prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "C15 (16-4, Bulgaria) Divide an $8 \\times 8$ chessboard into $p$ rectangles, such that the division does not cut through any cell (i.e., it must follow the grid lines of the chessboard), and satisfies the following two conditions:\n（1）Each rectangle contains the same number of white and black cell... | {
"ground_truth": "7",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three. (This question is worth 50 points) Given 10 points in space, where no four points lie on the same plane. Connect some of the points with line segments. If the resulting figure contains no triangles and no spatial quadrilaterals, determine the maximum number of line segments that can be draw... | {
"ground_truth": "15",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the maximum number $E$ such that the following holds: there is an edge-colored graph with 60 vertices and $E$ edges, with each edge colored either red or blue, such that in that coloring, there is no monochromatic cycles of length 3 and no monochromatic cycles of length 5.",
"role": "... | {
"ground_truth": "1350",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given \\( a_{n} = \\mathrm{C}_{200}^{n} \\cdot (\\sqrt[3]{6})^{200-n} \\cdot \\left( \\frac{1}{\\sqrt{2}} \\right)^{n} \\) for \\( n = 1, 2, \\ldots, 95 \\), find the number of integer terms in the sequence \\(\\{a_{n}\\}\\).",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "As shown in the diagram, \\( D \\), \\( E \\), and \\( F \\) are points on the sides \\( BC \\), \\( CA \\), and \\( AB \\) of \\(\\triangle ABC\\), respectively, and \\( AD \\), \\( BE \\), \\( CF \\) intersect at point \\( G \\). Given that the areas of \\(\\triangle BDG\\), \\(\\triangle CDG\\)... | {
"ground_truth": "63",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Among five externally identical coins, 3 are genuine and 2 are counterfeit, with the counterfeits weighing the same but it is unknown whether they are heavier or lighter than the genuine coins. How can you find at least one genuine coin with the fewest possible weighings?",
"role": "user"
}
... | {
"ground_truth": "2",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the internal angle that guarantees two isosceles triangles are similar. Express your answer as a single angle value in degrees, including the degree symbol (°).",
"role": "user"
}
] | {
"ground_truth": "60°",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "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 prime numbers $p$ and nonnegative integers $x\\neq y$ such that $x^4- y^4=p(x^3-y^3)$.\n\n[Solution]\n\n<paragraph_0>\nTo solve the equation \\( x^4 - y^4 = ... | {
"ground_truth": "-1",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. let $M$ be a finite set of real numbers with the following property: From every three different elements of $M$, two can always be selected whose sum lies in $M$. What is the maximum number of elements $M$ can have?\n\n## Solution",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A chess knight has injured his leg and is limping. He alternates between a normal move and a short move where he moves to any diagonally neighbouring cell.\n\n\n\nNormal m... | {
"ground_truth": "25",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1.49 On a grid paper of size $11 \\times 11$, mark 22 cells so that exactly two cells are marked in each row and each column. If one arrangement of the marked cells can be transformed into another arrangement by swapping rows with rows or columns with columns, then these two arrangements are consi... | {
"ground_truth": "14",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For all positive integers $n$, let $g(n)=\\log_{3003} n^2$. Calculate $g(7) + g(11) + g(13)$.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are $2024$ people, which are knights and liars and some of them are friends. Every person is asked for the number of their friends and the answers were $0,1, \\ldots, 2023$ . Every knight answered truthfully, while every liar changed the real answer by exactly $1$ . What is the minimal n... | {
"ground_truth": "1012",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "22. There are 4 people sitting together, some of them always tell the truth, while others always lie. According to their conversation, the number of people who always tell the truth is $\\qquad$ people.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's find the highest degree expression of $x$ such that\n\n$$\nn x^{n+1}-(n+1) x^{n}+1\n$$\n\nand $x^{n}-n x+n-1$\n\nare divisible.",
"role": "user"
}
] | {
"ground_truth": "(x-1)^2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. (7 points) Percival's castle had a square shape. One day, Percival decided to expand his domain and added a square extension to the castle. As a result, the perimeter of the castle increased by $10 \\%$. By what percentage did the area of the castle increase?",
"role": "user"
}
] | {
"ground_truth": "4",
