prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Find the number of ways to exchange a 2-jiao coin (20 fen) into 1-fen, 2-fen, and 5-fen coins by finding non-negative integer solutions to the equation x + 2y + 5z = 20, where x is the number of 1-fen coins, y is the number of 2-fen coins, and z is the number of 5-fen coins.",
"role": "user"
... | {
"ground_truth": "29",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Kayla draws three triangles on a sheet of paper. What is the maximum possible number of regions, including the exterior region, that the paper can be divided into by the sides of the triangles? \n\n*Proposed by Michael Tang*",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all natural numbers $ n $ for which there exists two natural numbers $ a,b $ such that $$ n=S(a)=S(b)=S(a+b) , $$ where $ S(k) $ denotes the sum of the digits of $ k $ in base $ 10, $ for any natural number $ k. $ *Vasile Zidaru* and *Mircea Lascu*",
"role": "user"
}
] | {
"ground_truth": "n=9k",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 2.1. Condition:\n\nIn the campus, rooms are numbered consecutively $1,2,3,4 \\ldots, 10,11, \\ldots$ For room numbering, stickers with digits were purchased, with the digits 1, 2, and 3 being purchased in equal quantities, and the digit 5 being purchased three more than the digit 6. How many roo... | {
"ground_truth": "66",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A set of points $M$ in the plane satisfies the following conditions:\n(a) No three points are collinear;\n(b) Each point in $M$ can be colored either red or blue such that every triangle with vertices of the same color has at least one point of the other color inside it.\n\nDetermine the maximum p... | {
"ground_truth": "8",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the drawing to the side, triangle $ABC$ is equilateral and $BD = CE = AF = \\frac{AB}{3}$. The ratio $\\frac{EG}{GD}$ can be written in the form $\\frac{m}{n}, \\operatorname{gcd}(m, n)=1$. What is the value of $m+n$?\n\n![](https://cdn.mathpix.com/cropped/2024_05_01_12f29789e10e6749ebb9g-37.jp... | {
"ground_truth": "5",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that the domain of function $f(x)$ is $\\mathbf{R}$, $f''(x)$ is the derivative of $f(x)$, and $f''(x) - 2f(x) > 0$, with $f(\\frac{1}{2}) = e$, where $e$ is the base of the natural logarithm, determine the solution set for the inequality $f(\\frac{1}{2}\\ln{x}) < x$. Express your answer in ... | {
"ground_truth": "(0, e)",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Inside the circle $\\omega$ are two intersecting circles $\\omega_{1}$ and $\\omega_{2}$, which intersect at points $K$ and $L$, and are tangent to the circle $\\omega$ at points $M$ and $N$. It turns out that the points $K$, $M$, and $N$ are collinear. Find the radius of the circle $\\omega$, giv... | {
"ground_truth": "8",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. [4] A sphere is the set of points at a fixed positive distance $r$ from its center. Let $\\mathcal{S}$ be a set of 2010dimensional 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 $n$.",
"role": "u... | {
"ground_truth": "2",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two positive integers differ by 8 and their product is 168. What is the larger integer?",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The number of right-angled triangles with integer side lengths $a$ and $b$ (where $b < 2011$), and hypotenuse length $b + 1$ is .",
"role": "user"
}
] | {
"ground_truth": "31",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 3. The numbers $2,3,4, \\ldots, 29,30$ 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 board? [... | {
"ground_truth": "5",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. For any natural number $n$, let us form all possible \"words\" of length $n$ from the letters $A$ and $B$, and let $p_{n}$ denote the number of those words that do not contain the quadruple $AAAA$ of consecutive letters $A$, nor the triple $BBB$ of consecutive letters $B$. Determine the value o... | {
"ground_truth": "2",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[Example 3.3.7] In the plane, there are 100 lines. Can there be 1985 intersection points among them.",
"role": "user"
}
] | {
"ground_truth": "1985",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a budget-conscious backpacker planning a trip to three different cities. He has found a budget airline that offers flights between the cities with the following costs: $50 from City A to City B, $30 from City B to City C, and $40 from City A to City C. Alex also plans to spend $20 per day ... | {
