prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Square $PQRS$ has side length $2$ units. Points $T$ and $U$ are on sides $PQ$ and $SQ$, respectively, with $PT = SU$. When the square is folded along the lines $RT$ and $RU$, sides $PR$ and $SR$ coincide and lie on diagonal $RQ$. Find the length of segment $PT$ which can be expressed in the form $... | {
"ground_truth": "10",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Let $A$ and $B$ be two sets, and let set $X$ satisfy\n$$\nA \\cap X=B \\cap \\dot{X}=A \\cap B, A \\cup B \\cup X=A \\cup B \\text {, }\n$$\n\nthen $X=$ $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "A \\cap B",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. In a school quiz, 100 students participated. After the results were tallied, it turned out that any 66 of them together earned no less than $50 \\%$ of the total prize points. What is the highest percentage of points that one participant could have earned?",
"role": "user"
}
] | {
"ground_truth": "25",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a cycling competition with $14$ stages, one each day, and $100$ participants, a competitor was characterized by finishing $93^{\\text{rd}}$ each day.What is the best place he could have finished in the overall standings? (Overall standings take into account the total cycling time over all... | {
"ground_truth": "2",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Pizzas are sized by diameter. What percent increase in area results if Lorrie’s pizza increases from a 16-inch pizza to an 18-inch pizza?",
"role": "user"
}
] | {
"ground_truth": "26.5625\\%",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Shapovalov A.V.\n\nEach face of a cube $6 \\times 6 \\times 6$ is divided into $1 \\times 1$ cells. The cube is covered with $2 \\times 2$ squares such that each square covers exactly four cells, no squares overlap, and each cell is covered by the same number of squares. What is the maximum value ... | {
"ground_truth": "3",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. The elements of set $A$ are positive integers, with the property: if $a \\in A$, then $42-a \\in A$. Therefore, the number of such sets $A$ is $\\qquad$.\n\nTranslating the text into English while preserving the original formatting and line breaks, the result is as follows:\n\n5. The elements o... | {
"ground_truth": "2^{21}-1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "As shown in the figure, find the sum of the angles \\( \\angle 1 + \\angle 2 + \\angle 3 + \\angle 4 + \\angle 5 + \\angle 6 + \\angle 7 \\). Express your answer in degrees (\\( ^\\circ \\)) as a whole number.",
"role": "user"
}
] | {
"ground_truth": "540",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct trees with exactly 7 vertices are there? A tree is defined in the language of graph theory as a connected graph with no cycles, simply understood as a graph that connects \\( n \\) vertices with \\( n-1 \\) edges. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Stevens, a businessman, owned and operated a small retail shop in Boone Mall from 1995 to 2015. During his first year in business, he sold 1,200 items. Over the next 10 years, his sales increased by 150 items each year. In his final year of business, he decided to have a closing sale and manag... | {
"ground_truth": "47750",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A tetrahedron has one face that is a regular triangle with 6 unit edges, and its other edges are 3, 4, and 5 units long. What is the distance between the straight line of the 3-unit edge and the straight line of the opposite edge?",
"role": "user"
}
] | {
"ground_truth": "3.0356",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Solve the inequality $n^{3}-n<n$! on the set of positive integers. ( $n$! denotes the product of integers from 1 to $n$.)",
"role": "user"
}
] | {
"ground_truth": "1n\\geq6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 Solve the equation $3^{x}+4^{x}=5^{x}$.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly. \n\nHowever, since the provided text is already in English, here is the confirmation of the text with the ... | {
"ground_truth": "x=2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a right triangle $XYZ$, medians are drawn from points $X$ and $Y$ to segments $\\overline{YZ}$ and $\\overline{XZ}$, respectively, dividing these segments in half. The lengths of the medians from $X$ and $Y$ are 5 units and $3\\sqrt{5}$ units, respectively. The area of triangle $XYZ$ is 30 squa... | {
