prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "6. (10 points) A deck of playing cards, excluding the joker, has 4 suits totaling 52 cards, with each suit having 13 cards, numbered from 1 to 13. Feifei draws 2 hearts, 3 spades, 4 diamonds, and 5 clubs. If the sum of the face values of these 14 cards Feifei drew is exactly 35, then how many of t... | {
"ground_truth": "4",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the greatest positive integer \\(n\\) for which there exists a sequence of distinct positive integers \\(s_1\\), \\(s_2\\), \\(\\ldots\\), \\(s_n\\) satisfying \\[s_1^{s_2}=s_2^{s_3}=\\cdots=s_{n-1}^{s_n}.\\]\n\n[i]Proposed by Holden Mui[/i]",
"role": "user"
}
] | {
"ground_truth": "n = 5",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a tech enthusiast who values originality and has a keen eye for spotting counterfeits. He recently attended a tech convention where he found a booth selling authentic new gadgets and another booth selling counterfeit copies. At the authentic booth, a new gadget costs $120 each, while at th... | {
"ground_truth": "240",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 9.8. On the side $CD$ of trapezoid $ABCD (AD \\| BC)$, a point $M$ is marked. A perpendicular $AH$ is dropped from vertex $A$ to segment $BM$. It turns out that $AD = HD$. Find the length of segment $AD$, given that $BC = 16$, $CM = 8$, and $MD = 9$.\n\n![](https://cdn.mathpix.com/cropped/... | {
"ground_truth": "18",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. (1986, 1st Northeast China Three Provinces Mathematics Invitational) Calculate the sum $\\sum_{n=0}^{502}\\left[\\frac{305 n}{503}\\right]$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"rol... | {
"ground_truth": "76304",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A club consists of three board members and a certain number of regular members. Every year, the board members retire and are not replaced. Each regular member recruits one new person to join as a regular member. Initially, there are nine people in the club total. How many people total will be in t... | {
"ground_truth": "96",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Find all triples of integers $(x, y, z)$ that satisfy $8^{x}+15^{y}=17 x$.",
"role": "user"
}
] | {
"ground_truth": "(2,2,2)",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Chloe and Zoe are both students in Ms. Demeanor's math class. Last night, they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only $80\\%$ of the problems she solved alone, but overall $88\\%$ of her answers... | {
"ground_truth": "93",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider 9 points in the plane with no alignment. What is the minimum value of $n$ such that if we color $n$ edges connecting two of the points in red or blue, we are sure to have a monochromatic triangle regardless of the coloring?\n\n(IMO 1992)",
"role": "user"
}
] | {
"ground_truth": "33",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many of the twelve pentominoes pictured below have at least one line of reflectional symmetry? [asy] unitsize(5mm); defaultpen(linewidth(1pt)); draw(shift(2,0)*unitsquare); draw(shift(2,1)*unitsquare); draw(shift(2,2)*unitsquare); draw(shift(1,2)*unitsquare); draw(shift(0,2)*unitsquare); draw(... | {
"ground_truth": "6",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9-6. Petya wants to place 99 coins in the cells of a $2 \\times 100$ board so that no two coins are in cells that share a side, and no more than one coin is in any cell. How many ways are there to place the coins?",
"role": "user"
}
] | {
"ground_truth": "396",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\underline{\\text { Folklore }}$\n\nCan some of the minuses in the expression $2013^{2}-2012^{2}-\\ldots-2^{2}-1^{2}$ be replaced with pluses so that the value of the resulting expression equals 2013?",
"role": "user"
}
] | {
"ground_truth": "2013",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the inequality x^2 - 5x + 6 < 0 and the polynomial function p(x) = x^2 + 5x + 6, calculate the range of p(x). Express your answer as an interval.",
"role": "user"
}
] | {
"ground_truth": "[20, 30)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Point $D$ is on side $AC$ of triangle $ABC$, $\\angle ABD=15^{\\circ}$ and $\\angle DBC=50^{\\circ}$. What is the measure of angle $BAD$, in degrees?\n\n[asy]draw((-43,0)--(43,0)--(43,40)--cycle);\ndraw((-4,0)--(43,40));\ndraw((39,4)--(39,0));\ndraw((39,4)--(43,4));\ndraw((-1,36)--(22.5,26),Arrow... | {