"ground_truth": "395",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the function $f(x)=\\left\\{{\\begin{array}{l}{(a-3)x+2a, x<1}\\\\{a{x^2}+(a+1)x, x\\geq 1}\\end{array}}\\right.$, find the range of real number $a$ such that $f(x)$ is a monotonically increasing function on $\\mathbb{R}$. Express your answer as an interval or a union of intervals.",
"ro... | {
"ground_truth": "(3, 4]",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $d$ be a complex number. Suppose there exist distinct complex numbers $a$, $b$, and $c$ such that for every complex number $z$, we have:\n\\[\n(z - a)(z - b)(z - c) = (z - d^2a)(z - d^2b)(z - d^2c).\n\\]\nCompute the number of distinct possible values of $d$.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Charles Dickens' 200th anniversary was celebrated on February 7, 2012, which was a Tuesday. A year is a leap year if it is divisible by 400 or divisible by 4 but not by 100. Using this rule, calculate the day of the week on which Charles Dickens was born. Express your answer as the full day of the... | {
"ground_truth": "Friday",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sarah is a hardcore fan of The Telescopes and has a grand collection of their records and merchandise. In her collection, she has 25 vinyl albums, 12 EPs, 18 singles, and 5 exclusive merchandise items. She recently attended a fan convention where she bought 3 more rare vinyl albums, 2 exclusive EP... | {
"ground_truth": "14",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. (10 points) Cut a pentagon along a straight line into two polygons, then cut one of the polygons along a straight line into two parts, resulting in three polygons, and then cut one of the polygons along a straight line into two parts, $\\cdots$, and so on. To have 20 pentagons among the result... | {
"ground_truth": "38",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. From 30 people with distinct ages, select two groups, the first with 12 people and the second with 15 people, such that the oldest person in the first group is younger than the youngest person in the second group. How many ways are there to select these groups?",
"role": "user"
}
] | {
"ground_truth": "4060",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Adva is a regular tetrahedron with side length \\( s \\), and there are three spheres associated with it. The first sphere passes through the vertices of the tetrahedron, the second intersects the midpoints of the edges, and the third is inscribed such that it touches the faces of the tetrahedron.... | {
"ground_truth": "9:3:1",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let S be the set of integers between 1 and 2^40 that contain two 1’s when written in base 2. What is the probability that a random integer from S is divisible by 9?",
"role": "user"
}
] | {
"ground_truth": "0.1705",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct trees with exactly 7 vertices are there? A tree is defined in the language of graph theory as a connected graph with no cycles, simply understood as a graph that connects \\( n \\) vertices with \\( n-1 \\) edges. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the greatest integer $A$ for which in any permutation of the numbers $1, 2, \\ldots , 100$ there exist ten consecutive numbers whose sum is at least $A$ .",
"role": "user"
}
] | {
"ground_truth": "505",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A point $ M$ is taken on the perpendicular bisector of the side $ AC$ of an acute-angled triangle $ ABC$ so that $ M$ and $ B$ are on the same side of $ AC$ . If $ \\angle BAC\\equal{}\\angle MCB$ and $ \\angle ABC\\plus{}\\angle MBC\\equal{}180^{\\circ}$ , find $ \\angle BAC.$ ",
... | {
"ground_truth": "30^\\circ",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A9. A unit square has an equilateral triangle drawn inside it, with a common edge. Four of these squares are placed together to make a larger square. Four vertices of the triangles are joined up to form a square, which is shaded and shown in the diagram. What is the area of the shaded square?",
... | {
"ground_truth": "2",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.5. In the list $1,2, \\ldots, 2016$, two numbers $a<b$ were marked, dividing the sequence into 3 parts (some of these parts might not contain any numbers at all). After that, the list was shuffled in such a way that $a$ and $b$ remained in their places, and no other of the 2014 numbers remained ... | {
