prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Let \\[\\mathbf{M} = \\begin{pmatrix} a & b & 0 \\\\ 0 & a & b \\\\ b & 0 & a \\end{pmatrix}\\] be a matrix with complex entries such that $\\mathbf{M}^3 = \\mathbf{I}$. If $ab = 1$, find the possible values of $a^3 + b^3$.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At a university in Budapest, the most successful students can apply for two types of scholarships. One of the conditions for the outstanding scholarship is that the average of the grades earned in the last semester must be above 4.5. For the republican scholarship, however, an average of at least ... | {
"ground_truth": "51",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Milton spilled some ink on his homework paper again. He can't read the coefficient of \\(x^2\\), but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain?\n\n[asy]\ndraw((0,0)--(3,0)--(3,... | {
"ground_truth": "26",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For the expression $\\frac{\\sqrt{5}}{5}\\left(\\frac{\\sqrt{5}+1}{2}\\right)^{2013}$, when written as a decimal, find the digit before the decimal point.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Define a function \\( f \\) on the set of positive integers \\( N \\) as follows:\n(i) \\( f(1) = 1 \\), \\( f(3) = 3 \\);\n(ii) For \\( n \\in N \\), the function satisfies\n\\[ \n\\begin{aligned}\n&f(2n) = f(n), \\\\\n&f(4n+1) = 2f(2n+1) - f(n), \\\\\n&f(4n+3) = 3f(2n+1) - 2f(n).\n\\end{aligned}... | {
"ground_truth": "92",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5 Suppose we have a $4 \\times 4$ grid where each cell is colored differently. Each cell is filled with either 0 or 1, such that the product of the numbers in any two adjacent cells is 0. How many different ways are there to fill the grid with numbers?\n\n(2007, Korean Mathematical Olympia... | {
"ground_truth": "1234",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. A thin beam of light falls normally on a plane-parallel glass plate. Behind the plate, at some distance from it, stands an ideal mirror (its reflection coefficient is equal to one). The plane of the mirror is parallel to the plate. It is known that the intensity of the beam that has passed thro... | {
"ground_truth": "0.75",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The diagram below shows the regular hexagon $BCEGHJ$ surrounded by the rectangle $ADFI$. Let $\\theta$\u0012 be the measure of the acute angle between the side $\\overline{EG}$ of the hexagon and the diagonal of the rectangle $\\overline{AF}$. There are relatively prime positive integers $m$ and $... | {
"ground_truth": "55",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A bungee cord is 30.0 m long and, when stretched a distance x, it exerts a restoring force of magnitude kx. Your father-in-law (mass 95.0 kg) stands on a platform 45.0 m above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him... | {
"ground_truth": "0.602",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Let M be a set of six distinct positive integers whose sum is 60. We will write all of them on the faces of a cube, with exactly one on each face. In one step, we choose any three faces of the cube that share a common vertex and increase each of the numbers on these three faces by 1. Determine ... | {
"ground_truth": "84",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 In $\\triangle A B C$, $a, b, c$ are the sides opposite to $A, B, C$ respectively, then $\\frac{a A+b B+c C}{a+b+c}-\\frac{\\pi}{3}$ (fill in $\\left.\\geq 、 \\leq 、=\\right)$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output ... | {
"ground_truth": "\\geq",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five 1x1 squares are arranged as shown in the diagram. Calculate the percentage of the total area of the five squares that is shaded. Express your answer as a percentage, including the percent sign (%).",
"role": "user"
}
] | {
"ground_truth": "40%",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A can complete a piece of work in 12 days. B is 33% less efficient than A. Determine the number of days it takes B to do the same piece of work.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all positive integers $n>1$ such that \n\\[\\tau(n)+\\phi(n)=n+1\\]\nWhich in this case, $\\tau(n)$ represents the amount of positive divisors of $n$ , and $\\phi(n)$ represents the amount of positive integers which are less than $n$ and relatively prime with $n$ .\n\n*Raja Oktovin,... | {
