prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "1. The increasing interval of the function $y=\\left(\\frac{1}{2}\\right)^{\\mathrm{i} g x \\mid}$ is",
"role": "user"
}
] | {
"ground_truth": "(0,1)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the fictional country of Mahishmati, there are $50$ cities, including a capital city. Some pairs of cities are connected by two-way flights. Given a city $A$, an ordered list of cities $C_1,\\ldots, C_{50}$ is called an [i]antitour[/i] from $A$ if\n[list]\n[*] every city (including $A$) appears... | {
"ground_truth": " (25!)^2 ",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. If $a>0, a^{2}-2 a b+c^{2}=0, b c>a^{2}$, then the size relationship of the real numbers $a, b, c$ is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "b>c>a",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. Let $\\left(1+x-x^{2}\\right)^{10}=a_{0}+a_{1} x+\\cdots+a_{20} x^{20}$. Then $a_{0}+a_{1}+2 a_{2}+\\cdots+20 a_{20}=$ $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "-9",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nConsider all possible quadratic polynomials $x^2 + px + q$ with a positive discriminant, where the coefficients $p$ and $q$ are integers divisible by 5. Find the largest natural number $n$ such that for any polynomial with the described properties, the sum of the hundredth powers of the roots is... | {
"ground_truth": "50",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex loves watching educational segments about math and science and frequently engages with them on social media. Each week, Alex watches 4 different segments and posts feedback on them. For each segment, Alex sparks 3 discussions with friends and followers. If Alex’s comments inspire 5 additional... | {
"ground_truth": "288",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Greedy Vovochka has 25 classmates. For his birthday, he brought 200 candies to class. Vovochka's mother, so that he does not eat everything himself, ordered him to distribute the candies in such a way that any 16 of his classmates have at least 100 candies in total. What is the maximum number of c... | {
"ground_truth": "37",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a six-page homework assignment, we need to place four figures. The order of the figures is fixed, and a maximum of two figures can be on one page. In how many ways can this be done? (We do not consider the position of the figures on a page.)",
"role": "user"
}
] | {
"ground_truth": "90",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. The Earth's orbit around the Sun is an ellipse, with the equation set as $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$. The Sun is located at the left focus $F_{1}$, and the endpoints of the major axis are $A$ and $B$ (with $A$ to the left of point $F_{1}$). It is known that when the Ear... | {
"ground_truth": "0.017",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The numbers \\(2^{2000}\\) and \\(5^{2000}\\) are written consecutively. How many digits are written in total?",
"role": "user"
}
] | {
"ground_truth": "2001",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sample data with a capacity of 10 is grouped, and the group intervals and frequencies are as follows: [1,2), 1; [2,3), 1; [3,4), 2; [4,5), 3; [5,6), 1; [6,7), 2. Calculate the frequency of the sample in the interval [1,5). Express your answer as a decimal value rounded to two decimal places.",
... | {
"ground_truth": "0.70",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A father purchases 4 yellow cups, 3 blue cups, and 2 red cups. He wants to arrange these cups in a circular pattern on a tray. How many ways can he arrange these cups if he does not want the 2 red cups to be next to each other?",
"role": "user"
}
] | {
"ground_truth": "105",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sara, a homesteader living off the grid, has a sustainable farm where she grows vegetables and raises chickens. She collects eggs from her chickens every morning. This week, Sara collected the following number of eggs each day: Monday - 12, Tuesday - 15, Wednesday - 10, Thursday - 13, Friday - 11.... | {
"ground_truth": "110",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $A$ and $B$ be two sets of non-negative integers, define $A+B$ as the set of the values obtained when we sum any (one) element of the set $A$ with any (one) element of the set $B$ . For instance, if $A=\\{2,3\\}$ and $B=\\{0,1,2,5\\}$ so $A+B=\\{2,3,4,5,7,8\\}$ .\nDetermine the l... | {
"ground_truth": "32",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. (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 the 4 cards Feifei draws is exactly 34, then among them, the... | {
"ground_truth": "4",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Daniel writes over a board, from top to down, a list of positive integer numbers less or equal to 10. Next to each number of Daniel's list, Martin writes the number of times exists this number into the Daniel's list making a list with the same length. If we read the Martin's list from down to top,... | {
