prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "A curriculum specialist is designing a gamified lesson plan for a class of 30 students. She wants to divide the class into teams of 5 students each to participate in a math challenge. For each team, she plans to prepare a set of 10 math puzzles. Each puzzle requires 3 minutes to solve. If the less... | {
"ground_truth": "10",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A certain quadratic polynomial is known to have the following properties: its leading coefficient is equal to one, it has integer roots, and its graph (parabola) intersects the line \\( y = 2017 \\) at two points with integer coordinates. Can the ordinate of the vertex of the parabola be uniquely ... | {
"ground_truth": "-1016064",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The increasing sequence of positive integers $a_1, a_2, a_3, \\dots$ is defined by the rule\n\\[a_{n + 2} = a_{n + 1} + a_n\\]\nfor all $n \\ge 1.$ If $a_7 = 210$, then find $a_8.$",
"role": "user"
}
] | {
"ground_truth": "340",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the greatest possible value of a three-digit number $NNM$ when the two-digit integer $MM$, where both digits are $M$, is multiplied by the integer $M$, with the condition that $M \\times M$ modulo 10 must equal $M$.",
"role": "user"
}
] | {
"ground_truth": "396",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task A-2.4.\n\nFive sides of a wooden cube are painted blue, while one side remains unpainted. The cube is then cut into smaller, congruent cubes, of which 649 have exactly one blue side. How many of the smaller cubes have exactly two blue sides?",
"role": "user"
}
] | {
"ground_truth": "92",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Calculate: $1 \\times 2+5 \\times 5+9 \\times 8+13 \\times 11+\\cdots+101 \\times 77=$",
"role": "user"
}
] | {
"ground_truth": "69927",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the square shown, find the value of x. Express your answer in degrees as a whole number.",
"role": "user"
}
] | {
"ground_truth": "45",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If\n\\[1 \\cdot 1500 + 2 \\cdot 1499 + 3 \\cdot 1498 + \\dots + 1499 \\cdot 2 + 1500 \\cdot 1 = 1500 \\cdot 751 \\cdot x,\\]\ncompute the integer $x.$",
"role": "user"
}
] | {
"ground_truth": "501",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three, given $x, y \\in N$, find the largest $y$ value such that there exists a unique $x$ value satisfying the following inequality:\n$$\n\\frac{9}{17}<\\frac{x}{x+y}<\\frac{8}{15} \\text {. }\n$$",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "F11 (29-3, UK) Let $\\mathbf{N}^{*}$ be the set of positive integers, and define the function $f$ on $\\mathbf{N}^{*}$ as follows:\n(1) $f(1)=1, f(3)=3$;\n(2) For $n \\in \\mathbf{N}^{*}$, we have\n$$\n\\begin{array}{c}\nf(2 n)=f(n), \\\\\nf(4 n+1)=2 f(2 n+1)-f(n), \\\\\nf(4 n+3)=3 f(2 n+1)-2 f(n)... | {
"ground_truth": "92",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 213: If $m, n \\in Z^{+}, (m, n)=1, m<n$, and the decimal representation of $\\frac{\\mathrm{m}}{\\mathrm{n}}$ contains $\\overline{251}$, find the minimum value of $\\mathrm{n}$.",
"role": "user"
}
] | {
"ground_truth": "127",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. In the city of liars and knights, there are 366 residents, all born on different days of a leap year. All residents of the city answered two questions. To the question “Were you born in February?” 100 people answered affirmatively, and to the question “Were you born on the 30th?” 60 people answ... | {
"ground_truth": "29",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that \\( A \\) and \\( B \\) are two subsets of the set \\(\\{1,2,3, \\cdots, 100\\}\\), satisfying \\( |A| = |B| \\) and \\( A \\cap B = \\varnothing \\). If \\( x \\in A \\) always implies \\( 2x + 2 \\in B \\), what is the maximum number of elements in the set \\( A \\cup B \\)?",
"ro... | {
"ground_truth": "66",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a 6 by 6 grid, each of the 36 small squares measures 1.5 cm by 1.5 cm. The grid is fully shaded in grey. Six unshaded shapes are then added: one medium hexagon, four small circles placed symmetrically, and one larger circle in the center. The diameter of the small circles equals the side of a s... | {
