prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Tiles $I, II, III$ and $IV$ are translated so one tile coincides with each of the rectangles $A, B, C$ and $D$. In the final arrangement, the two numbers on any side common to two adjacent tiles must be the same. Which of the tiles is translated to Rectangle $C$? [asy] size(400); defaultpen(linewi... | {
"ground_truth": "IV",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a function f(x) defined on R, where f''(x) < f''(-x) for any x in (0, +inf), and non-zero real numbers a and b satisfying f(a) - f(b) > f(-b) - f(-a), determine the relationship between a^2 and b^2. Express your answer as a relationship between a^2 and b^2.",
"role": "user"
}
] | {
"ground_truth": "a^2 < b^2",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7. Compute the integral\n\n$$\nI=\\int_{|z|=3} \\frac{z^{17}}{\\left(z^{2}+2\\right)^{3}\\left(z^{3}+3\\right)^{4}} d z\n$$",
"role": "user"
}
] | {
"ground_truth": "2\\pii",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\triangle ABC$ have vertices $A$ at the origin $(0,0)$, $B$ at $(8,0)$, and $C$ at $(1,7)$. Suppose you guess that the point $P = (3,4)$ might be a point of interest (e.g., aiming to minimize some combined distance property). Calculate the sum of distances from $P$ to $A$, $B$, and $C$ and e... | {
"ground_truth": "60",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Min-jun's video had a score of $120$, and $75\\%$ of the votes were likes. Determine how many total votes were cast on his video at that point.",
"role": "user"
}
] | {
"ground_truth": "240",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jenna, whose spouse was a miner who tragically lost their life in a mining accident, is now committed to advocating for stricter safety regulations in the mining industry. She decides to organize a community meeting to raise awareness and gather support. Jenna plans to invite 85 people to the meet... | {
"ground_truth": "247.50",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. Find positive integers $\\boldsymbol{n}$ and $m, n>m \\geqslant 1$, such that the last three digits of $1978^{n}$ and $1978^{m}$ are equal, and make $n+m$ as small as possible. (20th International Mathematical Olympiad Problem)",
"role": "user"
}
] | {
"ground_truth": "106",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's calculate the edge angle at the apex of a regular square pyramid, given that the centers of the inscribed and circumscribed spheres coincide.\n\n---\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.... | {
"ground_truth": "45",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a $4\\times 4\\times 3$ rectangular parallelepiped, vertices $A$, $B$, and $C$ are adjacent to vertex $D$. The perpendicular distance from $D$ to the plane containing $A$, $B$, and $C$ is closest to [asy] size(120); import three; currentprojection=orthographic(1, 4/5, 1/3); draw(box(O, (4,4,3))... | {
"ground_truth": "2.1",
"mean_reward": 0.34375
} | 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\nSelect numbers $a$ and $b$ between 0 and 1 independently and at random, and let $c$ be their sum. Let $A$, $B$, and $C$ be the results when $a$, $b$, and $c$, respect... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. Let the line $y=\\sqrt{3} x+b$ intersect the parabola $y^{2}=2 p x(p>0)$ at points $A, B$. The circle passing through $A, B$ intersects the parabola $y^{2}=2 p x(p>0)$ at two other distinct points $C, D$. Find the angle of intersection between the lines $A B$ and $C D$.",
"role": "user"
... | {
"ground_truth": "60",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task B-4.4.\n\nPoints $A, B$, and $C$ are the vertices of a triangle. On side $\\overline{A B}$, 6 points are marked, on side $\\overline{B C}$, 7 points are marked, and on side $\\overline{C A}$, 8 points are marked. The vertices of the triangle are not among the marked points. How many differ... | {
"ground_truth": "4347",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the diagram, \\(ABCD\\) is a square with a side length of 10. If \\(AY = CX = 8\\), calculate the area of the shaded region. Express your answer as a single numerical value.",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The base three representation of $x$ is \n\\[12112211122211112222\\]\nFind the first digit of the base nine representation of $x$. Express your answer as a single digit.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The quadratic polynomial $P(x),$ with real coefficients, satisfies\n\\[P(x^3 + x) \\ge P(x^2 + 1)\\]for all real numbers $x.$ Find the sum of the roots of $P(x).$",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Fill the numbers $1,2, \\cdots, 36$ into a $6 \\times 6$ grid, with each cell containing one number, such that the numbers in each row are in increasing order from left to right. The minimum value of the sum of the six numbers in the third column is $\\qquad$\n$(2015$, National Junior High Scho... | {
