"
}
] | {
"ground_truth": "78.3526",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the de Broglie Wavelength, in nm, of an electron with kinetic energy 50 eV.",
"role": "user"
}
] | {
"ground_truth": "0.17",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The clock runs 3 minutes fast every 24 hours. The clock was set accurately. After what minimum time will the clock show the correct time again?",
"role": "user"
}
] | {
"ground_truth": "240",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three boys played a \"Word\" game in which they each wrote down ten words. For each word a boy wrote, he scored three points if neither of the other boys had the same word; he scored one point if only one of the other boys had the same word. No points were awarded for words which all three boys ha... | {
"ground_truth": "25",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Given a three-digit number $\\overline{a b c}$, the last three digits of its square are also $\\overline{a b c}$. Then, the sum of all such three-digit numbers is $\\qquad$\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the transla... | {
"ground_truth": "1001",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is a positive integer s such that there are s solutions to the equation $64sin^2(2x)+tan^2(x)+cot^2(x)=46$ in the interval $(0,\\frac{\\pi}{2})$ all of the form $\\frac{m_k}{n_k}\\pi$ where $m_k$ and $n_k$ are relatively prime positive integers, for $k = 1, 2, 3, . . . , s$ . Find ... | {
"ground_truth": "100",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A number is written on the board. In one move, you can either increase or decrease any of its digits by three (if the resulting digit is valid) or swap two adjacent digits. Show how to obtain the number 654321 from the number 123456 in 11 moves.",
"role": "user"
}
] | {
"ground_truth": "654321",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. There are 99 bags, each containing $1,2,3,4, \\cdots \\cdots, 99$ gold coins respectively. Each time the fairy wields her magic wand over some of the bags, the number of gold coins in these bags increases by the same amount. To make the number of gold coins in each bag exactly 100, the fairy ne... | {
"ground_truth": "7",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a positive integer \\(n\\), let \\(f(n)\\) be the total count of (not necessarily distinct) prime factors of \\(n\\) (with \\(f(1)=0\\)). Define \\(g(n)\\) to be the number of integers \\(k \\le n\\) such that \\(f(k)\\) is at least as large as \\(f(j)\\) for all \\(j \\le n\\). Compute \\(g(1... | {
"ground_truth": "136",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Piercarlo chooses \\( n \\) integers from 1 to 1000 inclusive. None of his integers is prime, and no two of them share a factor greater than 1. What is the greatest possible value of \\( n \\)?",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4.1. Find the area of the figure defined on the coordinate plane by the system\n\n$$\n\\left\\{\\begin{array}{l}\n2 \\pi\\left(x^{2}+y^{2}\\right) \\leqslant 15 \\\\\nx^{4}-y^{4} \\leqslant x y-x^{3} y^{3}\n\\end{array}\\right.\n$$",
"role": "user"
}
] | {
"ground_truth": "3.75",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nCompute the area of the ellipse $25x^2 +4 y^2 = 16.$\n\n[Solution]\n\n<paragraph_0>\nTo find the area of the ellipse given by the equation \\(25x^2 + 4y^2 = 16\\), we... | {
"ground_truth": "-1",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\(p,\\) \\(q,\\) and \\(r\\) be constants, and suppose that the inequality \\[\\frac{(x-p)(x-q)}{x-r} \\ge 0\\]is true if and only if either \\(x > 5\\) or \\(3 \\le x \\le 7.\\) Given that \\(p < q,\\) find the value of \\(p + 2q + 3r.\\)",
"role": "user"
}
] | {
"ground_truth": "32",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a$ and $b$ be constants. Suppose that the equation \\[\\frac{(x+a)(x+b)(x+10)}{(x+4)^2} = 0\\] has exactly $3$ distinct roots, while the equation \\[\\frac{(x+2a)(x+4)(x+5)}{(x+b)(x+10)} = 0\\] has exactly $1$ distinct root. Compute $100a + b.$",
"role": "user"
}
] | {
"ground_truth": "205",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "LIX OM - I - Task 7\n\nIn an $ n $-person association, there are $ 2n-1 $ committees (any non-empty set of association members\nforms a committee). A chairperson must be selected in each committee. The following condition must be met: If\ncommittee $ C $ is the union $ C = A\\cup B $ of two commit... | {
