prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "## 255. Math Puzzle $8 / 86$\n\nFelix rides his bicycle on a straight route between two towns that are ten kilometers apart, and the round trip takes him one hour.\n\nThe next day, a strong wind blows, so he rides 5 km/h faster on the way there and 5 km/h slower on the way back compared to his ave... | {
"ground_truth": "4",
"mean_reward": 0.15625
} | 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\nIs there an integer $n$ such that $\\sqrt{n-1}+\\sqrt{n+1}$ is a rational number?\n\n[Solution]\n\n<paragraph_0>\nTo solve this problem, let's start by examining the ... | {
"ground_truth": "-1",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.5. On a 10 by 10 cell board, some 10 cells are marked. For what largest $n$ is it always possible, regardless of which cells are marked, to find a rectangle consisting of several cells, the perimeter of which will be at least $n$? The length or width of the rectangle can be equal to one cell.",
... | {
"ground_truth": "20",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a triangle \\( \\triangle KLM \\), point \\( A \\) lies on the extension of \\( LK \\). Construct a rectangle \\( ABCD \\) such that points \\( B \\), \\( C \\), and \\( D \\) lie on the lines containing \\( KM \\), \\( KL \\), and \\( LM \\), respectively.",
"role": "user"
}
] | {
"ground_truth": "ABCD",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the minimum number of points that can be chosen on a circle with a circumference of 1956 so that for each of these points there is exactly one chosen point at a distance of 1 and exactly one at a distance of 2 (distances are measured along the circle)?",
"role": "user"
}
] | {
"ground_truth": "1304",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a software engineer working on privacy controls for a tech company. This week, Alex needs to update the privacy settings for a new feature. The feature is used by 150 employees and each employee requires 5 different privacy settings. For each privacy setting, Alex has to write 3 lines of c... | {
"ground_truth": "32",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. [7] Consider the graph in 3-space of\n$$\n0=x y z(x+y)(y+z)(z+x)(x-y)(y-z)(z-x) \\text {. }\n$$\n\nThis graph divides 3 -space into $N$ connected regions. What is $N$ ?",
"role": "user"
}
] | {
"ground_truth": "48",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "One, (40 points) Integers $a, b, c, d$ satisfy $ad - bc = 1$. Find the minimum value of $a^2 + b^2 + c^2 + d^2 + ab + cd - ac - bd - bc$, and determine all quadruples $(a, b, c, d)$ that achieve this minimum value.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the area of the triangle bounded by the axes and the curve $y = (x-5)^2 (x+3)$.",
"role": "user"
}
] | {
"ground_truth": "300",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. (8 points) Solve the equation\n\n$$\n\\sqrt{a^{2}+c-1-2 x-x^{2}}+\\sqrt{b^{2}+c-1-2 x-x^{2}}=\\sqrt{x^{2}+2 x+1-c+(a+b)^{2}}\n$$\n\nIn your answer, write the sum of the squares of all possible pairwise differences of the real roots of the equation. Numbers $a, b>0$.",
"role": "user"
}
] | {
"ground_truth": "4c",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5. Find the flux of the vector field $\\mathbf{a} = \\boldsymbol{y}^{2} \\mathbf{j} + z \\mathbf{k}$ through the part of the surface $z = x^{2} + y^{2}$, cut off by the plane $z = 2$. The normal is taken outward with respect to the region bounded by the paraboloid.\n\n![](https://cdn.mathp... | {
"ground_truth": "-2\\pi",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. A wooden rectangular prism has edges of length 8, 10, and 15. From two of its vertices, one cube each is cut out, with the lengths of their edges being natural numbers. First, a cube of the largest possible volume is cut from the prism, and then a cube of the smallest possible volume. What perc... | {
"ground_truth": "42.75",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Riley has 64 cubes with dimensions \\(1 \\times 1 \\times 1\\). Each cube has its six faces labeled with a 2 on two opposite faces and a 1 on each of its other four faces. The 64 cubes are arranged to build a \\(4 \\times 4 \\times 4\\) cube. Riley determines the total of the numbers on the outsid... | {
"ground_truth": "49",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. The sum of a set of numbers is the sum of all its elements. Let $S$ be a set of positive integers not exceeding 15, such that the sums of any two disjoint subsets of $S$ are not equal, and among all sets with this property, the sum of $S$ is the largest. Find the sum of the set $S$.\n(4th Ameri... | {