"ground_truth": "508536",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the polynomial equation \\( z^{4} + a z^{3} + b z^{2} + c z + d = 0 \\) with real coefficients \\( a, b, c, d \\), and all roots of the polynomial lying on the circle with center at the origin and radius 1 in the complex plane, find the sum of the reciprocals of these roots. Express your ans... | {
"ground_truth": "-a",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of the two smallest possible values of $x^\\circ$ (in degrees) that satisfy the following equation if $x$ is greater than $2017^\\circ$ : $$ \\cos^59x+\\cos^5x=32\\cos^55x\\cos^54x+5\\cos^29x\\cos^2x\\left(\\cos9x+\\cos x\\right). $$ *2017 CCA Math Bonanza Individual Round #10... | {
"ground_truth": "4064",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three, 18 football teams are participating in a single round-robin tournament, meaning each round the 18 teams are divided into 9 groups, with each group's two teams playing one match. In the next round, the teams are regrouped to play, for a total of 17 rounds, ensuring that each team plays one m... | {
"ground_truth": "7",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2 Draw three rays $O A, O B, O C$ from point $O$, with the angles between each pair being $60^{\\circ}, 90^{\\circ}, 120^{\\circ}$, respectively. What is the minimum value of the angles between the angle bisectors of these three angles?",
"role": "user"
}
] | {
"ground_truth": "45",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7 Let $S=\\{1,2, \\cdots, 2005\\}$. If any set of $n$ pairwise coprime numbers in $S$ contains at least one prime number, find the minimum value of $n$.\n\n",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alisha wrote an integer in each square of a 4x4 grid, such that integers in squares with a common edge differed by 1. She wrote a 3 in the top-left corner and a 9 somewhere in the grid. How many distinct integers did she write in the grid? Express your answer as a single integer.",
"role": "us... | {
"ground_truth": "7",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "122. Digits and Cubes. Professor Rackbrain recently asked his young friends to find all five-digit squares for which the sum of the numbers formed by the first two and the last two digits is a perfect cube. For example, if we take the square of 141, which is 19881, and add 81 to 19, we get 100 - a... | {
"ground_truth": "3",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15 Find the smallest positive integer $n(n \\geqslant 3)$, such that in any set of $n$ points in the plane with no three points collinear, there must be three points that are the vertices of a non-isosceles triangle.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students. [asy] size(8cm); void drawbar(real x, real h) { fill((x-0.15,0.5)-... | {
"ground_truth": "4.36",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "70. A tiger and a cheetah are having a 100-meter race. The tiger can stride 2 meters in one step, while the cheetah can stride 3 meters in one step. In the time it takes the tiger to take 4 steps, the cheetah can only take 3 steps. So, $\\qquad$ who will reach the finish line first.",
"role": ... | {
"ground_truth": "Cheetah",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. The border of a square with a side of 9, cut out of white cardboard, is painted red. It is necessary to cut the square into 6 equal-area parts, the boundaries of which contain segments painted red with the same total length.\n\n## Solutions\n\nOption 1\n\nProblem 1",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. On the table, there are three cones standing on their bases, touching each other. The radii of their bases are 10, 15, and 15. A truncated cone is placed on the table with its smaller base down, and it shares a generatrix with each of the other cones. Find the area of the smaller base of the tr... | {
"ground_truth": "4\\pi",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The line $y = b-x$ where $0 < b < 6$ intersects the $y$-axis at $P$ and the line $x=6$ at $S$. If the ratio of the area of triangle $QRS$ to the area of triangle $QOP$ is 4:9, what is the value of $b$? Express the answer as a decimal to the nearest tenth.",
"role": "user"
}
] | {
"ground_truth": "3.6",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A round robin tournament is held with $2016$ participants. Each player plays each other player once and no games result in ties. We say a pair of players $A$ and $B$ is a [i]dominant pair[/i] if all other players either defeat $A$ and $B$ or are defeated by both $A$ and $B$. Find the maximum numbe... | {