"ground_truth": "n!",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "42nd Putnam 1981 Problem A6 A, B, C are lattice points in the plane. The triangle ABC contains exactly one lattice point, X, in its interior. The line AX meets BC at E. What is the largest possible value of AX/XE? Solution",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 4: Given 1 one-yuan note, 1 two-yuan note, 1 five-yuan note, 4 ten-yuan notes, and 2 fifty-yuan notes, how many different amounts of money can be paid using these notes?\n(1986 Shanghai Competition Question)",
"role": "user"
}
] | {
"ground_truth": "119",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If we write every day of 2014 in the form of an eight-digit number, for example, 20140125 represents January 25, 2014, how many eight-digit numbers have the digits '1', '2', '0' appearing the same number of times?",
"role": "user"
}
] | {
"ground_truth": "43",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A pyramid \\( S A B C D \\) has a trapezoid \\( A B C D \\) as its base, with bases \\( B C \\) and \\( A D \\). Points \\( P_1, P_2, P_3 \\) lie on side \\( B C \\) such that \\( B P_1 < B P_2 < B P_3 < B C \\). Points \\( Q_1, Q_2, Q_3 \\) lie on side \\( A D \\) such that \\( A Q_1 < A Q_2 < A ... | {
"ground_truth": "2028",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In the 100th year of Besmiki's tenure as the President of the Currency Authority, he decided to issue new gold coins. In this year, he put into circulation an unlimited number of gold coins with a face value of $2^{100}-1$ yuan. In the following year, he put into circulation an unlimited number... | {
"ground_truth": "200",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.3. On one main diagonal and all edges of a cube, directions are chosen. What is the smallest length that the sum of the resulting 13 vectors can have, if the edge length is 1, and the length of the main diagonal is $\\sqrt{3}$.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{3}",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nGiven a right-angled triangle \\(15 ABC\\) with \\(\\angle BAC = 90^\\circ\\), squares \\(ABDE\\) and \\(BCFG\\) are constructed on sides \\(AB\\) and \\(BC\\) respectively. The area of square \\(ABDE\\) is \\(8 \\ \\text{cm}^2\\) and the area of square \\(BCFG\\) is \\(26 \\ \\text{cm}^2\\). Fi... | {
"ground_truth": "6",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.4. What is the minimum number of kings that need to be placed on a chessboard so that they attack all unoccupied squares? (A king attacks the squares that are adjacent to its square by side or corner).\n\n![](https://cdn.mathpix.com/cropped/2024_05_06_39d633e886f69700a0e8g-1.jpg?height=462&width... | {
"ground_truth": "9",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Call a lattice point visible if the line segment connecting the point and the origin does not pass through another lattice point. Given a positive integer $k$, denote by $S_{k}$ the set of all visible lattice points $(x, y)$ such that $x^{2}+y^{2}=k^{2}$. Let $D$ denote the set of all positive ... | {
"ground_truth": "20",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13th CanMO 1981 Problem 5 11 groups perform at a festival. Each day any groups not performing watch the others (but groups performing that day do not watch the others). What is the smallest number of days for which the festival can last if every group watches every other group at least once during... | {
"ground_truth": "6",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We have 50 numbered chips from 1 to 50, and they need to be colored either red or blue. We know that chip 5 is blue. For the coloring of the remaining chips, the following rules are followed:\n\na) If the chip with number $x$ and the chip with number $y$ are of different colors, then the chip with... | {
"ground_truth": "2",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $z=1-2 i$. Find $\\frac{1}{z}+\\frac{2}{z^{2}}+\\frac{3}{z^{3}}+\\cdots$.",
"role": "user"
}
] | {
"ground_truth": "(2i-1)/4",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14.2. For 9 identical books, more than 11 rubles were paid, and for 13 such books, less than 16 rubles were paid. How much does one book cost?\n\n$$\n(6-7 \\text { grade) }\n$$",
"role": "user"
}
] | {