"ground_truth": "25^\\circ",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 100 light bulbs arranged in a row on a Christmas tree. The bulbs are then toggled according to the following algorithm: initially, all the bulbs are turned on; after one second, every second bulb is turned off; after another second, every third bulb is toggled (turned off if it was on, t... | {
"ground_truth": "0.1",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of positive integers $m$ for which there exist nonnegative integers $x_0$ , $x_1$ , $\\dots$ , $x_{2011}$ such that \\[m^{x_0} = \\sum_{k = 1}^{2011} m^{x_k}.\\]",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. The figure on the right is a military layout of a region. Now, some cannons need to be placed in the grid, with the requirement that each grid can have at most one cannon, and no two grids with cannons can be adjacent by an edge. What is the maximum number of cannons that can be placed?\n\n\n\n... | {
"ground_truth": "8",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the number of labelled forests on 10 vertices with 5 connected components, such that vertices 1, 2, 3, 4, 5 all belong to different connected components?",
"role": "user"
}
] | {
"ground_truth": "50000",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3 [ Constructions on a Projection Drawing ]\n\nIn a regular quadrilateral pyramid with a lateral edge of 20, the angle between the lateral edges lying in the same face is $\\frac{\\pi}{3}$. A line perpendicular to one of the lateral edges and passing through a point on this edge intersects the hei... | {
"ground_truth": "17",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a class with $23$ students, each pair of students have watched a movie together. Let the set of movies watched by a student be his *movie collection*. If every student has watched every movie at most once, at least how many different movie collections can these students have?",
"role": "u... | {
"ground_truth": "23",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $ABCD$ be a convex quadrilateral with $AC=20$, $BC=12$ and $BD=17$. If $\\angle{CAB}=80^{\\circ}$ and $\\angle{DBA}=70^{\\circ}$, then find the area of $ABCD$.\n\n[i]2017 CCA Math Bonanza Team Round #7[/i]",
"role": "user"
}
] | {
"ground_truth": "85",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If an irrational number $a$ multiplied by $\\sqrt{8}$ is a rational number, write down one possible value of $a$ as ____.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A company sells a brand of cars in locations A and B, with profits (in units of ten thousand yuan) given by $L_1 = 5.06x - 0.15x^2$ and $L_2 = 2x$ respectively, where $x$ is the sales volume (in units of vehicles). If the company sells a total of 15 cars in both locations, calculate the maximum pr... | {
"ground_truth": "45.6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "21. Baron Münchhausen told a story. \"A whole crowd gathered. We reached a crossroads. Then half of our group turned left, a third - right, and a fifth - straight ahead.\" \"But excuse me,\" the duke noticed, - the sum of a half, a third, and a fifth is not equal to one, so you are lying!\" The ba... | {
"ground_truth": "37",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10.3. Initially, there are three piles of 100, 101, and 102 stones on the table, respectively. Ilya and Kostya are playing the following game. On each turn, each of them can take one stone from any pile except the one from which they took a stone on their previous turn (on their first turn, each p... | {
"ground_truth": "Ilya",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3-rd 5. When dividing the polynomial \\(x^{1951}-1\\) by \\(x^{4}+x^{3}+2 x^{2}+x+1\\), a quotient and a remainder are obtained. Find the coefficient of \\(x^{14}\\) in the quotient.",
"role": "user"
}
] | {
"ground_truth": "-1",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. (8 points) There is a magical tree with 123 fruits on it. On the first day, 1 fruit will fall from the tree. Starting from the second day, the number of fruits that fall each day is 1 more than the previous day. However, if the number of fruits on the tree is less than the number that should fa... | {
"ground_truth": "17",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At the rehabilitation center, the staff member is planning a week of activities for the patients. She organizes a daily exercise class, an arts and crafts session, and a relaxation hour each day from Monday to Friday. For each activity, she needs 3 volunteers to assist, and she has 10 volunteers a... | {