"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\nDhruv is older than Bev. Bev is older than Elcim. Elcim is younger than Andy. Andy is younger than Bev. Bev is younger than Cao. Who is the third oldest?\n\n[Solution... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. An $A M C$ exam consists of 30 questions, with the scoring rules specifying 5 points for each correct answer, 0 points for each wrong answer, and 2 points for each unanswered question. \nThe sum of the points a participant earns for each question is called the participant's total score. Assumin... | {
"ground_truth": "145",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The function \\[f(x) = \\left\\{ \\begin{aligned} 2x + 1 & \\quad \\text{ if } x < 3 \\\\ x^2 & \\quad \\text{ if } x \\ge 3 \\end{aligned} \\right.\\] has an inverse $f^{-1}.$ Compute the value of $f^{-1}(-3) + f^{-1}(0) + \\dots + f^{-1}(4) + f^{-1}(9).$",
"role": "user"
}
] | {
"ground_truth": "3.5",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2 After a round-robin volleyball tournament, it was found that for any two teams, there is always a third team that has defeated both of these teams. How many teams participated in the tournament at the very least?",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two positive integers differ by 5 and their product is 88. What is the larger integer?",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Compute the number of ordered quadruples $(a,b,c,d)$ of distinct positive integers such that $\\displaystyle \\binom{\\binom{a}{b}}{\\binom{c}{d}}=21$.\n\n[i]Proposed by Luke Robitaille[/i]",
"role": "user"
}
] | {
"ground_truth": "13",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 6 people standing in a line numbered 1 through 6 in a left to right order.\nEach person has the following attributes: Beverage, Food, Hobby, Pet.\nThe attributes have the following possible values:\n- Beverage: almond-milk, milk, mirinda, soy-milk, sprite, tea\n- Food: apricot, banana, ... | {
"ground_truth": "cooking",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The perimeter of a semicircle with an area of ______ square meters is 15.42 meters.",
"role": "user"
}
] | {
"ground_truth": "14.13",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Two players, A and B, are playing a game on a $2^{100} \\times 100$ grid. They take turns filling in symbols in the empty cells of the first row, with A starting first. In each turn, A selects an empty cell in the first row and fills it with “$\\times$”, then B selects an empty cell in the firs... | {
"ground_truth": "2^{50}",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ such that\n\n$$\ny^{2} f(x)+x^{2} f(y)+x y=x y f(x+y)+x^{2}+y^{2}\n$$\n\nfor all real numbers $x, y$.",
"role": "user"
}
] | {
"ground_truth": "f(x)=ax+1",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Let's call a natural number an almost palindrome if it can be transformed into a palindrome by changing one of its digits. How many nine-digit almost palindromes exist? (20 points)",
"role": "user"
}
] | {
"ground_truth": "3240000",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 173, Given that a square has three vertices on the parabola $y=x^{2}$, find the minimum value of the area of such a square.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly. \n\n(Note: The note its... | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Vintik and Shpuntik built a machine called \"Tug-Push,\" which moves forward on syrup with a fuel consumption of Zl/km, and backward on orange juice with a fuel consumption of 5l/km. Leaving home, they drove the machine in turns. Vintik drove 12 km in both directions. Shpuntik drove forward hal... | {
"ground_truth": "9",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a cube with edges of length 2 units, point Q is the intersection of the diagonals of one face. Calculate the length of QR. Express your answer as a radical.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{6}",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. $z$ is a complex number, then the minimum value of $T=|z|+|z-2|+|z+\\sqrt{3} i|$ is what?\n\n---\n\nThe translation maintains the original format and line breaks as requested.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{13}",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B1. Above the campsite where Huub is camping, there is a cable car with $n$ numbered gondolas.\n\nThe gondolas hang in a loop at equal distances from each other. After gondola 1 comes gondola 2, after gondola 2 comes gondola 3, and so on, and after gondola $n$ comes gondola 1 again. At a certain m... | {
"ground_truth": "202",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. (2 points) A chess piece called a quadraliner attacks two verticals and two horizontals adjacent to the square it occupies. What is the maximum number of non-attacking quadraliners that can be placed on a $10 \\times 10$ board?",
"role": "user"
}
] | {
