prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "The number of passengers on the bus remained constant from departure to the second stop. Then, it was observed that at each stop, as many people boarded as had boarded at the two previous stops, and as many people disembarked as had boarded at the previous stop. The tenth stop from departure is th... | {
"ground_truth": "21",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "59. The fox and the weasel are having a jumping contest. The fox jumps 4.5 meters each time, while the weasel jumps 2.75 meters each time. They start jumping at the same time and jump exactly once every second. Along the way, there is a trap every 12.375 meters from the starting point. When one of... | {
"ground_truth": "40.5",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ms. Smith, an experienced PYP educator, is planning a special project for her class to demonstrate the importance of a well-rounded, holistic education. She decides to integrate art, math, and science into a single project. She has a total of 30 students in her class, and she wants to divide them ... | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An oreo shop now sells $5$ different flavors of oreos, $3$ different flavors of milk, and $2$ different flavors of cookies. Alpha and Gamma decide to purchase some items. Since Alpha is picky, he will order no more than two different items in total, avoiding replicas. To be equally strange, Gamma ... | {
"ground_truth": "2100",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's find a four-digit square number where two adjacent digits are equal!",
"role": "user"
}
] | {
"ground_truth": "7744",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The figure $ABCDE$ is a star pentagon (each line segment of the pentagon has 2 vertices on one side and 1 vertex on the other side). What is the sum of the angles $A B C, B C D, C D E, D E A, E A B$?",
"role": "user"
}
] | {
"ground_truth": "180^\\circ",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The ancient Chinese mathematical text, \"The Nine Chapters on the Mathematical Art,\" presents the following problem: \"There is a gold bar that is 5 feet long. When 1 foot is cut from the thicker end, it weighs 4 pounds; when 1 foot is cut from the thinner end, it weighs 2 pounds. What is the wei... | {
"ground_truth": "6",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "18. (USA 5) Inside triangle \\( A B C \\) there are three circles \\( k_{1}, k_{2}, k_{3} \\) each of which is tangent to two sides of the triangle and to its incircle \\( k \\). The radii of \\( k_{1}, k_{2}, k_{3} \\) are 1, 4, and 9. Determine the radius of \\( k \\).",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For which integers $n > 2$ is the following statement true? \"Any convex $n$-gon has a side such that neither of the two angles at its endpoints is an acute angle.\"",
"role": "user"
}
] | {
"ground_truth": "n \\geq 7",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Circle $\\omega$ has radius 5 and is centered at $O$. Point $A$ lies outside $\\omega$ such that $OA=13$. The two tangents to $\\omega$ passing through $A$ are drawn, and points $B$ and $C$ are chosen on them (one on each tangent), such that line $BC$ is tangent to $\\omega$ and $\\omega$ lies out... | {
"ground_truth": "17",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.43*. In a city, there are 10 streets parallel to each other, and 10 streets intersecting them at right angles. What is the minimum number of turns a closed bus route can have, passing through all intersections?",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the least positive integer $n$ such that the decimal representation of the binomial coefficient $\\dbinom{2n}{n}$ ends in four zero digits.",
"role": "user"
}
] | {
"ground_truth": "313",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Combinatorics (miscellaneous) $]$ $[$ Estimation + example ]\n\nIn a pond, 30 pikes were released, which gradually eat each other. A pike is considered full if it has eaten at least three pikes (full or hungry). What is the maximum number of pikes that can become full?",
"role": "user"
}
... | {
"ground_truth": "9",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the number of labelled rooted forests on 6 vertices",
"role": "user"
}
] | {
"ground_truth": "16807",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Evokimov M.A.\n\nA gold prospector has a pile of gold sand weighing 37 kg (and he has no more sand), a two-pan balance, and two weights of 1 and 2 kg. The prospector can perform actions of two types:\n\n- balance the scales, i.e., if the scales are currently not in equilibrium, he can pour some sa... | {