"ground_truth": "10",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "(IMO SL 1992)(M-D) $a, b>0$ Determine the solutions $f: \\mathbb{R}^{+} \\rightarrow \\mathbb{R}^{+}$ such that $f(f(x))+$ $a f(x)=b(a+b) x$.",
"role": "user"
}
] | {
"ground_truth": "f(x)=bx",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 7.2. Answer. $31.5 \\%$.",
"role": "user"
}
] | {
"ground_truth": "31.5",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 6.20. 600 corn seeds are planted with a probability of 0.9 for each seed to germinate. Find the boundary of the absolute value of the deviation of the frequency of germinated seeds from the probability $p=0.9$, if this boundary is to be guaranteed with a probability $P=0.995$.",
"role"... | {
"ground_truth": "0.034",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. (10 points) There is a cup filled with a 15% saltwater solution. There are large, medium, and small iron balls, with volume ratios of 10: 5: 3. First, the small ball is submerged in the saltwater cup, causing 10% of the saltwater to overflow. The small ball is then removed. Next, the medium ba... | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The number $6\\,21H\\,408\\,3G5$ is divisible by $6$. If $H$ and $G$ each represent a single digit, what is the sum of all distinct possible values of the product $HG$?",
"role": "user"
}
] | {
"ground_truth": "0",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A Haiku is a Japanese poem of seventeen syllables, in three lines of five, seven, and five.\n\nTake five good haikus\nScramble their lines randomly\nWhat are the chances\nThat you end up with\nFive completely good haikus\n(With five, seven, five)?\nYour answer will be\nm over n where m,n\nAre numb... | {
"ground_truth": "3004",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "While driving along a main road, there are eight traffic lights. The probability that a light will be showing red when we arrive is 0.4. What is the probability that we will not encounter two consecutive stop signals?",
"role": "user"
}
] | {
"ground_truth": "0.38",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given $\\omega = -\\frac{1}{2} + \\frac{1}{2}i\\sqrt{3}$, define $T$ as the set of all points in the complex plane of the form $a + b\\omega + c\\omega^2$, where $0 \\leq a, b, c \\leq 2$. Find the area of $T$.",
"role": "user"
}
] | {
"ground_truth": "6\\sqrt{3}",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. A bouncy ball falls from point $A$ to the ground, bounces up to point $B$, then falls to a platform $20 \\mathrm{~cm}$ high, bounces up to point $C$, and finally falls to the ground. Each time it bounces, the height it reaches is $80 \\%$ of the height from which it fell. It is known that poin... | {
"ground_truth": "132",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. At the conference, there were 15 alien races. Each alien greeted at least 30 representatives from each race (including representatives from their own race). What is the maximum number of aliens from one race that could have been at the conference, if the total number of participants was 2018?",... | {
"ground_truth": "1584",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Answer: there are two such students.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two positive integers $a_{1}, a_{2}, \\cdots, a_{2006}$ (which can be the same) are such that $\\frac{a_{1}}{a_{2}}, \\frac{a_{2}}{a_{3}}, \\cdots, \\frac{a_{2005}}{a_{2006}}$ are all distinct. How many different numbers are there at least among $a_{1}$, $a_{2}, \\cdots, a_{2006}$?\n（Chen Yonggao,... | {
"ground_truth": "46",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the equation of the ellipse $\\frac{x^{2}}{16} + \\frac{y^{2}}{9} = 1$, calculate the length of the focal distance using the formula $c=\\sqrt{a^2-b^2}$ and then $2c$. Express your answer as a numerical value.",
"role": "user"
}
] | {
"ground_truth": "2\\sqrt{7}",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct digits can appear as the units digit of an integral perfect-square number under modulo 6?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3.3.3 Let $S$ be a set composed of some positive integers not greater than 15, and any two disjoint subsets of $S$ have unequal sums of elements. Find the maximum value of the sum of elements in $S$ with this property.",
"role": "user"
}
] | {
"ground_truth": "61",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Point $P$ lies outside a circle, and two rays are drawn from $P$ that intersect the circle as shown. One ray intersects the circle at points $A$ and $B$ while the other ray intersects the circle at $M$ and $N$ . $AN$ and $MB$ intersect at $X$ . Given that $\\angle AXB$ measures ... | {
