prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "The real number \\(x\\) satisfies the equation \\(x + \\frac{1}{x} = \\sqrt{3}\\). Evaluate the expression \\(x^{7} - 5x^{5} + x^{2}\\).",
"role": "user"
}
] | {
"ground_truth": "-1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all positive integers $n$ such that for any integer $k$ there exists an integer $a$ for which $a^3+a-k$ is divisible by $n$ .\n\n*Warut Suksompong, Thailand*",
"role": "user"
}
] | {
"ground_truth": "n = 3^k",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find $x$ such that $\\lceil x \\rceil \\cdot x = 156$. Express $x$ as a decimal.",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are \\(100\\) countries participating in an olympiad. Suppose \\(n\\) is a positive integers such that each of the \\(100\\) countries is willing to communicate in exactly \\(n\\) languages. If each set of \\(20\\) countries can communicate in exactly one common language, and no language is ... | {
"ground_truth": "20",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Subtract $(C A F E)_{16}$ from $(F E E D)_{16}$.",
"role": "user"
}
] | {
"ground_truth": "33 E F",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The numbers \\(a, b,\\) and \\(c\\) (not necessarily integers) satisfy the conditions\n\n\\[\na + b + c = 0 \\quad \\text{and} \\quad \\frac{a}{b} + \\frac{b}{c} + \\frac{c}{a} = 100\n\\]\n\nWhat is the value of \\(\\frac{b}{a} + \\frac{c}{b} + \\frac{a}{c}\\)?",
"role": "user"
}
] | {
"ground_truth": "-101",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. (10 points) A convoy of trucks is delivering supplies to a disaster victim resettlement point. Each truck has a carrying capacity of 10 tons. If each tent is allocated 1.5 tons of supplies, there will be less than one truck's worth of supplies left over. If each tent is allocated 1.6 tons of su... | {
"ground_truth": "213",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. (2 points) Boy Vasya wrote down the non-zero coefficients of the polynomial $P(x)$ of the tenth degree in his notebook. Then he calculated the derivative of the resulting polynomial and wrote down its non-zero coefficients, and so on, until he obtained a constant, which he also wrote down.\n\nW... | {
"ground_truth": "10",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given an acute $\\triangle ABC$ with circumcenter $O$. Line $AO$ intersects $BC$ at point $D$. Let $E$ and $F$ be the circumcenters of $\\triangle ABD$ and $\\triangle ACD$, respectively. If $AB > AC$ and $EF = BC$, then $\\angle C - \\angle B = \\qquad$",
"role": "user"
}
] | {
"ground_truth": "60^{\\circ}",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the number of different ways to arrange 2014 points into either a triangular or a trapezoidal point lattice, where the difference in the number of points between two adjacent rows is always 1, and there are at least two layers. Express your answer as a single integer.",
"role": "user... | {
"ground_truth": "3",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.2. Daniil has 6 cards with letters, from which he managed to form the word WNMWNM shown in the picture. Note that this word has a remarkable property: if you rotate it 180 degrees, you get the same word. How many words with such a property can Daniil form using all 6 cards at once?\n\n![](https:... | {
"ground_truth": "12",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A basket is called \"*Stuff Basket*\" if it includes $10$ kilograms of rice and $30$ number of eggs. A market is to distribute $100$ Stuff Baskets. We know that there is totally $1000$ kilograms of rice and $3000$ number of eggs in the baskets, but some of market's baskets include either... | {
"ground_truth": "99",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below. [asy] size(300); defaultpen(linewidth(0.8)+fontsize(13)); real r = 0.05; draw((0.9,0)--(3.5,0),EndArrow(size=7)); filldraw((4,2.5)--(7,2.5)--(7,-2.5)--(4,-2.5)--cycle,gray(0.65))... | {
"ground_truth": "83",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. The diagram shows two circles and a square with sides of length $10 \\mathrm{~cm}$. One vertex of the square is at the centre of the large circle and two sides of the square are tangents to both circles. The small circle touches the large circle. The radius of the small circle is $(a-b \\sqrt{2... | {
"ground_truth": "50",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Use euler's method to find the solution to the differential equation $\\frac{\\partial y}{\\partial x} = 3x + 4y$ at $x=1$ with the initial condition y(0) = 0 and step size $h=0.25$. What is y(1)?",
"role": "user"
}
] | {
"ground_truth": "2.0625",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A safari company offers unique experiences in a region of Africa known for its diverse wildlife and beautiful landscapes. They have designed a 5-day safari package that includes daily 4-hour guided tours. On each tour, guests can expect to see an average of 12 different animal species. If the safa... | {