"ground_truth": " n = 4 ",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Four, (50 points) A town has $n(n \\geqslant 3)$ villages, some of which are connected by roads, and each road connects only two villages. Any two villages are connected by at most one road, and there are no crossroads at road intersections, but there are bridges or tunnels. It is known that any t... | {
"ground_truth": "2n-3",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The owner of a large cleaning company is worried about the rise of small cleaning services that offer flexible scheduling and efficient communication channels. These smaller companies manage to complete 15 cleaning jobs per week. To stay competitive, the owner wants to ensure their company complet... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Four, (50 points) Find all positive integers $n$, such that $2^{n}+2n$ is a factorial of a positive integer.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly. \n\nNote: The provided text is already in Engli... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## 47.\n\nOne day, Alice met the Lion and the Unicorn resting under a tree. They made the following statements.\n\nLion. Yesterday was one of the days when I lie.\n\nUnicorn. Yesterday was one of the days when I also lie.\n\nFrom these two statements, Alice (a very smart girl) was able to deduce w... | {
"ground_truth": "Thursday",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Friends Vasya, Petya, and Kolya live in the same house. One day, Vasya and Petya went fishing at the lake on foot. Kolya stayed home, promising to meet his friends on a bicycle on their way back. Vasya was the first to head home, and at the same time, Kolya set out on a bicycle to meet him. Pet... | {
"ground_truth": "2",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "33rd Swedish 1993 Problem 6 For reals a, b define the function f(x) = 1/(ax+b). For which a, b are there distinct reals x 1 , x 2 , x 3 such that f(x 1 ) = x 2 , f(x 2 ) = x 3 , f(x 3 ) = x 1 .",
"role": "user"
}
] | {
"ground_truth": "-b^2",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Compute the remainder when\n\\[\n\\prod_{i=1}^{1903} \\Big(2^i+5\\Big)\n\\]\nis divided by 1000.",
"role": "user"
}
] | {
"ground_truth": "931",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1.39. A point $O$ inside a convex quadrilateral of area $S$ is reflected symmetrically with respect to the midpoints of its sides. Find the area of the quadrilateral with vertices at the resulting points.\n\n## §4. Auxiliary Congruent Triangles\n\nTranslate the text above into English, please keep... | {
"ground_truth": "2S",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The photographer wants to arrange three boys and three girls in a row such that a boy or a girl could be at each end, and the rest alternate in the middle, calculate the total number of possible arrangements.",
"role": "user"
}
] | {
"ground_truth": "72",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.8 Dima calculated the reciprocal of the factorial of each integer from 80 to 100. He printed the resulting decimal fractions on 19 infinitely long strips of paper (for example,\n\nSasha cut a segment from one of the strips, which had exactly $n$ digits without a decimal point. If Sasha doesn't w... | {
"ground_truth": "155",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Putnam 1994 Problem B3 Let R be the reals and R + the positive reals. f : R → R + is differentiable and f '(x) > f(x) for all x. For what k must f(x) exceed e kx for all sufficiently large k? Solution",
"role": "user"
}
] | {
"ground_truth": "k\\leq1",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. The number $a_{n}$ is formed by writing down the first n consecutive natural numbers in sequence, for example, $a_{13}=12345678910111213$. Determine how many numbers divisible by 24 are among the numbers $a_{1}, a_{2}, \\ldots, a_{10000}$.",
"role": "user"
}
] | {
"ground_truth": "834",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Given a cube and 12 colors. Find the number of ways to paint the faces of this cube using these colors (each face in one color) such that adjacent faces are of different colors. Colorings that differ by a rotation are considered different.",
"role": "user"
}
] | {
"ground_truth": "987360",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Distinct positive integers $a, b, c, d$ satisfy\n\n$$\n\\left\\{\\begin{array}{l}\na \\mid b^{2}+c^{2}+d^{2}, \\\\\nb \\mid a^{2}+c^{2}+d^{2}, \\\\\nc \\mid a^{2}+b^{2}+d^{2}, \\\\\nd \\mid a^{2}+b^{2}+c^{2},\n\\end{array}\\right.\n$$\n\nand none of them is larger than the product of the three oth... | {