"ground_truth": "26",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all positive integers $n$ with $n \\ge 2$ such that the polynomial \\[ P(a_1, a_2, ..., a_n) = a_1^n+a_2^n + ... + a_n^n - n a_1 a_2 ... a_n \\] in the $n$ variables $a_1$ , $a_2$ , $\\dots$ , $a_n$ is irreducible over the real numbers, i.e. it cannot be factored as the product of ... | {
"ground_truth": " n \\ge 4 ",
"mean_reward": 0.078125
} | 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\nDetermine all functions $f: \\mathbb{Z}\\to\\mathbb{Z}$ satisfying \\[f\\big(f(m)+n\\big)+f(m)=f(n)+f(3m)+2014\\] for all integers $m$ and $n$.\n\n[i]\n\n[Solution]\n... | {
"ground_truth": "-1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For what values of \\( k \\) does the equation\n\\[ |x-2007| + |x+2007| = k \\]\nhave \\((-\\infty, -2007) \\cup (2007, +\\infty)\\) as its solution set?",
"role": "user"
}
] | {
"ground_truth": "k > 4014",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Let $A$ be any set of 7 real numbers, and let the set $B=\\{x y \\mid x, y \\in A$ and $x \\neq y\\}$, denote the number of elements in set $B$ as $|B|$, then $|B|_{\\text {max }}+|B|_{\\text {min }}=$ $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the ordered pair of relatively prime positive integers \\( (p, q) \\) of the successive ratios of segments cut by the curve \\( y = \\sin x \\) when it intersects the horizontal line \\( y = \\sin 60^\\circ \\) in the interval from \\( 0^\\circ \\) to \\( 360^\\circ \\).",
"role": "u... | {
"ground_truth": "(1, 4)",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same speed, how many miles would she have ridden? [asy] import graph; /* this is a label */ Label f; f.p=fontsize(0); xaxis(-0.9,20,Ticks(f, 5.0, 5.0)); yaxis(-0.9,20, Ticks(f, 22.0,5.0... | {
"ground_truth": "6",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We divided a chord $AB$ of a circle, which has the length of the radius, and the shorter arc $AB$ into three equal parts each. The line connecting the division points closer to $A$ intersects the line connecting the division points closer to $B$ at point $P$. What is the measure of angle $APB$?",
... | {
"ground_truth": "20",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.3. Answer. $A=376,625$.",
"role": "user"
}
] | {
"ground_truth": "376,625",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nFind all functions $f$ and $g$ defined from $\\mathbb{R}_{>0}$ to $\\mathbb{R}_{>0}$ such that for all $x, y > 0$ the two equations hold\n$$ (f(x) + y - 1)(g(y) + x -... | {
"ground_truth": "5",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A and B play a number-changing game on a $5 \\times 5$ grid: A starts and both take turns filling empty spaces, with A filling each space with the number 1 and B filling each space with the number 0. After the grid is completely filled, the sum of the numbers in each $3 \\times 3$ square is calcul... | {
"ground_truth": "6",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In Figure 1, \\( P R S \\) is a straight line, \\( P Q = P R = Q S \\) and \\( \\angle Q P R = 30^{\\circ} \\). If \\( \\angle R Q S = w^{\\circ} \\), find the value of \\( w \\).",
"role": "user"
}
] | {
"ground_truth": "45^\\circ",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of real solutions of the equation\n\\[\\frac{x}{50} = \\cos x.\\]",
"role": "user"
}
] | {
"ground_truth": "31",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Clever Dusya arranges six cheat sheets in four secret pockets so that the 1st and 2nd cheat sheets end up in the same pocket, the 4th and 5th cheat sheets also end up in the same pocket, but not in the same pocket as the 1st. The others can be placed anywhere, but only one pocket can remain emp... | {
"ground_truth": "144",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The rectangular spiral shown in the diagram is constructed as follows. Starting at $(0,0)$, line segments of lengths $1,1,2,2,3,3,4,4, \\ldots$ are drawn in a clockwise manner, as shown. The integers from 1 to 1000 are placed, in increasing order, wherever the spiral passes through a point with in... | {
"ground_truth": "10944",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The line \\( K M_{1} \\) intersects the extension of \\( A B \\) at point \\( N \\). Find the measure of angle \\( DNA \\).",
"role": "user"
}
] | {