"ground_truth": "180",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Define a sequence recursively by $f_1(x)=|x-1|$ and $f_n(x)=f_{n-1}(|x-n|)$ for integers $n>1$. Find the least value of $n$ such that the sum of the zeros of $f_n$ exceeds $500,000$.",
"role": "user"
}
] | {
"ground_truth": "101",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the sign of the expression sin(2)cos(3)tan(4). Is the value of the expression positive, negative, or zero? Provide your answer in the form \"positive\", \"negative\", or \"zero\".",
"role": "user"
}
] | {
"ground_truth": "negative",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a $4 \\times 4 \\times 3$ rectangular parallelepiped, vertices $A$, $B$, and $C$ are adjacent to vertex $D$. The perpendicular distance from $D$ to the plane containing $A$, $B$, and $C$ is closest to",
"role": "user"
}
] | {
"ground_truth": "2.1",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.5. Lёsha colors cells inside a $6 \\times 6$ square drawn on graph paper. Then he marks the nodes (intersections of the grid lines) to which the same number of colored and uncolored squares are adjacent. What is the maximum number of nodes that can be marked?",
"role": "user"
}
] | {
"ground_truth": "45",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the flux of the vector field \\(\\mathbf{a} = 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 vector is taken to be outward with respect to the region bounded by the paraboloid.",
"role": "user"
}
] | {
"ground_truth": "-2\\pi",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task B-1.2.\n\nIvo, Alen, Vanja, Marko, and Saša are chefs in a hotel. Alen and Marko are responsible for preparing breakfast and lunch, Ivo and Vanja work on preparing lunch and dinner, while Saša is available for all three meals. In how many ways can their daily cooking schedule be arranged i... | {
"ground_truth": "4",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a rectangular cuboid $ABCDEFGHIJ$, consider the following 12 lines: $AB', BA', CD', DC', AD', DA', BC', CB', AC, A'C', BD, B'D'$. Calculate the number of pairs of skew lines among them. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Altitudes \\( \\overline{AD} \\) and \\( \\overline{BE} \\) of an acute triangle \\( \\triangle ABC \\) intersect at point \\( H \\). If \\( HD = 8 \\) and \\( HE = 3 \\), compute \\( (BD)(DC) - (AE)(EC) \\).",
"role": "user"
}
] | {
"ground_truth": "55",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a plane with 7 assigned seats, the first passenger sits in the wrong seat. Each subsequent passenger sits in their assigned seat if available, or else chooses a random available seat. If you are the last to board, what is the probability that you sit in your own seat?",
"role": "user"
}
] | {
"ground_truth": "5/12",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Someone in 1860 placed 100,000 frt at 5% interest for the purpose of building and maintaining an orphanage for 100 orphans at some point. When can the construction and opening of the orphanage take place if the construction and equipment costs are 100,000 frt, the staff of the orphanage costs 3,96... | {
"ground_truth": "1896",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given points $P$ and $Q$ are $8$ units apart in a plane, determine the number of lines containing $P$ and $Q$ that are $4$ units from $P$ and $6$ units from $Q$.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five children (Tian Tian, Shi Tou, Kimi, Cindy, Angela) need to switch fathers, with each child choosing any one of the other four fathers except their own. What is the total number of different combinations of choices for the five children? Express your answer as a single integer.",
"role": "... | {
"ground_truth": "44",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the set $I=\\{1,2,3,4,5\\}$. Choose two non-empty subsets $A$ and $B$ from $I$ such that the smallest number in $B$ is greater than the largest number in $A$. The number of different ways to choose such subsets $A$ and $B$ is ______.",
"role": "user"
}
] | {
"ground_truth": "49",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A solid rectangular block is created using $N$ congruent 1-cm cubes adhered face-to-face. When observing the block to maximize visibility of its surfaces, exactly $252$ of the 1-cm cubes remain hidden from view. Determine the smallest possible value of $N.$",
"role": "user"
}
] | {
"ground_truth": "392",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that $\\angle \\text{CBD}$ is a right angle, the sum of the angles around point B is $180^\\circ$ and $\\angle \\text{ABD} = 30^\\circ$, find the measure of $\\angle \\text{ABC}$.",
"role": "user"
}
] | {