"ground_truth": "61",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a polynomial equation \\( z^{4} + a z^{3} + b z^{2} + c z + d = 0 \\) with real coefficients, where all roots lie on the unit circle in the complex plane, find the sum of the reciprocals of these roots. Express your answer as a single value.",
"role": "user"
}
] | {
"ground_truth": "-a",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the equation of the trajectory of points that are equidistant from both coordinate axes. Express your answer as an equation using standard mathematical notation.",
"role": "user"
}
] | {
"ground_truth": "y^2 = x^2",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are two hourglasses - one for 7 minutes and one for 11 minutes. An egg needs to be boiled for 15 minutes. How can you measure this amount of time using the hourglasses?",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Emily is a statistician who loves using numbers to help her community. She is working on a project to measure the impact of a new community center in her town. At the start of the year, the town had 240 children attending various after-school programs. After the community center opened, 5 new prog... | {
"ground_truth": "330",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two players, Blake and Ruby, play the following game on an infinite grid of unit squares, all initially colored white. The players take turns starting with Blake. On Blake's turn, Blake selects one white unit square and colors it blue. On Ruby's turn, Ruby selects two white unit squares and colors... | {
"ground_truth": "4",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In triangle $A B C$, side $B C$ is 19 cm. The perpendicular $D F$, drawn from the midpoint of side $A B$ - point $D$, intersects side $B C$ at point $F$. Find the perimeter of triangle $A F C$, if side $A C$ is $10 \\, \\text{cm}$.",
"role": "user"
}
] | {
"ground_truth": "29",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $n$ be a natural number. An integer $a>2$ is called $n$-decomposable, if $a^n-2^n$ is divisible by all the numbers of the form $a^d+2^d$, where $d\\neq n$ is a natural divisor of $n$. Find all composite $n\\in \\mathbb{N}$, for which there's an $n$-decomposable number.",
"role": "user"
}... | {
"ground_truth": " n = 2^k ",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 8 Suppose $N$ consecutive positive integers satisfy the following conditions: the sum of the digits of the 1st number is divisible by 1, the sum of the digits of the 2nd number is divisible by 2, $\\cdots$. The sum of the digits of the $N$th number is divisible by $N$. Find the maximum pos... | {
"ground_truth": "21",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find a positive integer that is divisible by 18 and has a square root between 30 and 30.2.",
"role": "user"
}
] | {
"ground_truth": "900",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $P(r,t,T)$ denote the price at time $t$ of $1 to be paid with certainty at time $T, t\\leT$, if the short rate at time $t$ is equal to $r$. For a Vasicek model you are given: $P(0.04, 0, 2)=0.9445$, $P(0.05, 1, 3)=0.9321$, $P(r^*, 2, 4)=0.8960$. What is $r^*$?",
"role": "user"
}
] | {
"ground_truth": "0.08",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the solution set of the inequality $x^2-2x+3<0$. Describe your answer using interval notation or clear descriptive text, and indicate if the solution set is empty.",
"role": "user"
}
] | {
"ground_truth": "\\emptyset",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If $x$ is a real number, let $\\lfloor x \\rfloor$ be the greatest integer that is less than or equal to $x$ . If $n$ is a positive integer, let $S(n)$ be defined by\n\\[\n S(n) \n = \\left\\lfloor \\frac{n}{10^{\\lfloor \\log n \\rfloor}} \\right\\rfloor\n + 10 \\left( n - 10... | {
"ground_truth": "108",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In triangle \\( \\triangle ABC \\), \\( AM \\) and \\( CN \\) are the medians to sides \\( BC \\) and \\( AB \\), respectively, intersecting at point \\( O \\). \\( P \\) is the midpoint of \\( AC \\), and \\( MP \\) intersects \\( CV \\) at \\( Q \\). If the area of \\( \\triangle OMQ \\) is \\( ... | {
