prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Example 4 Given two points $M(-1,0), N(1,0)$, and point $P$ such that $\\overrightarrow{M P} \\cdot \\overrightarrow{M N}, \\overrightarrow{P M} \\cdot \\overrightarrow{P N}, \\overrightarrow{N M} \\cdot \\overrightarrow{N P}$ form an arithmetic sequence with a common difference less than zero, fi... | {
"ground_truth": "x^2+y^2=3",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In triangle $ABC$, $AD=DC$ where $D$ is a point on $\\overline{AC}$, and $BD$ is a point on $\\overline{BC}$ such that $BD = BC$. If $\\overline{BD}$ bisects angle $ABC$, what is the measure, in degrees, of angle $B$?",
"role": "user"
}
] | {
"ground_truth": "120^\\circ",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Isosceles $\\triangle ABC$ has equal side lengths $AB$ and $BC$. In the figure below, segments are drawn parallel to $\\overline{AC}$ so that the shaded portions of $\\triangle ABC$ have the same area. The heights of the two unshaded portions are 11 and 5 units, respectively. What is the height of... | {
"ground_truth": "14.6",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.82 Suppose there are 128 ones written on the blackboard. In each step, you can erase any two numbers $a$ and $b$ on the blackboard, and write $ab+1$. After 127 such steps, only one number remains. Let the maximum possible value of this remaining number be $A$. Find the last digit of $A$.\n\n",
... | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Line segment $\\overline{AB}$ is extended past $B$ to $P$ such that $AP:PB = 4:5.$ Then\n\\[\\overrightarrow{P} = s \\overrightarrow{A} + v \\overrightarrow{B}\\] for some constants $s$ and $v.$ Determine the ordered pair $(s, v).$",
"role": "user"
}
] | {
"ground_truth": "(5, -4)",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A gear wheel has 12 teeth on the smaller wheel and 32 teeth on the larger one. Due to a manufacturing defect, one tooth on the small wheel and one gap on the large wheel are faulty, causing them to rattle when they meet. How often will we hear the rattling if the time for one revolution of the lar... | {
"ground_truth": "9",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a tennis tournament, 512 schoolchildren participate. For a win, 1 point is awarded, for a loss, 0 points. Before each round, pairs are drawn from participants with an equal number of points (those who do not have a pair are awarded a point without playing). The tournament ends as soon as a sole... | {
"ground_truth": "84",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $s(a)$ denote the sum of digits of a given positive integer a. The sequence $a_1, a_2,..., a_n, ...$ of positive integers is such that $a_{n+1} = a_n+s(a_n)$ for each positive integer $n$ . Find the greatest possible n for which it is possible to have $a_n = 2008$ .",
"role": "use... | {
"ground_truth": "6",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a faded piece of paper it is possible to read the following:\n\\[(x^2 + x + a)(x^{15}- \\cdots ) = x^{17} + x^{13} + x^5 - 90x^4 + x - 90.\\]\nSome parts have got lost, partly the constant term of the first factor of the left side, partly the majority of the summands of the second factor. It wo... | {
"ground_truth": "2",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the angle of inclination of the line y = -√3x + 2√3. Express your answer in degrees, including the degree symbol (°).",
"role": "user"
}
] | {
"ground_truth": "120°",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n10.4. A positive integer is called simple if its ordinary decimal representation consists entirely of zeroes and ones. Find the least positive integer $k$ such that each positive integer $n$ can be written as $n=a_{1} \\pm a_{2} \\pm a_{3} \\pm \\cdots \\pm a_{k}$, where $a_{1}, \\ldots, a_{k}$ ... | {
"ground_truth": "9",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the least positive integer $n$ for which $2^n + 5^n - n$ is a multiple of $1000$.",
"role": "user"
}
] | {
"ground_truth": "797",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The area of two parallel plane sections of a sphere are $9 \\pi$ and $16 \\pi$. The distance between the planes is given. What is the surface area of the sphere?",
"role": "user"
}
] | {
"ground_truth": "100\\pi",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 1.\n\n| West | Non-West | Russia |\n| :--- | :--- | :--- |\n| 3rd place | 2nd place | 1st place |\n| 55,084 barrels/person | 214,59 barrels/person | 1038,33 barrels/person |",
"role": "user"
}
] | {