"ground_truth": "60^\\circ",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A regular hexagon is drawn on the plane with a side length of 1. Using only a ruler, construct a segment whose length is $\\sqrt{7}$.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{7}",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Let $E$ be a moving point inside square $ABCD$. It is known that the minimum value of the sum of the distances from $E$ to points $A$, $B$, and $C$ is $\\sqrt{2}+\\sqrt{6}$. Try to find the side length of this square.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 7 balls of each of the three colors: red, blue, and yellow. Each set of 7 balls of the same color is numbered from 1 to 7. If we randomly pick 3 balls with different numbers, and these 3 balls are of different colors and their numbers are not consecutive, find the number of ways to do th... | {
"ground_truth": "60",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a, b, c, x, y$, and $z$ be complex numbers such that $a=\\frac{b+c}{x-2}, \\quad b=\\frac{c+a}{y-2}, \\quad c=\\frac{a+b}{z-2}$. If $x y+y z+z x=67$ and $x+y+z=2010$, find the value of $x y z$.",
"role": "user"
}
] | {
"ground_truth": "-5892",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The weight of grain in a sample of 256 grains is 18 grains, and the total weight of rice is 1536 dan. Calculate the amount of mixed grain in the total batch of rice.",
"role": "user"
}
] | {
"ground_truth": "108",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2.3. The master's day shift lasts $30 \\%$ longer than the apprentice's shift. If the apprentice worked as long as the master, and the master worked as long as the apprentice, they would produce the same number of parts. By what percentage does the master produce more parts per day than the appren... | {
"ground_truth": "69",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many rectangles are there whose four vertices are points on this grid? [asy]\nsize(50);\ndot((0,0));\ndot((5,0));\ndot((10,0));\ndot((0,5));\ndot((0,10));\ndot((5,5));\ndot((5,10));\ndot((10,5));\ndot((10,10));\n[/asy]",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Piercarlo chooses $n$ integers from 1 to 1000 inclusive. None of his integers is prime, and no two of them share a factor greater than 1 .\nWhat is the greatest possible value of $n$ ?",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a convex polygon with the sum of its interior angles equal to $3140^\\circ$, calculate the degree measure of the missing angle.",
"role": "user"
}
] | {
"ground_truth": "100",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $x,$ $y,$ $z$ be nonnegative real numbers. Let\n\\begin{align*}\nA &= \\sqrt{x + 2} + \\sqrt{y + 5} + \\sqrt{z + 10}, \\\\\nB &= \\sqrt{x + 1} + \\sqrt{y + 1} + \\sqrt{z + 1}.\n\\end{align*}Find the minimum value of $A^2 - B^2.$",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5 Let $a=\\frac{20052005}{20062006}, b=\\frac{20062006}{20072007}$, $c=\\frac{20072007}{20082008}$.\nTry to compare the sizes of $a$, $b$, and $c$.",
"role": "user"
}
] | {
"ground_truth": "a<b<c",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of all $x$ from $2$ to $1000$ inclusive such that $$ \\prod_{n=2}^x \\log_{n^n}(n+1)^{n+2} $$ is an integer.\n\n*Proposed by Deyuan Li and Andrew Milas*",
"role": "user"
}
] | {
"ground_truth": "739",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Given $\\sqrt{ } 30=5.477$, find the value of $\\sqrt{0.027}$ is",
"role": "user"
}
] | {
"ground_truth": "0.1643",
"mean_reward": 0.3125
} | 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, Hobby, Beverage, Music-Genre, Nationality, Pet.\nThe attributes have the following possible values:\n- Job: lawyer, manager, nurse, scientist, software-developer\n-... | {
"ground_truth": "folk",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Use the digits $0,2,4,6,8$ once each to form a two-digit number and a three-digit number. The maximum product of these two numbers 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.",
"... | {
"ground_truth": "52480",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "(2) Solve the equation $2 \\times 7^{2 x-3}-3 \\times 7^{x-2}-5=0$.\n\nTranslate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "\\log_{7}35",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "G8.1 If the area of the rectangle $A B C D$ is $a+4 \\sqrt{3}$, find the value of $a$.\nThe lines joining the centres form an equilateral triangle, side $=2$.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. A bent thin homogeneous rod $ABC$, with small loads $m_{1}=2$ kg and $m_{2}$ located at its ends, is in equilibrium relative to a support placed at point $B$. The mass per unit length of the rod $\\lambda=2$ kg. It is known that $AB=7$ m, $BC=5$ m, $BO=4$ m, $OC=3$ m. Find $m_{2}$.\n\n(10 point... | {
"ground_truth": "10.75",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly $10^14$ times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both be... | {
"ground_truth": "4600.0",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Rectangular prism P Q R S W T U V has a square base P Q R S. Point X is on the face T U V W so that P X = 12, Q X = 10, and R X = 8. Determine the maximum possible area of rectangle P Q U T.",
"role": "user"
}
] | {