"ground_truth": "63",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest $r$ such that $4$ balls each of radius $r$ can be packed into a regular tetrahedron with side length $1$ . In a packing, each ball lies outside every other ball, and every ball lies inside the boundaries of the tetrahedron. If $r$ can be expressed in the form $\\frac{\\s... | {
"ground_truth": " 15 ",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "78. A person is walking along the road, and a car comes from the opposite direction. He asks the driver: \"Was there a bicycle behind you?\" The driver answers: \"I passed a bicycle 10 minutes ago.\" The person continues walking for 10 minutes and meets the bicycle. If the bicycle's speed is 3 tim... | {
"ground_truth": "7",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find an eight-digit palindrome that is a multiple of three, composed of the digits 0 and 1, given that all its prime divisors only use the digits 1, 3, and %. (Palindromes read the same forwards and backwards, for example, 11011).",
"role": "user"
}
] | {
"ground_truth": "10111101",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$10 \\cdot 52 \\quad 1990-1980+1970-1960+\\cdots-20+10$ equals:",
"role": "user"
}
] | {
"ground_truth": "1000",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( n \\) be a positive integer. Determine the smallest number \\( k \\) of colors needed to color the edges of any directed simple graph with \\( n \\) vertices such that there is no monochromatic cycle.",
"role": "user"
}
] | {
"ground_truth": "k = 2",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A young artist named Mia recently moved to the neighborhood of Bermondsey, where she found inspiration in its rich history. She decided to create a series of 5 paintings depicting different historical events from Bermondsey's past. Each painting takes her 3 days to complete. After finishing all th... | {
"ground_truth": "750",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. On the island, there are 217 residents, 17 of whom are knights, and the remaining 200 are tricksters. One day, a private detective arrived on the island and decided to find out who is who. For this, he asked each resident to write a list of 200 people they consider to be tricksters. The detecti... | {
"ground_truth": "13",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"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": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The stem-and-leaf plot shows the number of minutes and seconds of one ride on each of the 21 top-rated water slides in the world. In the stem-and-leaf plot, $1 \\ 45$ represents 1 minute, 45 seconds, which is equivalent to 105 seconds. What is the median of this data set? Express your answer in se... | {
"ground_truth": "135",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Rectangle $ABCD$, pictured below, shares $50\\%$ of its area with square $EFGH$. Square $EFGH$ shares $20\\%$ of its area with rectangle $ABCD$. What is $\\frac{AB}{AD}$?",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that a new kitchen mixer is listed in a store for $\\textdollar 129.99$ and an online advertisement offers the same mixer for four easy payments of $\\textdollar 29.99$ and a one-time shipping and handling fee of $\\textdollar 19.99$, calculate how many cents are saved by purchasing the mixe... | {
"ground_truth": "996",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the area enclosed by the graph \\( x^{2}+y^{2}=|x|+|y| \\) on the \\( xy \\)-plane.",
"role": "user"
}
] | {
"ground_truth": "\\pi + 2",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sphere is the set of points at a fixed positive distance \\( r \\) from its center. Let \\(\\mathcal{S}\\) be a set of 2010-dimensional spheres. Suppose that the number of points lying on every element of \\(\\mathcal{S}\\) is a finite number \\( n \\). Find the maximum possible value of \\( n \... | {