"ground_truth": "1038.33",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "28. On the number line, draw line segments according to the following rules:\n(1) The numbers corresponding to the endpoints of the line segments are non-negative numbers not exceeding 2020;\n(2) The number corresponding to the midpoint of the line segment is an integer.\nThe number of such line s... | {
"ground_truth": "1020100",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\{a_n\\}$ be a geometric sequence, $\\{b_n\\}$ be an arithmetic sequence, and $b_1=0$, $c_n=a_n+b_n$. If $\\{c_n\\}$ is $1$, $1$, $2$, $\\ldots$, find the sum of the first $10$ terms of the sequence $\\{c_n\\}$.",
"role": "user"
}
] | {
"ground_truth": "978",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Lisa is a cat-loving gamer who has a collection of 15 cat-themed video games. She decided to buy more games to add to her collection. She found a gaming store that has a special offer: buy 2 cat-themed games and get the 3rd one free. If Lisa buys 6 cat-themed games, how many games in total will sh... | {
"ground_truth": "24",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. In her fourth year at Hogwarts, Hermione was outraged by the infringement of house-elf rights and founded the Association for the Restoration of Elven Independence. Of course, even the brightest and noblest idea requires funding for promotion, so Hermione decided to finance her campaign by prod... | {
"ground_truth": "7.682",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A former diplomat is attending a conference to discuss diplomatic conflicts. There are 15 countries participating in the conference. Each country brings 3 delegates, including the former diplomat himself, who represents his own country. During the conference, the former diplomat holds a private me... | {
"ground_truth": "210",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In any permutation of the numbers \\(1, 2, 3, \\ldots, 18\\), we can always find a set of 6 consecutive numbers whose sum is at least \\(m\\). Find the maximum value of the real number \\(m\\).",
"role": "user"
}
] | {
"ground_truth": "57",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a semicircle O whose diameter lies along the base AB of a trapezoid ABCD, and BC, CD, DA are tangent to the semicircle, with BC = 2 and DA = 3, calculate the length of AB. Express your answer as a single numerical value.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 5.1. At a physical education class, 27 seventh-graders arrived, some of them brought one ball each. Sometimes during the class, one of the seventh-graders would give their ball to another seventh-grader who didn't have one.\n\nAt the end of the class, $N$ seventh-graders said: \"I received... | {
"ground_truth": "13",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Define: For any three-digit natural number $m$, if $m$ satisfies that the tens digit is $1$ greater than the hundreds digit, and the units digit is $1$ greater than the tens digit, then this three-digit number is called an \"upward number\"; for any three-digit natural number $n$, if $n$ satisfies... | {
"ground_truth": "531",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. A diagonal of a convex polygon (i.e., a polygon where all interior angles are less than $180^{\\circ}$) is called \"bisecting\" if and only if the diagonal simultaneously bisects the area and the perimeter of the polygon. How many diagonals of a convex pentagon can be bisecting at most?\n\n---\... | {
"ground_truth": "2",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task No. 1.1\n\n## Condition:\n\nFive friends - Masha, Nastya, Irina, Olya, and Anya - meet in the park every day after buying ice cream from the shop around the corner. One day, the girls had a conversation.\n\nIrina: I was the first in line!\n\nOlya: No one was after me.\n\nAnya: Only one person... | {
"ground_truth": "3",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A pedestrian walked 5.5 kilometers in 1 hour but did not reach point \\( B \\) (short by \\(2 \\pi - 5.5\\) km). Therefore, the third option is longer than the first and can be excluded.\n\nIn the first case, they need to cover a distance of 5.5 km along the alley. If they move towards each other,... | {
"ground_truth": "11/51",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In Longtown, the streets are all $30$ feet wide and the blocks they enclose are rectangles with sides $500$ feet and $300$ feet in length. Jenny runs around the block along the $500$-foot side of the street, while Jeremy runs on the opposite side of the street. How many more feet than Jenny does J... | {