"ground_truth": "3",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In base $b$, there are exactly one hundred forty-four three-digit numbers whose digits are all distinct and each number includes the digit 1 at least once. What is $b$?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Find the smallest natural number $n$, for which it is possible to cover a table of dimensions $n \\times n$ without overlapping using the same number of tiles\n\n\n\nS... | {
"ground_truth": "6",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given {(x1,x2,x3,x4) ⊆ {x | (x-3) * sin(πx) = 1, x > 0}}, find the minimum value of x1+x2+x3+x4.",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Emily, a neighborhood kid who grew up playing in the streets of Chelmsford, loves organizing games with her friends. One sunny afternoon, she decided to organize a game of street soccer. She invited 18 kids from the neighborhood to join. She wants to make sure that each team has an equal number of... | {
"ground_truth": "5",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. For the complex number $x$, the minimum value of the expression $u=|x|+|x-i|+|x-\\sqrt{3}|$ is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{7}",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the value of $-1 + 2 + 3 + 4 - 5 - 6 - 7 - 8 - 9 + \\dots + 12100$, where the signs change after each perfect square.",
"role": "user"
}
] | {
"ground_truth": "1331000",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.4. How to cut a $5 \\times 5$ square with straight lines so that the resulting pieces can be used to form 50 equal squares? It is not allowed to leave unused pieces or overlap them.",
"role": "user"
}
] | {
"ground_truth": "50",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Vertices $A$ and $B$ of the prism $A B C A 1 B 1 C 1$ lie on the axis of the cylinder, while the other vertices lie on the lateral surface of the cylinder. Find the dihedral angle in this prism with edge $A B$.",
"role": "user"
}
] | {
"ground_truth": "120",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sequence of natural numbers is constructed by listing the first $4$, then skipping one, listing the next $5$, skipping $2$, listing $6$, skipping $3$, and on the $n$th iteration, listing $n+3$ and skipping $n$. The sequence begins $1,2,3,4,6,7,8,9,10,13$. What is the $500,\\!000$th number in the... | {
"ground_truth": "996,506",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Let $A=\\left\\{a_{1}, a_{2}, \\cdots, a_{7}\\right\\}$. Here $a_{i} \\in \\mathbf{Z}^{\\prime}$, and let $n_{A}$ denote the number of triples $(x, y, z)$ such that: $x<y$, $x+y=z, x, y, z \\in A$. Then the maximum possible value of $n_{A}$ is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2 Let $S=\\{1,2,3,4\\}, n$ terms of the sequence: $a_{1}, a_{2}, \\cdots, a_{n}$ have the following property, for any non-empty subset $B$ of $S$ (the number of elements in $B$ is denoted as $|B|$), there are adjacent $\\mid B$ | terms in the sequence that exactly form the set $B$, find th... | {
"ground_truth": "8",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Zhang Ming, Wang Liang, Li Yang, and Zhao Xu are four athletic students who will form a 4×100 meter relay team. They have the following conversation:\n\nZhang Ming: I won't run the first or second leg.\n\nWang Liang: I won't run the first or fourth leg.\n\nLi Yang: I also won't run the first or fo... | {
"ground_truth": "Li Yang",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given two points on a plane and a line parallel to the line segment connecting the two points, along with the angle $\\alpha$. Construct the segment on the parallel line that appears at an angle $\\alpha$ from both points!",
"role": "user"
}
] | {
"ground_truth": "CD",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Yamenniko i.v.\n\nThe numbers 2, 3, 4, ..., 29, 30 are written on the board. For one ruble, you can mark any number. If a number is already marked, you can freely mark its divisors and numbers that are multiples of it. What is the minimum number of rubles needed to mark all the numbers on the boar... | {
"ground_truth": "5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find $x$, given that $x$ is neither zero nor one and the numbers $\\{x\\}$, $\\lfloor x \\rfloor$, and $x$ form a geometric sequence in that order. (Recall that $\\{x\\} = x - \\lfloor x\\rfloor$).",
"role": "user"
}
] | {
"ground_truth": "1.618",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many sequences $ a_1,a_2,...,a{}_2{}_0{}_0{}_8$ are there such that each of the numbers $ 1,2,...,2008$ occurs once in the sequence, and $ i \\in (a_1,a_2,...,a_i)$ for each $ i$ such that $ 2\\le i \\le2008$?",