"ground_truth": "90^\\circ",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nIn \"The Three-Body Problem,\" the operation involves intercepting the \"Judgment Day\" ship with a \"nano-blade\" material at the Panama Canal locks. As long as the \"Judgment Day\" ship passes through the \"nano-blade\" material completely undetected, the operation is a success. If the entire ... | {
"ground_truth": "40",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Chad runs a rare candy store. At six specified times during the day, one student randomly chooses to buy a candy. Boxes of candy contain $3$ candies at a cost of \\$3, and each candy is sold for \\$1.50. Any opened box’s remaining candies are discarded. Chad may refuse sales. If he acts optimally,... | {
"ground_truth": "121",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Shaq sees the numbers $1$ through $2017$ written on a chalkboard. He repeatedly chooses three numbers, erases them, and writes one plus their median. (For instance, if he erased $-2, -1, 0$ he would replace them with $0$ .) If $M$ is the maximum possible final value remaining on the board... | {
"ground_truth": "2014",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Find the smallest 10-digit number, the sum of whose digits is greater than that of any smaller number.",
"role": "user"
}
] | {
"ground_truth": "1999999999",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Given the set $A=\\{1,2, \\cdots, 104\\}, S$ is a subset of $A$. If $x \\in S$, and at the same time $x-1 \\notin S$ and $x+1 \\notin S$, then $x$ is called an \"isolated point\" of $S$. The number of all 5-element subsets of $A$ with no \"isolated points\" is . $\\qquad$",
"role": "user"
... | {
"ground_truth": "10000",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jenny rolls a die by placing it flat on the ground and rolling it along an edge for each step. Initially, the face with 1 pip is up. In how many ways can she roll the die for 6 steps such that the 1 face is up at the end?",
"role": "user"
}
] | {
"ground_truth": "704",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n\nIn the airspace, there are clouds. It turned out that the space can be divided by ten planes into parts such that no more than one cloud is in each part. What is the ... | {
"ground_truth": "11",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the smallest integer $n > 0$ such that for any integer m in the range $1, 2, 3, ... , 1992$ we can always find an integral multiple of $\\frac{1}{n}$ in the open interval $(\\frac{m}{1993}, \\frac{m+1}{1994})$?",
"role": "user"
}
] | {
"ground_truth": "3987",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a $16 \\times 16$ torus as shown all 512 edges are colored red or blue. A coloring is good if every vertex is an endpoint of an even number of red edges. A move consists of switching the color of each of the 4 edges of an arbitrary cell. What is the largest number of good colorings such that no... | {
"ground_truth": "4",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a qualification football round there are six teams and each two play one versus another exactly once. No two matches are played at the same time. At every moment the difference between the number of already played matches for any two teams is $0$ or $1$. A win is worth $3$ points, a draw is wor... | {
"ground_truth": "9",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A marksman shoots at a target, expecting to continue until hitting it for the first time. The probability of hitting the target with each shot is 0.6. If there are 4 bullets available, calculate the expected number of remaining bullets after the first hit. Express your answer as a decimal value wi... | {
"ground_truth": "2.376",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. Find the sum of all the prime factors of $27,000,001$.",
"role": "user"
}
] | {
"ground_truth": "652",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given $a=\\sqrt{2}$ and $b=\\sqrt{10}$, express $\\sqrt{20}$ in terms of $a$ and $b$. Provide your answer as an algebraic expression in terms of $a$ and $b$.",
"role": "user"
}
] | {
"ground_truth": "ab",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 1. Let $x$ and $y$ be two non-zero natural numbers such that $2015^{x}-2013=x+y$. Verify whether $y$ is a perfect square, given that:\n\n$$\n3 x+6 x+9 x+\\ldots+102 x=3570\n$$\n\nGratiela Popa, Slatina",
"role": "user"
}
] | {