"ground_truth": "0",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The term containing \\(x^7\\) in the expansion of \\((1 + 2x - x^2)^4\\) arises when \\(x\\) is raised to the power of 3 in three factors and \\(-x^2\\) is raised to the power of 1 in one factor.",
"role": "user"
}
] | {
"ground_truth": "-8",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Vasya thought of a two-digit number and told Petya the product of the digits of this number, while Sasha was told the sum of these digits. The following dialogue took place between the boys:\n\nPetya: \"I can guess the conceived number in three attempts, but two may not be enough for me.\"\n\nSash... | {
"ground_truth": "10",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For example, if $0<\\alpha<\\frac{\\pi}{2}, 0<\\beta<\\frac{\\pi}{2}$, find the extremum of $\\frac{1}{\\cos ^{2} \\alpha}+\\frac{1}{\\sin ^{2} \\alpha \\sin ^{2} \\beta \\cos ^{2} \\beta}$, and the corresponding values of $\\alpha$ and $\\beta$.",
"role": "user"
}
] | {
"ground_truth": "9",
"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\n200 points are equally spaced on the circumference of a circle. How many squares can be formed with 4 of the 200 points as vertices?\n\n[Solution]\n\n<paragraph_0>\n... | {
"ground_truth": "-1",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given two skew lines $a$ and $b$ that form an angle of $50^\\circ$, and a point $P$ in space, determine the number of lines passing through point $P$ that form an angle of $30^\\circ$ with both lines $a$ and $b$. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How should a rook move across the chessboard to visit each square exactly once and make the fewest number of turns?\n\n#",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Using 4 different colors to paint the 4 faces of a regular tetrahedron (each face is an identical equilateral triangle) so that different faces have different colors, how many different ways are there to paint it? (Coloring methods that remain different even after any rotation of the tetrahedron a... | {
"ground_truth": "2",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the convex quadrilateral $ABCD$, the sum of $AB+BD+DC$ is at most 2, and the area of the quadrilateral is $1/2$. What can be the length of diagonal $AC$?",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given in $\\bigtriangleup ABC$, $AB = 75$, and $AC = 120$. A circle with center $A$ and radius $AB$ intersects $\\overline{BC}$ at points $B$ and $X$. Moreover, $\\overline{BX}$ and $\\overline{CX}$ have integer lengths. Find the length of $BC$.",
"role": "user"
}
] | {
"ground_truth": "117",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three mad painters started painting the floor each in their own color. One managed to paint 75% of the floor red, another 70% green, and the third 65% blue. What part of the floor is definitely painted with all three colors?",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A surveyor uses a steel measuring tape that is exactly 50.000 m long at a temperature of 20°C. The markings on the tape are calibrated for this temperature. When it is 35°C, the surveyor uses the tape to measure a distance. The value that she reads off the tape is 35.794 m. What is the actual dist... | {
"ground_truth": "35.8",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The price of an item is decreased by 20%. To bring it back to its original value and then increase it by an additional 10%, the price after restoration must be increased by what percentage.",
"role": "user"
}
] | {
"ground_truth": "37.5\\%",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "28. Each face of a cube has one of the numbers from 1 to 6, and they are all different. The following are views of the cube from different perspectives. What number does “?” represent?",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given three congruent circles with centers $P$, $Q$, and $R$ tangent to the sides of rectangle $ABCD$, the circle centered at $Q$ has a diameter of $6$ and passes through points $P$ and $R$. Compute the area of rectangle $ABCD$.",
"role": "user"
}
] | {
"ground_truth": "72",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "As shown in the figure, the diagonal $BD$ of square $ABCD$ is 20 cm long, and $BDFE$ is a rectangle. What is the area of the pentagon $ABEF D$ in square centimeters?",
"role": "user"
}
] | {
"ground_truth": "300",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15.27 Find the smallest natural number $n$ with the following property: if the set $\\{1,2, \\cdots, n\\}$ is arbitrarily divided into two disjoint subsets, then one of the subsets contains three distinct numbers, the product of two of which equals the third.\n（29th International Mathematical Olym... | {