"ground_truth": "123",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rug is made with three different colors as shown. The areas of the three differently colored regions form an arithmetic progression. The inner rectangle is one foot wide, and each of the two shaded regions is $1$ foot wide on all four sides. What is the length in feet of the inner rectangle? [as... | {
"ground_truth": "2",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the Tenth Kingdom, there are 17 islands, each with 119 inhabitants. The inhabitants are divided into two castes: knights, who always tell the truth, and liars, who always lie. During a population census, each person was first asked, \"Not including yourself, are there an equal number of knights... | {
"ground_truth": "1013",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "18. There is a batch of wooden materials in the shape of a regular triangular prism, 2 meters long, with a base edge length of 12 cm. Now, 1000 wooden balls need to be processed, and the wooden balls should be as large as possible. Therefore, at least $\\qquad$ pieces of this material are needed (... | {
"ground_truth": "36",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "(11) (25 points) The sum of $n$ positive integers $x_{1}, x_{2}, \\cdots, x_{n}$ is 2009. If these $n$ numbers can be divided into 41 groups with equal sums and also into 49 groups with equal sums, find the minimum value of $n$.\n\n",
"role": "user"
}
] | {
"ground_truth": "89",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangular prism has 6 faces (2 rectangular and 4 square faces), 12 edges, and 8 vertices. Choose one of its square faces as the base of a new pyramid. The numbers of external faces, vertices, and edges of the resulting shape (the combination of the prism and pyramid) are added. What is the max... | {
"ground_truth": "34",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $n$ be a positive integer with the following property: $2^n-1$ divides a number of the form $m^2+81$ , where $m$ is a positive integer. Find all possible $n$ . ",
"role": "user"
}
] | {
"ground_truth": " n = 2^k ",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 2023 cups numbered from 1 through 2023. Red, green, and blue balls are placed in the cups according to the following rules.\n- If cups $m$ and $n$ both contain a red ball, then $m-n$ is a multiple of 2 .\n- If cups $m$ and $n$ both contain a green ball, then $m-n$ is a multiple of 3 .\n-... | {
"ground_truth": "538",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Natural numbers $1, 2, 3, \\cdots$ are written consecutively to form a number $123456789101112 \\cdots$. At what point does the formed number first become divisible by 72? This number is $\\qquad$ _. $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A triangle is composed of circular cells arranged in $5784$ rows: the first row has one cell, the second has two cells, and so on (see the picture). The cells are divided into pairs of adjacent cells (circles touching each other), so that each cell belongs to exactly one pair. A pair of adjacent... | {
"ground_truth": "2892",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.1. In a circle, 58 balls of two colors - red and blue - are arranged. It is known that the number of triples of consecutive balls, among which there are more red ones, is the same as the number of triples with a majority of blue ones. What is the smallest number of red balls that could be presen... | {
"ground_truth": "20",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Putnam 1993 Problem B1 What is the smallest integer n > 0 such that for any integer m in the range 1, 2, 3, ... , 1992 we can always find an integral multiple of 1/n in the open interval (m/1993, (m + 1)/1994)? Solution",
"role": "user"
}
] | {
"ground_truth": "3987",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\\left[\\begin{array}{l}{[\\text { Decimal numeral system }]} \\\\ {[\\text { Case enumeration }}\\end{array}\\right]\n\nAuthor: Raskina I.V.\n\nThe year 2009 has the following property: by rearranging the digits of the number 2009, it is impossible to obtain a smaller four-digit number (numbers d... | {
"ground_truth": "2022",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At each of the sixteen circles in the network below stands a student. A total of $3360$ coins are distributed among the sixteen students. All at once, all students give away all their coins by passing an equal number of coins to each of their neighbors in the network. After the trade, all students... | {