"ground_truth": "2",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In Papa Carlo's room, there is a clock on each wall, and they all show incorrect times: the first clock is off by 2 minutes, the second by 3 minutes, the third by 4 minutes, and the fourth by 5 minutes. One day, Papa Carlo decided to find out the exact time before leaving the house, and he saw the... | {
"ground_truth": "14:58",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The fraction \\(\\frac{1}{99^2}=0.\\overline{b_{n-1}b_{n-2}\\ldots b_2b_1b_0},\\) where $n$ is the length of the period of the repeating decimal expansion. What is the sum $b_0+b_1+\\cdots+b_{n-1}$?",
"role": "user"
}
] | {
"ground_truth": "883",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If\n\\[\n\\sum_{n=1}^{\\infty}\\frac{\\frac11 + \\frac12 + \\dots + \\frac 1n}{\\binom{n+100}{100}} = \\frac pq\n\\]\nfor relatively prime positive integers $p,q$ , find $p+q$ .\n\n*Proposed by Michael Kural*",
"role": "user"
}
] | {
"ground_truth": "9901",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.4. Does there exist a six-digit natural number that, when multiplied by 9, is written with the same digits but in reverse order?",
"role": "user"
}
] | {
"ground_truth": "109989",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "John was born on a Wednesday. Alison was born 72 days later. On what day of the week was Alison born? Express your answer as the full day of the week.",
"role": "user"
}
] | {
"ground_truth": "Friday",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Rational numbers $x, y, z$ satisfy $(|x+2|+|x-4|)(|y-2|+|y-5|)(|z-2|+|z+3|)=90$, then the maximum value of $(x-2 y+3 z)^{2}$ is $\\qquad$\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role":... | {
"ground_truth": "441",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is $\\frac{2468_{10}}{123_{5}} \\times 107_{8} + 4321_{9}$? Express your answer in base 10.",
"role": "user"
}
] | {
"ground_truth": "7789",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Place some white and black pieces in the following pattern, then the 27th piece is ( ) in color.",
"role": "user"
}
] | {
"ground_truth": "Black",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The 26 letters of the English alphabet are listed in an infinite, repeating loop:\n\nABCDEFGHIJKLMNOPQRSTUVWXYZABC...\n\nFind the letter at the 258th position in this sequence. Express your answer as a single letter.",
"role": "user"
}
] | {
"ground_truth": "\\text{X}",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. A chessboard $(8 \\times 8)$ was cut into several equal parts in such a way that all white cells remained uncut, while each black cell was cut. How many parts could have been obtained?",
"role": "user"
}
] | {
"ground_truth": "32",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sarah runs a popular Bachelor-themed podcast and records an episode every week to discuss the latest happenings on the show. Each episode is 45 minutes long. Sarah spends 20 minutes preparing notes for each contestant she discusses, and she talks about 3 contestants in each episode. After recordin... | {
"ground_truth": "135",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the minimum number of operations required to transform 2014 into 1, where an operation is defined as adding, subtracting, multiplying, or dividing by a single-digit number (1-9)?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. 10 athletes participate in a table tennis round-robin tournament, with each pair of athletes playing exactly one match. During the round-robin process, the first participant wins $x_{1}$ matches and loses $y_{1}$ matches, and so on,\n$$\n\\begin{array}{l}\nx_{1}{ }^{2}+x_{2}{ }^{2}+\\cdots+x_{1... | {
"ground_truth": "0",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Denote by $\\mathbb{Q}^+$ the set of positive rational numbers. A function $f : \\mathbb{Q}^+ \\to \\mathbb{Q}$ satisfies\n\n• $f(p) = 1$ for all primes $p$ , and\n\n• $f(ab) = af(b) + bf(a)$ for all $ a,b \\in \\mathbb{Q}^+ $ .\n\nFor which positive integers $n$ does the equation $nf... | {
"ground_truth": " n ",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. Let $x, y$ be real numbers. Then\n$$\n\\max _{S x^{2}+4 y^{2}=10 x}\\left(x^{2}+y^{2}\\right)=\n$$\n$\\qquad$",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "XXII OM - III - Problem 5\n\nFind the largest integer $ A $ such that for every permutation of the set of natural numbers not greater than 100, the sum of some 10 consecutive terms is at least $ A $.",