"ground_truth": "96",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Problem 7. (3 points)\n\nIt is known that $20 \\%$ of people own no less than $80 \\%$ of all the money in the world. For what minimum percentage of all people can it be guaranteed that these people own $90 \\%$ of all the money?\n\n#",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given two four-digit numbers \\( M \\) and \\( N \\) which are reverses of each other, and have \\( q^{p}-1 \\) identical positive divisors, \\( M \\) and \\( N \\) can be factorized into prime factors as \\( p q^{q} r \\) and \\( q^{p+q} r \\) respectively, where \\( p \\), \\( q \\), and \\( r \... | {
"ground_truth": "1998",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14. 3 piles of peaches have the numbers $93, 70, 63$, respectively. A monkey moves peaches between the 3 piles. It is known that the monkey can move a maximum of 5 peaches each time, and will eat 1 peach during the move from one pile to another. When the number of peaches in the 3 piles is equal, ... | {
"ground_truth": "4",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "283 Find the unit digit of $\\left(\\frac{5+\\sqrt{21}}{2}\\right)^{2010}$.\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": "7",
"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 solutions to the inequality \\[\\frac{1}{2} \\le \\frac{x+1}{x} \\le \\frac{3}{2}.\\]\n\n[Solution]\n\n<paragraph_0>\nTo solve the inequality \\(\\dfrac{1}{2... | {
"ground_truth": "3",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7th Junior Balkan 2003 Problem 2 A 1 , A 2 , ... , A n are points in the plane, so that if we take the points in any order B 1 , B 2 , ... , B n , then the broken line B 1 B 2 ...B n does not intersect itself. What is the largest possible value of n?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Centered at each lattice point in the coordinate plane are a circle radius $\\frac{1}{10}$ and a square with sides of length $\\frac{1}{5}$ whose sides are parallel to the coordinate axes. The line segment from $(0,0)$ to $(1001, 429)$ intersects $m$ of the squares and $n$ of the circles. Find $m ... | {
"ground_truth": "574",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Tokaeva I.\n\nLet $F_{1}, F_{2}, F_{3}, \\ldots$ be a sequence of convex quadrilaterals, where $F_{k+1}$ (for $k=1,2,3, \\ldots$) is obtained by cutting $F_{k}$ along a diagonal, flipping one of the parts, and gluing it back along the cut line to the other part. What is the maximum number of diffe... | {
"ground_truth": "6",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 In a finite sequence of real numbers, the sum of any seven consecutive terms is negative, while the sum of any eleven consecutive terms is positive. How many terms can such a sequence have at most?\n\nTranslate the above text into English, please keep the original text's line breaks and ... | {
"ground_truth": "16",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $1 \\leq k \\leq n$ be integers. How many $k$-element subsets of the set $\\{1,2, \\ldots, n\\}$ can be chosen such that any two of them consist of the $k$ smallest elements of their union?",
"role": "user"
}
] | {
"ground_truth": "n-k+1",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.5. In a city, there are 10 streets parallel to each other and 10 others intersect them at right angles. What is the minimum number of turns a closed route can have, passing through all intersections?",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If the total sum of squared deviations of a set of data is 100, and the correlation coefficient is 0.818, then the sum of squared residuals is.",
"role": "user"
}
] | {
"ground_truth": "33.0876",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. A test paper consists of four multiple-choice questions, each with three options $\\mathrm{A}$, $\\mathrm{B}$, and $\\mathrm{C}$. Several students take the exam, and after grading, it is found that any three students have different answers to at least one question, and no student leaves any que... | {
"ground_truth": "9",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Fractal geometry is a new discipline founded by French-American mathematician Benoit B. Mandelbrot in the 1970s. Its creation has provided new ideas for solving numerous problems in various fields of traditional science. The following figure grows according to fractal rules into a tree-like dia... | {