"ground_truth": "2\\sqrt{14}",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task 1 - 291211\n\nDetermine the number of all natural numbers $z$ with the following properties:\n\n(1) The decimal representation of $z$ consists of five pairwise distinct digits.\n\n(2) The first and the last digit in it are different from 0.\n\n(3) If $z^{\\prime}$ is the number whose digit... | {
"ground_truth": "56",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A farmer's rectangular field is partitioned into $2$ by $2$ grid of $4$ rectangular sections as shown in the figure. In each section the farmer will plant one crop: corn, wheat, soybeans, or potatoes. The farmer does not want to grow corn and wheat in any two sections that share a border, and the ... | {
"ground_truth": "84",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4-2. A circle touches the sides of an angle at points $A$ and $B$. The distance from a point $C$ lying on the circle to the line $A B$ is 6. Find the sum of the distances from point $C$ to the sides of the angle, given that one of these distances is 5 more than the other.",
"role": "user"
}
... | {
"ground_truth": "13",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 14. Problem 14\n\nFull score -6\n\nA zero-coupon bond is redeemed at its nominal value of 1000 rubles in one year. Determine the market value of the bond if the market rate of return is $10 \\%$ per annum.",
"role": "user"
}
] | {
"ground_truth": "909",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. July 1, 2021 is the 100th anniversary of the founding of our Party, recorded as 20210701, where the sum of the digits in the odd positions is $1+7+1+0=9$ and the sum of the digits in the even positions is $0+0+2+2=4$, with a ratio of $9: 4$; among the 8-digit numbers formed by $0 \\sim 9$ (no r... | {
"ground_truth": "2304",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. (20 points) Given the ellipse $C: \\frac{x^{2}}{25}+\\frac{y^{2}}{9}=1$, and the moving circle $\\Gamma: x^{2}+y^{2}=r^{2}(3<r<5)$. If $M$ is a point on the ellipse $C$, and $N$ is a point on the moving circle $\\Gamma$, and the line $M N$ is tangent to both the ellipse $C$ and the moving circ... | {
"ground_truth": "2",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "(7) As shown in the figure, $AB$ is the diameter of semicircle $O$, and $C, D$ are two moving points on the semicircle, with $CD \\parallel AB$. If the radius of the semicircle is 1, then the maximum value of the perimeter of trapezoid $ABCD$ is . $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest positive integer \\( n \\) such that the inequality \\(\\frac{8}{15} < \\frac{n}{n+k} < \\frac{7}{13}\\) holds for exactly one integer \\( k \\). (5th American Mathematics Invitational, 1987)",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ward and Gabriëlle are playing a game on a large sheet of paper. At the beginning, there are 999 ones written on the paper. Ward and Gabriëlle take turns, with Ward starting. A player whose turn it is may choose two numbers $a$ and $b$ from the paper for which $\\operatorname{ggd}(a, b)=1$, erase ... | {
"ground_truth": "Gabriëlle",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B3. We start with a square with side 1. In the first minute, squares with side $\\frac{1}{3}$ grow in the middle of the vertical sides. In the next minute, squares with sides of $\\frac{1}{3}$ of the length of those line segments grow in the middle of all vertical line segments of the new figure. ... | {
"ground_truth": "84",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jamie, a sports broadcaster, is preparing for a live basketball game commentary. To make the commentary more engaging, Jamie relies on video clips edited by Alex, the video editor. Alex has prepared 5 highlights for the first quarter, 7 for the second quarter, 4 for the third quarter, and 6 for th... | {
"ground_truth": "14",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10.3. 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": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Carlos is constructing a rectangular storage unit using one-foot cubical blocks. The storage unit is 15 feet long, 12 feet wide, and 8 feet high. The walls and the floor are 1.5 feet thick. Calculate the total number of blocks contained in the storage unit.",
"role": "user"
}
] | {