"role": "user"
}
] | {
"ground_truth": "505",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Evaluate $\\lfloor0.999\\rfloor+\\lceil2.001\\rceil$.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A movie producer specializing in CGI technology is working on a new film that features realistic animal characters. For one scene, the producer needs to create 8 different animals. Each animal requires 5 hours of CGI work to look realistic. Additionally, each animal character needs a 2-hour post-C... | {
"ground_truth": "28",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "assume you are Indonesian. In 2010, the rupiah exchange rate was around IDR15,000/USD, and the consumer price index in Indonesia and the United States was at 100. In 2019, the exchange rate changed to IDR14,000/USD. Simultaneously, Indonesia’s inflation rose 5% due to the consumer price index risi... | {
"ground_truth": "14666.67",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Igor and Pasha are playing a game, taking turns placing natural numbers at the vertices of a regular hexagon (each can choose any free vertex and place any natural number in it). After six moves, when the game ends, the judge writes the product of the numbers at the two ends of each side of the... | {
"ground_truth": "Pasha",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In $10\\times 10$ square we choose $n$ cells. In every chosen cell we draw one arrow from the angle to opposite angle. It is known, that for any two arrows, or the end of one of them coincides with the beginning of the other, or\nthe distance between their ends is at least 2. What is the maxi... | {
"ground_truth": "50",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a tournament with $55$ participants, one match is played at a time, with the loser dropping out. In each match, the numbers of wins so far of the two participants differ by not more than $1$. What is the maximal number of matches for the winner of the tournament?",
"role": "user"
}
] | {
"ground_truth": " 8 ",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 8 For a positive integer $n$, find the smallest integer $k$ such that for any given real numbers $a_{1}, a_{2}, \\cdots, a_{d}$, we have\n$$\n\\begin{array}{l}\na_{1}+a_{2}+\\cdots+a_{d}=n, \\\\\n0 \\leqslant a_{i} \\leqslant 1(i=1,2, \\cdots, d),\n\\end{array}\n$$\n\nthese real numbers ca... | {
"ground_truth": "2n-1",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three years ago, you invested some money at $12\\%$ interest. You now have $\\$504.32$ in the account. If the interest was compounded yearly, how much did you invest 3 years ago?",
"role": "user"
}
] | {
"ground_truth": "359",
"mean_reward": 0.046875
} | 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. The refractive index of the glass $n=1.6$. The angle of refraction for the first ray $\\beta=30^{\\circ}$. Determine the angle between the refracted rays.",
"r... | {
"ground_truth": "52",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The pentagon $ABCDE$ is inscribed in a circle. Points $M, Q, N,$ and $P$ are the bases of the perpendiculars dropped from vertex $E$ to the sides $AB, BC, CD$ (or their extensions) and diagonal $AD$ respectively. It is known that $|EP|=d$, and the ratio of the area of triangle $MQE$ to the area of... | {
"ground_truth": "d \\sqrt{k}",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In how many ways can you form 5 quartets from 5 violinists, 5 violists, 5 cellists, and 5 pianists?",
"role": "user"
}
] | {
"ground_truth": "(5!)^3",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. In the country of Landia, which breeds an elite breed of horses, an annual festival is held to test their speed, in which only one-year-old, two-year-old, three-year-old, and four-year-old horses can participate. For each horse that meets the speed standard, the festival organizers pay a fixed ... | {
"ground_truth": "200",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7.14 Find the number of second-kind circular permutations made from 2 $a$s, 2 $b$s, 2 $c$s.",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A smaller square was cut out from a larger square in such a way that one side of the smaller square lies on a side of the original square. The perimeter of the resulting octagon is $40\\%$ greater than the perimeter of the original square. By what percentage is the area of the octagon less than th... | {