"ground_truth": "y",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Given $a<b<c$. Try to find the minimum value of the function $y=|x-a|+|x-b|+|x-c|$.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly. \n\n4. Given $a<b<c$. Try to find the minimum value of the function $... | {
"ground_truth": "c-a",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Simplify the product \\[\\frac{6}{2}\\cdot\\frac{10}{6}\\cdot\\frac{14}{10} \\dotsm \\frac{4n+2}{4n} \\dotsm \\frac{1004}{1000}.\\]",
"role": "user"
}
] | {
"ground_truth": "502",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$2 \\cdot 29$ Let $T=\\left\\{9^{k} \\mid k\\right.$ be an integer, $\\left.0 \\leqslant k \\leqslant 4000\\right\\}$, it is known that $9^{4000}$ has 3817 digits, and its leftmost digit is 9, how many elements in $T$ have 9 as their leftmost digit?",
"role": "user"
}
] | {
"ground_truth": "184",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sum of the absolute values of the terms of a finite arithmetic progression is 100. If all its terms are increased by 1 or all its terms are increased by 2, the sum of the absolute values of the terms of the resulting progression will also be 100. What values can the quantity $n^{2} d$ take und... | {
"ground_truth": "400",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( S(n) \\) denote the sum of the digits of a natural number \\( n \\). For example, \\( S(123) = 1 + 2 + 3 = 6 \\). If two different positive integers \\( m \\) and \\( n \\) satisfy the following conditions:\n\\[ \n\\begin{cases}\nm < 100 \\\\\nn < 100 \\\\\nm > n \\\\\nm + S(n) = n + 2S(m)... | {
"ground_truth": "99",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a$ and $b$ be constants. Suppose that the equation \\[\\frac{(x+a)(x+b)(x+12)}{(x+3)^2} = 0\\]has exactly $3$ distinct roots, while the equation \\[\\frac{(x+2a)(x+3)(x+6)}{(x+b)(x+12)} = 0\\]has exactly $1$ distinct root. Compute $100a + b.$",
"role": "user"
}
] | {
"ground_truth": "156",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The square root of half the total number of bees in the swarm flew to a jasmine bush; $\\frac{8}{9}$ of the entire swarm remained in place; one bee is flying around her beloved, who is buzzing inside a lotus, where he flew at night attracted by the aroma of this flower, which has now become his pr... | {
"ground_truth": "72",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. For sets $A$ and $B$, their union $A \\cup B=\\left\\{a_{1}, a_{2}\\right.$, $\\left.\\cdots, a_{n}\\right\\}$, when $A \\neq B$, $(A, B)$ and $(B, A)$ are considered different pairs. Then the number of such pairs $(A, B)$ is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "3^n",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": " $ABC$ is a triangle with points $D$ , $E$ on $BC$ with $D$ nearer $B$ ; $F$ , $G$ on $AC$ , with $F$ nearer $C$ ; $H$ , $K$ on $AB$ , with $H$ nearer $A$ . Suppose that $AH=AG=1$ , $BK=BD=2$ , $CE=CF=4$ , $\\angle B=60^\\circ$ and that $D$ , $E$ , $F$ , $G$ , $H$ ... | {
"ground_truth": "\\sqrt{3}",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A regular tetrahedron has two spheres that are inscribed in and circumscribed around it. Additionally, in each face of the regular tetrahedron and between it and the circumscribed sphere, there are four spheres touching the center of the face. Given that point P is inside the circumscribed sphere,... | {
"ground_truth": "0.19",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the least integer value of $x$ for which $3|x| - 2 > 13$.",
"role": "user"
}
] | {
"ground_truth": "-6",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a pyramid \\( S A B C \\) with a triangular base \\( A B C \\) that is equilateral, and all the plane angles at the vertex \\( S \\) are equal to \\( \\alpha \\). What is the smallest \\( \\alpha \\) for which we can claim that this pyramid is regular?",
"role": "user"
}
] | {
"ground_truth": "60^\\circ",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14, 43 students, each carrying a different amount of money ranging from 8 cents to 5 yuan. Each student spent all their money on picture cards. There are only two types of picture cards, 3 cents each and 5 cents each, and each student tried to buy as many 5-cent cards as possible. How many 3-cent ... | {
"ground_truth": "84",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Find the last non-zero digit of $50!=1 \\times 2 \\times \\cdots \\times 50$.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.6 On a circle with a circumference of 1956, what is the minimum number of points that should be selected so that for each of these points, there is exactly 1 point at a distance of 1, and exactly 1 point at a distance of 2 (the distance between two points is measured along the arc)?",