"ground_truth": "2015",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $$P(x)=\\bigl(x-3\\bigr)^m\\Bigl(x-\\frac{1}{3}\\Bigr)^n,$$ where $m,n$ are positive integers. For how many ordered pairs $(m,n)$ with $m,n\\le100$ does $P(x)$ (written in descending powers of $x$) have integer coefficients for its first three terms and its constant term?",
"role": "user"
... | {
"ground_truth": "517",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Assume that half of the mass of a 62-kg person consists of protons. If the half-life of the proton is 10^33 years, calculate the number of proton decays per day from the body.",
"role": "user"
}
] | {
"ground_truth": "3.5e-08",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "54. As shown in the figure, $\\angle A+\\angle B+\\angle C+\\angle D+\\angle E+\\angle F=$\n\nThe text above has been translated into English, preserving the original text's line breaks and format.",
"role": "user"
}
] | {
"ground_truth": "360",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When three planes divide the space into 7 parts, how many intersection lines are formed? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Two very small fleas are jumping on a large sheet of paper. The first jump of the fleas is along a straight line towards each other (their jumps may have different lengths). The first flea first jumps to the right, then up, then to the left, then down, then to the right again, and so on. Each j... | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest constant \\( m \\) such that for any positive real numbers \\( x, y, z, \\) and \\( w \\)\n\\[\n\\sqrt{\\frac{x}{y+z+x}} + \\sqrt{\\frac{y}{x+z+w}} + \\sqrt{\\frac{z}{x+y+w}} + \\sqrt{\\frac{w}{x+y+z}} > m.\n\\]",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Several chips of two colors are arranged in a row (both colors are present). It is known that the chips that are 10 or 15 chips apart are the same.\n\nWhat is the maximum number of chips possible?",
"role": "user"
}
] | {
"ground_truth": "25",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A regular hexagon is divided into 6 equilateral triangles. How many parallelograms can be formed within the hexagon? Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "(5) In a simple graph with eight vertices, what is the maximum number of edges in a graph that does not contain a quadrilateral? (A simple graph is one where no vertex is connected to itself, and any two vertices are connected by at most one edge.)",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\(\\left(x^{2}+2x-2\\right)^{6}=a_{0}+a_{1}(x+2)+a_{2}(x+2)^{2}+\\cdots+a_{12}(x+2)^{12}\\), where \\(a_{i} (i=0,1,2,\\ldots,12)\\) are real constants. Determine the value of \\(a_{0}+a_{1}+2a_{2}+3a_{3}+\\cdots+12a_{12}\\).",
"role": "user"
}
] | {
"ground_truth": "64",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The master magician, known for their secretive nature, has 5 different magic tricks that they perform at special shows. Each trick requires a unique set of magic cards, and the magician has a total of 60 magic cards in their collection. To prevent anyone from learning their secrets, the magician e... | {
"ground_truth": "16",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a sequence \\( A = (a_1, a_2, \\cdots, a_{10}) \\) that satisfies the following four conditions:\n1. \\( a_1, a_2, \\cdots, a_{10} \\) is a permutation of \\{1, 2, \\cdots, 10\\};\n2. \\( a_1 < a_2, a_3 < a_4, a_5 < a_6, a_7 < a_8, a_9 < a_{10} \\);\n3. \\( a_2 > a_3, a_4 > a_5, a_6 > a_7, a... | {
"ground_truth": "42",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Zadatak B-1.6.\n\nU nizu brojeva\n\n$$\n20,202,2020,20202,202020, \\ldots\n$$\n\nsvaki se sljedeći broj dobije dopisivanjem znamenke 2 ili 0 prethodnom broju, naizmjence. Izračunajte zbroj znamenaka prvih sto brojeva toga niza koji su djeljivi s 202.\n\n",
"role": "user"
}
] | {
"ground_truth": "10200",
"mean_reward": 0.046875
} | 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 regular tetrahedron is a pyramid with four faces, each of which is an equilateral triangle.\n\nLet $ABCD$ be a regular tetrahedron and let $P$ be the unique point e... | {
"ground_truth": "4",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a high school student who loves watching math videos from a popular content creator, Mr. MathWhiz, to help with their remote learning. Mr. MathWhiz uploads 3 new math videos every week, which Alex watches diligently. Each video is about 15 minutes long. After watching these videos for 4 we... | {