"ground_truth": "88.875",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $M$ be the intersection point of the medians $AD$ and $BE$ of a right triangle $ABC$ ( $\\angle C=90^\\circ$ ). It is known that the circumcircles of triangles $AEM$ and $CDM$ are tangent. Find the angle $\\angle BMC.$ ",
"role": "user"
}
] | {
"ground_truth": "90^\\circ",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $n$ be a positive integer and $a,b,c,d$ be integers such that $a\\equiv c^{-1} \\pmod{n}$ and $b\\equiv d^{-1} \\pmod{n}$. What is the remainder when $(ab + cd)$ is divided by $n$?",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The orchestra has more than 150 members but fewer than 300 members. When they line up in rows of 6 there are two extra people; when they line up in rows of 8 there are four extra people; and when they line up in rows of 9 there are six extra people. How many members are in the orchestra?",
"ro... | {
"ground_truth": "212",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2 Find a three-digit decimal number such that the ratio of the number to the sum of its digits is minimized.\n\nKeep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "199",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task 3 - 250513\n\nThree customers in a hardware store bought screws. Each screw cost 7 pfennigs. The second customer bought four more screws than the first customer. The third customer bought twice as many screws as the second customer. The three customers paid a total of 5 marks and 32 pfenni... | {
"ground_truth": "2.80",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given\n$$\nS_{n}=|n-1|+2|n-2|+\\cdots+10|n-10| \\text {, }\n$$\nwhere \\( n \\in \\mathbf{Z}_{4} \\). Find the minimum value of \\( S_{n} \\).",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The cells of a $100 \\times 100$ table are painted white. In one move, you are allowed to choose any 99 cells from one row or one column and repaint each of them in the opposite color – from white to black or from black to white. What is the minimum number of moves needed to obtain a table with a ... | {
"ground_truth": "100",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7. The number of natural numbers $n$ that make $n^{2}-19 n+91$ a perfect square is?\n\nWill the above text be translated into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10,11\n\nThe radius of the base of the cylinder is equal to $r$, and the height is equal to $5 r$. A parallelepiped is circumscribed around the cylinder, the ratio of the volume of which to the volume of the cylinder is $\\frac{\\tilde{5}}{\\pi}$. Find the length of the segment of the larger diago... | {
"ground_truth": "3r",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4.1. $[7-8.3$ (15 points)] In three flasks, there is concentrated acid: in the first 10 g, in the second 20 g, in the third 30 g. There is also a fourth flask with water. If some amount of water from the fourth flask is added to the first flask, and the remaining water is poured into the second fl... | {
"ground_truth": "10.5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 10 Find the largest integer $n$ such that all non-zero solutions of the equation $(z+1)^{n}=z^{n}+1$ lie on the unit circle.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nFind the minimum value of the expression\n\n\\[\n(3 \\sqrt{2(1+\\cos 2 x)}-\\sqrt{8-4 \\sqrt{3}} \\sin x+2) \\cdot(3+2 \\sqrt{11-\\sqrt{3}} \\cos y-\\cos 2 y)\n\\]\n\nIf the answer is not an integer, round it to the nearest whole number.",
"role": "user"
}
] | {
"ground_truth": "-33",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a regular quadrilateral pyramid $S-ABCD$, points $P$ and $Q$ are the midpoints of $SB$ and $SD$ respectively. The plane passing through points $A$, $P$, and $Q$ divides $S-ABCD$ into two parts with volumes $V_1$ and $V_2$ such that $V_1 < V_2$. Calculate the ratio $\\frac{V_2}{V_1}$. Express... | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. In an arm wrestling tournament, 510 athletes are participating. 1 point is awarded for a win, and 0 points for a loss. If the winner initially had fewer points than the opponent, the winner additionally receives one point from the loser. In each round, participants with a difference of no more ... | {
"ground_truth": "9",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A car departed from point A to point B, and with some delay, a second car followed. When the first car had traveled half the distance, the second car had traveled $26 \\frac{1}{4}$ km. When the second car had traveled half the distance, the first car had traveled $31 \\frac{1}{5}$ km. After overta... | {