"ground_truth": "240",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Use $1,2,3,4,5,6$ to form a six-digit number without repeating digits. By arbitrarily extracting any two adjacent digits, you can get 5 different two-digit numbers. What is the maximum sum of these 5 two-digit numbers?\n\nTranslate the above text into English, please retain the original text's ... | {
"ground_truth": "219",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. Let \\( \\left.T=\\left|9^{k}\\right| k \\in \\mathbf{Z}, 0 \\leqslant k \\leqslant 4000\\right\\} \\), given that \\( 9^{4000} \\) is a 3817-digit number. And its leading digit is 9, then in \\( T \\), there are \\(\\qquad\\) numbers whose leading digit is 9.",
"role": "user"
}
] | {
"ground_truth": "184",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Let $x, y, z$ be non-negative real numbers, and satisfy $\\left\\{\\begin{array}{l}x+y-z=4 \\\\ x-y+3 z=6\\end{array}\\right.$, then the minimum value of $4 x+3 y+2 z$ is\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translati... | {
"ground_truth": "19",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Cyclic quadrilateral $ABCD$ has $AC\\perp BD$ , $AB+CD=12$ , and $BC+AD=13$ . FInd the greatest possible area of $ABCD$ . ",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "28.2.11 ** Let $M$ be a set of $n$ points in the plane, satisfying:\n(1) $M$ contains 7 points which are the 7 vertices of a convex heptagon;\n(2) For any 5 points in $M$, if these 5 points are the 5 vertices of a convex pentagon, then this convex pentagon contains at least one point from $M$ insi... | {
"ground_truth": "11",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A region is bounded by four quarter-circle arcs constructed at each corner of a square whose sides measure $4/\\pi$. Calculate the perimeter of this region.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The price of Grandma Margit's favorite chocolate increased by 30%, while her pension also rose by $15$%. By what percentage will Grandma Margit's chocolate consumption decrease if she can only spend $15$% more on chocolate?",
"role": "user"
}
] | {
"ground_truth": "11.54",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Zadatak A-2.5.\n\nDan je trapez $A B C D$ s osnovicama $\\overline{A B}$ i $\\overline{C D}$, takav da je trokut $A B C$ šiljastokutan. Neka je $O$ središte kružnice opisane trokutu $A B C$, a točka $E$ sjecište pravaca $O B$ i $C D$. Ako je $\\varangle D B C=\\varangle C E B+10^{\\circ}$, odre... | {
"ground_truth": "80",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. If $m+2019 n$ and $n+2019 m$ are divisible by $d$, then the number\n\n$$\n2019(m+2019 n)-(n+2019 m)=(2019^2-1) n\n$$\n\nis also divisible by $d$. If $n$ is divisible by $d$, and $m+2019 n$ is divisible by $d$, then $m$ is divisible by $d$ and the numbers $m$ and $n$ are not coprime. Therefore, ... | {
"ground_truth": "101",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 6 balls of each of the four colors: red, blue, yellow, and green. Each set of 6 balls of the same color is numbered from 1 to 6. If 3 balls with different numbers are randomly selected, and these 3 balls have different colors and their numbers are not consecutive, the number of ways to d... | {
"ground_truth": "96",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. From $1,2, \\cdots, 10$ choose 3 different numbers $a, b, c$ as the coefficients of the quadratic equation $a x^{2}+b x=c$. Then the number of equations with different solutions is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "654",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Let's consider the members of the finite sequence\n\n$$\n\\left[\\frac{k^{2}}{1998}\\right], \\quad k=1,2, \\ldots, 1997\n$$\n\nwhere $[x]$ denotes the integer part of $x$. How many different members are there in this sequence?\n\n(Greek)",
"role": "user"
}
] | {
"ground_truth": "1498",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two right triangles share a side such that the common side AB has a length of 8 units, and both triangles ABC and ABD have respective heights from A of 8 units each. Calculate the area of triangle ABE where E is the midpoint of side CD and CD is parallel to AB. Assume that side AC = side BC.",
... | {
"ground_truth": "16",
"mean_reward": 0.28125
} | 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\nFind all functions $f : \\mathbb{R} \\to\\mathbb{R}$ such that $f(0)\\neq 0$ and\n\\[f(f(x)) + f(f(y)) = f(x + y)f(xy),\\]\nfor all $x, y \\in\\mathbb{R}$.\n\n[Soluti... | {
"ground_truth": "5",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The \"Middle School Eight\" basketball conference has $8$ teams. Every season, each team plays every other conference team twice (home and away), and each team also plays $4$ games against non-conference opponents. What is the total number of games in a season involving the \"Middle School Eight\"... | {