"role": "user"
}
] | {
"ground_truth": "2^{2007}",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A brand of orange juice is available in shop $A$ and shop $B$ at an original price of $\\$2.00$ per bottle. Shop $A$ provides a \"buy 4 get 1 free\" promotion and shop $B$ provides a $15\\%$ discount if one buys 4 bottles or more. Find the minimum cost (in cents) if one wants to buy 13 bottles of ... | {
"ground_truth": "2160",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "20. Given a finite number of polygons in the plane, if for any two of them, there is a line passing through the origin that intersects both, then these polygons are said to be properly placed.\n\nFind the smallest positive integer $m$, such that for any set of properly placed polygons, it is possi... | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Convex Polygons ]\n\nAmong all such numbers $n$, that any convex 100-gon can be represented as the intersection (i.e., common part) of $n$ triangles, find the smallest.",
"role": "user"
}
] | {
"ground_truth": "50",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. If the sum of 12 distinct positive integers is 2016, then the maximum value of the greatest common divisor of these positive integers is $\\qquad$\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.",
... | {
"ground_truth": "24",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For reals $x\\ge3$ , let $f(x)$ denote the function\n\\[f(x) = \\frac {-x + x\\sqrt{4x-3} } { 2} .\\]Let $a_1, a_2, \\ldots$ , be the sequence satisfying $a_1 > 3$ , $a_{2013} = 2013$ , and for $n=1,2,\\ldots,2012$ , $a_{n+1} = f(a_n)$ . Determine the value of\n\\[a_1 + \\sum_{i=1}^{2012} ... | {
"ground_truth": "4025",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B. If $k$ numbers are chosen from 2, $, 8, \\cdots, 101$ these 34 numbers, where the sum of at least two of them is 43, then the minimum value of $k$ is: $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "28",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 2. Lёnya has cards with digits from 1 to 7. How many ways are there to glue them into two three-digit numbers (one card will not be used) so that their product is divisible by 81, and their sum is divisible by 9?",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. In the school, after classes, someone broke a mirror in the vestibule. The last to leave were 9 students. The school principal asked each of them: \"Who broke the mirror?\" The answers were as follows. Roland: \"It was Percy.\" Alex: \"No, it wasn't Percy.\" Ted: \"I broke the mirror.\" Fred: \... | {
"ground_truth": "Walter",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Line segments PQ and RS are parallel. Points T, U, and V are placed so that ∠QTV = 30°, ∠SUV = 40°, and ∠TVU = x°, as shown. Find the value of x. Express your answer in degrees as a whole number.",
"role": "user"
}
] | {
"ground_truth": "70",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7 Given positive real numbers $x, y, z$ satisfy\n$$\n\\left\\{\\begin{array}{l}\nx^{2}+x y+y^{2}=9, \\\\\ny^{2}+y z+z^{2}=16, \\\\\nz^{2}+z x+x^{2}=25 .\n\\end{array}\\right.\n$$\n\nFind the value of $x y+y z+z x$.",
"role": "user"
}
] | {
"ground_truth": "8 \\sqrt{3}",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Determine all natural numbers $n \\geq 2$ such that for all integers $0 \\leq i, j \\leq n$:\n\n$$\ni+j \\equiv\\binom{n}{i}+\\binom{n}{j} \\quad(\\bmod 2)\n$$\n\nAnswer: The solutions are all numbers of the form $n=2^{k}-2$ with $k \\geq 2$.",
"role": "user"
}
] | {
"ground_truth": "2^{k}-2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7 Let $S=\\{1,2, \\cdots, 15\\}$, and take $n$ subsets $A_{1}, A_{2}, \\cdots, A_{n}$ from $S$, satisfying the following conditions:\n(i) $\\left|A_{i}\\right|=7, i=1,2, \\cdots, n$;\n(ii) $\\left|A_{i} \\cap A_{j}\\right| \\leqslant 3,1 \\leqslant i<j \\leqslant n$;\n(iii) For any three-e... | {
"ground_truth": "15",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Express $537_8 + 1C2E_{16}$ as a base 10 integer, where $C$ and $E$ denote the hexadecimal digits with values 12 and 14 respectively.",
"role": "user"
}
] | {
"ground_truth": "7565",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the monotonic decreasing interval of the function $y=\\sqrt{3-2x-x^2}$. Express your answer as an interval in standard interval notation.",
"role": "user"
}
] | {