"ground_truth": "280",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the smallest number of plastic snap-together cubes that can be snapped together such that only receptacle holes are showing, with all protruding snaps hidden? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 7.1. Inside a large square, there is a small square, the corresponding sides of which are parallel. The distances between some sides of the squares are marked on the diagram. By how much is the perimeter of the large square greater than the perimeter of the small square?\n\n![](https://cdn... | {
"ground_truth": "32",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For any positive integer, if the number of $2$'s in its digits is greater than the number of $3$'s in its digits, we call that is a [b]good[/b] number. And if the number of $3$'s in its digits is more than the number of $2$'s in its digits, we call that is a [b]bad[/b] number. For example, there a... | {
"ground_truth": "22",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A farmer bought $749$ sheep. He sold $700$ of them for the price paid for the $749$ sheep. The remaining $49$ sheep were sold at the same price per head as the other $700$. Based on the cost, the percent gain on the entire transaction is:",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\underline{\\text { Folklore }}$\n\nPetya wants to make an unusual die, which, as usual, should have the shape of a cube, with dots drawn on its faces (different numbers of dots on different faces), but at the same time, on any two adjacent faces, the number of dots must differ by at least two (... | {
"ground_truth": "27",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? (For clarification: If the polynomial is $ax^2+bx+c, a \\neq 0,$ and the roots are $r$ and $s,$ then the requirement is that $\\{a,b,c\\}=\\{r,s\\}$.)",
"role": "user"
}... | {
"ground_truth": "4",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five children (Tian Tian, Shi Tou, Kimi, Cindy, Angela) need to switch fathers (each child can choose any one of the other four fathers except their own). Find the total number of different combinations of choices for the five children. Express your answer as a single integer.",
"role": "user"... | {
"ground_truth": "44",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 19 (Problem 1506 from \"Mathematics Bulletin\") In $\\triangle A B C$, $A B=A C$, the angle bisector of $\\angle B$ intersects $A C$ at $D$, and $B C=B D+A D$. Find $\\angle A$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output t... | {
"ground_truth": "100",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are $5$ accents in French, each applicable to only specific letters as follows:\n\n\n\n- The cédille: ç\n- The accent aigu: é\n- The accent circonflexe: â, ê, î, ô, û\n- The accent grave: à, è, ù\n- The accent tréma: ë, ö, ü\n\n\nCédric needs to write down a phrase in French. He knows that... | {
"ground_truth": "4",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a$ , $b$ , $c$ , $d$ , $e$ , $f$ and $g$ be seven distinct positive integers not bigger than $7$ . Find all primes which can be expressed as $abcd+efg$ ",
"role": "user"
}
] | {
"ground_truth": "179",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the triangle. The sides and the height of a certain triangle are expressed by four consecutive integers. What is the area of this triangle?",
"role": "user"
}
] | {
"ground_truth": "84",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Humanity has discovered 15 habitable planets, where 7 are \"Earth-like\" and 8 are \"Mars-like\". Colonizing an Earth-like planet requires 3 units of colonization, while a Mars-like planet requires 1 unit. If humanity has 21 units available for colonization, determine how many different combinatio... | {
"ground_truth": "981",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Seven students count from 1 to 1000 as follows: Alice says all the numbers, except she skips the middle number in each consecutive group of three numbers. That is, Alice says 1, 3, 4, 6, 7, 9, . . ., 997, 999, 1000. Barbara says all of the numbers that Alice doesn't say, except she also skips the ... | {