"ground_truth": "39",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Optimus Prime and Bumblebee set off from Earth and Cybertron simultaneously, heading towards each other. The speed ratio of Bumblebee to Optimus Prime is $4: 5$. One hour after they set off, Bumblebee encounters Megatron's interception and fights for half an hour. Then Bumblebee continues, but ... | {
"ground_truth": "504",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all possible three-digit numbers that can be obtained by removing three digits from the number 112277. Sum them and write the result as the answer.",
"role": "user"
}
] | {
"ground_truth": "1159",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 6 people standing in a line numbered 1 through 6 in a left to right order.\nEach person has the following attributes: Job, Hobby, Nationality, Sport, Transport.\nThe attributes have the following possible values:\n- Job: architect, designer, engineer, lawyer, manager, mechanic\n- Hobby:... | {
"ground_truth": "argentine",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Cube [ Properties of parts obtained by cutting ]\n\nThe surface of a 3 x 3 x 3 Rubik's cube consists of 54 cells. What is the maximum number of cells that can be marked so that the marked cells do not share any vertices?",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The numbers $1,2,\\ldots,49,50$ are written on the blackboard. Ann performs the following operation: she chooses three arbitrary numbers $a,b,c$ from the board, replaces them by their sum $a+b+c$ and writes $(a+b)(b+c)(c+a)$ to her notebook. Ann performs such operations until only two numb... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Šárka enjoys celebrating, so in addition to birthdays, she came up with antibirthdays: the date of the antibirthday is created by swapping the day and month numbers in the birth date. She was born on 8.11., so her antibirthday is on 11.8. Her mother cannot celebrate her antibirthday: she was born ... | {
"ground_truth": "132",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In $\\triangle A B C$, it is known that $\\angle A=60^{\\circ}, \\angle C=$ $75^{\\circ}, A B=10$, points $D, E, F$ are on sides $A B, B C, C A$ respectively. Then the minimum perimeter of $\\triangle D E F$ is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "5 \\sqrt{6}",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2. Using the trapezoidal rule with an accuracy of 0.01, calculate $\\int_{2}^{3} \\frac{d x}{x-1}$.",
"role": "user"
}
] | {
"ground_truth": "0.6956",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "James, a middle-aged executive, spends his weekends at the country club to learn golf and release stress. On a typical Saturday, he practices his swing for 2 hours and then plays 9 holes. On Sunday, he practices for 1 hour and plays another 9 holes. After each session, he relaxes by the clubhouse ... | {
"ground_truth": "2050",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n1. Alice and Ben play the game on a board with 72 cells around a circle. First, Ben chooses some cells and places one chip on each of them. Each round, Alice first chooses one empty cell and then Ben moves a chip from one of the adjacent cell onto the chosen one. If Ben fails to do so, the game ... | {
"ground_truth": "36",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sequence of integers $ a_{1},a_{2},a_{3},\\ldots$ is defined as follows: $ a_{1} \\equal{} 1$ and for $ n\\geq 1$, $ a_{n \\plus{} 1}$ is the smallest integer greater than $ a_{n}$ such that $ a_{i} \\plus{} a_{j}\\neq 3a_{k}$ for any $ i,j$ and $ k$ in $ \\{1,2,3,\\ldots ,n \\plus{} 1\\}$, not ... | {
"ground_truth": "4494",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find out the maximum possible area of the triangle $ABC$ whose medians have lengths satisfying inequalities $m_a \\le 2, m_b \\le 3, m_c \\le 4$ .",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Third question: For all real numbers $x_{1}, x_{2}, \\ldots, x_{60} \\in[-1,1]$, find the maximum value of $\\sum_{i=1}^{60} x_{i}^{2}\\left(x_{i+1}-x_{i-1}\\right)$, where $x_{0}=x_{60}, x_{61}=x_{1}$.",
"role": "user"
}
] | {
"ground_truth": "40",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Here is a fairly simple puzzle: EH is four times greater than OY. AY is four times greater than OH. Find the sum of all four.",
"role": "user"
}
] | {
"ground_truth": "150",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The efficiency of an ideal heat engine is $40\\%$. What will it become if the temperature of the heater is increased by $40\\%$ and the temperature of the cooler is decreased by $40\\%$?",
"role": "user"
}
] | {
"ground_truth": "74\\%",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. [5] Dragoons take up $1 \\times 1$ squares in the plane with sides parallel to the coordinate axes such that the interiors of the squares do not intersect. A dragoon can fire at another dragoon if the difference in the $x$-coordinates of their centers and the difference in the $y$-coordinates o... | {