"ground_truth": "64",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Elara, a storyteller known for her ghost tours and urban legends in European cities, is planning a special event for Halloween. She will tell 5 unique ghost stories in each of 3 different cities: Prague, Edinburgh, and Rome. Each story takes 15 minutes to tell. After each story, she takes a 5-minu... | {
"ground_truth": "5",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that for the positive numbers $x, y, z$,\n\n$$\nx^{2}+x y+y^{2}=9, \\quad y^{2}+y z+z^{2}=16, \\quad z^{2}+z x+x^{2}=25 .\n$$\n\nDetermine the value of $x y+y z+z x$.",
"role": "user"
}
] | {
"ground_truth": "8\\sqrt{3}",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that \\( A \\) and \\( B \\) are two subsets of \\(\\{1, 2, \\ldots, 100\\}\\) such that \\( |A| = |B| \\), \\( A \\cap B = \\emptyset \\), and for any \\( x \\in A \\), \\( 2x + 2 \\in B \\). Find the maximum value of \\( |A \\cup B| \\).",
"role": "user"
}
] | {
"ground_truth": "66",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The base three representation of $x$ is \n\\[12112211122211112222\\]\nFind the first digit of the base nine representation of $x$. Express your answer as a single digit.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Find the smallest natural number $n$, such that in any simple graph with 10 vertices, $n$ edges, and two-colored edges, there always exists a monochromatic triangle or a monochromatic quadrilateral.",
"role": "user"
}
] | {
"ground_truth": "31",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a class of 33 students, 22 swim and 22 play soccer every day. Everyone participates in at least one of the exercises every day. Of those who play soccer today, 15 swam and 15 played soccer yesterday, and the same situation applies to those who swim today. How many students swam only every day?"... | {
"ground_truth": "4",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five years ago, there were 25 trailer homes on Maple Street with an average age of 12 years. Since then, a group of brand new trailer homes was added, and 5 old trailer homes were removed. Today, the average age of all the trailer homes on Maple Street is 11 years. How many new trailer homes were ... | {
"ground_truth": "20",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Van has equal-sized balls, of which 2 are red, 2 are white, and 2 are blue. Among the monochromatic balls, one is made of gold, and the other is made of silver. What is the minimum number of weighings needed to select the three gold balls using a two-pan balance? (Balls made of the same material h... | {
"ground_truth": "2",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. From what country is the only the second South East Asian mathematician who recently received what is considered the highest recognition in mathematics, the Fields Medal.",
"role": "user"
}
] | {
"ground_truth": "Vietnam",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the vertices of a unit square, perpendiculars are erected to its plane. On them, on one side of the plane of the square, points are taken at distances of 3, 4, 6, and 5 from this plane (in order of traversal). Find the volume of the polyhedron whose vertices are the specified points and the ver... | {
"ground_truth": "4.5",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. (15 points) Fengfeng, Leilei, and Feifei have different eating habits. The table below shows today's lunch menu at the school cafeteria. A “ $\\checkmark$ ” indicates that they like the food, and a “ $\\times$ ” indicates that they refuse the food. If each of the three people orders 1 dish they... | {
"ground_truth": "51",
"mean_reward": 0.09375
} | 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\nA tangent from the point $(2 \\cdot 1994, 2 \\cdot 1994)$ to the circle $x^2 + y^2 = 1994^2$ touches circle at the point $(a,b).$ Compute $a + b.$\n\n[Solution]\n\n<... | {
"ground_truth": "3",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Problem Statement\n\nCalculate approximately using the differential.\n\n$y=x^{11} \\cdot x=1.021$",
"role": "user"
}
] | {
"ground_truth": "1.231",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the area of a quadrilateral with vertices at $(0,0)$, $(4,3)$, $(7,0)$, and $(4,4)$?",
"role": "user"
}
] | {