"ground_truth": "25",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The owner of a modern auto parts chain wants to expand into the nostalgia market by selling classic car parts. They decide to launch their new product line with 5 different types of vintage hubcaps, each priced at $25. On the first day of the launch, the store sells 3 sets of each type of hubcap. ... | {
"ground_truth": "825",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 10. Points $M, N$, and $K$ are located on the lateral edges $A A_{1}, B B_{1}$, and $C C_{1}$ of the triangular prism $A B C A_{1} B_{1} C_{1}$ such that $A M: A A_{1}=1: 2, B N: B B_{1}=1: 3, C K: C C_{1}=1: 4$. Point $P$ belongs to the prism. Find the maximum possible value of the volume... | {
"ground_truth": "4",
"mean_reward": 0.15625
} | 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 6, 24, and 24. 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 radius of the smaller base of the t... | {
"ground_truth": "2",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex, a film critique with a passion for old Christmas movies, is planning a holiday movie marathon. He has a collection of 12 classic Christmas films, each with a soundtrack composed by different artists. However, 5 of these soundtracks were composed by his favorite composer, Harry Gregson-Willia... | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of real roots of the equation x/100 = sin(x) over the entire real number line.",
"role": "user"
}
] | {
"ground_truth": "63",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Triangle $ABC$ is isosceles with $AC = BC$ and $\\angle ACB = 106^\\circ.$ Point $M$ is in the interior of the triangle so that $\\angle MAC = 7^\\circ$ and $\\angle MCA = 23^\\circ.$ Find the number of degrees in $\\angle CMB.$\n[asy] pointpen = black; pathpen = black+linewidth(0.7); size(220); /... | {
"ground_truth": "83",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 4 people standing in a line numbered 1 through 4 in a left to right order.\nEach person has the following attributes: Job, Food, Beverage, Movie-Genre, Nationality, Transport.\nThe attributes have the following possible values:\n- Job: engineer, freelancer, pilot, videographer\n- Food: ... | {
"ground_truth": "malaysian",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest solution to \\[\n\\lfloor x \\rfloor = 7 + 150 \\{ x \\},\n\\] where $\\{x\\} = x - \\lfloor x \\rfloor$.",
"role": "user"
}
] | {
"ground_truth": "156.9933",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Given the function $f(x)=x^{2}-1$ with domain $D$, and the range is $\\{-1,0,1,3\\}$. Determine the maximum number of such sets $D$.\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": "27",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given $a,x\\in\\mathbb{R}$ and $x\\geq 0$ , $a\\geq 0$ . Also $\\sin(\\sqrt{x+a})=\\sin(\\sqrt{x})$ . What can you say about $a$ ??? Justify your answer.",
"role": "user"
}
] | {
"ground_truth": " a = 0 ",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Over the course of three years, Marina did not invest the funds in her Individual Investment Account (IIA) into financial instruments and therefore did not receive any income from it. However, she gained the right to an investment tax deduction for depositing her own money into the IIA.\n\nThe tax... | {
"ground_truth": "3.55\\%",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "18. N1 (BUL) $M$ is a subset of $\\{1,2,3, \\ldots, 15\\}$ such that the product of any three distinct elements of $M$ is not a square. Determine the maximum number of elements in $M$.",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "16. Team A and Team B each send out 7 players to compete in a Go broadcast tournament, following a predetermined order. The competition starts with the No. 1 players from both teams. The loser is eliminated, and the winner then faces the No. 2 player from the losing team, $\\cdots$, until all play... | {
"ground_truth": "210",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given in $\\triangle A B C$, $A B=A C, \\angle A=20^{\\circ}$, $D$ is on $A C$ and $E$ is on $A B$. If $\\angle A B D=10^{\\circ}, \\angle B D E$ $=20^{\\circ}$, find the degree measure of $\\angle A C E$.",
"role": "user"
}
] | {
"ground_truth": "20^{\\circ}",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jamie is a community organizer who is campaigning for a new after-school program. To gain support, Jamie decides to distribute flyers on a bus route that is popular with local families. Jamie talks to the bus driver, who agrees to help by allowing Jamie to leave flyers on the bus every day for a w... | {
"ground_truth": "24",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a$ be a positive real number, $n$ a positive integer, and define the [i]power tower[/i] $a\\uparrow n$ recursively with $a\\uparrow 1=a$, and $a\\uparrow(i+1)=a^{a\\uparrow i}$ for $i=1,2,3,\\ldots$. For example, we have $4\\uparrow 3=4^{(4^4)}=4^{256}$, a number which has $155$ digits. For... | {
"ground_truth": " x_{42} ",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine all integers $k$ such that there exists infinitely many positive integers $n$ [b]not[/b] satisfying \n\\[n+k |\\binom{2n}{n}\\]",