"ground_truth": "168",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "According to national regulations, only adults aged between 18 and 70 are eligible to apply for a motor vehicle driver's license. A sixth-grade student, Li Ming, says, \"My dad has a driver's license. His age equals the product of the month and day of his birth, and that product is 2975.\" How old... | {
"ground_truth": "35",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. (19th Austrian Mathematical Competition) Find $N=$ $19^{88}-1$ for all divisors $d=2^{2} \\cdot 3^{b}$ (where $a, b$ are natural numbers) and determine the sum of these divisors $d$.",
"role": "user"
}
] | {
"ground_truth": "744",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A2 From each of the eight vertices of a cube, a piece is sawn off so that instead of a vertex, a triangular face with three vertices appears. Each pair of the 24 vertices of the resulting body is connected by a line segment.\n\nHow many of these line segments lie, except for their endpoints, entir... | {
"ground_truth": "120",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a positive integer $n$ , let $f(n)$ be the sum of the positive integers that divide at least one of the nonzero base $10$ digits of $n$ . For example, $f(96)=1+2+3+6+9=21$ . Find the largest positive integer $n$ such that for all positive integers $k$ , there is some positive integer... | {
"ground_truth": "15",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the vertices of triangle $\\triangle ABC$ as $A(2,0)$, $B(0,4)$, and $C(4,1)$, where $AE$ is the angle bisector of $\\angle BAC$, calculate the coordinates of a directional vector of line $AE$. Express your answer as a vector in the form $(x, y)$.",
"role": "user"
}
] | {
"ground_truth": "(1,3)",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five line segments are drawn inside a rectangle, creating a decagon (10-sided polygon). Find the sum of the six marked angles. Express your answer in degrees as a whole number.",
"role": "user"
}
] | {
"ground_truth": "1080^\\circ",
"mean_reward": 0.0625
} | 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": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10.9. 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": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Given that $a, b, c$ are rational numbers, and $\\sqrt{2}(a+b+\\sqrt{2})+\\sqrt{3}(b+c+2)+2(a+c)=0$, then $3 a-2 b+c=$ $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 3, 7, and 7, as shown. What is the area of the shaded quadrilateral?",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. Let $S=\\{1,2, \\cdots, 2005\\}$. If any set of $n$ pairwise coprime numbers in $S$ contains at least one prime number, find the minimum value of $n$.\n\n",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The finite sequence 1, $2^3$, $2^6$, $2^9$, …, $2^{3n+6}$ is given. Find the number of terms in this sequence. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "n+3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. Six positive integers $a, b, c, d, e, f$ are arranged in alphabetical order to form a sequence, where $a=1$. If a certain positive integer is greater than 1, then the number that is one less than this positive integer must appear to its left. For example, if $d>1$, then one of $a, b, c$ must b... | {
"ground_truth": "203",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.2. 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": 0.078125
} | 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": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Compute the integer $n > 2$ for which\n\\[\\log_{10} (n - 2)! + \\log_{10} (n - 1)! + 1 = 2 \\log_{10} n!.\\]",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "31. (5 points)\nThe careless Pigsy failed to notice the dots above the repeating decimals when calculating $2.0 \\ddot{2} 1 \\times 165000$. His result was less than the correct result by $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "35",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1.3. Rex, Dzhulbars, Tarzan, Barbos and Sharik are frolicking on the lawn. Rex has bitten the one who has bitten Dzhulbars, Dzhulbars - the one who has bitten Tarzan, Tarzan - the one who has bitten Barbos, Barbos - the one who has bitten Sharik, Sharik - the one who has bitten Rex. Who, then, has... | {
"ground_truth": "Tarzan",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Second Pump Find all real numbers $p$ such that the cubic equation\n$$\n5 x^{3}-5(p+1) x^{2}+(71 p-1) x+1=66 p\n$$\n\nhas three roots that are all natural numbers.",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A strip of paper that is 5 cm wide is wound around a cylindrical tube with a diameter of 2 cm for 600 turns, forming a cylindrical shape with a diameter of 10 cm. Assuming the paper strip forms 600 concentric cylindrical layers, with their diameters uniformly increasing from 2 cm to 10 cm, calcula... | {