"role"... | {
"ground_truth": "1304",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A set of positive integers is said to be [i]pilak[/i] if it can be partitioned into 2 disjoint subsets $F$ and $T$, each with at least $2$ elements, such that the elements of $F$ are consecutive Fibonacci numbers, and the elements of $T$ are consecutive triangular numbers. Find all positive intege... | {
"ground_truth": "30",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## 236. How old is Willie?\n\n- Is this problem your teacher gave you? - I asked Willie. - It looks quite boring.\n- No, - Willie replied, - I came up with it myself. - See this polynomial? My age is its root. I mean, if you substitute the number of years I was when I last celebrated my birthday f... | {
"ground_truth": "14",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 217, Determine the smallest possible value of the largest term in an arithmetic sequence composed of seven distinct prime numbers.\n\nTranslate the above text into English, keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
... | {
"ground_truth": "907",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "17. (5 points) Factory A and Factory B produce the same type of clothing. Factory A produces 2700 sets of clothing per month, with the time ratio for producing tops and pants being 2:1; Factory B produces 3600 sets of clothing per month, with the time ratio for producing tops and pants being 3:2. ... | {
"ground_truth": "6700",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many four-digit integers $abcd$, with $a \\neq 0$, have the property that the three two-digit integers $ab<bc<cd$ form an increasing arithmetic sequence? One such number is $4692$, where $a=4$, $b=6$, $c=9$, and $d=2$.",
"role": "user"
}
] | {
"ground_truth": "17",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. A hotel has 90 vacant rooms, each with a unique key. 100 guests arrive, and keys need to be distributed so that any 90 of them can stay in the 90 rooms, with each person getting one room (assuming there is no limit to the number of keys that can be issued for each room or the number of keys eac... | {
"ground_truth": "990",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 3. CONDITION\n\nPerpendiculars $B E$ and $D F$, dropped from vertices $B$ and $D$ of parallelogram $A B C D$ to sides $A D$ and $B C$ respectively, divide the parallelogram into three parts of equal area. On the extension of diagonal $B D$ beyond vertex $D$, segment $D G$ is laid off, equal to s... | {
"ground_truth": "1:1",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In each cell of a chessboard with $2$ rows and $2019$ columns a real number is written so that:\n[LIST]\n[*] There are no two numbers written in the first row that are equal to each other.[/*]\n[*] The numbers written in the second row coincide with (in some another order) the numbers written in ... | {
"ground_truth": "4032",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a table $n \\times 9$ ( $n$ rows and $9$ columns), determine the maximum of $n$ that we can write one number in the set $\\left\\{ {1,2,...,9} \\right\\}$ in each cell such that these conditions are satisfied:\n\n1. Each row contains enough $9$ numbers of the set $\\left\\{ {1,2,..... | {
"ground_truth": " 8! ",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a $5 \\times 5$ board, two players alternately mark numbers on empty cells. The first player always marks 1's, the second 0's. One number is marked per turn, until the board is filled. For each of the nine $3 \\times 3$ squares, the sum of the nine numbers on its cells is computed. Denote by \\... | {
"ground_truth": "6",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[arubber $\\mathbf{M .}$\n\nIn a class, there are 15 boys and 15 girls. On March 8, some boys called some girls to congratulate them on the holiday (no boy called the same girl twice). It turned out that the children could be uniquely divided into 15 pairs such that in each pair, there is a boy wh... | {
"ground_truth": "120",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## [ equations in integers ] Decompositions and partitions $\\quad]$ [ GCD and LCM. Mutual simplicity ]\n\nOstap Bender organized a giveaway of elephants to the population in the city of Fux. 28 union members and 37 non-members showed up for the giveaway, and Ostap distributed the elephants equall... | {