"role": "user"
}
] | {
"ground_truth": "k \\neq 1",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that $f'\"({x}_{0})=-3$, calculate the limit: $\\lim\\limits_{h\\to0} \\frac{f\\left({x}_{0}+h\\right)-f\\left({x}_{0}-3h\\right)}{h}$. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "-12",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. At night, snow fell and evenly covered a circular area with a radius of five meters with a layer 36 centimeters high. What is the maximum height (in meters) that children can build a snowman, assuming the snowman is two spheres, one placed on top of the other? Neglect the change in snow density... | {
"ground_truth": "6",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "IMO 1988 Problem A3 A function f is defined on the positive integers by: f(1) = 1; f(3) = 3; f(2n) = f(n), f(4n + 1) = 2f(2n + 1) - f(n), and f(4n + 3) = 3f(2n + 1) - 2f(n) for all positive integers n. Determine the number of positive integers n less than or equal to 1988 for which f(n) = n. Solut... | {
"ground_truth": "92",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The pentagon \\(ABCDE\\) is inscribed around a circle. The angles at its vertices \\(A\\), \\(C\\), and \\(E\\) are \\(100^{\\circ}\\). Find the angle \\(ACE\\).",
"role": "user"
}
] | {
"ground_truth": "40^\\circ",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Van 4 points on a plane. The distance between any two points is at most 1. What is the maximum possible sum of the squares of the 6 distances between the 4 points?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a chess tournament, a team of schoolchildren and a team of students, each consisting of 15 participants, compete against each other. During the tournament, each schoolchild must play with each student exactly once, with the condition that everyone can play at most once per day. Different number... | {
"ground_truth": "120",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Find all real numbers $p$ such that the cubic equation $5 x^{3}-5(p+1) x^{2}+(71 p-1) x+1=66 p$ has three positive integer roots.\n\n untranslated text remains the same as requested.",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a sequence ${a_n}$ defined by $|a_{n+1}|+|a_n|=3$ for any positive integer $n$ and $a_1=2$, find the minimum value of the sum $S_{2019}$ of its first 2019 terms.",
"role": "user"
}
] | {
"ground_truth": "-3025",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. On the sides of a rectangle with length $8 \\mathrm{~cm}$ and width $6 \\mathrm{~cm}$, points are placed starting from one vertex, each $2 \\mathrm{~cm}$ apart. How many different lines do these points determine?\n\nNATIONAL MATHEMATICS COMPETITIONPrimošten, April 4-6, 2016.6th grade-elementary... | {
"ground_truth": "63",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a lake there are several sorts of fish, in the following distribution: $ 18\\%$ catfish, $ 2\\%$ sturgeon and $ 80\\%$ other. Of a catch of ten fishes, let $ x$ denote the number of the catfish and $ y$ that of the sturgeons. Find the expectation of $ \\frac {x}{y \\plus{} 1}$",
"role": "us... | {
"ground_truth": "1.6461",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a set $ P$ of five points in the plane, no three of them being collinear, let $ s(P)$ be the numbers of acute triangles formed by vertices in $ P$ .\r\nFind the maximum value of $ s(P)$ over all such sets $ P$ .",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. find all triples $(p, q, r)$ of prime numbers such that the three differences\n\n$$\n|p-q|, \\quad|q-r|, \\quad|r-p|\n$$\n\nare all prime numbers.\n\n## Solution:",
"role": "user"
}
] | {
"ground_truth": "(2,5,7)",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest number $n$ having the following properties:\n\n(a) No two digits of $n$ are equal.\n\n(b) The number formed by reversing the digits of $n$ is divisible by 8 .\n\nRemark. $n$ cannot start with 0 , but it can end with 0 .",
"role": "user"
}
] | {
"ground_truth": "8697543210",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Integers $x, y$ satisfy the equation $15 x^{2} y^{2}=35 x^{2} \\cdots$ $3 y^{2}+412$. Then $15 x^{2} y^{2}=$",
"role": "user"
}
] | {
"ground_truth": "960",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A Gauss brand light bulb will work for 24999 hours. If it is used for exactly 2 hours every day starting on a Monday, on what day of the week will it stop working? Express your answer as a day of the week (e.g. Monday, Tuesday, etc.).",
"role": "user"
}
] | {
"ground_truth": "Friday",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Armen paid \\$190 to buy movie tickets for a group of \\( t \\) people, consisting of some adults and some children. Movie tickets cost \\$5 for children and \\$9 for adults. How many children's tickets did he buy?",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Parallelogram $A B C D$ can be divided into four equilateral triangles with a side length\n\n(8) of $2 \\mathrm{~cm}$. What is the length of the longer diagonal of the parallelogram?",
