prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "10. $1991^{2000}$ divided by $10^{6}$, the remainder is",
"role": "user"
}
] | {
"ground_truth": "880001",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The squares in a $7\\times7$ grid are colored one of two colors: green and purple. The coloring has the property that no green square is directly above or to the right of a purple square. Find the total number of ways this can be done.",
"role": "user"
}
] | {
"ground_truth": "3432",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An $8 \\times 8$ chessboard is divided into $p$ rectangles such that no single square is cut in half. Each such division must satisfy the following conditions:\n\n(a) Each rectangle must contain an equal number of white and black squares.\n\n(b) If $a_{i}$ denotes the number of white squares in th... | {
"ground_truth": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Square $ABCD$ in the coordinate plane has vertices at the points $A(1,1), B(-1,1), C(-1,-1),$ and $D(1,-1).$ Consider the following four transformations: $\\quad\\bullet\\qquad$ $L,$ a rotation of $90^{\\circ}$ counterclockwise around the origin; $\\quad\\bullet\\qquad$ $R,$ a rotation of $90^{\\c... | {
"ground_truth": "2^{38}",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangular box has integer side lengths in the ratio $1: 3: 4$. Which of the following could be the volume of the box?",
"role": "user"
}
] | {
"ground_truth": "96",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We have 21 pieces of type $\\Gamma$ (each formed by three small squares). We are allowed to place them on an $8 \\times 8$ chessboard (without overlapping, so that each piece covers exactly three squares). An arrangement is said to be maximal if no additional piece can be added while following thi... | {
"ground_truth": "16",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many three-digit positive integers $\\underline{a} \\ \\underline{b} \\ \\underline{c}$ are there whose nonzero digits $a,b,$ and $c$ satisfy \\[0.\\overline{\\underline{a}~\\underline{b}~\\underline{c}} = \\frac{1}{3} (0.\\overline{a} + 0.\\overline{b} + 0.\\overline{c})?\\] (The bar indicate... | {
"ground_truth": "13",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. (12 points) In a city, from 7:00 to 8:00 in the morning is the peak hour, during which all vehicles travel at half their original speed. Every morning at 6:50, two people, A and B, start from points $A$ and $B$ respectively, heading towards each other, and meet at a point 24 kilometers away fr... | {
"ground_truth": "42",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangular plot $ABCD$ is divided into two rectangles as shown in the diagram and is contracted to two households, Jia and Yi. Jia's vegetable greenhouse has the same area as Yi’s chicken farm, while the remaining part of Jia's area is 96 acres more than Yi's. Given that $BF = 3 CF$, what is th... | {
"ground_truth": "192",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Tangent circles [ Opposite the larger side lies the larger angle ]\n\nTwo circles of radii $r$ and $p (r < p)$ touch each other externally and both touch internally a circle of radius $R$. It is known that the triangle with vertices at the centers of the circles is isosceles, and the angle betwe... | {
"ground_truth": "R-r",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For every integer $n\\ge2$, let $\\text{pow}(n)$ be the largest power of the largest prime that divides $n$. For example $\\text{pow}(144)=\\text{pow}(2^4\\cdot3^2)=3^2$. What is the largest integer $m$ such that $2010^m$ divides\n\n$\\prod_{n=2}^{5300}\\text{pow}(n)$?",
"role": "user"
}
] | {
"ground_truth": "77",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the last digit of the decimal expansion of $\\frac{1}{3^{15}}$?",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A man was building a house for himself. Only the roof remains to be completed. The builder wanted the raindrops falling on the roof to roll off as quickly as possible. Determine the angle of inclination of the roof required to achieve this goal. Ignore friction between the raindrops and the roof."... | {
"ground_truth": "45^\\circ",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the 33rd digit after the decimal point of $(\\\\sqrt{10} + 3)^{2001}$? Express your answer as a single digit.",
"role": "user"
}
] | {