"ground_truth": "(-1,1)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $S$ be the set of all permutations of $\\{1, 2, 3, 4, 5\\}$. For $s = (a_1, a_2,a_3,a_4,a_5) \\in S$, define $\\text{nimo}(s)$ to be the sum of all indices $i \\in \\{1, 2, 3, 4\\}$ for which $a_i > a_{i+1}$. For instance, if $s=(2,3,1,5,4)$, then $\\text{nimo}(s)=2+4=6$. Compute \\[\\sum_{s\\... | {
"ground_truth": "9765",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is a 3-hour time difference between Vancouver and Toronto, with Vancouver being behind Toronto. For example, when it is 1:00 p.m. in Vancouver, it is 4:00 p.m. in Toronto. What time is it in Vancouver when it is 6:30 p.m. in Toronto? Express your answer in 12-hour clock format, including the... | {
"ground_truth": "3:30 p.m.",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 6. Father's age is 48 years old, son's age is 20 years old. How many years later will the father's age be 3 times the son's age?",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Out of 24 matchsticks of the same length, use some of them to form 6 triangles in a plane where each side of the equilateral triangle is one matchstick. Then, use the remaining matchsticks to form squares in the plane where each side of the square is one matchstick. What is the maximum number of s... | {
"ground_truth": "4",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sorrelkova N.P.\n\nUnder one of the cells of an $8 \\times 8$ board, a treasure is buried. Under each of the other cells, there is a sign indicating the minimum number of steps required to reach the treasure from that cell (one step allows moving from a cell to an adjacent cell by side). What is t... | {
"ground_truth": "3",
"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\nAn integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition.... | {
"ground_truth": "-1",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.14 The lock opens only if a specific three-digit number is entered. An attempt consists of randomly selecting three digits from the five given. The number was guessed only on the last of all attempts. How many attempts preceded the successful one?",
"role": "user"
}
] | {
"ground_truth": "124",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13.336. Coal delivered to the warehouse is intended for two plants. Coal delivery to the first plant started on June 1st at a rate of $m$ tons daily, including Sundays, and to the second plant - on June 8th at a rate of $n$ tons daily, including Sundays. By the end of June 16th, half of the initia... | {
"ground_truth": "June28",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A lumberjack is building a non-degenerate triangle out of logs. Two sides of the triangle have lengths $\\log 101$ and $\\log 2018$ . The last side of his triangle has side length $\\log n$ , where $n$ is an integer. How many possible values are there for $n$ ?\n\n*2018 CCA Math Bonanza Ind... | {
"ground_truth": "203797",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a, b, c, d$ be real numbers. Suppose that all the roots of $z^4+az^3+bz^2+cz+d=0$ are complex numbers lying on a circle in the complex plane centered at $0+0i$ and having radius $1$. The sum of the reciprocals of the roots is necessarily",
"role": "user"
}
] | {
"ground_truth": "-a",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal $\\overline{BD}$ of square $ABCD$? [asy] defaultpen(linewidth(1)); for ( int x = 0; x < 5; ++x ) { draw((0,x)--(4,x)); draw((x,0)--(x,4)); } fill((1,0)--(2,0)--(2,1)--(1,1)--cy... | {
"ground_truth": "4",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "24. Find the number of permutations $a_{1} a_{2} a_{3} a_{4} a_{5} a_{6}$ of the six integers from 1 to 6 such that for all $i$ from 1 to $5, a_{i+1}$ does not exceed $a_{i}$ by 1 .",
"role": "user"
}
] | {
"ground_truth": "309",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Entrepreneurs Vasiliy Petrovich and Petr Gennadievich opened a clothing factory \"ViP.\" Vasiliy Petrovich invested 200 thousand rubles, while Petr Gennadievich invested 350 thousand rubles. The factory was successful, and after a year, Anastasia Alekseevna approached them with an offer to buy par... | {
"ground_truth": "1000000",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. A reservoir of water in a national park is replenished with 1 hectoliter of water every day. A herd of 38 elephants will drink all the water from the reservoir in one day, while a herd of 8 elephants will drink all the water from the reservoir in 5 days. If each elephant drinks the same amount ... | {