"role": "user"
}
] | {
"ground_truth": "2\\sqrt{7}",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A test consists of 6 multiple-choice questions. The grading rule is as follows: each person initially scores 6 points, each correct answer adds 4 points, each incorrect answer deducts 1 point, and no answer gets 0 points. If 51 students take the test, what is the minimum number of students who mus... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 68: Given $a, b \\in R$, such that the equation $x^{4}+a x^{3}+2 x^{2}+b x+1=0$ has real roots, find the minimum possible value of $a^{2}+b^{2}$.\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": "8",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is 56. Find the area of the polygon.\n\n[asy]\nunitsize(0.5 cm);\n\ndraw((3,0)--(4,0)--(4,1)--(5,1)--(5,2)--(6,2)--(6,3)--(7,3)--(7,4)--(6,4)--(6,5)--(5,5)-... | {
"ground_truth": "100",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Today is Barbara's birthday, and Alberto wants to give her a gift playing the following game. The numbers 0,1,2,...,1024 are written on a blackboard. First Barbara erases $2^{9}$ numbers, then Alberto erases $2^{8}$ numbers, then Barbara $2^{7}$ and so on, until there are only two numbers a,b left... | {
"ground_truth": "32",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct sets of $5$ distinct positive integers $A$ satisfy the property that for any positive integer $x\\le 29$ , a subset of $A$ sums to $x$ ?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sum of the positive divisors of a positive integer of the form $2^i5^j$ is equal to $930$. What is $i + j$?",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is a set of points \\( M \\) on a plane and seven different circles \\( C_{1}, C_{2}, \\cdots, C_{7} \\). Circle \\( C_{7} \\) passes through exactly 7 points in \\( M \\), circle \\( C_{6} \\) passes through exactly 6 points in \\( M \\), and so on, with circle \\( C_{1} \\) passing through... | {
"ground_truth": "12",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Four consecutive three-digit numbers are divided respectively by four consecutive two-digit numbers. What minimum number of different remainders can be obtained? \n\n*(A. Golovanov)*",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Compute the integral $\\iint_D xy^2 dA$, where $D$ is the rectangle defined by 0 <= x <= 2 and 0 <= y <= 1.",
"role": "user"
}
] | {
"ground_truth": "0.66667",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a given positive integer $m$ , the series $$ \\sum_{k=1,k\\neq m}^{\\infty}\\frac{1}{(k+m)(k-m)} $$ evaluates to $\\frac{a}{bm^2}$ , where $a$ and $b$ are positive integers. Compute $a+b$ .",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the state of Karnataka, there are 224 assembly constituencies. During the last election, Party A won 56 seats, Party B won 78 seats, and Party C won 62 seats. The remaining seats were won by independent candidates. If the total number of votes cast in the election was 10,000,000 and each consti... | {
"ground_truth": "44643",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.2. The year 2009 has the property that by rearranging its digits, it is impossible to form a smaller four-digit number (numbers do not start with zero). In which year will this property reoccur for the first time?\n\n(I. V. Raskina)",
"role": "user"
}
] | {
"ground_truth": "2022",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Marie has $10$ identical candies and $5$ identical boxes. How many ways are there for her to distribute all of the candies among the boxes, if only the number of candies in each box matters?",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum $m + n$ where $m$ and $n$ are integers, such that the positive difference between the two roots of the quadratic equation $2x^2 - 5x - 12 = 0$ can be expressed as $\\frac{\\sqrt{m}}{n}$, and $m$ is not divisible by the square of any prime number.",
"role": "user"
}
] | {
"ground_truth": "123",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the function y=x^2 with a range of [1,4], determine the number of such functions that can be defined within the domain that meets this range. Express your answer as a numerical value if finite, or as 'infinite' if appropriate.",
"role": "user"
}
] | {
"ground_truth": "infinite",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the maximum number of principals that can serve at Lincoln High School during an 8-year period, given that each principal serves exactly one 3-year term? Provide your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sum $\\frac{2}{3\\cdot 6} +\\frac{2\\cdot 5}{3\\cdot 6\\cdot 9} +\\ldots +\\frac{2\\cdot5\\cdot \\ldots \\cdot 2015}{3\\cdot 6\\cdot 9\\cdot \\ldots \\cdot 2019}$ is written as a decimal number. Find the first digit after the decimal point.",
"role": "user"
}
] | {