"ground_truth": "0",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "It is known that solution A has a salinity of $8\\%$, and solution B has a salinity of $5\\%$. After mixing both solutions, the resulting salinity is $6.2\\%$. What will be the concentration when a quarter of solution A is mixed with a sixth of solution B?",
"role": "user"
}
] | {
"ground_truth": "6.5\\%",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. The right side of the inequality is zero when $|x| \\leqslant 10$ (for other $x$ it is undefined). Denoting $\\alpha=\\frac{\\pi x}{4}$, we get:\n\n$$\n\\begin{aligned}\n& \\frac{\\sin 2 \\alpha-\\cos 2 \\alpha+1}{\\sin 2 \\alpha+\\cos 2 \\alpha-1} \\geqslant 0 \\Longleftrightarrow \\frac{2 \\s... | {
"ground_truth": "-12",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7 (2003 Belarusian Mathematical Olympiad) Given a convex pentagon $A B C D E$ satisfying $A B=B C, C D=$ $D E, \\angle A B C=150^{\\circ}, \\angle C D E=30^{\\circ}, B D=2$. Find the area of pentagon $A B C D E$.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the sequence $\\left\\{a_{n}\\right\\}$, if $a_{n}^{2}-a_{n-1}^{2}=p$ (where $n \\geq 2, n \\in \\mathbf{N^{*}}$, and $p$ is a constant), then $\\left\\{a_{n}\\right\\}$ is called an \"equal variance sequence.\" Below are the judgments for the \"equal variance sequence\":\n\n1. The sequence $\\... | {
"ground_truth": "1234",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $O$ and $I$ be the circumcenter and incenter of triangle $ABC$ . The perpendicular from $I$ to $OI$ meets $AB$ and the external bisector of angle $C$ at points $X$ and $Y$ respectively. In what ratio does $I$ divide the segment $XY$ ?",
"role": "user"
}
] | {
"ground_truth": " 1:2 ",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find $x$ such that $\\lceil x \\rceil \\cdot x = 210$. Express $x$ as a decimal.",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sandy wants to cover the exterior wall, which measures 8 feet wide by 10 feet high, and two identical roof faces, each 8 feet wide that slant upward at 45 degrees over an additional 7 feet, with special weather-resistant siding. Each sheet of siding measures 8 feet by 12 feet and costs \\$32.80. A... | {
"ground_truth": "\\$98.40",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the value of $-1 + 2 + 3 + 4 - 5 - 6 - 7 - 8 - 9 + \\dots + 10000$, where the signs change after each perfect square.",
"role": "user"
}
] | {
"ground_truth": "1000000",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Arrange 2002 students numbered from 1 to 2002 in a row from left to right. Counting from left to right from 1 to 11, the student who is counted as 11 remains in place, while the others leave the row. Then, the remaining students count from left to right from 1 to 11 again, and the student who is c... | {
"ground_truth": "1331",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\left.\\frac{\\text { Auxiliary similar triangles }}{[\\quad \\text { Law of Cosines }}\\right]$\n\nIn triangle $ABC$, a point $D$ is taken on side $AC$, such that $AD=3$, $\\cos \\angle BDC=13/20$, and $\\angle B+\\angle ADB=180^{\\circ}$. Find the perimeter of triangle $ABC$ if $BC=2$.",
"... | {
"ground_truth": "11",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.5. 16 travelers, each of whom is either a liar or a knight (liars always lie, knights always tell the truth), settled into 3 rooms of a hotel. When everyone gathered in their rooms, Basil, who was staying in the first room, said: \"There are more liars than knights in this room right now. Althou... | {
"ground_truth": "9",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two sisters were picking currants: the older one was using a 4-liter bucket, and the younger one was using a 3.5-liter bucket. The older sister was always working faster than the younger one. When the older sister had collected three-quarters of her bucket, and the younger sister had collected mor... | {
"ground_truth": "1.5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In one year, what is the maximum number of months that can have five Sundays? Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. In the right figure, there are 10 beads on each of the three rods of the abacus. By dividing the beads on each rod into upper and lower parts, we get two three-digit numbers. The upper part must be a three-digit number with all different digits, and it must be a multiple of the lower three-digi... | {