"ground_truth": "88",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What flowchart symbol can have two directions of exit? Express your answer as the name of the symbol.",
"role": "user"
}
] | {
"ground_truth": "Decision",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. (13 points) In a dance ensemble, there are 8 boys and 16 girls. Some of them form mixed (boy and girl) dance pairs. It is known that in each pair, at least one of the partners does not belong to any other pair. What is the maximum number of dance pairs that can be formed in this ensemble?",
... | {
"ground_truth": "22",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a set $I=\\{1,2,3,4,5\\}$, select two non-empty subsets $A$ and $B$ such that the largest number in set $A$ is less than the smallest number in set $B$. The total number of different selection methods is $\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | {
"ground_truth": "49",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Among 30 people with different ages, select two groups: the first group with 12 people and the second group with 15 people, such that the oldest person in the first group is younger than the youngest person in the second group. Determine the number of ways to make this selection.",
"role": "us... | {
"ground_truth": "4060",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Can the number of diagonals of a polygon be exactly twice the number of its sides?",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let triangle $ABC$ with incenter $I$ satisfy $AB = 10$ , $BC = 21$ , and $CA = 17$ . Points $D$ and E lie on side $BC$ such that $BD = 4$ , $DE = 6$ , and $EC = 11$ . The circumcircles of triangles $BIE$ and $CID$ meet again at point $P$ , and line $IP$ meets the altitude fr... | {
"ground_truth": "85",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. The Black Demon stole a time-space gem from the divine tower and then fled in a straight line to the west. When the Black Demon had run 100 meters, the guards noticed the anomaly and set off from the divine tower at 1.5 times the speed of the Black Demon. At the moment of being caught, the Bla... | {
"ground_truth": "1500",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. (5 points)\nThe amusement park \"Forest River Adventure\" has a circular river, as shown in the figure. At 8:00, Feifei sets off downstream in a small boat. Feifei's rowing speed in still water is 4 kilometers per hour, and the current speed is 2 kilometers per hour. Feifei rests for 5 minutes... | {
"ground_truth": "11",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4・183 Find the number of real number pairs $(a, b)$ that make the system of equations $\\left\\{\\begin{array}{l}a x+b y=1, \\\\ x^{2}+y^{2}=50 .\\end{array}\\right.$ have at least one solution, and all solutions are integer solutions.",
"role": "user"
}
] | {
"ground_truth": "72",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "II. Find the maximum number of elements in a set $S$ that satisfies the following conditions:\n(1) Each element in $S$ is a positive integer not exceeding 100;\n(2) For any two different elements $a, b$ in $S$, there exists an element $c$ in $S$ such that the greatest common divisor (gcd) of $a$ a... | {
"ground_truth": "72",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest integer $m$ such that every digit of $m$ is either $8$ or $0$ and $m$ is a multiple of $18$. Compute $\\frac{m}{18}$.",
"role": "user"
}
] | {
"ground_truth": "493827160",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a set of 4027 points on a plane, called a \"Colombian point set,\" where no three points are collinear. Among these points, 2013 are red, and 2014 are blue. A set of lines drawn on the plane can divide the plane into several regions. A set of lines is considered a \"good line set\" for a Col... | {
"ground_truth": "2013",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Russian 2000 Problem 17 S is a finite set of numbers such that given any three there are two whose sum is in S. What is the largest number of elements that S can have?",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A Russian artist is planning an exhibition to showcase contemporary Russian art to gain more recognition. To organize the event, the artist has created 3 different series of paintings. Each series consists of 8 paintings. The artist also plans to invite 5 art critics to review the exhibition, and ... | {