"ground_truth": "67.82",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many numbers should there be in a lottery for the probability of getting an ambo to be $\\frac{5}{473}$, when drawing five numbers?",
"role": "user"
}
] | {
"ground_truth": "44",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the number of one-foot cubical blocks Maria uses to construct a fort with exterior dimensions of 15 feet in length, 12 feet in width, and 7 feet in height, given that the floor and the four walls are all 1.5 feet thick.",
"role": "user"
}
] | {
"ground_truth": "666",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a rectangle with a length of 8 and a width of 4, it is folded along a diagonal and pressed flat. Find the area of the overlapping part (grey triangle).",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. 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 drive for 4 hours to reach $B$, while Car B only drives for 1 hour to reach $A$, then when the two cars... | {
"ground_truth": "86",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n\nAuto: Evendokiioo $M$.\n\nPoint $O$ is the center of the circumcircle $\\Omega$ of an acute triangle $ABC$. The circumcircle $\\omega$ of triangle $AOC$ intersects s... | {
"ground_truth": "45",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Given $\\cos (\\alpha+\\beta)=\\cos \\alpha+\\cos \\beta$, find the maximum value of $\\cos \\alpha$.\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": "\\sqrt{3}-1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. One side of a large rectangle is 5, dividing this large rectangle into a square and a smaller rectangle, one part of which has an area of 4. There are $\\qquad$ possible cases for such a large rectangle.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider a forward contract on a 4-year bond with maturity 1 year. The current value of the bond is $1018.86, it has a face value of $1000 and a coupon rate of 10% per annum. A coupon has just been paid on the bond and further coupons will be paid after 6 months and after 1 year, just prior to del... | {
"ground_truth": "999.998976",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Thanh, a local resident of Khương Đình, Hanoi, loves to share historical stories with his neighbors. One day, he decided to organize a walking tour to explore some significant historical sites in the area. The tour starts at the Khương Đình Pagoda, built in the year 1010, and includes stops at... | {
"ground_truth": "713",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a country there are two-way non-stopflights between some pairs of cities. Any city can be reached from any other by a sequence of at most $100$ flights. Moreover, any city can be reached from any other by a sequence of an even number of flights. What is the smallest $d$ for which one can al... | {
"ground_truth": "200",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Using a suitable substitution, determine the number of roots of the equation\n\n$$\n8 x\\left(1-2 x^{2}\\right)\\left(8 x^{4}-8 x^{2}+1\\right)=1\n$$\n\nthat lie within the interval $[0,1]$.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. In the right figure, each of the three rods of the abacus has 10 beads. Dividing the beads on each rod into upper and lower parts, we get two three-digit numbers. The upper part should be a three-digit number with all different digits, and it must be a multiple of the three-digit number from th... | {
"ground_truth": "925",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Given that two cars, A and B, start from points $A$ 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 drive for 4 hours to reach $B$, while car B only drives for 1 hour to reach $A$, then when... | {
"ground_truth": "86",
"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 three of its vertices, such that the fou... | {
"ground_truth": "2",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Five students $A, B, C, \\ldots D, E$ participate in a competition. Someone guessed the result of the competition to be $A B C D E$, but did not guess any of the ranks correctly, nor did they guess any student's rank immediately following another's.\n\nAnother person guessed the competition res... | {
"ground_truth": "E D A C B",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that \\( f(x) \\) and \\( g(x) \\) are functions which satisfy \\( f(g(x)) = x^3 \\) and \\( g(f(x)) = x^4 \\) for all \\( x \\ge 1 \\). If \\( g(81) = 81 \\), compute \\( [g(3)]^4 \\).",
"role": "user"
}
] | {
"ground_truth": "81",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A point \\(A_{1}\\) is taken on the side \\(AC\\) of triangle \\(ABC\\), and a point \\(C_{1}\\) is taken on the extension of side \\(BC\\) beyond point \\(C\\). The length of segment \\(A_{1}C\\) is 85% of the length of side \\(AC\\), and the length of segment \\(BC_{1}\\) is 120% of the length o... | {