"ground_truth": "348",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 5 different lines on a plane, forming $m$ intersection points. How many different values can $m$ take?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The graphs of four functions, labelled (2) through (5), are provided. The domain of function (3) is $$\\{-6,-5,-4,-3,-2,-1,0,1,2,3\\}.$$ Identify the labels of the functions which are invertible and find their product. The functions are described as follows:\n- Function (2): $f(x) = x^3 - 3x$\n- F... | {
"ground_truth": "15",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a $3 \\times 3$ table, natural numbers (not necessarily distinct) are placed such that the sums in all rows and columns are different. What is the minimum value that the sum of the numbers in the table can take?\n",
"role": "user"
}
] | {
"ground_truth": "17",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Cedric has deposited $12,000 into an account that pays $6\\%$ interest compounded annually.\n\nDaniel has deposited $12,000 into an account that pays $8\\%$ simple annual interest.\n\nAfter 20 years, Cedric and Daniel compare their respective balances. What is the positive difference between their... | {
"ground_truth": "7286",
"mean_reward": 0
} | 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 circle has the same center as an ellipse and passes through the foci $F_1$ and $F_2$ of the ellipse. The two curves intersect in 4 points. Let $P$ be any point of... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. As shown in the figure, 10 identical regular pentagons are joined edge-to-edge, forming a regular decagon in the middle. 3 identical regular $n$-sided polygons are joined edge-to-edge, forming a regular triangle in the middle. What is the value of $n$? $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Dr. Star, an astrophysicist who studies exoplanets, discovered a new exoplanet orbiting a distant star. She determined that this exoplanet's orbit takes 365 Earth days to complete one full revolution around its star. Dr. Star also found that the exoplanet has 4 moons. Each moon orbits the exoplane... | {
"ground_truth": "30",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Masha looked at the drawing and said: \"There are seven rectangles drawn here: one large and six small ones.\" \"There are also various medium rectangles here\" - said Mom. How many rectangles are there in total on this drawing? Explain your answer.\n\n##\n\n![](https://cdn.mathpix.com/cropped/202... | {
"ground_truth": "18",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "G3.3 $A B C D$ is a cyclic quadrilateral. $A C$ and $B D$ intersect at $G$. Suppose $A C=16 \\mathrm{~cm}, B C=C D=8 \\mathrm{~cm}$, $B G=x \\mathrm{~cm}$ and $G D=y \\mathrm{~cm}$. If $x$ and $y$ are integers and $x+y=c$, find the value of $c$.",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\(x\\) and \\(y\\) be real numbers such that:\n\\[\nxy + \\frac{x}{y} + \\frac{y}{x} = 3.\n\\]\nFind the sum of all possible values of \\((x + 1)(y + 1).\\)",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two sages are playing the following game. The numbers $0,1,2, \\ldots, 1024$ are written down. The first sage crosses out 512 numbers (of his choice), the second crosses out 256 of the remaining, then the first crosses out 128 numbers, and so on. On the tenth step, the second sage crosses out one ... | {
"ground_truth": "32",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $n \\leq 100$ be an integer. Hare puts real numbers in the cells of a $100 \\times 100$ table. By asking Hare one question, Wolf can find out the sum of all numbers of a square $n \\times n$ , or the sum of all numbers of a rectangle $1 \\times (n - 1)$ (or $(n - 1) \\times 1$ ). Find ... | {
"ground_truth": "51",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five towns are connected by a system of roads. There is exactly one road connecting each pair of towns. Find the number of ways there are to make all the roads one-way in such a way that it is still possible to get from any town to any other town using the roads (possibly passing through other tow... | {
"ground_truth": "544",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Compute $\\frac{x^{10} - 32x^5 + 1024}{x^5 - 32}$ when $x=8$.",
"role": "user"
}
] | {