"ground_truth": "24",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Oleg and Sergey take turns writing down one digit from left to right until a nine-digit number is formed. At the same time, they cannot write down digits that have already been written. Oleg starts (and finishes). Oleg wins if the resulting number is divisible by 4; otherwise, Sergey wins. Who ... | {
"ground_truth": "Sergey",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A person contracted the flu, and after two rounds of infection, a total of 196 people were infected. Calculate the average number of people infected by one person in each round of infection. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "13",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the minimum number of cells that need to be coloured in a 5x5 square grid so that every 1x4 or 4x1 rectangle in the grid has at least one coloured cell? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A street has parallel curbs 60 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is 20 feet and each stripe is 50 feet long. Find the distance, in feet, between the stripes.",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ten identical books cost no more than 11 rubles, whereas 11 of the same books cost more than 12 rubles. How much does one book cost?",
"role": "user"
}
] | {
"ground_truth": "110",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A square and a regular pentagon are coplanar and share a common side \\( \\overline{AD} \\). Determine the degree measure of the exterior angle \\( BAC \\).",
"role": "user"
}
] | {
"ground_truth": "162^\\circ",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A marathon is $26$ miles and $400$ yards. One mile equals $1760$ yards.\n\nMark has run fifteen marathons in his life. If the total distance Mark covered in these marathons is $m$ miles and $y$ yards, where $0 \\leq y < 1760$, what is the value of $y$?",
"role": "user"
}
] | {
"ground_truth": "720",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Estimate the value of $\\sqrt{90} - \\sqrt{88}$.",
"role": "user"
}
] | {
"ground_truth": "0.11",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 56, Find the value of $a$ that makes $\\sin 4 x \\cdot \\sin 2 x-\\sin x \\cdot \\sin 3 x=a$ have a unique solution in $[0, \\pi)$.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "... | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest real number \\( p \\) such that all three roots of the equation below are positive integers:\n\\[ \n5x^{3} - 5(p+1)x^{2} + (71p-1)x + 1 = 66p .\n\\]",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Four consecutive three-digit numbers are divided respectively by four consecutive two-digit numbers. What minimum number of different remainders can be obtained? \n\n[i](A. Golovanov)[/i]",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Determine all integers greater than 1 by which some fraction of the form\n\n$$\n\\frac{3 p-q}{5 p+2 q}\n$$\n\ncan be divided, where $p$ and $q$ are coprime integers.\n\nThe written part of the school round in category A takes place\n\n## on Tuesday, December 2, 2008\n\nso that it starts in the ... | {
"ground_truth": "11",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The South China tiger is a first-class protected animal in our country. To save the species from the brink of extinction, the country has established a South China tiger breeding base. Due to scientific artificial cultivation, the relationship between the number of South China tigers $y$ (individu... | {
"ground_truth": "46",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "22. In the figure below, if\n$$\n\\angle A+\\angle B+\\angle C+\\angle D+\\angle E+\\angle F+\\angle G=x \\text { degrees, }\n$$\nthen what is $x$ ?",
"role": "user"
}
] | {
"ground_truth": "540",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "As shown in the figure, Leilei uses 12 small wooden sticks to form a $3 \\times 3$ square. Fanfan uses 9 small wooden sticks to cut it into 3 small $1 \\times 2$ rectangles and 3 small $1 \\times 1$ squares. If Leilei uses 40 small wooden sticks to form an $8 \\times 12$ rectangle, then Fanfan nee... | {
"ground_truth": "116",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a chess festival that is held in a school with $2017$ students, each pair of students played at most one match versus each other. In the end, it is seen that for any pair of students which have played a match versus each other, at least one of them has played at most $22$ matches. What is t... | {
"ground_truth": "43890",
"mean_reward": 0.1875
} | 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\nIf $n$ gives a remainder of 3 when divided by 7, then what remainder does $2n+1$ give when divided by 7?\n\n[Solution]\n\n<paragraph_0>\nGiven that \\( n \\) gives a ... | {