"ground_truth": "925",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. In a hat, there are 11 slips of paper with numbers $0,1,2,3,4,5,6,7,8,9,10$ (one with each number). Each of the eleven students takes one slip. Then they announce in alphabetical order the sentence \"so far, at least $k$ students have told a lie,\" where $k$ is the number on the drawn slip. How... | {
"ground_truth": "6",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\(\\triangle ABC\\) have side lengths \\(AB=30\\), \\(BC=32\\), and \\(AC=34\\). Point \\(X\\) lies in the interior of \\(\\overline{BC}\\), and points \\(I_1\\) and \\(I_2\\) are the incenters of \\(\\triangle ABX\\) and \\(\\triangle ACX\\), respectively. Find the minimum possible area of \... | {
"ground_truth": "126",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the 10 by 10 grid of squares shown, point \\( P \\) can be at any of the 41 points of intersection of pairs of gridlines inside (and not on) \\(\\triangle F G H\\). For each possible location of \\( P \\), exactly three triangles are formed: \\(\\triangle F P G\\), \\(\\triangle G P H\\), \\(\\... | {
"ground_truth": "9",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A professional scriptwriter named Alex is working on a new holiday movie screenplay. To make the movie unique, Alex decides to include 5 different holiday traditions from various cultures. Each tradition is to be featured in a 10-minute scene. Alex also wants to include 2 musical numbers, each las... | {
"ground_truth": "-3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a class, there are 15 boys and 15 girls. On Women's Day, some boys called some girls to congratulate them (no boy called the same girl more than once). It turned out that the children can be uniquely divided into 15 pairs, such that each pair consists of a boy and a girl whom he called. What is... | {
"ground_truth": "120",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2 Given that $\\alpha$ is a root of the equation $x^{2}-x-1=0$. Try to find the value of $\\alpha^{18}+323 \\alpha^{-6}$.\n\n \n\nTranslating the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "us... | {
"ground_truth": "5796",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 17 (2002-2003 British Mathematical Olympiad) Find all positive integers $a, b, c$ such that $a, b, c$ satisfy\n$$\n(a!)(b!)=a!+b!+c!.\n$$",
"role": "user"
}
] | {
"ground_truth": "3,3,4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A Moskvich car was sent to transport mail from the post office to the airfield. The plane carrying the mail landed earlier than expected, and the delivered mail was sent to the post office by a passing truck. After driving for 30 minutes, the truck met the Moskvich on the road, which received the ... | {
"ground_truth": "40",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The eleven members of a cricket team are numbered $1,2,...,11$ . In how many ways can the entire cricket team sit on the eleven chairs arranged around a circular table so that the numbers of any two adjacent players differ by one or two ?",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task Condition\n\nApproximately calculate using the differential.\n\n$y=x^{4}, x=3,998$",
"role": "user"
}
] | {
"ground_truth": "255.488",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nNT3 Let $s(a)$ denote the sum of digits of a given positive integer $a$. The sequence $a_{1}, a_{2}, \\ldots a_{n}, \\ldots$ of positive integers is such that $a_{n+1}=a_{n}+s\\left(a_{n}\\right)$ for each positive integer $n$. Find the greatest possible $n$ for which it is possible to have $a_{... | {
"ground_truth": "6",
"mean_reward": 0.25
} | 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\nOn the Cartesian plane, the midpoint between two points $A(a,b)$ and $B(c,d)$ is $M(m,n)$. If $A$ is moved vertically upwards 20 units and horizontally to the right 1... | {
"ground_truth": "6",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In Zuminglish, all words consist only of the letters $M, O,$ and $P$. As in English, $O$ is said to be a vowel and $M$ and $P$ are consonants. A string of $M's, O's,$ and $P's$ is a word in Zuminglish if and only if between any two $O's$ there appear at least two consonants. Let $N$ denote the num... | {
"ground_truth": "936",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A flowchart is executed with the following initial conditions and loop structure:\n- Initial values: S = 1, n = 1\n- Loop condition: n > 3\n- Loop body: S = S + 2n, n = n + 1\n\nCalculate the final value of S after executing the loop.",