"ground_truth": "24n",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a dihedral angle α-PQ-β, points A and B are on half-plane α, and point C is on half-plane β (A, B, and C are not on PQ, and the distances from A and B to PQ are not equal). Determine the number of trapezoids that can be constructed with A, B, and C as vertices, such that the fourth vertex al... | {
"ground_truth": "2",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a convex pentagon $ABCDE$ with $AB=BC, CD=DE, \\angle ABC=150^o, \\angle CDE=30^o, BD=2$. Find the area of $ABCDE$.\n\n(I.Voronovich)",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Zkov G.\n\nA bank serves a million customers, the list of whom is known to Ostap Bender. Each has a six-digit PIN code, and different customers have different codes. In one move, Ostap Bender can choose any customer he has not yet chosen and peek at the digits of the code at any $N$ positions (he ... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. (8 points) One day, Xiao Ming was chatting with his brother. Xiao Ming said to his brother: \"I am particularly looking forward to the year 2013, because 2, 0, 1, and 3 are four different digits. I have never experienced such a year before.\" His brother smiled and said: \"Yes, we can call such... | {
"ground_truth": "1987",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[Arithmetic. Mental arithmetic, etc.] [Theory of algorithms (other).]\n\nThere are two hourglasses - one for 7 minutes and one for 11 minutes. An egg needs to be boiled for 15 minutes. How can you measure this time using the available hourglasses?\n\n#",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. Given a function $f(x)$ defined on $[0,1]$, $f(0)=0, f(1)=1$, and satisfies the following conditions:\n(a) For any $x \\in[0,1], f(x) \\geq 0$;\n(b) For any two numbers $x_{1} \\geq 0, x_{2} \\geq 0, x_{1}+x_{2} \\leq 1$, it holds that $f\\left(x_{1}+x_{2}\\right) \\geq f\\left(x_{1}\\right)+f... | {
"ground_truth": "2",
"mean_reward": 0.390625
} | 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\nAlex has four books of different sizes which he wishes to place on a bookshelf. Unfortunately, the bookshelf has a conspicuous hole at one end through which only the ... | {
"ground_truth": "0",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 8/88 The number of all ordered pairs $(x ; y)$ of integers $x$ and $y$, which are solutions to the inequalities\n\n$$\n8 \\cdot \\sqrt{8+8}+8+\\frac{8}{8} \\leq|x|+|y| \\leq 8 \\cdot 8 \\cdot \\sqrt{8+8}+\\sqrt{8+8}+8+\\frac{8}{8}\n$$\n\nis sought, increased by 8. Insert a dot after the first... | {
"ground_truth": "1.4.1988",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From the positive integers, $m,m+1,\\dots,m+n$ , only the sum of digits of $m$ and the sum of digits of $m+n$ are divisible by $8$ . Find the maximum value of $n$ .",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Berolov s.l.\n\nThe incircle of triangle $ABC$ touches sides $AB$ and $AC$ at points $X$ and $Y$ respectively. Point $K$ is the midpoint of the arc $AB$ of the circumcircle of triangle $ABC$ (not containing point $C$). It turns out that line $XY$ bisects segment $AK$. What can the angle $BAC$ be?"... | {
"ground_truth": "120",
"mean_reward": 0.265625
} | 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\nTriangle $ABC$ is an isosceles right triangle with a right angle at $A$. Segments $BD$ and $BE$ trisect angle $ABC$. What is the degree measure of angle $BDE$?\n\n[as... | {
"ground_truth": "0",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. $[\\mathbf{3}]$ A $3 \\times 3 \\times 3$ cube composed of 27 unit cubes rests on a horizontal plane. Determine the number of ways of selecting two distinct unit cubes from a $3 \\times 3 \\times 1$ block (the order is irrelevant) with the property that the line joining the centers of the two c... | {
"ground_truth": "60",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( ABC \\) be a triangle in which \\( \\angle ABC = 60^\\circ \\). Let \\( I \\) and \\( O \\) be the incentre and circumcentre of \\( ABC \\), respectively. Let \\( M \\) be the midpoint of the arc \\( BC \\) of the circumcircle of \\( ABC \\), which does not contain the point \\( A \\). Det... | {
"ground_truth": "30",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Petya's favorite TV game is called \"Lottery on the Couch.\" During the game, viewers can send SMS messages with three-digit numbers containing only the digits 1, 2, 3, and 4. At the end of the game, the host announces a three-digit number, also consisting only of these digits. An SMS is considere... | {