"ground_truth": "738",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a 6 by 5 grid, how many 10-step paths are there from $W$ to $X$ that must pass through a point $H$? Assume $W$ is located at the top-left corner, $X$ at the bottom-right corner, and $H$ is three squares to the right and two squares down from $W$.",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "59. An electronic watch uses 5 two-digit numbers (including two-digit numbers with a leading 0) to indicate time and date, such as 15:23:45/06/18 representing June 18, 15:23:45. There are some special moments when all ten digits on the electronic watch are different. Among these special moments, t... | {
"ground_truth": "153",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The center of circle $k$ is $O$. Points $A, B, C, D$ are consecutive points on the circumference of $k$ such that $\\angle AOB = \\angle BOC = \\angle COD = \\alpha < 60^\\circ$. Point $E$ is the projection of $D$ onto the diameter $AO$. Point $F$ is the trisection point of segment $DE$ closer to ... | {
"ground_truth": "60^\\circ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a planet, there are $2^{N}$ countries $(N \\geqslant 5)$. Each country has a flag composed of a line of $N$ squares of side 1, each being yellow or blue. The flags are all distinct from each other. A set of $N$ flags is diverse if they can be placed in a certain order to form an $N \\times N$ s... | {
"ground_truth": "2^{N-2}+1",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. All three-digit numbers from 100 to 999 are written in a row without spaces. Kostya underlined \\( k \\) consecutive digits in this sequence, and Andrey underlined other \\( k \\) consecutive digits in this sequence. It turned out that the \\( k \\)-digit numbers underlined by the boys are equa... | {
"ground_truth": "5",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A bus ticket is numbered with six digits: from 000000 to 999999. You buy one ticket. What is the probability that you will get a ticket whose digits are in ascending (or descending) order?",
"role": "user"
}
] | {
"ground_truth": "0.00042",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A weighted dice has six faces. The probability of rolling a 2 is $\\frac{1}{4}$, the probability of rolling a 5 is $\\frac{1}{2}$, and the probability of rolling any other number is $\\frac{1}{12}$ for each number. You win $\\$4$ if you roll a 2, $\\$6$ if you roll a 5, and lose $\\$3$ for rolling... | {
"ground_truth": "\\$3",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Add $(A B A B)_{16}$ and $(B A B A)_{16}$.",
"role": "user"
}
] | {
"ground_truth": "16665_{16}",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A high school has three math teachers. To facilitate students, math teachers are scheduled for duty from Monday to Friday, with two teachers on duty on Monday. If each teacher is on duty for two days a week, then there are ________ possible duty schedules for a week.",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the solution set of the inequality $x(2-x) > 3$. Express your answer as a set using proper set notation.",
"role": "user"
}
] | {
"ground_truth": "\\emptyset",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In an isosceles trapezoid, the angle at the base is $50^{\\circ}$, and the angle between the diagonals, facing the lateral side, is $40^{\\circ}$. Is the center of the circumscribed circle inside or outside the trapezoid?",
"role": "user"
}
] | {
"ground_truth": "Outside",
"mean_reward": 0.296875
} | 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 functions $f:\\mathbb{R}\\rightarrow \\mathbb{R}$ such that for all real numbers $x$ and $y$ , \\[(f(x)+xy)\\cdot f(x-3y)+(f(y)+xy)\\cdot f(3x-y)=(f(x+y))^2.... | {
"ground_truth": "-1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A $3 \\times 3 \\times 3$ cube composed of 27 unit cubes rests on a horizontal plane. Determine the number of ways of selecting two distinct unit cubes from a $3 \\times 3 \\times 1$ block (the order is irrelevant) such that the line joining the centers of the two cubes makes a $45^{\\circ}$ angle... | {
"ground_truth": "60",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Theorem of the length of a tangent and a secant; the product of the entire secant and its external part [ Mean proportionals in a right triangle\n\nIn rhombus $A B C D$, angle $B A D$ is acute. A circle inscribed in this rhombus touches sides $A B$ and $C D$ at points $M$ and $N$ respectively an... | {
"ground_truth": "1:9",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9 | |\n\nIn a square table of $9 \\times 9$ cells, 9 cells are marked at the intersections of the second, fifth, and eighth rows with the second, fifth, and eighth columns. How many ways are there to get from the bottom-left cell to the top-right cell, moving only through unmarked cells upwards o... | {