"ground_truth": "75",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the number of solutions to the equation 10 sin(x + π/6) = x within the bounds -10 ≤ x ≤ 10.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[Equilateral (Equiangular) Triangle]\n\n[Properties and Characteristics of a Parallelogram]\n\n[Auxiliary Congruent Triangles]\n\n[Rotation Helps Solve the Problem.\n\nOn the sides $AB, BC$, and $CA$ of an equilateral triangle $ABC$, points $D, E$, and $F$ are chosen respectively such that $DE \\p... | {
"ground_truth": "60",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the triangle ABC, the side lengths opposite to angles A, B, and C are a, b, and c respectively. If the height h from angle A to side AC equals c - a, then find the value of sin((C - A)/2) + cos((C + A)/2). Express your answer as a single numerical value.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Old Mr. Thompson, a retired gentleman with a penchant for storytelling, fondly recalls the days when he would enjoy a smoke while chatting with friends. Although those days are behind him, he always finds a way to see the silver lining in every situation. One sunny afternoon, while reminiscing abo... | {
"ground_truth": "2190",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider an equilateral triangle of side length $n$, which is divided into unit triangles, as shown. Let $f(n)$ be the number of paths from the triangle in the top row to the middle triangle in the bottom row, such that adjacent triangles in our path share a common edge and the path never travels ... | {
"ground_truth": "(2004)!",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a certain triangle, the difference of two sides: $b-c$ is twice the distance of the angle bisector $f_{\\alpha}$, originating from the common endpoint $A$ of the two sides, from the altitude foot $M$. What is the angle $\\alpha$ enclosed by the two sides?",
"role": "user"
}
] | {
"ground_truth": "60^\\circ",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex, an education technology expert, is invited to give a presentation about the future of library technology at a conference. For the presentation, Alex plans to use a total of 5 gadgets: 2 tablets, 1 laptop, and 2 smartboards. Each tablet requires 3 hours to charge fully, the laptop requires 4 ... | {
"ground_truth": "8",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the statements: ① the four interior angles of a square are equal; ② the four interior angles of a rectangle are equal; ③ a square is a rectangle, determine the correct sequence of these statements to form a valid syllogism for the major premise, minor premise, and conclusion, respectively. E... | {
"ground_truth": "②③①",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the minimum value of $k$ such that there exists two sequence ${a_i},{b_i}$ for $i=1,2,\\cdots ,k$ that satisfies the following conditions.\n\n(i) For all $i=1,2,\\cdots ,k,$ $a_i,b_i$ is the element of $S=\\{1996^n|n=0,1,2,\\cdots\\}.$ (ii) For all $i=1,2,\\cdots, k, a_i\\ne b_i.$... | {
"ground_truth": "1997",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "16. Two cars are driving on a highway, 100 meters apart, both traveling at 60 kilometers per hour. The highway has different speed points (the speed points are far apart). After each car passes the first speed point, their speed immediately increases to 80 kilometers per hour; after passing the se... | {
"ground_truth": "200",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that a high school senior year has 12 classes, with exactly 8 classes to be proctored by their own homeroom teachers, find the number of different proctoring arrangements for the math exam.",
"role": "user"
}
] | {
"ground_truth": "4455",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A large square is divided into a small square surrounded by four congruent rectangles as shown. The perimter of each of the congruent rectangles is $14$. What is the area of the large square? [asy]pathpen = black+linewidth(0.7); D((0,0)--(7,0)--(7,7)--(0,7)--cycle); D((1,0)--(1,6)); D((0,6)--(6,6)... | {
"ground_truth": "49",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. It is given that the sequence $\\left(a_{n}\\right)_{n=1}^{\\infty}$, with $a_{1}=a_{2}=2$, is given by the recurrence relation\n$$\n\\frac{2 a_{n-1} a_{n}}{a_{n-1} a_{n+1}-a_{n}^{2}}=n^{3}-n\n$$\nfor all $n=2,3,4, \\ldots$. Find the integer that is closest to the value of $\\sum_{k=2}^{2011} \... | {
"ground_truth": "3015",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , $X$ in centimeters?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the result of $655_6 - 222_6 + 111_6$ in base-6.",
"role": "user"
}
] | {