"ground_truth": "3.5",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5: A and B take turns picking distinct numbers from $0,1, \\cdots, 81$, with A starting first, and each person picks one number from the remaining numbers each time. After all 82 numbers are picked, let $A$ and $B$ be the sums of all numbers chosen by A and B, respectively. During the proc... | {
"ground_truth": "41",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Rhombus $ABCD$ has $\\angle BAD < 90^\\circ.$ There is a point $P$ on the incircle of the rhombus such that the distances from $P$ to the lines $DA,AB,$ and $BC$ are $9,5,$ and $16,$ respectively. Find the perimeter of $ABCD.$",
"role": "user"
}
] | {
"ground_truth": "125",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 7.7. The numbers from 1 to 200 were arranged in a random order on a circle such that the distances between adjacent numbers on the circle are the same.\n\nFor any number, the following is true: if you consider 99 numbers standing clockwise from it and 99 numbers standing counterclockwise f... | {
"ground_truth": "114",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a young American soccer enthusiast who loves learning about the history of the game. He recently discovered that the United States hosted the FIFA World Cup in 1994, a year before he was born. Alex learned that during the 1994 World Cup, a total of 52 matches were played, and the total att... | {
"ground_truth": "68991",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Serge and Tanya want to show Masha a magic trick. Serge leaves the room. Masha writes down a sequence $(a_1, a_2, \\ldots , a_n)$ , where all $a_k$ equal $0$ or $1$ . After that Tanya writes down a sequence $(b_1, b_2, \\ldots , b_n)$ , where all $b_k$ also equal $0$ or $1$ . Then Mash... | {
"ground_truth": " n ",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. At the hitmen convention, 1000 participants gathered, each receiving a registration number from 1 to 1000. By the end of the convention, it turned out that all hitmen, except number 1, were killed. It is known that each hitman could only kill hitmen with higher numbers, and the number of his vi... | {
"ground_truth": "10",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Given $p$ is a prime number, the fractional part of $\\sqrt{p}$ is $x$, and the fractional part of $\\frac{1}{x}$ is $\\frac{\\sqrt{p}-31}{75}$. Find all prime numbers $p$ that satisfy the condition.",
"role": "user"
}
] | {
"ground_truth": "2011",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If the graph of the function \\( f(x) \\) is symmetric about the points \\( (a, b) \\) and \\( (m, n) \\) (where \\( a \\neq m \\)), then for every \\( x \\) in the domain of the function \\( f(x) \\), the sequence \\( \\left\\{ y_{k} \\right\\} \\) formed by \\( y_{k} = f[x + 2k(a - m)] \\) (\\( ... | {
"ground_truth": "2(b-n)",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The Wolf and the three little pigs wrote a detective story \"The Three Little Pigs-2\", and then, together with Little Red Riding Hood and her grandmother, a cookbook \"Little Red Riding Hood-2\". The publisher gave the fee for both books to the pig Naf-Naf. He took his share and handed the remain... | {
"ground_truth": "700",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Problem B2\n\n$\\mathrm{P}_{1}, \\mathrm{P}_{2}, \\ldots, \\mathrm{P}_{\\mathrm{n}}$ are points in the plane and $\\mathrm{r}_{1}, \\mathrm{r}_{2}, \\ldots, \\mathrm{r}_{\\mathrm{n}}$ are real numbers such that the distance between $P_{i}$ and $P_{j}$ is $r_{i}+r_{j}$ (for $i$ not equal to $j$ ... | {
"ground_truth": "4",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The yearly changes in the population census of a town for four consecutive years are, respectively, 25% increase, 25% increase, 25% decrease, 25% decrease. The net change over the four years, to the nearest percent, is:",
"role": "user"
}
] | {
"ground_truth": "-12",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Egor wrote a number on the board and encrypted it according to the rules of letter puzzles (different letters correspond to different digits, the same letters correspond to the same digits). The result was the word \"GUATEMALA\". How many different numbers could Egor have initially written if h... | {
"ground_truth": "67200",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sum of 9 standard dice rolled has the same probability of occurring as the sum of 20. Find the value of the sum of 9 standard dice that shares this same probability.",
"role": "user"
}
] | {