"ground_truth": "8",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Carlos is a political columnist living in Puerto Rico, and he writes articles for a local newspaper. Each week, he writes about the latest political developments both locally and internationally. On average, Carlos writes 4 articles per week. Each article takes him 3 hours to research and 2 hours ... | {
"ground_truth": "96",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A quadratic polynomial $f(x)$ (of exact degree 2 with integer coefficients) is called *sparse* if there exists a nonzero polynomial $g(x)$ with integer coefficients such that $f(x)g(x)$ has degree at most 3 and has at most two nonzero coefficients. Find the number of sparse quadratics whose coeffi... | {
"ground_truth": "228",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A polynomial of degree 3n has the value 2 at 0, 3, 6, ... , 3n, the value 1 at 1, 4, 7, ... , 3n-2, and the value 0 at 2, 5, 8, ..., 3n-1. Its value at 3n+1 is 730. What is n?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In trapezoid \\(ABCD\\), the angles \\(A\\) and \\(D\\) at the base \\(AD\\) are \\(60^{\\circ}\\) and \\(30^{\\circ}\\) respectively. Point \\(N\\) lies on the base \\(BC\\) such that \\(BN : NC = 2\\). Point \\(M\\) lies on the base \\(AD\\), the line \\(MN\\) is perpendicular to the bases of th... | {
"ground_truth": "3:4",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An 8 by 6 grid is placed in the first quadrant with its edges along the axes. A total of 32 of the squares in the grid are shaded. A line is drawn through (0,0) and (8, c) cutting the shaded region into two equal areas. What is the value of c?",
"role": "user"
}
] | {
"ground_truth": "c = 4",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. (5 points) Given: $1-\\frac{1}{6+\\frac{1}{6+\\frac{1}{6}}}=\\frac{1}{\\mathrm{~A}+\\frac{1}{\\mathrm{~B}+\\frac{1}{1}}}$ where $A$, $B$, and $C$ are all natural numbers greater than 0 and distinct from each other,\nthen $(A+B) \\div C=$\n\nTranslate the above text into English, preserving the ... | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Tim is choosing between two internet plans for his new apartment. Plan X does not have a base charge but costs 25 cents per GB of data used. Plan Y has an initial setup fee of $15 and charges 15 cents per GB of data used. How many gigabytes of data must Tim use for Plan Y to become the more cost-e... | {
"ground_truth": "150",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "You walk a spiraling maze on the Cartesian plane as follows: starting at \\((0,0)\\) and the first five stops are at \\(A(1,0)\\), \\(B(1,1)\\), \\(C(0,1)\\), \\(D(-1,1)\\), and \\(E(-1,0)\\). Your ninth stop is at the point \\((2,-1)\\). What is the \\(x\\)-coordinate of the point which you would... | {
"ground_truth": "3",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The returns on a stock are 2.45% at 2018, 5.42% at 2019, -13.83% at 2020. What is the compound annual rate (between -1 and 1) of return over the three years.",
"role": "user"
}
] | {
"ground_truth": "-0.023669",
"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\nLet $\\{fn\\}$ be the Fibonacci sequence $\\{1, 1, 2, 3, 5, \\dots.\\}. $\n\n(a) Find all pairs $(a, b)$ of real numbers such that for each $n$, $af_n +bf_{n+1}$ is a... | {
"ground_truth": "6",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A curious and passionate student is researching the impact of Georgetown University on local communities. The student discovers that the university hosts 150 community events annually. Each event attracts an average of 75 local residents. If the student finds that 60% of these residents participat... | {
"ground_truth": "7031",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Find the last four digits of $7^{7^{-7}}$ (100 sevens).\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": "2343",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 5. In class 5A, a survey was conducted on what fruits the students like. It turned out that 13 students like apples, 11 like plums, 15 like peaches, and 6 like melons. A student can like more than one fruit. Every student who likes plums also likes either apples or peaches (but not both at th... | {
"ground_truth": "22",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Exercise 8. A coloring of the integers $\\{1,2, \\cdots, 2020\\}$ in blue and red is said to be pleasant if there do not exist two distinct integers in $\\{1,2, \\cdots, 2020\\}$ of the same color whose sum is a power of 2. How many such colorings exist?",
"role": "user"
}
] | {