"ground_truth": "678",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. How many four-digit numbers are there, the sum of whose digits is twenty, and the number of hundreds is greater than 19 and does not exceed twenty-two",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Let $\\left(x_{1}, x_{2}, \\cdots, x_{20}\\right)$ be a permutation of $(1,2, \\cdots, 20)$, and satisfy $\\sum_{i=1}^{20}\\left(\\left|x_{i}-i\\right|+\\left|x_{i}+i\\right|\\right)=620$, then the number of such permutations is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "(10!)^2",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. (12 points) Five students, Jia, Yi, Bing, Ding, and Wu, ranked in the top 5 (no ties) in a math competition and stood in a row for a photo. They each said the following:\n\nJia said: The two students next to me have ranks that are both behind mine;\nYi said: The two students next to me have ran... | {
"ground_truth": "23514",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Each of the thirty sixth-graders has one pen, one pencil, and one ruler. After their participation in the Olympiad, it turned out that 26 students lost a pen, 23 - a ruler, and 21 - a pencil. Find the smallest possible number of sixth-graders who lost all three items.",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A function f(x) defined on R satisfies f(0)=0, f(x)+f(1-x)=1, f(x/5)=1/2f(x), and f(x1) ≤ f(x2) when 0 ≤ x1 < x2 ≤ 1. Find the value of f(1/2007). Express your answer as a fraction in simplest form.",
"role": "user"
}
] | {
"ground_truth": "1/32",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A student has 6 pencils, all of different colors. He chooses some of them and puts them in his pencil case. How many possibilities are there?",
"role": "user"
}
] | {
"ground_truth": "64",
"mean_reward": 0
} | 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": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's round each addend in the following expressions to $n=1,2,3, \\ldots$ decimal places, and find the largest value of $n$ for which the rounded values of $K_{1}$ and $K_{2}$ are still equal. Also, examine the question for the case where the addends are rounded to the nearest unit, ten, hundred,... | {
"ground_truth": "4",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "79. If prime numbers $p, q$ satisfy: $3 q-p-4=0, p+q<111$, then the maximum value of $p q$ is\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": "1007",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Points $G$, $H$, $I$, and $J$ are collinear on a line with $GH = HI = IJ = 2$. Points $K$ and $L$ rest on another line, parallel to the first, and distanced such that $KL = 2$. Find the number of distinct possible values for the area of the triangle formed by any three of the six points.",
"ro... | {
"ground_truth": "3",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "196. Composite Squares. Can you find two three-digit squares (with no zeros) that, when written consecutively, form a six-digit number which itself is a square? For example, from 324 and $900\\left(18^{2}\\right.$ and $\\left.30^{2}\\right)$ we get $324900\\left(570^{2}\\right)$, but the number 90... | {
"ground_truth": "225625",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. 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(Tang Lihua)",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The diagonals of kite WXYZ intersect at P. If XP = 8, PZ = 8, WP = 6, and PY = 24, find ZY.",
"role": "user"
}
] | {
"ground_truth": "25.3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In triangle $ABC$, where $A$ is at the origin $(0,0)$, $B$ is now at $(12,0)$, and $C$ remains at $(3,5)$. If Wanda now guesses that the Fermat point $P$ is at $(5,3)$, calculate the sum of the distances from $P$ to the vertices of $\\triangle ABC$. If she obtains $m\\sqrt{a} + n\\sqrt{b}$, where ... | {
"ground_truth": "4",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the addition problem, each digit has been replaced by a letter. If different letters represent different digits then what is the value of $C$? [asy] unitsize(18); draw((-1,0)--(3,0)); draw((-3/4,1/2)--(-1/4,1/2)); draw((-1/2,1/4)--(-1/2,3/4)); label(\"$A$\",(0.5,2.1),N); label(\"$B$\",(1.5,2.1)... | {
"ground_truth": "1",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Senderovv B.A.\n\nFind all such triples of prime numbers $p, q, r$, such that the fourth power of each of them, decreased by 1, is divisible by the product of the other two.",
"role": "user"
}
] | {