"ground_truth": " 6 ",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Given $f(x)=\\sqrt{a x^{2}+2 b x}$, there exists at least one positive number $b$, such that the domain and range of $f(x)$ are the same. Then the value of the real number $a$ that satisfies the condition is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "0or-4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A palace is shaped like a square and divided into $2003 \\times 2003$ rooms, similar to the squares on a large chessboard. There is a door between two rooms if and only if they share a wall. The main entrance allows entry into the palace from the outside into the room located at the northwest corn... | {
"ground_truth": "99",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "96. Processing a batch of parts, if A works for 5 hours first, then B joins to work together, A will have made 400 more parts than B when completed; if B works for 5 hours first, then A joins to work together, B will have made 40 more parts than A when completed. If A and B start working together ... | {
"ground_truth": "180",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A test consists of 6 multiple-choice questions. The grading rule is as follows: each person initially scores 6 points, each correct answer adds 4 points, each incorrect answer deducts 1 point, and no answer gets 0 points. If 51 students take the test, what is the minimum number of students who mus... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two dice (each die has sides numbered from 1 to 6) are rolled sequentially and land on a horizontal surface, recording the numbers facing up as x and y. Let event A be “x+y is an even number”, and event B be “one of x or y is an even number, and x!= y”. Calculate the conditional probability P(B|A)... | {
"ground_truth": "1/3",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Dinesh has several squares and regular pentagons, all with side length $ 1$. He wants to arrange the shapes alternately to form a closed loop (see diagram). How many pentagons would Dinesh need to do so?\n[img]https://cdn.artofproblemsolving.com/attachments/8/9/6345d7150298fe26cfcfba554656804ed25a... | {
"ground_truth": "10",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The large cube shown is made up of $27$ identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. Fold a rope 4 times, cut it from the middle, the rope will be divided into many small segments, these segments have two lengths, among which the longer ones have $\\qquad$ segments.",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Arrange students A, B, C, D, and E from left to right. Calculate the total number of arrangements where A and B are adjacent and there is exactly one student between A and C. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "20.16. Some of the 20 metal cubes, identical in size and appearance, are aluminum, the rest* are duralumin (heavier). How can you determine the number of duralumin cubes using 11 weighings on a balance with two pans and no weights?",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.1875
} | 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\nWhat is the smallest positive integer $n$ such that, out of the $n$ unit fractions $\\frac{1}{k}$ where $1 \\le k \\le n$, exactly half of the fractions give a termin... | {
"ground_truth": "4",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Thompson is a high school teacher who loves educating his students on global issues. He often uses marketing case studies from his cousin's international marketing firm to make his lessons more engaging. In one of his classes, he wants to illustrate the impact of advertising on sales. He prese... | {
"ground_truth": "1686",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 9.7. In front of a sweet-tooth lie five boxes of candies: the first box contains 11 candies, the second - 22 candies, the third - 33 candies, the fourth - 44 candies, the fifth - 55 candies. In one move, the sweet-tooth can take four candies from one box and distribute them, one candy to e... | {
"ground_truth": "159",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three workers are digging a hole. They take turns working, with each one working as long as it takes the other two to dig half the hole. Working in this way, they finished digging the hole. How many times faster would they have finished the job if they had worked simultaneously?",
"role": "use... | {
"ground_truth": "3",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In parallelogram $A B C D$ with angle $A$ equal to $60^{\\circ}$, the bisector of angle $B$ intersects side $C D$ at point $E$. A circle with radius $R$ is inscribed in triangle $E C B$. Another circle is inscribed in trapezoid $A B E D$. Find the distance between the centers of these circles.",
... | {
"ground_truth": "R\\sqrt{7}",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Problem 5\n\nA polynomial of degree $3 n$ has the value 2 at $0,3,6, \\ldots, 3 n$, the value 1 at $1,4,7, \\ldots, 3 n-2$ and the value 0 at $2,5,8, \\ldots, 3 n-1$. Its value at $3 n+1$ is 730 . What is $n$ ?\n\n",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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