"ground_truth": "36 \\pi",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In triangle \\(ABC\\), points \\(P\\) and \\(Q\\) are taken on the base \\(AC\\) such that \\(AP < AQ\\). The lines \\(BP\\) and \\(BQ\\) divide the median \\(AM\\) into three equal parts. It is known that \\(PQ = 3\\).\n\nFind \\(AC\\).",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of the prime factors of $67208001$, given that $23$ is one.\n\n[i]Proposed by Justin Stevens[/i]",
"role": "user"
}
] | {
"ground_truth": "781",
"mean_reward": 0.109375
} | 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": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. If the integer $k$ is added to $36,300,596$, respectively, the results are the squares of three consecutive terms in an arithmetic sequence, find the value of $k$.",
"role": "user"
}
] | {
"ground_truth": "925",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a mapping f: {1, 2, 3} → {1, 2, 3} that satisfies f(1) < f(2) < f(3) and f(f(x)) = 3x, find the value of f(1). Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 5.4. For a physical education class, 29 seventh-graders came, some of them brought one ball each. Sometimes during the class, one of the seventh-graders would give their ball to another seventh-grader who didn't have one.\n\nAt the end of the class, \\( N \\) seventh-graders said: “I recei... | {
"ground_truth": "14",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The venusian prophet Zabruberson sent to his pupils a $ 10000$ -letter word, each letter being $ A$ or $ E$ : the *Zabrubic word*. Their pupils consider then that for $ 1 \\leq k \\leq 10000$ , each word comprised of $ k$ consecutive letters of the Zabrubic word is a *prophetic word* of len... | {
"ground_truth": "504",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 233: Let the difference between any two adjacent interior angles of a convex $\\mathrm{n}$-sided polygon be $20^{\\circ}$, find the maximum possible value of $\\mathrm{n}$.",
"role": "user"
}
] | {
"ground_truth": "34",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. (3 points) Anya, Vanya, Danya, Sanya, and Tanya were collecting apples. It turned out that each of them collected a whole percentage of the total number of collected apples, and all these numbers were different and greater than zero. Then Tanya, who collected the most apples, ate her apples. Af... | {
"ground_truth": "20",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Let set $A$ consist entirely of positive integers, and for any $x, y \\in A (x \\neq y)$, we have $|x-y| \\geqslant \\frac{1}{25} x y$. How many numbers can $A$ contain at most?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.03125
} | 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 $(a_n)_{n\\geq0}$ and $(b_n)_{n \\geq 0}$ be two sequences of natural numbers. Determine whether there exists a pair $(p, q)$ of natural numbers that satisfy\n\\[... | {
"ground_truth": "3",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\(\\triangle ABC\\) be a scalene triangle. Let \\(h_{a}\\) be the locus of points \\(P\\) such that \\(|PB - PC| = |AB - AC|\\). Let \\(h_{b}\\) be the locus of points \\(P\\) such that \\(|PC - PA| = |BC - BA|\\). Let \\(h_{c}\\) be the locus of points \\(P\\) such that \\(|PA - PB| = |CA - ... | {
"ground_truth": "2",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mark had a box of chocolates. He consumed $\\frac{1}{4}$ of them and then gave $\\frac{1}{3}$ of what remained to his friend Lucy. Mark and his father then each ate 20 chocolates from what Mark had left. Finally, Mark's sister took between five and ten chocolates, leaving Mark with four chocolates... | {
"ground_truth": "104",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "69. The gym has 3 types of balls: soccer, basketball, and volleyball. 50 students go to borrow balls, with each person borrowing at least 1 ball and at most 2 balls. At least one student borrows the same number and type of balls.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Marie changed her dice by replacing 1, 3, and 5 with -1, -3, and -5 respectively. She left the even numbers unchanged. If she throws two such dice, what is the total that cannot be achieved? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$n$ coins are simultaneously flipped. The probability that two or fewer of them show tails is $\\frac{1}{4}$. Find $n$.",
"role": "user"
}
] | {
"ground_truth": "n = 5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sequence of positive integers is to be placed in each box. The product of any four adjacent integers is always 120. Given the sequence:\n\n| | | 2 | | | 4 | | x | | | 3 | | |\n\nFind the value of x. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. On an island, there are two tribes: the tribe of knights, who always tell the truth, and the tribe of liars, who always lie. On the main holiday, 2017 islanders sat around a large round table. Each islander said the phrase: \"my neighbors are from the same tribe.\" It turned out that two liars ... | {