"ground_truth": "2072",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The café has enough chairs to seat $312_8$ people. If $3$ people are supposed to sit at one table, how many tables does the café have?",
"role": "user"
}
] | {
"ground_truth": "67",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "G7.4 If $x+k$ is a factor of $3 x^{2}+14 x+a$, find $k$. ( $k$ is an integer.)",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Tiana is a young woman from the Cook Islands who dreams of becoming a published author. She has decided to write a book about the beautiful islands and their rich culture. Tiana plans to write a total of 120 pages. She writes 3 pages each day during the week and doubles her effort by writing 6 pag... | {
"ground_truth": "32",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a race, all runners must start at point $A$, touch any part of a 1500-meter wall, and then stop at point $B$. Given that the distance from $A$ directly to the wall is 400 meters and from the wall directly to $B$ is 600 meters, calculate the minimum distance a participant must run to complete th... | {
"ground_truth": "1803",
"mean_reward": 0.015625
} | 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 book with 50 pages numbered 1 through 50 has its pages renumbered in reverse, from 50 to 1. For how many pages do both sets of page numbers share the same ones digi... | {
"ground_truth": "2",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Brian starts at the point $\\left(1,0\\right)$ in the plane. Every second, he performs one of two moves: he can move from $\\left(a,b\\right)$ to $\\left(a-b,a+b\\right)$ or from $\\left(a,b\\right)$ to $\\left(2a-b,a+2b\\right)$ . How many different paths can he take to end up at $\\lef... | {
"ground_truth": "70",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Giraldo wrote five distinct natural numbers on the vertices of a pentagon. And next he wrote on each side of the pentagon the least common multiple of the numbers written of the two vertices who were on that side and noticed that the five numbers written on the sides were equal. What is the smalle... | {
"ground_truth": "30",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. 2019 circles split a plane into a number of parts whose boundaries are arcs of those circles. How many colors are needed to color this geographic map if any two neighboring parts must be coloured with different colours?",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$a, b, c$. Find $a+b+c$.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 130. Given an angle of $54^{\\circ}$. Divide it into three equal parts using a compass and a straightedge.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Monica decides to tile the floor of her 15-foot by 20-foot dining room. She plans to create a two-foot-wide border using one-foot by one-foot square tiles around the edges of the room and fill in the rest of the floor with three-foot by three-foot square tiles. Calculate the total number of tiles ... | {
"ground_truth": "144",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $g$ be a function from the positive integers to the positive integers, such that:\n\n(i) $g$ is strictly increasing ($g(n+1) > g(n)$ for all $n$),\n(ii) $g(mn) = g(m) g(n)$ for all positive integers $m, n$,\n(iii) if $m \\neq n$ and $m^n = n^m$, then $g(m) = n$ or $g(n) = m$.\n\nFind the sum o... | {
"ground_truth": "144",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the given diagram, there are two regular polygons, a pentagon and a square. Find the sum of the measures of angles \\(ABC\\) and \\(ABD\\) in degrees.\n\n[asy]\ndraw(10dir(0)--10dir(72)--10dir(144)--10dir(216)--10dir(288)--cycle,linewidth(2));\ndraw(10dir(216)--10dir(288)--10dir(288)+(0,-10)--1... | {
"ground_truth": "198^\\circ",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 1. We call a collection of lines in the plane beautiful if each line in the collection intersects an odd number of the other lines in the collection.\n\nDetermine the smallest integer $k \\geq 0$ with the following property: for any 2018 different lines $\\ell_{1}, \\ell_{2}, \\ldots, \\ell_{... | {
"ground_truth": "1010",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the diagram, triangles $ABC$ and $CBD$ are isosceles. The perimeter of $\\triangle CBD$ is $24,$ the perimeter of $\\triangle ABC$ is $23,$ and the length of $BD$ is $10.$ What is the length of $AB?$",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "43. If $\\overline{a b c}+\\overline{c b a}=1009$, then how many such $\\overline{a b c}$ are there?",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find $XY$ in the triangle below.\n\n\n[asy]\nunitsize(1inch);\npair P,Q,R;\nP = (0,0);\nQ= (1,0);\nR = (0,1);\ndraw (P--Q--R--P,linewidth(0.9));\ndraw(rightanglemark(Q,P,R,3));\nlabel(\"$X$\",P,S);\nlabel(\"$Y$\",Q,S);\nlabel(\"$Z$\",R,N);\nlabel(\"$12\\sqrt{2}$\",R/2,W);\nlabel(\"$45^\\circ$\",(0... | {