"ground_truth": "{2,3,5}",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "56. As shown in the figure, $C, D$ are the trisection points of $A B$. At 8:00 AM, Jia starts walking from $A$ towards $B$, and at 8:12 AM, Yi starts walking from $B$ towards $A$. A few minutes later, Bing also starts walking from $B$ towards $A$. When Jia and Yi meet at $C$, Bing happens to be at... | {
"ground_truth": "16",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3.1. A chocolate bar weighed 250 g and cost 50 rubles. Recently, to save money, the manufacturer reduced the weight of the bar to 200 g, and increased its price to 52 rubles. By what percentage did the manufacturer's revenue increase?",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. C1 (UKR) On a $5 \\times 5$ board, two players alternately mark numbers on empty cells. The first player always marks 1's, the second 0's. One number is marked per turn, until the board is filled. For each of the nine $3 \\times 3$ squares the sum of the nine numbers on its cells is computed. D... | {
"ground_truth": "6",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Tokarev S.i.\n\nThe participants of the test olympiad were offered $n$ questions. The jury determines the difficulty of each question: a positive integer number of points awarded to participants for a correct answer to the question. For an incorrect answer, 0 points are awarded, and all points ear... | {
"ground_truth": "n",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n\nA frame for three square photographs has the same width everywhere (see the figure). The perimeter of one opening is 60 cm, and the perimeter of the entire frame is 180... | {
"ground_truth": "5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( a, b, c, x, y, \\) and \\( z \\) be complex numbers such that\n\\[ a = \\frac{b+c}{x-2}, \\quad b = \\frac{c+a}{y-2}, \\quad c = \\frac{a+b}{z-2}. \\]\n\nIf \\( 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": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $x = \\sqrt{\\frac{\\sqrt{53}}{2} + \\frac{3}{2}}.$ There exist unique positive integers $a,$ $b,$ $c$ such that\n\\[x^{100} = 2x^{98} + 14x^{96} + 11x^{94} - x^{50} + ax^{46} + bx^{44} + cx^{40}.\\]Find $a + b + c.$",
"role": "user"
}
] | {
"ground_truth": "157",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In chess, a king threatens another king if, and only if, they are on neighboring squares, whether horizontally, vertically, or diagonally . Find the greatest amount of kings that can be placed on a $12 \\times 12$ board such that each king threatens just another king. Here, we are not considerin... | {
"ground_truth": "72",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. Let $R S T U V$ be a regular pentagon. Construct an equilateral triangle $P R S$ with point $P$ inside the pentagon. Find the measure (in degrees) of angle $P T V$.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. January 1, 2015 was a Thursday, based on this information, we can calculate that March 9, 2015 was a Sunday\n\nAccording to the given information, January 1, 2015, was a Thursday. To find out what day of the week March 9, 2015, was, we need to count the total number of days from January 1, 201... | {
"ground_truth": "Monday",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In $\\triangle ABC$, $\\angle A = 42^{\\circ}$. If the trisectors of $\\angle B$ and $\\angle C$ meet at points $D$ and $E$ respectively, then find the measure of $\\angle BDC$. Express your answer in degrees as a whole number.",
"role": "user"
}
] | {
"ground_truth": "88^\\circ",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\triangle ABC$ have side lengths $AB=30$, $BC=32$, and $AC=34$. Point $X$ lies in the interior of $\\overline{BC}$, and points $I_1$ and $I_2$ are the incenters of $\\triangle ABX$ and $\\triangle ACX$, respectively. Find the minimum possible area of $\\triangle AI_1I_2$ as $X$ varies along ... | {
"ground_truth": "126",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. (10 points) There are 20 piles of stones, each containing 2006 stones. The rule is: taking one stone from each of any 19 piles and placing them into another pile is considered one operation. After fewer than 20 such operations, one pile has 1990 stones, and another pile has between 2080 and 21... | {
"ground_truth": "2090",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five friends were comparing how much scrap iron they brought to the collection. On average, it was $55 \\mathrm{~kg}$, but Ivan brought only $43 \\mathrm{~kg}$.\n\nWhat is the average amount of iron brought without Ivan?\n\n(Note: By how many kilograms does Ivan's contribution differ from the aver... | {