"ground_truth": "10945",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On the plane $S$ in a space, given are unit circle $C$ with radius 1 and the line $L$ . Find the volume of the solid bounded by the curved surface formed by the point $P$ satifying the following condition $(a),\\ (b)$ . $(a)$ The point of intersection $Q$ of the line passing through $P... | {
"ground_truth": "\\pi",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Problem No. 7 (15 points)\n\nFor a body completely submerged in a liquid to be in equilibrium, a force $F=2 H$ is applied to it. Determine the density of the body if its volume $V=1 \\pi$, and the density of the liquid $\\rho_{\\text {liq }}=1000$ kg $/ \\mathrm{m}^{3}$.\n\nAnswer: 1200 kg/m",
... | {
"ground_truth": "1200/^3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. (12 points) In the Sheep Sheep Sports Meet, Happy Sheep, Boiling Sheep, Lazy Sheep, Warm Sheep, and Big Bad Wolf participated in a 400-meter race. After the race, the five of them discussed the results.\nFirst place said: “Happy Sheep ran faster than Lazy Sheep.”\nSecond place said: “I ran fas... | {
"ground_truth": "2",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Eight students from Adams school worked for $4$ days, six students from Bentley school worked for $6$ days, and seven students from Carter school worked for $10$ days. If a total amount of $\\ 1020$ was paid for the students' work, with each student receiving the same amount for a day's work, dete... | {
"ground_truth": "517.39",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The base three representation of $x$ is \n\\[12112211122211112222\\]\nFind the first digit of the base nine representation of $x$. Express your answer as a single digit.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a sequence of positive integers starting from 1, some numbers are colored red according to the following rules: first color 1 red, then color the next 2 even numbers 2 and 4 red; next, color the 4 closest consecutive odd numbers after 4, which are 5, 7, 9, red; then color the 4 closest consecut... | {
"ground_truth": "103",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. In a football tournament where each team played against each other once, teams A, B, C, D, and E participated. For a win, a team received 3 points, for a draw 1 point, and for a loss 0 points. In the end, it turned out that teams A, B, C, D, and E each had 7 points. What is the maximum number o... | {
"ground_truth": "7",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( n = 2^{31} \\times 3^{19} \\times 5^7 \\). How many positive integer divisors of \\( n^2 \\) are less than \\( n \\) but do not divide \\( n \\)?",
"role": "user"
}
] | {
"ground_truth": "13307",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( n \\) be an integer greater than 3. Let \\( R \\) be the set of lattice points \\( (x, y) \\) such that \\( 0 \\leq x, y \\leq n \\) and \\( |x-y| \\leq 3 \\). Let \\( A_n \\) be the number of paths from \\( (0,0) \\) to \\( (n,n) \\) that consist only of steps of the form \\( (x, y) \\rig... | {
"ground_truth": "2+\\sqrt{2}",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the inequality $(x-a+2)(x^2-ax-2) \\geq 0$ for $x > 0$, find the exact value of the real number $a$.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In $\\triangle ABC$ , $AB= 425$ , $BC=450$ , and $AC=510$ . An interior point $P$ is then drawn, and segments are drawn through $P$ parallel to the sides of the triangle. If these three segments are of an equal length $d$ , find $d$ .",
"role": "user"
}
] | {
"ground_truth": "306",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3. As shown in the figure, $A D, B E, C F$ intersect at a point $P$ inside $\\triangle A B C$, dividing $\\triangle A B C$ into six smaller triangles, with the areas of four of these smaller triangles already given in the figure. Find the area of $\\triangle A B C$.",
"role": "user"
... | {
"ground_truth": "315",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the slope angle of the line $x- \\sqrt {3}y=3$. Express your answer in degrees, including the degree symbol (°).",
"role": "user"
}
] | {
"ground_truth": "30°",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a=\\log_{3}\\pi$, $b=\\log_{7}6$, $c=\\log_{2}0.8$. Determine the correct ordering of the values a, b, and c from largest to smallest. Express your answer in the format a [symbol] b [symbol] c, using >, <, or = as comparison symbols.",
"role": "user"
}
] | {
"ground_truth": "a>b>c",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A songwriter is trying to write a new song with unique and compelling lyrics. They decide that each verse of the song should have 8 lines. The songwriter plans to write 5 verses for the song. If they have a total of 120 unique words they can use, how many times will each word be used, on average, ... | {