"ground_truth": "102",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all real numbers \\( p \\) such that the cubic equation \\( 5x^{3} - 5(p+1)x^{2} + (71p - 1)x + 1 = 66p \\) has three roots, all of which are positive integers.",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We have $98$ cards, in each one we will write one of the numbers: $1, 2, 3, 4,...., 97, 98$.\nWe can order the $98$ cards, in a sequence such that two consecutive numbers $X$ and $Y$ and the number $X - Y$ is greater than $48$, determine how and how many ways we can make this sequence!!",
"rol... | {
"ground_truth": " 2 ",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a kingdom of animals, tigers always tell the truth, foxes always lie, and monkeys sometimes tell the truth and sometimes lie. There are 100 animals of each kind, divided into 100 groups, with each group containing exactly 2 animals of one kind and 1 animal of another kind. After grouping, Kung ... | {
"ground_truth": "76",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are $64$ booths around a circular table and on each one there is a chip. The chips and the corresponding booths are numbered $1$ to $64$ in this order. At the center of the table there are $1996$ light bulbs which are all turned off. Every minute the chips move simultaneously in a ci... | {
"ground_truth": "64",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "【Question 15】 \nZhao, Qian, Sun, and Li, four children, all like playing chess. Among them, someone likes playing Chinese chess, someone likes playing Go, and someone likes both types of chess. Therefore, the different ways these four people can like these two types of chess are $\\qquad$ kinds."... | {
"ground_truth": "36",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $s_1, s_2, s_3$ be the three roots of $x^3 + x^2 +\\frac92x + 9$.\n$$\\prod_{i=1}^{3}(4s^4_i + 81)$$ can be written as $2^a3^b5^c$. Find $a + b + c$.",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For each positive integer, define a function \\[ f(n)=\\begin{cases}0, &\\text{if n is the square of an integer} \\left\\lfloor\\frac{1}{\\{\\sqrt{n}\\}}\\right\\rfloor, &\\text{if n is not the square of an integer}\\end{cases}. \\] Find the value of $\\sum_{k=1}^{200} f(k)$ .",
"role": "use... | {
"ground_truth": "629",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. If in any permutation of $1,2,3, \\cdots, 18$, there always exists a sum of 6 consecutive numbers not less than $m$, then the maximum value of the real number $m$ is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "57",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Is the cumulative distribution function of the standard gaussian distribution $F(x)=1/\\sqrt{2 \\pi} \\int_{-\\infty}^x e^{-t^2/2} dt$ is log-concave? Return 1 for yes and 0 for no.",
"role": "user"
}
] | {
"ground_truth": "1.0",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. On each field of the chessboard, a number is written. The sum of the numbers written on any four fields that form a knight's path (in the shape of the letter Г) is constant. How many different numbers are written on the board? Explain your answer.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose Annie the Ant is walking on a regular icosahedron. Starting at point $A$, she takes a random path to reach the point $Z$ opposite to $A$, never moving further from $Z$. What is the expected number of moves she makes?",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that $n$ is the product of three consecutive integers and that $n$ is divisible by $7$. Which of the following is not necessarily a divisor of $n$?",
"role": "user"
}
] | {
"ground_truth": "28",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An amateur entomologist from Australia named Alex is studying a colony of ants. He observes that each day, the number of ants in the colony increases by 15. On Monday, he counted 120 ants in the colony. If he continues to observe the colony for 7 days, how many ants will there be by the end of Sun... | {
"ground_truth": "210",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For every integer $n \\ge 1$ , the function $f_n : \\left\\{ 0, 1, \\cdots, n \\right\\} \\to \\mathbb R$ is defined recursively by $f_n(0) = 0$ , $f_n(1) = 1$ and \\[ (n-k) f_n(k-1) + kf_n(k+1) = nf_n(k) \\] for each $1 \\le k < n$ . Let $S_N = f_{N+1}(1) + f_{N+2}(2) + \\cdots + f_{2N} ... | {
"ground_truth": "26",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "90. Given that January 1, 2017 is a Sunday, then November 11, 2017 is a \n\nSaturday",
"role": "user"
}
] | {
"ground_truth": "Saturday",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. (8 points) The figure below is composed of 54 identical unit equilateral triangles, some of which have already been shaded. If you want to make the figure symmetrical about an axis, then, at least $\\qquad$ more unit equilateral triangles need to be shaded.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2.017. $\\frac{x-1}{x^{3 / 4}+x^{1 / 2}} \\cdot \\frac{x^{1 / 2}+x^{1 / 4}}{x^{1 / 2}+1} \\cdot x^{1 / 4}+1$.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{x}",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nIn the diagram, there is a map consisting of 8 cities connected by 12 roads. How many ways are there to close 5 roads simultaneously for repairs such that it is still possible to travel from any city to any other city?",