"ground_truth": "58",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 10 Solve the equation $\\cos \\frac{x^{2}+x}{2}-2^{x-1}-2^{-x-1}=0$.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly. \n\nHowever, since the request is to translate the given text, here is the tran... | {
"ground_truth": "x=0",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. (5 points) If a natural number has an even number of even digits, it is called a \"Hope Number\", for example: 26, 201, 533 are Hope Numbers, while 8, 36, 208 are not Hope Numbers. Therefore, if all Hope Numbers are arranged in ascending order, the 2010th Hope Number is $\\qquad$",
"role": ... | {
"ground_truth": "4019",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The set $X$ of $N$ four-digit numbers formed from the digits $1,2,3,4,5,6,7,8$ satisfies the following condition:\n\n\n[i]for any two different digits from $1,2,3,4,,6,7,8$ there exists a number in $X$ which contains both of them. [/i]\\\\\n\nDetermine the smallest possible value of $N$.",
"ro... | {
"ground_truth": "6",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.68. Using a compass and a ruler, divide an angle of $19^{\\circ}$ into 19 equal parts.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all positive integers $k$ such that for any positive numbers $a, b, c$ that satisfy the inequality $k(a b+b c+c a)>5\\left(a^{2}+b^{2}+c^{2}\\right)$, there always exists a triangle with side lengths $a, b, c$.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nLet \\( N \\) be a natural number whose base-2016 representation is \\( ABC \\). Working now in base-10, what is the remainder when \\( N - (A + B + C + k) \\) is divided by 2015, if \\( k \\in \\{ 1, 2, \\ldots, 2015 \\} \\)?",
"role": "user"
}
] | {
"ground_truth": "2015 - k",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A4. Twenty students go abseiling during a school trip. In each round, one student gets a turn to abseil, so after twenty rounds, everyone has safely descended. To determine who goes first in round 1, cards with numbers 1 to 20 are distributed to the students. The one who gets the 1 starts. In roun... | {
"ground_truth": "66",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. From the odd natural numbers from 1 to 47, 12 fractions less than 1 were formed, using each number exactly once. The resulting fractions were divided into groups of equal values. What is the smallest number of groups that could have been obtained? (I. Rubanov)",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4.1. A train of length $L=600$ m, moving by inertia, enters a hill with an angle of inclination $\\alpha=30^{\\circ}$ and stops when exactly a quarter of the train is on the hill. What was the initial speed of the train $V$ (in km/h)? Provide the nearest whole number to the calculated speed. Negle... | {
"ground_truth": "49",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Primary School No.1 and Primary School No.2 have the same number of students participating in the Golden Cup Competition. The schools use cars to transport the students to the examination site. Primary School No.1 uses cars that can seat 15 people each, while Primary School No.2 uses cars that ... | {
"ground_truth": "184",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A 4-dimensional hyperparallelepiped $ABCDEFGHJKLMN$ is generated by vectors $\\overrightarrow{AB},$ $\\overrightarrow{AD},$ $\\overrightarrow{AE},$ and $\\overrightarrow{AF},$ with $A$ at the origin. Compute\n\\[\n\\frac{AG^2 + BK^2 + CM^2 + DN^2}{AB^2 + AD^2 + AE^2 + AF^2}.\n\\]",
"role": "us... | {
"ground_truth": "4",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Know-it-all told Don't-know-it that to convert kilolunes (a unit of mass used by the little people on the Moon) to kilograms, one needs to divide the mass in kilolunes by 4 and then decrease the obtained number by $4 \\%$. Don't-know-it decided that to convert from kilograms to kilolunes, one s... | {
"ground_truth": "0.16",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a positive integer $k$, let the set\n$$\nR_{n}=\\left\\{\\begin{array}{l}\n\\{-k,-(k-1), \\cdots,-1,1, \\cdots, k-1, k\\}, \\quad n=2 k ; \\\\\n\\{-k,-(k-1), \\cdots,-1,0,1, \\cdots, k-1, k\\}, \\quad n=2 k+1 .\n\\end{array}\\right.\n$$\n\nA device contains some balls and red or white strings ... | {
"ground_truth": "2n-1",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all the pairs of positive numbers such that the last\ndigit of their sum is 3, their difference is a primer number and\ntheir product is a perfect square.",