"ground_truth": "365",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "88. The Chase (I). Ship $P$ has spotted ship $Q$, which is sailing in a direction perpendicular to $P Q$, maintaining its course. Ship $P$ is chasing $Q$, always heading directly towards $Q$; the speed of both ships is the same at any moment (but can vary over time). Without calculations, it is cl... | {
"ground_truth": "5",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In right triangle $ABC$, we have $\\angle A = 40^\\circ$, $\\angle B = 90^\\circ$, and $BC = 12$. Find $AB$ to the nearest tenth. You may use a calculator for this problem.",
"role": "user"
}
] | {
"ground_truth": "14.3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Square $ABCD$ has an area of $144$. Point $E$ lies on side $\\overline{BC}$ such that $BE:EC = 3:1$. Points $F$ and $G$ are the midpoints of $\\overline{AE}$ and $\\overline{DE}$, respectively. Given that quadrilateral $BEGF$ has area $25$, find the area of triangle $GCD$.",
"role": "user"
}... | {
"ground_truth": "9",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $z_1=18+83i,~z_2=18+39i,$ and $z_3=78+99i,$ where $i=\\sqrt{-1}.$ Let $z$ be the unique complex number with the properties that $\\frac{z_3-z_1}{z_2-z_1}~\\cdot~\\frac{z-z_2}{z-z_3}$ is a real number and the imaginary part of $z$ is the greatest possible. Find the real part of $z$.",
"role... | {
"ground_truth": "56",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Rectangle $A B C D$ has an area of 2011 square centimeters. The vertices of trapezoid $A F G E$ are such that $F$ is on $B C$, and $D$ is the midpoint of the leg $E G$. Find the area of trapezoid $A F G E$.",
"role": "user"
}
] | {
"ground_truth": "2011",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "47. The school has bought a batch of science fiction novels and distributed them to 10 groups. After each group received 5 books, there were not enough books left to distribute. What is the minimum number of science fiction novels in this batch?",
"role": "user"
}
] | {
"ground_truth": "51",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the least number of colors needed to shade the tessellation shown, such that no two tiles sharing a side are the same color? The tessellation includes interlocking hexagons and squares as depicted below:\n\n[asy]\nunitsize(1cm);\nint i;\nfor(i=0; i < 7; i = i + 2){\n draw(shift(2*i,0)*p... | {
"ground_truth": "3",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. In the vertices of a regular 300-gon, numbers from 1 to 300 are placed once each in some order. It turns out that for each number a, among the 15 nearest numbers to it in the clockwise direction, there are as many numbers less than a as there are among the 15 nearest numbers to it in the counte... | {
"ground_truth": "10",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the smallest \\( n > 4 \\) for which we can find a graph on \\( n \\) points with no triangles and such that for every two unjoined points we can find just two points joined to both of them.",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. The last digit of $\\sum_{k=0}^{201}(10 k+7)^{k+1}$ is\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that for the positive numbers \\( x \\), \\( y \\), and \\( z \\),\n\n\\[ x^2 + xy + y^2 = 9, \\quad y^2 + yz + z^2 = 16, \\quad z^2 + zx + x^2 = 25. \\]\n\nDetermine the value of \\( xy + yz + zx \\).",
"role": "user"
}
] | {
"ground_truth": "8 \\sqrt{3}",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a,$ $b,$ and $c$ be constants, and suppose the inequality \\[\\frac{(x-a)(x-b)}{x-c} \\geq 0\\] is true if and only if either $x < -6$ or $20 \\leq x \\leq 23.$ Given that $a < b,$ find the value of $a + 2b + 3c.$",
"role": "user"
}
] | {
"ground_truth": "48",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. City $A$ has 4 suburban counties $(B, C, D, E)$, as shown in Figure 2. There are 5 colors available. How many different coloring methods are there such that no two adjacent areas share the same color, and each area is painted with only one color?",
"role": "user"
}
] | {
"ground_truth": "420",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given integers $a$ and $b$ satisfy: $a-b$ is a prime number, and $ab$ is a perfect square. When $a \\geq 2012$, find the minimum value of $a$.",
"role": "user"
}
] | {
"ground_truth": "2025",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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