"role": "user"
}
] | {
"ground_truth": "384",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$8 \\cdot 30$ Two players, A and B, play a number-filling game on a $5 \\times 5$ grid: A goes first, and the two players take turns filling in the empty cells, with A writing a one in a cell and B writing a zero. After the grid is filled, the sum of the 9 numbers in each $3 \\times 3$ square is c... | {
"ground_truth": "6",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. The smallest positive period of the function $f(x)=\\frac{\\cot x+\\cos x}{1+\\sin x}$ is",
"role": "user"
}
] | {
"ground_truth": "2\\pi",
"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\nA natural number $n$ is given. Determine all $(n - 1)$-tuples of nonnegative integers $a_1, a_2, ..., a_{n - 1}$ such that\n$$\\lfloor \\frac{m}{2^n - 1}\\rfloor + \\... | {
"ground_truth": "2",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Determine the number of the form $\\overline{a b c}$ such that $10 \\cdot\\left(\\frac{\\overline{a b}}{c}-1\\right)+\\frac{\\overline{b c}}{a}=82$.\n\nNicolae Stănică, G.M.",
"role": "user"
}
] | {
"ground_truth": "386",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the rug display featuring sections in three distinct colors, where the areas of these sections form an arithmetic progression, and the width of the center section is 2 feet, and each of the two colored rings around the center section extends outward by 2 feet on all sides, determine the leng... | {
"ground_truth": "4",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. In a tennis tournament, 512 schoolchildren are participating. 1 point is awarded for a win, and 0 points for a loss. Before each round, pairs are formed by lottery among participants with the same number of points (those who do not find a pair are awarded a point without playing). The tournamen... | {
"ground_truth": "84",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine how many more digits the base-3 representation of the number \\(1357_{10}\\) has than both the base-5 and base-8 representations combined of the same number.",
"role": "user"
}
] | {
"ground_truth": "-2",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. A regular tetrahedron with edge length $x$ is inside a cube with edge length 6, and the tetrahedron can rotate freely within the cube. The maximum value of $x$ is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "2\\sqrt{6}",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 1. (1989, Jilin Provincial Competition Question) Simplify\n$$\n\\frac{a^{2}\\left(\\frac{1}{b}-\\frac{1}{c}\\right)+b^{2}\\left(\\frac{1}{c}-\\frac{1}{a}\\right)+c^{2}\\left(\\frac{1}{a}-\\frac{1}{b}\\right)}{a\\left(\\frac{1}{b}-\\frac{1}{c}\\right)+b\\left(\\frac{1}{c}-\\frac{1}{a}\\righ... | {
"ground_truth": "a+b+c",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.8. In the vertices of a regular 100-gon, 100 chips numbered $1, 2, \\ldots, 100$ were placed, in exactly that order clockwise. In one move, it is allowed to swap two adjacent chips if their numbers differ by no more than $k$. For what smallest $k$ can a series of such moves result in a configur... | {
"ground_truth": "50",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Kevin colors three distinct squares in a $3\\times 3$ grid red. Given that there exist two uncolored squares such that coloring one of them would create a horizontal or vertical red line, find the number of ways he could have colored the original three squares.",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. Two people are walking towards each other from points $A$ and $B$ with speeds $v_{1}=6 \\mathrm{~m} / \\mathrm{s}$ and $v_{2}=4 \\mathrm{~m} / \\mathrm{s}$. At the moment of their meeting, one of them turned around and walked in the opposite direction, while the other continued in the same dire... | {
"ground_truth": "20",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. From 30 people with distinct ages, select two groups, the first group consisting of 12 people, and the second group consisting of 15 people, such that the oldest person in the first group is younger than the youngest person in the second group. The number of ways to select these groups is. $\\... | {
"ground_truth": "4060",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Arrange six positive integers \\(a, b, c, d, e, f\\) in a sequence in alphabetical order such that \\(a=1\\). If any positive integer is greater than 1, then the number that is one less than this integer must appear to its left. For example, \\(1,1,2,1,3,2\\) meets the requirement; \\(1,2,3,1,4,1\... | {
"ground_truth": "203",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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