"ground_truth": "-1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. The integers from 1 to $n$ are written on a circle, and the sum of any two adjacent integers is divisible by the integer that follows it (in the clockwise direction). Find all possible values of $n$.\n(1999, World Cities Mathematics Competition)",
"role": "user"
}
] | {
"ground_truth": "n=3",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Johnson, a retired bank security officer, often reminisces about his days of protecting the bank from criminals. One day, he decides to organize his old case files. He has 28 files, each representing a crime he helped prevent. He wants to divide these files into 4 equal stacks so he can easily... | {
"ground_truth": "8",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the decomposition rate $v$ of a certain type of garbage approximately satisfies the relationship $v=a\\cdot b^{t}$, where $a$ and $b$ are non-zero constants, and $v=5\\%$ after $6$ months and $v=10\\%$ after $12$ months, determine the time needed for this type of garbage to completely decomp... | {
"ground_truth": "32",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At a certain middle school, there are 110 teachers who know both English and Russian. According to the statistics, there are 75 teachers who know English and 55 teachers who know Russian. How many teachers at this school know English but not Russian?",
"role": "user"
}
] | {
"ground_truth": "55",
"mean_reward": 0.3125
} | 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\nThree friends Archie, Billie, and Charlie play a game. At the beginning of the game, each of them has a pile of $2024$ pebbles. Archie makes the first move, Billie ma... | {
"ground_truth": "9",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. Let the polynomial $1-x+x^{2}-x^{8}+\\cdots+x^{16}$ $-x^{17}$ be written as $a_{0}+a_{1} y+a_{2} y^{2}+a_{3} y^{3}+\\cdots$ $+a_{10} y^{16}+a_{17} y^{17}$,\n\nwhere $y=x+1$, and all $a_{\\mathrm{i}}$ are constants, find $a_{2}$.",
"role": "user"
}
] | {
"ground_truth": "816",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$15 A B C$ is a right-angled triangle with $\\angle B A C=90^{\\circ}$. A square is constructed on the side $A B$ and $B C$ as shown. The area of the square $A B D E$ is $8 \\mathrm{~cm}^{2}$ and the area of the square $B C F G$ is $26 \\mathrm{~cm}^{2}$. Find the area of triangle $D B G$ in $\\ma... | {
"ground_truth": "6",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B4. On a grid, a kind of spiral is drawn as follows. The spiral starts at point $(0,0)$\n\n$1^{\\text {st }}$ step: 1 to the right\n\n$2^{\\text{nd}}$ step: 1 diagonally to the top right\n\n$3^{\\text{rd}}$ step: 2 up\n\n$4^{\\text{th}}$ step: 2 diagonals to the top left\n\n$5^{\\text{th }}$ step:... | {
"ground_truth": "(1502,503)",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Covering with percentages and ratios ] [ Inclusion-exclusion principle ]\n\nThree crazy painters started painting the floor each in their own color. One managed to paint $75 \\%$ of the floor red, another $70 \\%$ green, and the third $65 \\%$ blue. What part of the floor is definitely painted w... | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a highway, there are checkpoints D, A, C, and B arranged in sequence. A motorcyclist and a cyclist started simultaneously from A and B heading towards C and D, respectively. After meeting at point E, they exchanged vehicles and each continued to their destinations. As a result, the first person... | {
"ground_truth": "340",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider 7 islands $A_{1}, \\ldots, A_{7}$. We are allowed to build bridges, either between an island $A_{i}$ and the next island $A_{i+1}$ (for $i \\in\\{1,2, \\ldots, 6\\}$), or between an island $A_{i}$ and the last one $A_{7}$ (for $i \\in\\{1,2, \\ldots, 6\\}$). In how many ways can these con... | {
"ground_truth": "144",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Point \\( K \\) lies on edge \\( AB \\) of pyramid \\( ABCD \\). Construct the cross-section of the pyramid with a plane passing through point \\( K \\) parallel to lines \\( BC \\) and \\( AD \\).",
"role": "user"
}
] | {
"ground_truth": "K L M N",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4.40 Find the smallest positive integer $n$, such that in any two-coloring of $K_{n}$, there exist two monochromatic triangles of the same color with no common edge.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider the graph of the function $y=g(x)$, characterized by the function $g(x) = \\frac{x^2}{Px^2 + Qx + R}$, where $P$, $Q$, and $R$ are integers. For $x > 5$, it is true that $g(x) > 0.5$. From the graph, it is observed that there are vertical asymptotes at $x = -3$ and $x = 4$, and the horizo... | {