"ground_truth": "544_6",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The integer sequence \\(\\left\\{a_{n}\\right\\}\\) is defined as \\(a_{1}=1\\), \\(a_{2}=2\\), and \\(a_{n+2}=5a_{n+1}+a_{n}\\). Evaluate the expression \\(\\left[\\frac{a_{2}}{a_{1}}\\right] \\left\\{\\left[\\frac{a_{3}}{a_{2}}\\right\\} \\left\\{\\frac{a_{4}}{a_{3}}\\right\\} \\cdots \\left\\{\... | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rook has traveled across an \\( n \\times n \\) board, visiting each cell exactly once, where each of its moves was exactly one cell. The cells are numbered from 1 to \\( n^2 \\) in the order of the rook's path. Let \\( M \\) be the maximum difference between the numbers of adjacent (by side) ce... | {
"ground_truth": "2n - 1",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Rory uses four identical standard dice to build a solid. Whenever two dice touch, the numbers on the touching faces are the same. The numbers on some faces of the solid are shown. Given that the numbers on opposite faces of a standard die add up to 7, what number is written on the face marked with... | {
"ground_truth": "5",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $ABC$ be at triangle with incircle $\\Gamma$ . Let $\\Gamma_1$ , $\\Gamma_2$ , $\\Gamma_3$ be three circles inside $\\triangle ABC$ each of which is tangent to $\\Gamma$ and two sides of the triangle and their radii are $1,4,9$ . Find the radius of $\\Gamma$ .",
"role": "user"... | {
"ground_truth": "11",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If a polynomial with real coefficients of degree $d$ has at least $d$ coefficients equal to $1$ and has $d$ real roots, what is the maximum possible value of $d$?\n\n(Note: The roots of the polynomial do not have to be different from each other.)",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $c_1,c_2,\\ldots,c_{6030}$ be 6030 real numbers. Suppose that for any 6030 real numbers $a_1,a_2,\\ldots,a_{6030}$ , there exist 6030 real numbers $\\{b_1,b_2,\\ldots,b_{6030}\\}$ such that \\[a_n = \\sum_{k=1}^{n} b_{\\gcd(k,n)}\\] and \\[b_n = \\sum_{d\\mid n} c_d a_{n/d}\\] for $n=1,2... | {
"ground_truth": "528",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The owner of an art restoration studio, Ms. Lee, offers apprenticeships to recent art school graduates. Each apprentice works on restoring paintings under her guidance. The studio has received 15 paintings for restoration this month. Ms. Lee has 3 apprentices working in her studio. Each apprentice... | {
"ground_truth": "0",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 Find all positive integers $k$ such that the indeterminate equation $x^{2}+y^{2}=k x y-1$ has positive integer solutions for $x$ and $y$.\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": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Yashchenko I.V.\n\nThe numbers 2, 3, 4, ... 29, 30 are written on the board. For one ruble, you can mark any number. If a number is already marked, you can freely mark its divisors and numbers that are multiples of it. What is the minimum number of rubles needed to mark all the numbers on the boar... | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sum of a set of numbers is the sum of all its elements. Let \\( S \\) be a set consisting of positive integers not exceeding 15, where the sums of any two disjoint subsets of \\( S \\) are not equal. Among all sets with this property, find the \\( S \\) with the maximum sum, and determine the ... | {
"ground_truth": "61",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 181, Given sets $A, B, C \\subseteq\\{1,2, \\ldots, 2020\\}$, and $A \\subseteq C, B \\subseteq C$, find the number of ordered set groups $(A, B, C)$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result dire... | {
"ground_truth": "5^{2020}",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 9.4. It is known that the number 400000001 is the product of two prime numbers $p$ and $q$. Find the sum of the natural divisors of the number $p+q-1$.\n\n---\n\nThe text has been translated while preserving the original formatting and line breaks.",
"role": "user"
}
] | {
"ground_truth": "45864",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "16. For a plane region $D$, let $N(D)$ denote the number of all integer points (i.e., points on the $X O Y$ plane where both coordinates $x, y$ are integers) within $D$. If $A$ represents the region enclosed by the curve $y=x^{2} (x \\geqslant 0)$ and the two lines $x=10, y=1$ (including the bound... | {
"ground_truth": "1010",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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