"ground_truth": "32768",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n4. There are 100 countries participating in an olympiad. Suppose $n$ is a positive integer such that each of the 100 countries is willing to communicate in exactly $n$ languages. If each set of 20 countries can communicate in at least one common language, and no language is common to all 100 cou... | {
"ground_truth": "20",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many ways to fill the board $ 4\\times 4$ by nonnegative integers, such that sum of the numbers of each row and each column is 3?",
"role": "user"
}
] | {
"ground_truth": "2008",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 5 people standing in a line numbered 1 through 5 in a left to right order.\nEach person has the following attributes: Job, Food, Movie-Genre, Nationality, Sport.\nThe attributes have the following possible values:\n- Job: architect, dancer, designer, electrician, police-officer\n- Food:... | {
"ground_truth": "pear",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$15 \\cdot 26$ Let the natural number $n(n>3)$ have the following property: when the set $S_{n}=\\{3,4, \\cdots, n\\}$ is arbitrarily divided into two groups, there is always a group containing three numbers $a, b, c$ (allowing $a=b$), such that $a b=c$. Find the smallest value of such $n$.\n(Chin... | {
"ground_truth": "243",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 5 people standing in a line numbered 1 through 5 in a left to right order.\nEach person has the following attributes: Nationality, Food, Music-Genre, Beverage, Transport.\nThe attributes have the following possible values:\n- Nationality: egyptian, italian, japanese, pakistani, spanish\... | {
"ground_truth": "spanish",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jean Boucher is a history enthusiast who loves exploring her family's past. She recently discovered that her ancestors, the Bouchers, had a tradition of collecting historical artifacts. In the 18th century, the Boucher family acquired 45 artifacts. Each generation, starting with the 19th century, ... | {
"ground_truth": "105",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In four-dimensional space, the 24-cell of side length $\\sqrt{2}$ is the convex hull of all permutations of $(\\pm1,\\pm1,0,0)$. Find its 4-dimensional volume.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three, (50 points) A positive integer is called \"simple\" if it does not have any square factors greater than 1. Determine how many numbers in $1,2, \\cdots, 2010$ are simple.\n\n",
"role": "user"
}
] | {
"ground_truth": "1221",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Let $x>1, y>1$, and $2 \\log _{x} y-2 \\log _{x} x+3=0$, then the minimum value of $x^{2}-4 y^{2}$ is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "-4",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( M \\) be a set of \\( n \\) points in the plane such that:\n1. There are 7 points in \\( M \\) that form the vertices of a convex heptagon.\n2. For any 5 points in \\( M \\), if these 5 points form a convex pentagon, then the interior of this convex pentagon contains at least one point fro... | {
"ground_truth": "11",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. To transmit a three-letter word through a channel, the following method is used. Each letter of the word is assigned a pair of digits according to the rule: А -00, Б $-01, \\mathrm{~B}-02, \\ldots$, Я - 32. After that, the obtained sequence of digits $m_{1}, m_{2}, \\ldots, m_{6}$. is transform... | {
"ground_truth": "миф",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "【Example 2】Using 4 different colors to color the 4 sides of a small square wooden block, with each side painted a different color, how many different coloring patterns can there be?",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Diane has five identical blue disks, two identical red disks, and one yellow disk. She wants to place them on an 8-cell grid so that each cell contains exactly one disk. The two red disks must not be placed in cells that share a common edge. Calculate the total number of different-looking complete... | {
"ground_truth": "108",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "It is known that the polynomial \\( f(x) = 8 + 32x - 12x^2 - 4x^3 + x^4 \\) has 4 distinct real roots \\(\\{x_{1}, x_{2}, x_{3}, x_{4}\\}\\). The polynomial of the form \\( g(x) = b_{0} + b_{1} x + b_{2} x^2 + b_{3} x^3 + x^4 \\) has roots \\(\\{x_{1}^2, x_{2}^2, x_{3}^2, x_{4}^2\\}\\). Find the c... | {
"ground_truth": "-1216",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "46. In a convex quadrilateral $A B C D$, point $M$ is the midpoint of side $A D$, $C M \\| A B$, $A D=B D$ and $3 \\angle B A C=\\angle A C D$. Find the angle $A C B$.\n\n(S. Berlov)",