"ground_truth": "-24",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Inside triangle $A B C$, a point $M$ is taken such that $\\angle C M B=100^{\\circ}$. The perpendicular bisectors of $B M$ and $C M$ intersect sides $A B$ and $A C$ at points $P$ and $Q$, respectively. Points $P, Q$, and $M$ lie on the same line. Find the measure of $\\angle C A B$.",
"role... | {
"ground_truth": "20",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.4. In the tetrahedron $E F G H$, it is known that $E F=G H=7, E G=F H=10, E H=F G=11$. Points $K, L, M, N$ are the centers of the circles inscribed in triangles $E F G, E F H$, $E G H$ and $F G H$. Find the volume of the tetrahedron $K L M N$. Round the answer to the nearest hundredth if necessa... | {
"ground_truth": "2.09",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If\n\\[1 \\cdot 1992 + 2 \\cdot 1991 + 3 \\cdot 1990 + \\dots + 1991 \\cdot 2 + 1992 \\cdot 1 = 1992 \\cdot 996 \\cdot x,\\]\ncompute the integer $x.$",
"role": "user"
}
] | {
"ground_truth": "665",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Person A and Person B start simultaneously from points A and B respectively, walking towards each other. Person A starts from point A, and their speed is 4 times that of Person B. The distance between points A and B is \\( S \\) kilometers, where \\( S \\) is a positive integer with 8 factors. The... | {
"ground_truth": "105",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In some foreign country's government, there are 12 ministers. Each minister has 5 friends and 6 enemies in the government (friendship/enemyship is a symmetric relation). A triplet of ministers is called [b]uniform[/b] if all three of them are friends with each other, or all three of them are enemi... | {
"ground_truth": "40",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Exercise 5. A number has been written on the board. At each step, we add to it the largest of its digits (for example, if 142 is written, the next number will be 146). What is the maximum number of odd numbers that can be written consecutively by proceeding in this way?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. In the final stage of a professional bowling tournament, the top five players compete as follows: First, the fifth-place player competes with the fourth-place player, the loser gets fifth place, the winner competes with the third-place player; the loser gets third place, the winner competes wit... | {
"ground_truth": "16",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. The sequence $\\left|a_{n}\\right|$ satisfies $a_{1}=19, a_{2}=98, a_{n}+2=a_{n}-\\frac{2}{a_{n 11}}$, then when $a_{n s}=0$, $m$ is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "933",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Andjans A.\n\nIn a table with $m$ rows and $n$ columns, a horizontal move is defined as a permutation of the elements in the table such that each element remains in the same row it was in before the permutation; similarly, a vertical move is defined (\"row\" in the previous definition is replaced ... | {
"ground_truth": "3",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 6 Let $S=\\{1,2, \\cdots, 50\\}$, find the smallest natural number $k$, such that in any $k$-element subset of $S$ there exist two distinct numbers $a$ and $b$, satisfying $(a+b) \\mid a b$.\n(1993 China Winter Camp Problem)",
"role": "user"
}
] | {
"ground_truth": "39",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Eight strangers are preparing to play bridge. How many ways can they be grouped into two bridge games, meaning into unordered pairs of unordered pairs of people?",
"role": "user"
}
] | {
"ground_truth": "315",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many kilometers will a traveler cover in 17 days, spending 10 hours a day on this, if he has already covered 112 kilometers in 29 days, traveling 7 hours each day?",
"role": "user"
}
] | {
"ground_truth": "93.79",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "David works at a widget factory. On Monday, David produces $w$ widgets every hour for $t$ hours, knowing that $w = 2t$. Feeling more motivated on Tuesday, he works for one fewer hour and increases his production rate by $5$ widgets per hour. Determine how many more widgets David produces on Monday... | {
"ground_truth": "-3t + 5",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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