"role": "user"
}
] | {
"ground_truth": "13",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that $A_k = \\frac {k(k - 1)}2\\cos\\frac {k(k - 1)\\pi}2,$ find $|A_{19} + A_{20} + \\cdots + A_{98}|.$",
"role": "user"
}
] | {
"ground_truth": "40",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "To understand the vision of 600 students, system sampling was used to extract a sample of 20. Calculate the number of groups the students should be divided into to perform the sampling. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task 23/85\n\nGiven the $n$-digit natural number $z_{n}=1985$!. Form the natural number $z_{n-1}$ by removing the units digit of $z_{n}$ and subtracting it from the remaining $(n-1)$-digit number. Continue this process until a single-digit number $z$ is obtained. What is $z$?",
"role": "use... | {
"ground_truth": "0",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Four congruent rectangles are placed as shown. The area of the outer square is $4$ times that of the inner square. What is the ratio of the length of the longer side of each rectangle to the length of its shorter side? [asy] unitsize(6mm); defaultpen(linewidth(.8pt)); path p=(1,1)--(-2,1)--(-2,2)-... | {
"ground_truth": "3",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $M$.\n\nOn an island, there live knights, liars, and yes-men; each knows who everyone else is. All 2018 residents were lined up and asked to answer \"Yes\" or \"No\" to the question: \"Are there more knights than liars on the island?\". The residents answered in turn, and everyone could hear t... | {
"ground_truth": "1009",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "253. Garden Fence. A garden fence, similar to the one shown in the figure, had the same number of columns in each section (between two vertical posts), and each vertical post (except the two outermost ones) divided one of the columns in half. Absent-mindedly counting all the columns from end to en... | {
"ground_truth": "23",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider the parabolas defined by $y = 2(x - 2)^2$ and $x - 1 = 2(y + 1)^2$. Find the sum of all $x$ and $y$ coordinates of their intersection points.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. (20 points) Two mutually perpendicular rays, propagating in the same vertical plane, fall from air onto a horizontal glass surface.\n\nThe refractive index of the glass $n=1.5$. The angle of refraction for the first ray $\\beta=25^{\\circ}$. Determine the angle between the refracted rays.",
... | {
"ground_truth": "56",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A carpenter wishes to cut a wooden 3 x 3 x 3 cube into twenty-seven 1 x 1 x 1 cubes. What is the minimum number of cuts needed if he is allowed to rearrange the pieces after each cut? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three points with integer coordinates between 1 and 2020 are chosen uniformly at random. The triangle they form has area (via the shoelace formula) an integer if a certain numerator is even. If the probability that the triangle’s area is an integer is \\(\\frac{a}{b}\\) in lowest terms, find \\(a+... | {
"ground_truth": "13",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. (10 points) As shown in the figure, $ABCD$ is a rectangle, and the small horizontal lines drawn from $G$, $F$, and $E$ are all parallel to $AB$. If $AD$ $=12$, then what is $AG$ equal to?",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sequence $(a_n)$ satisfies $a_0=0$ and $a_{n + 1} = \\frac85a_n + \\frac65\\sqrt {4^n - a_n^2}$ for $n\\geq 0$. Find the greatest integer less than or equal to $a_{10}$.",
"role": "user"
}
] | {
"ground_truth": "983",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $S=\\{1,2, \\cdots, 2005\\}$. If any set of $n$ pairwise coprime numbers in $S$ contains at least one prime number, find the minimum value of $n$. (Tang Lihua)",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In the country of Ouo, the numbers are only even, there are no odd numbers. The sum of all three-digit numbers in Ouo is",
"role": "user"
}
] | {