"ground_truth": "1",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Tim is organizing a week-long series of pranks. On Monday, he gets his friend Joe to help. On Tuesday, he can choose between two friends, either Ambie or John. For Wednesday, there are four new people willing to help. However, on Thursday, none of these previous individuals can participate, but Ti... | {
"ground_truth": "40",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task A-1.5.\n\nAndrija and Boris have 2014 cards labeled with numbers from 1 to 2014. Andrija has all the cards with even numbers, and Boris has all the cards with odd numbers. Andrija has arranged his cards in a circle in order, from 2 to 2014, in a clockwise direction so that the numbers on t... | {
"ground_truth": "503",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Combinatorics (miscellaneous).]\n$[$ Estimation + example $]$\n\nIn a pond, 30 pikes were released, which gradually eat each other. A pike is considered full if it has eaten at least three pikes (full or hungry). What is the maximum number of pikes that can become full?",
"role": "user"
}
... | {
"ground_truth": "9",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Giuseppe has a sheet of plywood that measures $22 \\times 15$. Giuseppe wants to cut out as many rectangular pieces of $3 \\times 5$ as possible from it. How can he do this?",
"role": "user"
}
] | {
"ground_truth": "22",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Equilateral $\\triangle ABC$ has side length $600$. Points $P$ and $Q$ lie outside the plane of $\\triangle ABC$ and are on opposite sides of the plane. Furthermore, $PA=PB=PC$, and $QA=QB=QC$, and the planes of $\\triangle PAB$ and $\\triangle QAB$ form a $120^{\\circ}$ dihedral angle (the angle ... | {
"ground_truth": "450",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If from point $P$ two perpendicular chords are drawn to a given circle, then the sum of the squares of the resulting four segments is constant.",
"role": "user"
}
] | {
"ground_truth": "4r^2",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.2. In triangle $A B C$, angle $A$ is the largest. Points $M$ and $N$ are symmetric to vertex $A$ with respect to the angle bisectors of angles $B$ and $C$ respectively. Find $\\angle A$, if $\\angle M A N=50^{\\circ}$.",
"role": "user"
}
] | {
"ground_truth": "80",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13th APMO 2001 Problem 5 What is the largest n for which we can find n + 4 points in the plane, A, B, C, D, X 1 , ... , X n , so that AB is not equal to CD, but for each i the two triangles ABX i and CDX i are congruent?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Interior numbers begin in the third row of Pascal's Triangle. Find the sum of the interior numbers of the eighth row.",
"role": "user"
}
] | {
"ground_truth": "126",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From the three-digit numbers \\(100, 101, 102, \\ldots, 699, 700\\), choose \\(n\\) different numbers such that you can always find three of them with the same sum of digits. What is the minimum value of \\(n\\)?",
"role": "user"
}
] | {
"ground_truth": "47",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Liliane has $50\\%$ more soda than Jacqueline, and Alice has $25\\%$ more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alice have?",
"role": "user"
}
] | {
"ground_truth": "20\\%",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The museum curator is designing a new exhibit about ancient writing systems. The exhibit will have 5 sections, each dedicated to a different ancient civilization's writing. The curator plans to display 12 artifacts in each section. In addition, the curator decides to add a special interactive disp... | {
"ground_truth": "5",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 9.8. On the side $CD$ of trapezoid $ABCD (AD \\| BC)$, a point $M$ is marked. A perpendicular $AH$ is dropped from vertex $A$ to segment $BM$. It turns out that $AD = HD$. Find the length of segment $AD$, given that $BC = 16$, $CM = 8$, and $MD = 9$.\n\n![](https://cdn.mathpix.com/cropped/... | {
"ground_truth": "18",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "25. $[\\mathbf{1 4}]$ Let $n$ be an integer greater than 3 . Let $R$ be the set of lattice points $(x, y)$ such that $0 \\leq x, y \\leq n$ and $|x-y| \\leq 3$. Let $A_{n}$ be the number of paths from $(0,0)$ to $(n, n)$ that consist only of steps of the form $(x, y) \\rightarrow(x, y+1)$ and $(x,... | {