"ground_truth": "43",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The keystone arch is an ancient architectural feature. It is composed of congruent isosceles trapezoids fitted together along the non-parallel sides, as shown. The bottom sides of the two end trapezoids are horizontal. In an arch made with $9$ trapezoids, let $x$ be the angle measure in degrees of... | {
"ground_truth": "100",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the dense jungle, a skilled poacher named Carlos competes with another poacher for prized exotic birds. Each day, Carlos manages to capture twice as many birds as his competitor. On Monday, Carlos captured 12 exotic birds. The following day, his competitor captured 5 more birds than he did on M... | {
"ground_truth": "33",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock? Express your answer in degrees, including the degree symbol (°).",
"role": "user"
}
] | {
"ground_truth": "60°",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the minimum number of fence posts required to fence a rectangular garden plot measuring 30 m by 50 m, where the fourth side is an existing 80 m wall.",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A local political analyst in West Bengal, India, is studying the distribution of funds among various Panchayati Raj institutions in a rural district. The district has 5 villages, each with its own Panchayat. The total budget allocated for rural development is ₹500,000. The analyst discovers that e... | {
"ground_truth": "400000",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 4 people standing in a line numbered 1 through 4 in a left to right order.\nEach person has the following attributes: Nationality, Food, Movie-Genre, Beverage, Sport, Transport.\nThe attributes have the following possible values:\n- Nationality: egyptian, mexican, nigerian, polish\n- Fo... | {
"ground_truth": "egyptian",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( P \\) be a point inside regular pentagon \\( ABCDE \\) such that \\( \\angle PAB = 48^\\circ \\) and \\( \\angle PDC = 42^\\circ \\). Find \\( \\angle BPC \\), in degrees.",
"role": "user"
}
] | {
"ground_truth": "84",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Problem 2.\n\nIn a football tournament, each team is supposed to play one match against each of the others. But during the tournament, half of all the teams were disqualified and withdrew from further participation. As a result, 77 matches were played, and the teams that withdrew had managed to ... | {
"ground_truth": "14",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Find the largest positive integer $n$, such that the inequality $\\frac{8}{15}<$ $-\\frac{n}{n+k}<\\frac{7}{13}$ holds for exactly one integer $k$.",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alice and Bob have an $8 \\times 8$ chessboard in front of them. Initially, all the squares are white. Each turn, Alice selects a white square and colors it black. Bob then chooses to color one of the neighboring squares (sharing an edge) black or does nothing. Alice can stop the game whenever she... | {
"ground_truth": "16",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.45*. What is the maximum number of points that can be placed on a segment of length 1 so that on any segment of length $d$ contained in this segment, there are no more than $1+1000 d^{2}$ points?\n\nSee also problems $15.1,17.20$.\n\n## §7. Extremal Properties of Regular Polygons",
"role": ... | {
"ground_truth": "32",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Interior numbers begin in the third row of Pascal's Triangle. Calculate the sum of the squares of the interior numbers in the eighth row.",
"role": "user"
}
] | {
"ground_truth": "3430",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\underline{\\text { Akulich I.F. }}$\n\nThere are 40 identical gas cylinders, the pressure values in which are unknown to us and may be different. It is allowed to connect any cylinders to each other in a quantity not exceeding a given natural number $k$, and then disconnect them; in this case, ... | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three, (16 points) Let $n$ be a positive integer, and $d_{1}<d_{2}<$ $d_{3}<d_{4}$ be the 4 smallest consecutive positive integer divisors of $n$. If $n=d_{1}^{2}+d_{2}^{2}+d_{3}^{2}+d_{4}^{2}$, find the value of $n$.",
"role": "user"
}
] | {
"ground_truth": "130",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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