"role": "user"
}
] | {
"ground_truth": "90",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A.2 Calculate the minimum value of the momentum of an electron that allows it to escape the inner part of the detector in the radial direction. The inner part of the detector has a cylindrical shape with a radius of 1.1 meters, and the electron is produced in the collision point exactly in the cen... | {
"ground_truth": "p=330",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of real solutions of the equation\n\\[\\frac{x}{100} = \\sin x.\\]",
"role": "user"
}
] | {
"ground_truth": "63",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10、The number of positive integers not exceeding 2012 that have exactly three positive divisors 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": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On $5\\times 5$ squares, we cover the area with several S-Tetrominos (=Z-Tetrominos) along the square so that in every square, there are two or fewer tiles covering that (tiles can be overlap). Find the maximum possible number of squares covered by at least one tile.",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that \\( x, y, z \\in \\mathbb{R}_{+} \\), and \\( s = \\sqrt{x+2} + \\sqrt{y+5} + \\sqrt{z+10} \\), \\( t = \\sqrt{x+1} + \\sqrt{y+1} + \\sqrt{z+1} \\), find the minimum value of \\( s^{2} - t^{2} \\).",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The numbers on the faces of this cube are consecutive whole numbers. The sum of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is [asy] draw((0,0)--(3,0)--(3,3)--(0,3)--cycle); draw((3,0)--(5,2)--(5,5)--(2,5)--(0,3)); draw((3,3)--(5,... | {
"ground_truth": "81",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose $z=a+bi$ is a solution of the polynomial equation \\[c_4z^4+ic_3z^3+c_2z^2+ic_1z+c_0=0,\\] where $c_0, c_1, c_2, c_3, a,$ and $b$ are real constants and $i^2=-1.$ Which of the following must also be a solution?",
"role": "user"
}
] | {
"ground_truth": "-a+bi",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On the ceiling of a room hang 15 lamps, numbered from 1 to 15. Initially, all the lamps are off. In another room are 15 switches: one switch for lamp 1 and 2, one switch for lamp 2 and 3, one switch for lamp 3 and 4, and so on, up to a switch for lamp 15 and 1. When the switch for such a pair of l... | {
"ground_truth": "4",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. If we remove one or more digits from the beginning and/or end of a positive integer and still have a positive integer left, we call that a fragment of the original number. Thus, 2, 1, 9, 20, 19, and 201 are fragments of 2019.\n\nWhat is the smallest positive integer $n$ with the property: there... | {
"ground_truth": "1836",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Timur and Alexander are counting the trees growing around the house. They move in the same direction but start counting from different trees. How many trees are growing around the house if the tree that Timur counted as the 12th, Alexander counted as the 33rd, and the tree that Timur counted as th... | {
"ground_truth": "118",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. (15 points) A light ray falls at an angle $\\alpha=60^{\\circ}$ on the front surface of a parallel glass plate. The refractive index of the glass is $n=1.6$. By what angle is the ray, reflected from the back surface of the plate and exiting back through the front surface, deflected from the dir... | {
"ground_truth": "60",
"mean_reward": 0.203125
} | 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\nFor a convex quadrilateral $P$, let $D$ denote the sum of the lengths of its diagonals and let $S$ denote its perimeter. Determine, with proof, all possible values of... | {
"ground_truth": "1",
"mean_reward": 0.21875
} | 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\nLet \\(n \\geq 3\\) be a fixed integer. The number 1 is written \\(n\\) times on a blackboard. Below the blackboard, there are two buckets that are initially empty. A... | {
"ground_truth": "3",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the complex number $z=i(3-2i)$, where $i$ is the imaginary unit, calculate $\\overset{.}{z}$. Express your answer as a complex number in the form $a+bi$, including the imaginary unit $i$.",
"role": "user"
}
] | {
"ground_truth": "2-3i",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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