"ground_truth": "2^{11}",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Maria ordered a certain number of televisions at $R \\$ 1994.00$ each. She noticed that in the total amount to pay, there are no 0, 7, 8, or 9. What is the smallest number of televisions she ordered?\n\n## Solutions from List 4\n\nTranslate the above text into English, please retain the original t... | {
"ground_truth": "56",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If five pairwise coprime distinct integers \\( a_{1}, a_{2}, \\cdots, a_{5} \\) are randomly selected from \\( 1, 2, \\cdots, n \\) and there is always at least one prime number among them, find the maximum value of \\( n \\).",
"role": "user"
}
] | {
"ground_truth": "48",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The number $2.29^{\\star \\star} N$ is an integer. Its representation in base $b$ is 777. Find the smallest positive integer $b$ such that $N$ is a perfect fourth power.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Maria, a biologist and a politician from Angola, is studying the growth of a rare plant species found in the rainforests of Angola. She is also planning a community event to discuss environmental policies. Maria observes that each plant grows 3 new leaves every week. She starts with 5 plants, each... | {
"ground_truth": "234",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. Given $0 \\leqslant a_{k} \\leqslant 1(k=1,2, \\cdots, 2002)$, let $a_{2003}=a_{1}, a_{2004}=a_{2}$. The maximum value of $\\sum_{k=1}^{20002}\\left(a_{k}-a_{k+1} a_{k+2}\\right)$ is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "1001",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14. (12 points) There is a sequence of numbers: $\\frac{1}{1}, \\frac{1}{2}, \\frac{2}{2}, \\frac{1}{3}, \\frac{2}{3}, \\frac{3}{3}, \\frac{1}{4}, \\cdots$. What is the sum of the first 1996 numbers?",
"role": "user"
}
] | {
"ground_truth": "1022.52",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of the non–repeated roots of the polynomial $P(x)=x^6-5x^5-4x^4-5x^3+8x^2+7x+7$.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given \\( 0 \\leqslant a_{k} \\leqslant 1 \\) for \\( k = 1, 2, \\cdots, 2002 \\), and let \\( a_{2003} = a_{1} \\) and \\( a_{2004} = a_{2} \\), find the maximum value of \\( \\sum_{k=1}^{20002} \\left( a_{k} - a_{k+1} a_{k+2} \\right) \\).",
"role": "user"
}
] | {
"ground_truth": "1001",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Four congruent semicircles are drawn on the surface of a sphere with radius $2$, as shown, creating a close curve that divides the surface into two congruent regions. The length of the curve is $\\pi\\sqrt{n}$. What is $n$?",
"role": "user"
}
] | {
"ground_truth": "32",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Using the digits 2, 3, 5, 7, and 8 exactly once, form a five-digit integer that is as close as possible to 30000. What is the tens digit of this integer? Express your answer as a single digit.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $x$ and $y$ be positive integers such that $7x^5 = 11y^{13}.$ Find the prime factorization of the minimum possible value of $x$ and determine the sum of the exponents and the prime factors.",
"role": "user"
}
] | {
"ground_truth": "31",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Define a \"position\" as a point $(x, y)$ on the Cartesian plane, where $x$ and $y$ are positive integers not exceeding 20. Initially, all 400 positions are empty. Two players, A and B, take turns placing stones, starting with A. Each time it is A's turn, he places a new red stone on an empty posi... | {
"ground_truth": "100",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Every day at noon, a scheduled steamboat departs from Moscow to Astrakhan and from Astrakhan to Moscow. A steamboat departing from Moscow takes exactly four days to reach Astrakhan, then stays for two days, and at noon, two days after its arrival in Astrakhan, it departs for Moscow. A steamboat de... | {
"ground_truth": "13",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$A B C D E$ is a pyramid with square base $A B C D$. Point $E$ is directly above $A$ with $A E=1024$ and $A B=640$. The pyramid is cut into two pieces by a horizontal plane parallel to $A B C D$. This horizontal plane is a distance $h$ above the base $A B C D$. The portion of $A B C D E$ that is a... | {
"ground_truth": "85",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom and sides.\n\n[asy]/* AMC8 2002 #22 Problem */\ndraw((0,0)--(0,1)--(1,1)--(1,0)--cycle);\ndraw((0,1)--(0.5,1.5)--(1.5,1.5)--(1,1));\ndraw((1,0)--(1.5,0.5)--(... | {