"role": "user"
}
] | {
"ground_truth": " (9, 4) ",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $f(1)=1$, and for any integers $m, n, f(m+n)=f(m)+f(n)+3(4 m n \\cdots 1)$, then $f(19)=$ $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "2017",
"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\nWhat is the following value when expressed as a common fraction: $$\\frac{1}{2^{1}}+\\frac{1}{2^{2}}+\\frac{1}{2^{3}}+\\cdots + \\frac{1}{2^{8}}+\\frac{1}{2^{9}}+\\fr... | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 55 points marked on a plane: the vertices of a regular 54-gon and its center. Petya wants to color a set of three marked points in red so that the colored points form the vertices of a regular triangle. In how many ways can Petya do this?",
"role": "user"
}
] | {
"ground_truth": "72",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. (12 points) In a plane, there are 15 red points. Some line segments are drawn between these red points. If a red point is connected by several line segments, the number of line segments is marked on this red point. It is known that red points marked with the same number are not connected to ea... | {
"ground_truth": "85",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that December 21, 2013, is a Saturday, determine the day of the week for January 31, 2014. Express your answer as a day of the week (e.g., Monday, Tuesday, etc.).",
"role": "user"
}
] | {
"ground_truth": "Friday",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "38. Pete and Vasya take turns painting the edges of a 77-sided pyramid, one at a time. You can paint an edge that has not been painted yet, provided that all adjacent edges are not painted. The player who cannot make a move loses. Pete starts. Who among them can always win, regardless of how the o... | {
"ground_truth": "Vasya",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Decimal numeral system ] $[\\quad$ Case enumeration $\\quad]$\n\n## Author: Raskina I.V.\n\nThe year 2009 has the property that by rearranging the digits of the number 2009, it is impossible to obtain a smaller four-digit number (numbers do not start with zero). In which year will this property ... | {
"ground_truth": "2022",
"mean_reward": 0.390625
} | 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": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A health reporter named Alex is researching the impact of advanced diagnostics on patient care. During their investigation, Alex discovers that a new diagnostic tool can reduce the time it takes to diagnose patients by 30%. Previously, it took doctors 20 hours to diagnose a patient. Alex also lear... | {
"ground_truth": "300",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the distance between the foci of the ellipse\n\\[\\frac{x^2}{48} + \\frac{y^2}{12} = 3.\\]",
"role": "user"
}
] | {
"ground_truth": "4\\sqrt{3}",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Determination of reaction rate -3 points\n\nTotal: 8 points.\n\n## TASK 5\n\n## SOLUTION:\n\nConvert the temperature to the Kelvin scale: $T=273+95=368$ K. To calculate $\\Delta G^{0}{ }_{368}$, we will use the equation:\n\n$$\n\\Delta G^{\\mathrm{o}}{ }_{368}=\\Delta H^{o}-T \\Delta S^{o}\n$$\... | {
"ground_truth": "-140.9",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Maria is a single mother who decided to renovate her kitchen. She hired a contractor who promised to complete the renovation for $8,000. Unfortunately, the contractor turned out to be fraudulent and disappeared after receiving a $2,500 deposit from Maria, leaving the work unfinished. Maria later f... | {
"ground_truth": "500",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 9 representatives from different countries, with 3 people from each country. They sit randomly around a round table with 9 chairs. What is the probability that each representative has at least one representative from another country sitting next to them?",
"role": "user"
}
] | {
"ground_truth": "41/56",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a long straight stretch of one-way single-lane highway, cars all travel at the same speed and all obey the safety rule: the distance from the back of the car ahead to the front of the car behind is exactly one car length for each 15 kilometers per hour of speed or fraction thereof (Thus the fro... | {
"ground_truth": "375",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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