"ground_truth": "54400",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. A flask contains 40 liters of milk. How can you transfer 6 liters of milk from it into a 10-liter bucket using a 9-liter and a 5-liter bucket?",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "One hundred musicians are planning to organize a festival with several concerts. In each concert, while some of the one hundred musicians play on stage, the others remain in the audience assisting to the players. What is the least number of concerts so that each of the musicians has the chance to ... | {
"ground_truth": "9",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. $n$ chess players participate in a chess tournament, with each pair of players competing in one match. The rules are: the winner gets 1 point, the loser gets 0 points, and in the case of a draw, both players get 0.5 points. If it is found after the tournament that among any $m$ players, there i... | {
"ground_truth": "2m-3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "373. Cutting a Cube. In a mathematical journal, the following question and answer appeared.\n\nQuestion: \"A carpenter wants to cut a wooden cube with a side of 3 inches into 27 cubes with a side of 1 inch. He can easily do this by making 6 cuts while keeping the pieces together so they don't fall... | {
"ground_truth": "6",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We measured the elevation angles of a tower standing on a horizontal plane from points $50 \\mathrm{~m}$ and $100 \\mathrm{~m}$ away from the base of the tower. The sum of the measured angles is $45^{\\circ}$. How tall is the tower?",
"role": "user"
}
] | {
"ground_truth": "28.08",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Janice bought 40 items, each priced at 50 cents, $1.50, or $3.00. If her total purchase price was $\\$$45.00, how many 50-cent items did she purchase?",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Zhendarov R.G.\n\nIn the cells of a $4 \\times 4$ table, numbers are written such that the sum of the neighbors of each number is 1 (cells are considered neighbors if they share a side).\n\nFind the sum of all the numbers in the table.\n\n#",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10.5. The tsar has eight sons, and they are all fools. Every night the tsar sends three of them to guard the golden apples from the firebird. The tsareviches cannot catch the firebird, blame each other for it, and therefore no two of them agree to go on guard duty a second time. For how many night... | {
"ground_truth": "8",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At the mall's food court, Crystal and her friend Amy each want to buy a meal consisting of one entree, one drink, and one dessert. The table below lists both Crystal’s and Amy’s favorite foods from the food court. Assuming they could choose from a shared assortment and wanted to try different meal... | {
"ground_truth": "1260",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is a point source of light in an empty universe. What is the minimum number of solid balls (of any size) one must place in space so that any light ray emanating from the light source intersects at least one ball?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of all roots of the equation:\n\n$$\n\\begin{gathered}\n\\sqrt{2 x^{2}-2024 x+1023131} + \\sqrt{3 x^{2}-2025 x+1023132} + \\sqrt{4 x^{2}-2026 x+1023133} = \\\\\n= \\sqrt{x^{2}-x+1} + \\sqrt{2 x^{2}-2 x+2} + \\sqrt{3 x^{2}-3 x+3}\n\\end{gathered}\n$$",
"role": "user"
}
] | {
"ground_truth": "2023",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$12 \\cdot 144$ Find all real numbers $p$ such that the cubic equation\n$$\n5 x^{3}-5(p+1) x^{2}+(71 p-1) x+1=66 p\n$$\n\nhas three roots that are all natural numbers.\n(China High School Mathematics League, 1995)",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ana, Bob, and Cao bike at constant rates of $8.6$ meters per second, $6.2$ meters per second, and $5$ meters per second, respectively. They all begin biking at the same time from the northeast corner of a rectangular field whose longer side runs due west. Ana starts biking along the edge of the fi... | {
"ground_truth": "61",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a certain year, a specific date was never a Sunday in any month. Determine this date.",
"role": "user"
}
] | {
"ground_truth": "31",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$$\n\\begin{array}{l}\n\\frac{a^{2}\\left(\\frac{1}{b}-\\frac{1}{c}\\right)+b^{2}\\left(\\frac{1}{c}-\\frac{1}{a}\\right)+c^{2}\\left(\\frac{1}{a}-\\frac{1}{b}\\right)}{a\\left(\\frac{1}{b}-\\frac{1}{c}\\right)+b\\left(\\frac{1}{c}-\\frac{1}{a}\\right)+c\\left(\\frac{1}{a}-\\frac{1}{b}\\right)} \\... | {