"ground_truth": "26",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Two cars, A and B, depart from locations $A$ and $B$ respectively at the same time, and travel back and forth between $A$ and $B$ at a constant speed. If after the first meeting, car A continues to travel for 4 hours to reach $B$, while car B only travels for 1 hour to reach $A$, then when the ... | {
"ground_truth": "86",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "All three-digit numbers from 100 to 999 are written consecutively without spaces. Kostya underlined $k$ consecutive digits in this sequence, and Andrey underlined another $k$ consecutive digits in this sequence. The $k$-digit numbers underlined by the boys are equal. What is the largest possible v... | {
"ground_truth": "5",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a single-round-robin tournament, 10 chess players are participating. What is the minimum number of rounds after which a sole winner can be determined prematurely? (In each round, the participants are paired.\n\nWin - 1 point, draw - 0.5 points, loss - 0).\n\n#",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The function \\( f(n) \\) is an integer-valued function defined on the integers which satisfies \\( f(m + f(f(n))) = -f(f(m+1)) - n \\) for all integers \\( m \\) and \\( n \\). The polynomial \\( g(n) \\) has integer coefficients and satisfies \\( g(n) = g(f(n)) \\) for all \\( n \\). Find \\( f(... | {
"ground_truth": "-1992",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10.2. There are 2004 small boxes on the table, each containing 1 ball. It is known that some of the balls are white, and there are an even number of white balls. You are allowed to point to any 2 boxes and ask: \"Do they contain at least 1 white ball?\" How many times do you need to ask, at a mini... | {
"ground_truth": "2003",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 10.6. Find the largest possible number $A$ having the following property: if the numbers $1,2, \\ldots, 1000$ are ordered in arbitrary way then there exist 50 consecutive numbers with sum not less than $A$.\n\nIvan Landjev",
"role": "user"
}
] | {
"ground_truth": "25025",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "227. Find the triangle. The sides and height of a certain triangle are expressed by four consecutive integers. What is the area of this triangle?",
"role": "user"
}
] | {
"ground_truth": "84",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the function $f(x)=x^{2}-6x+4\\ln x$, find the x-coordinate of the quasi-symmetric point of the function.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "I4.3 Let $x, y$ and $z$ be positive integers. If $|x-y|^{2010}+|z-x|^{2011}=b$ and $c=|x-y|+|y-z|+|z-x|$, find the value of $c$.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the number of pairs of integers $(m, n)$ such that\n\n$$\n\\sqrt{n+\\sqrt{2016}}+\\sqrt{m-\\sqrt{2016}} \\in \\mathbb{Q}\n$$",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "76 Two perpendicular lines passing through the origin intersect the parabola $y^{2}=4 p(x+p)(p>0)$ at $A, B$ and $C, D$. When is $|A B|+|C D|$ minimized?",
"role": "user"
}
] | {
"ground_truth": "16p",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three, (25 points) Given that $a, b, c$ are positive integers, and the parabola $y=$ $a x^{2}+b x+c$ intersects the $x$-axis at two distinct points $A, B$. If the distances from $A, B$ to the origin are both less than 1, find the minimum value of $a+b+c$.\n\nTranslate the above text into English, ... | {
"ground_truth": "11",
"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\nLet $A(2,2)$ and $B(7,7)$ be points in the plane. Define $R$ as the region in the first quadrant consisting of those points $C$ such that $\\triangle ABC$ is an acute... | {
"ground_truth": "1",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\\section*{Problem 4 - 261014}\n\nJürgen claims that there is a positional system with base \\(m\\) in which the following calculation is correct:\n\n\\begin{tabular}{lllllll} \n& 7 & 0 & 1 &. & 3 & 4 \\\\\n\\hline 2 & 5 & 0 & 3 & & & \\\\\n& 3 & 4 & 0 & 4 & & \\\\\n\\hline 3 & 0 & 4 & 3 & 4 & &\n... | {
"ground_truth": "8",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Problem No. 6 (10 points)\n\nThe density of a body is defined as the ratio of its mass to the volume it occupies. A homogeneous cube with a volume of \\( V = 8 \\, \\text{m}^3 \\) is given. As a result of heating, each of its edges increased by 4 mm. By what percentage did the density of this cu... | {