"ground_truth": "2+\\sqrt{2}",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Inside a square, $n$ points are given. They are connected in pairs, as well as individual points with the vertices of the square, but in such a way that no two segments intersect at an interior point. How many segments can be constructed in this way?",
"role": "user"
}
] | {
"ground_truth": "3n+1",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Vasya thought of a natural number $n \\leq 2020$. Petya tries to guess it as follows: he names some natural number x and asks if his number is greater (is it true that $\\mathrm{x}<\\mathrm{n}$?), and Vasya answers him with \"yes\" or \"no\". Petya wins if he finds out the number, and loses if ... | {
"ground_truth": "64",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the parabola equation $y^2=2px$ ($p>0$), find the range of values for p such that a line passing through the focus of the parabola intersects the parabola at points A and B, and the length of AB is 4 units. Express your answer as an interval (e.g., (a, b)).",
"role": "user"
}
] | {
"ground_truth": "(0,2)",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 5 people standing in a line numbered 1 through 5 in a left to right order.\nEach person has the following attributes: Nationality, Movie-Genre, Pet, Sport, Transport.\nThe attributes have the following possible values:\n- Nationality: british, german, malaysian, polish, spanish\n- Movie... | {
"ground_truth": "biathlon",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A cylindrical, closable container has a diameter of 82 units and a length of 225 units. How many spheres with a diameter of 38 units can be placed inside, and then the container can be closed?",
"role": "user"
}
] | {
"ground_truth": "21",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Solve the congruence $15x + 3 \\equiv 9 \\pmod{21}$ for $x$, and express the solution as $x \\equiv a \\pmod{m}$, where $a < m$ and find $a + m$.",
"role": "user"
}
] | {
"ground_truth": "13",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The High School Ten basketball conference has 10 teams. Each team plays every other conference team twice and also plays 5 games against non-conference opponents. Calculate the total number of games in a season involving the High School Ten teams.",
"role": "user"
}
] | {
"ground_truth": "140",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two people, A and B, alternately pick distinct numbers from the set \\(\\{0, 1, \\cdots, 81\\}\\). A picks first, and each person picks one number per turn. After all 82 numbers are picked, let \\(S_A\\) and \\(S_B\\) be the sums of the numbers chosen by A and B, respectively. During the selection... | {
"ground_truth": "41",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the product of all even negative integers strictly greater than $-2020$, after adding 10 to the product, determine the sign and units digit of the result.",
"role": "user"
}
] | {
"ground_truth": "0",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ivan the Tsarevich fought with the three-headed and three-tailed Zmey Gorynych. With one blow, he could cut off either one head, one tail, two heads, or two tails. But if he cut off one tail, two would grow back; if he cut off two tails, a head would grow back; if he cut off a head, a new head wou... | {
"ground_truth": "9",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 4.1. Along the road connecting Masha's and Sasha's houses, there are 17 apple trees and 18 poplars. When Masha was going to visit Sasha, she took photos of all the trees. Right after the tenth apple tree, Masha's phone memory ran out, and she couldn't photograph the remaining 13 trees. The... | {
"ground_truth": "22",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A square $O P Q R$ is inscribed in $\\triangle A B C$. The areas of $\\triangle A O R$, $\\triangle B O P$, and $\\triangle C R Q$ are given as $S_{1}=1$, $S_{2}=3$, and $S_{3}=1$, respectively. Calculate the side length of the square $O P Q R$. Express your answer as a single number.",
"role"... | {
"ground_truth": "2",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. There is a cube fixed on legs, and six different paints. In how many ways can all the faces of the cube be painted (each in one color, not all paints have to be used) so that adjacent faces (having a common edge) are of different colors? (16 points)",
"role": "user"
}
] | {
"ground_truth": "4080",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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