"ground_truth": "a+b+c",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the sequence $\\{a_{n}\\}$ satisfying $a_{1}=1$, $a_{2}=4$, $a_{n}+a_{n+2}=2a_{n+1}+2$, find the sum of the first 2022 terms of the sequence $\\{b_{n}\\}$, where $\\left[x\\right)$ is the smallest integer greater than $x$ and $b_n = \\left[\\frac{n(n+1)}{a_n}\\right)$.",
"role": "user"
... | {
"ground_truth": "4045",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At the intersection of perpendicular roads, a highway from Moscow to Kazan intersects with a route from Vladimir to Ryazan. Dima and Tolya started traveling with constant speeds from Moscow to Kazan and from Vladimir to Ryazan, respectively. When Dima crossed the intersection, Tolya had 3500 meter... | {
"ground_truth": "9100",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Problem 4.\n\nA box contains 900 cards, numbered from 100 to 999. Cards are drawn at random (without replacement) from the box, and the sum of the digits of each card drawn is noted. What is the minimum number of cards that must be drawn to ensure that at least three of these sums are the same?... | {
"ground_truth": "53",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The chief information security officer of a major energy company is tasked with allocating resources to handle AI-driven threats. In one week, her team identifies 6 different AI threats. Each threat requires 3 team members and 4 hours to analyze. Additionally, for every threat analyzed, 2 hours ar... | {
"ground_truth": "108",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a dihedral angle α-PQ-β, points A and B are on half-plane α, and point C is on half-plane β (A, B, and C are not on PQ, and the distances from A and B to PQ are not equal). Construct a trapezoid with A, B, and C as three of its vertices, such that the fourth vertex also lies on the same half... | {
"ground_truth": "2",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. (5 points) Arrange the natural numbers $1,2,3,4$, in ascending order without any gaps, to get: 1234567891011121314. In this sequence of digits, when the first set of 5 consecutive even digits appears, the position of the first (even) digit from the left is the how many-th digit?",
"role": ... | {
"ground_truth": "490",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rain or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day $k$ is dependent on the weather on day $k-1$. We can write the transition ... | {
"ground_truth": "0.5167",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Use 2 red beads, 2 blue beads, and 2 purple beads to string into a bracelet as shown in the figure below. How many different bracelets can be made.\n\n\n\nPreserve the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. If $x^{4}+16 x=12$, then $x^{2}+2 x+4=$\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": "What is the number of labelled forests on 8 vertices with 5 connected components, such that vertices 1, 2, 3, 4, 5 all belong to different connected components?",
"role": "user"
}
] | {
"ground_truth": "320",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the order of the group S_3 * Z_2?",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. In each cell of a $2017 \\times 2017$ board, there is a chip. In one operation, you can remove a chip that has a non-zero even number of neighbors (neighbors are chips located in cells that share a side or a corner). What is the minimum number of chips that can be left on the board using such o... | {
"ground_truth": "2",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "(solved by Anca Arnautu and Adrien Laroche). Let $\\mathscr{P}$ be the parabola in the plane with equation $y=x^{2}$. Let $\\Gamma_{1}$ be the circle of diameter 1 tangent internally to $\\mathscr{P}$ at the origin. By recurrence, we define $\\Gamma_{n+1}$ as the circle tangent to $\\Gamma_{n}$ an... | {
"ground_truth": "4013",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Triangle \\(ABC\\) is isosceles \\((AB = BC)\\). Segment \\(AM\\) divides it into two isosceles triangles with bases \\(AB\\) and \\(MC\\). Find angle \\(B\\).",
"role": "user"
}
] | {