"ground_truth": "6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "43. As shown in the figure, the degree measure of $\\angle A+\\angle B+\\angle C+\\angle D+\\angle E$ is\n\nThe text above has been translated into English, preserving the original text's line breaks and format.",
"role": "user"
}
] | {
"ground_truth": "180",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Figures $I$, $II$, and $III$ are squares. The perimeter of $I$ is $12$ and the perimeter of $II$ is $24$. Find the perimeter of square $III$. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the base-nine representation of the number $N$ is $27,006,000,052_{\\rm nine}$, find the remainder when $N$ is divided by 5.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A carpenter wishes to cut a wooden 3 x 3 x 3 cube into twenty-seven 1 x 1 x 1 cubes. What is the minimum number of cuts needed if he is allowed to rearrange the pieces after each cut? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From the prime numbers less than 100, five need to be selected such that each of the digits 1, 2, ..., 9 appears exactly once among their digits. In how many ways can this be done?",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. There is a method of setting a six-digit password: the first 2 digits are the last 2 digits of the birth year, the middle 2 digits are the birth month, and the last 2 digits are the birth date. For example, if born on April 23, 1998, the six-digit password is set as 980423. The number of possib... | {
"ground_truth": "36525",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $m$ and $n$ be positive integers such that $\\gcd(m,n)=1$ and $$\\sum_{k=0}^{2020} (-1)^k {{2020}\\choose{k}} \\cos(2020\\cos^{-1}(\\tfrac{k}{2020}))=\\frac{m}{n}.$$ Suppose $n$ is written as the product of a collection of (not necessarily distinct) prime numbers. Compute the sum of the membe... | {
"ground_truth": "209601",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Fill in the squares with the numbers 1 $\\sim$ 9 so that all the inequalities hold. \"?\" =\n\n",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the order of operations in the expression\n\n$$\n1891-(1600: a+8040: a) \\times c \n$$\n\nand calculate its value when \\( a = 40 \\) and \\( c = 4 \\). Show how the expression can be modified without changing its numerical value.",
"role": "user"
}
] | {
"ground_truth": "927",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Compute the sum of all positive integers \\( n < 1000 \\) for which \\( a_{n} \\) is a rational number, given the sequence \\( \\{a_{n}\\} \\) defined by \\( a_{1} = 1 \\) and for all integers \\( n \\geq 1 \\):\n$$\na_{n+1} = \\frac{a_{n} \\sqrt{n^{2} + n}}{\\sqrt{n^{2} + n + 2 a_{n}^{2}}}.\n$$",... | {
"ground_truth": "131",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Given $f(x)=a \\sin x+b \\sqrt[3]{x}+c \\ln \\left(x+\\sqrt{x^{2}+1}\\right)+1003(a, b, c$ are real numbers $)$, and $f\\left(\\lg ^{2} 10\\right)=1$, then $f(\\lg \\lg 3)=$ $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "2005",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The stock of the CCC Corporation is currently valued at $12 and is assumed to possess all the properties of geometric Brownian motion. It has an expected annual return of 15%, an annual volatility of 20%, and the annual risk-free is 10%. Using a binomial lattice, determine the price of a call opti... | {
"ground_truth": "53.0",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Every month Ivan pays a fixed amount of his salary for a mortgage, and the remaining portion of his salary is spent on current expenses. In December, Ivan paid 40% of his salary for the mortgage. In January, Ivan's salary increased by 9%. By what percentage did the amount spent on current expenses... | {
"ground_truth": "15\\%",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$15 \\cdot 18$ in simplest form has a denominator of 30, find the sum of all such positive rational numbers less than 10.\n(10th American Invitational Mathematics Examination, 1992)",
"role": "user"
}
] | {
"ground_truth": "400",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In how many ways can the nine digits from 1 to 9 be placed in a $3 \\times 3$ grid so that the sums of the rows and the sums of the columns are all equal?",
"role": "user"
}
] | {
"ground_truth": "72",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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