"ground_truth": "1344",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Anikó, Béla, Csaba, and Dóra took out the figures from a deck of French cards. They distribute the remaining cards, each getting four. Then the bank pays $1 \\mathrm{Ft}$ for each jack, $3 \\mathrm{Ft}$ for each queen, $5 \\mathrm{Ft}$ for each king, and $7 \\mathrm{Ft}$ for each ace. In how many ... | {
"ground_truth": "643680",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 1.1. Condition:\n\nTwelve figures are made of matches - 3 triangles, 4 squares, and 5 pentagons. The figures have no common sides. Petya and Vasya take turns removing one match at a time. Vasya wants to leave as few untouched figures as possible, while Petya wants to leave as many untouched figu... | {
"ground_truth": "6",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 15 cities in a country, some of which are connected by roads. Each city is assigned a number equal to the number of roads leading out of it. It turns out that there are no roads between cities with the same number of roads. What is the maximum number of roads that can be in the country?"... | {
"ground_truth": "85",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A scientist stores the design of their time machine in a computer, and the file is protected by a password that is a permutation of the set $\\{1, 2, \\ldots, 64\\}$. They also design a program such that each time eight integers from 1 to 64 are inputted, the computer will indicate the order among... | {
"ground_truth": "45",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider the set of all four-digit rising numbers using the digits 1 through 7. Find the digit that the 35th number in the list from smallest to largest does not contain.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given sets A = {-2, -1, 0, 1, 2} and B = {1, 2, 3}, find the intersection A ∩ B. Express your answer as a set, listing all elements separated by commas.",
"role": "user"
}
] | {
"ground_truth": "{1, 2}",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. On a long strip of paper, the numbers $1, 2, 3, \\ldots, n$ are written in sequence. The long strip is cut into five segments, each containing some consecutive natural numbers (the digits of a single number are not split between different segments). We calculated the average of the numbers in ... | {
"ground_truth": "2014",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Graphistan has $2011$ cities and Graph Air (GA) is running one-way flights between all pairs of these cities. Determine the maximum possible value of the integer $k$ such that no matter how these flights are arranged it is possible to travel between any two cities in Graphistan riding only GA ... | {
"ground_truth": "1005",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Lina is an aspiring scientist from a country where the esteemed feminist historian, Dr. Maria, is highly celebrated for her work in promoting gender equality. Inspired by Dr. Maria, Lina decides to conduct a small survey on how many hours students spend on science and history subjects each week. S... | {
"ground_truth": "6",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many points can be placed inside a circle of radius 2 such that one of the points coincides with the center of the circle and the distance between any two points is not less than 1?",
"role": "user"
}
] | {
"ground_truth": "19",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A disadvantage of the contention approach for LANs, such as CSMA/CD, is the capacity wasted due to multiple stations attempting to access the channel at the same time. Suppose that time is divided into discrete slots, with each of 5 stations attempting to transmit with probability 0.35 during each... | {
"ground_truth": "0.572",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $A = {1, 2, 3, 4, 5}$ . Find the number of functions $f$ from the nonempty subsets of $A$ to $A$ , such that $f(B) \\in B$ for any $B \\subset A$ , and $f(B \\cup C)$ is either $f(B)$ or $f(C)$ for any $B$ , $C \\subset A$ ",
"role": "user"
}
] | {
"ground_truth": "120",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The first three numbers of a sequence are \\(1, 7, 8\\). Every subsequent number is the remainder obtained when the sum of the previous three numbers is divided by 4. Find the sum of the first 2011 numbers in this sequence.",
"role": "user"
}
] | {
"ground_truth": "3028",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A pentagon is obtained by joining, in order, the points \\((0,0)\\), \\((1,2)\\), \\((3,3)\\), \\((4,1)\\), \\((2,0)\\), and back to \\((0,0)\\). The perimeter of the pentagon can be written in the form \\(a + b\\sqrt{c} + d\\sqrt{e}\\), where \\(a\\), \\(b\\), \\(c\\), \\(d\\), and \\(e\\) are wh... | {
"ground_truth": "11",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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