"ground_truth": "36^\\circ",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. A rectangle is drawn on the board. It is known that if its width is increased by $30 \\%$, and its length is decreased by $20 \\%$, then its perimeter remains unchanged. How would the perimeter of the original rectangle change if its width were decreased by $20 \\%$, and its length were increas... | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine which is greater without using a calculator or logarithm table: \\(200!\\) or \\(100^{200}\\).",
"role": "user"
}
] | {
"ground_truth": "100^{200}",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many ways are there to arrange the letters of the word $\\text{B}_1\\text{A}_1\\text{N}_1\\text{A}_2\\text{N}_2\\text{A}_3\\text{B}_2$, where three A's, two N's, and two B's are all considered different within each letter group but identical between groups?",
"role": "user"
}
] | {
"ground_truth": "210",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Thompson, a retired engineer who loves solving Sudoku puzzles, is sharing his problem-solving strategies with a group of students. To make it fun, he decides to create a math challenge based on his Sudoku techniques. Mr. Thompson explains that in one of his favorite Sudoku strategies, he start... | {
"ground_truth": "8",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. There is a bag with 16 letters: А, А, А, А, В, В, Д, И, И, М, М, Н, Н, Н, Я, Я. Anna, Vanya, Danya, and Dima each took 4 letters from it, after which the bag was empty. How many of them could have successfully spelled out their names? Explain your answer.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Petl wrote on the board in a row $n$ two-digit octal numbers $(n \\geqslant 2)$, forming an arithmetic progression with a common difference of 8, and the first number does not contain the digit 2. Vasya thought that this was the octal representation of a natural number $x$, and he factored $x$ ... | {
"ground_truth": "3343",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For each of the nine natural numbers \\( n, 2n, 3n, \\ldots, 9n \\), the first digit from the left in its decimal representation was written on the board. \\( n \\) was chosen so that the number of different digits among the nine written digits is as small as possible. What is this minimum number ... | {
"ground_truth": "4",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2 Given that $A$ and $B$ are two subsets of the set $\\{1,2,3, \\cdots, 100\\}$, satisfying $|A|=|B|$, and $A \\cap$ $B=\\varnothing$. If $x \\in A$ always implies $2 x+2 \\in B$, then the maximum number of elements in the set $A \\cup B$ is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "66",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Figures $I$, $II$, and $III$ are squares. The perimeter of $I$ is $12$ and the perimeter of $II$ is $24$. Find the perimeter of square $III$. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "I2.4 Determine the unit digit, $\\delta$, of $\\left(\\left(\\gamma^{\\gamma}\\right)^{\\gamma}\\right)^{\\gamma}$.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose you have $27$ identical unit cubes colored such that $3$ faces adjacent to a vertex are red and the other $3$ are colored blue. Suppose further that you assemble these $27$ cubes randomly into a larger cube with $3$ cubes to an edge (in particular, the orientation of each cube is random). ... | {
"ground_truth": "53",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. In a $10 \\times 10$ grid, the centers of all unit squares are marked (a total of 100 points). What is the minimum number of lines, not parallel to the sides of the square, needed to cross out all the marked points?",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Dr. Alex, a computer scientist, is exploring the technical feasibility of teleportation devices described in a popular sci-fi author's books. In the novel, each teleportation device requires 5 energy crystals to function, and each crystal can only power the device for 3 hours. \n\nDr. Alex plans t... | {
"ground_truth": "1",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For example, October 1, 1949, was a Saturday.",
"role": "user"
}
] | {
"ground_truth": "Saturday",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given four distinct real numbers \\( a, b, c, d \\) such that \\(\\frac{a}{b} + \\frac{b}{c} + \\frac{c}{d} + \\frac{d}{a} = 4\\) and \\( ac = bd \\), find the maximum value of \\(\\frac{a}{c} + \\frac{b}{d} + \\frac{c}{a} + \\frac{d}{b} \\).",
"role": "user"
}
] | {
"ground_truth": "-12",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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