"ground_truth": "12\\sqrt{2}",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a$ , $b$ , $c$ be positive real numbers for which \\[\n \\frac{5}{a} = b+c, \\quad\n \\frac{10}{b} = c+a, \\quad \\text{and} \\quad\n \\frac{13}{c} = a+b. \\] If $a+b+c = \\frac mn$ for relatively prime positive integers $m$ and $n$ , compute $m+n$ .\n\n*Proposed by Evan Chen*",
... | {
"ground_truth": "55",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "20. (MON 4) Find the least natural number $n$ such that if the set $\\{1,2, \\ldots, n\\}$ is arbitrarily divided into two nonintersecting subsets, then one of the subsets contains three distinct numbers such that the product of two of them equals the third.",
"role": "user"
}
] | {
"ground_truth": "96",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all positive integers $n$ satisfying the following conditions simultaneously:\n\n(a) the number of positive divisors of $n$ is not a multiple of $8$ ;\n(b) for all integers $x$ , we have\n\\[x^n \\equiv x \\mod n.\\]\n*Proposed by usjl*",
"role": "user"
}
] | {
"ground_truth": " n = 1 ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For every point on the plane, one of $ n$ colors are colored to it such that:\r\n\r $ (1)$ Every color is used infinitely many times.\r\n\r $ (2)$ There exists one line such that all points on this lines are colored exactly by one of two colors.\r\n\r\nFind the least value of $ n$ such that ... | {
"ground_truth": " n = 5 ",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The \"Academy League\" basketball conference has 8 teams. Each team plays every other team in the conference twice, and 6 games against non-conference opponents. Calculate the total number of games in a season involving the \"Academy League\" teams.",
"role": "user"
}
] | {
"ground_truth": "104",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. The number of positive integers $n$ that make $\\frac{n}{100-n}$ a perfect square is.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On the lateral side \\( C D \\) of the trapezoid \\( A B C D \\) (\\( A D \\parallel B C \\)), a point \\( M \\) is marked. From the vertex \\( A \\), a perpendicular \\( A H \\) is dropped onto the segment \\( B M \\). It turns out that \\( A D = H D \\). Find the length of the segment \\( A D \\... | {
"ground_truth": "18",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Petya and Vasya calculated that if they walk at a speed of 4 km per hour to the neighboring village, which is 4 kilometers away, they will be 10 minutes late for the football match held there for the district championship. How should they proceed to arrive at the match on time and achieve the grea... | {
"ground_truth": "10",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. From point $A$ of a circular track, a car and a motorcycle started simultaneously and in the same direction. The car drove two laps without stopping in one direction. At the moment when the car caught up with the motorcyclist, the motorcyclist turned around and increased his speed by $16 \\math... | {
"ground_truth": "21",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "【Question 14】Select 5 digits from $1 \\sim 9$, to form a five-digit number, such that this five-digit number can be evenly divided by any of the 5 selected digits, but cannot be evenly divided by any of the 4 unselected digits. Then, the smallest value of this five-digit number is $\\qquad$.\n\n--... | {
"ground_truth": "14728",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We are considering all possible triangles with integer sides and a perimeter of 2000, as well as all possible triangles with integer sides and a perimeter of 2003. Which set of triangles is larger?",
"role": "user"
}
] | {
"ground_truth": "2003",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Points \\(M\\) and \\(N\\) lie on edges \\(BC\\) and \\(AA_1\\) of the parallelepiped \\(ABCD A_1 B_1 C_1 D_1\\). Construct the intersection point of line \\(MN\\) with the base plane \\(A_1 B_1 C_1 D_1\\).",
"role": "user"
}
] | {
"ground_truth": "P",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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