"ground_truth": "58",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A regular three-sided pyramid (its base is an equilateral triangle) is inscribed in a sphere, the diameter of which is nine times the height of the pyramid. What angle do two side faces enclose?",
"role": "user"
}
] | {
"ground_truth": "120",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Given that $x, y$ satisfy $2 x+5 y \\geq 7, 7 x-3 y \\leq 2$, then, the minimum value of $-27 x+35 y$ is\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. [35] Let $S$ be the set of ordered pairs of integers $(x, y)$ with $1 \\leq x \\leq 5$ and $1 \\leq y \\leq 3$. How many subsets $R$ of $S$ have the property that all the points of $R$ lie on the graph of a single cubic? A cubic is a polynomial of the form $y=a x^{3}+b x^{2}+c x+d$, where $a, b... | {
"ground_truth": "796",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "II. (This question is worth 25 points) Find all real numbers $p$ such that the cubic equation $5 x^{3}-5(p+1) x^{2}+(71 p-1) x+1=66 p$ has three roots that are all natural numbers.",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task A-1.1. (4 points)\n\nHow many squares of natural numbers are there between $4^{9}$ and $9^{4}$, not including these two numbers?",
"role": "user"
}
] | {
"ground_truth": "430",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Task 7.5\n\nOn a checkerboard of size $8 \\times 8$, Petya colors several cells. Vasya wins if he can cover all these cells with non-overlapping and non-protruding L-shaped corners consisting of three cells. What is the minimum number of cells Petya should color so that Vasya cannot win?\n\n## N... | {
"ground_truth": "64",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the Cartesian coordinate system, circle \\( C_1 \\) and circle \\( C_2 \\) intersect at points \\( P \\) and \\( Q \\), where the coordinates of point \\( P \\) are \\( (3, 2) \\). The product of the radii of the two circles is \\( \\frac{13}{2} \\). If the line \\( y = kx \\) (where \\( k > 0 ... | {
"ground_truth": "2 \\sqrt{2}",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a rectangular box-shaped fort with dimensions 15 feet in length, 12 feet in width, and 6 feet in height, and walls and floor uniformly 1.5 feet thick, calculate the total number of one-foot cubical blocks used to build the fort.",
"role": "user"
}
] | {
"ground_truth": "594",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 1 Given 20 numbers $1,2, \\cdots, 20$, two people, A and B, take turns placing a “+” or “-” sign in front of these numbers (the order of placement is not limited). After 20 steps, the absolute value $S$ of the resulting algebraic sum is calculated. A wants to make $S$ as small as possible,... | {
"ground_truth": "30",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Charles Dickens' 200th anniversary of birth was celebrated on February 7, 2012, which was a Tuesday. A year is a leap year if it is divisible by 400 or divisible by 4 but not by 100. Using this rule, calculate the day of the week on which Charles Dickens was born. Provide your answer as the full d... | {
"ground_truth": "Friday",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. From the three-digit numbers $100, 101, 102, \\ldots, 699, 700$, if $n$ different numbers are taken, such that there are always three numbers among them with the same sum of digits. Then the minimum value of $n$ is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "47",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The name of a river consists of three letters. The three numbers, which represent the positions of the letters in the $A B C$ (excluding J), add up to 35. If we increase the third number by one, the first two numbers and the new third number form an arithmetic sequence; if we add 3 to the first nu... | {
"ground_truth": "Ems",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The total in-store price for a blender is $\\textdollar 129.95$. A television commercial advertises the same blender for four easy payments of $\\textdollar 29.99$ and a one-time shipping and handling charge of $\\textdollar 14.95$. Calculate the number of cents saved by purchasing the blender thr... | {
"ground_truth": "496",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given \\(\\triangle DEF\\), where \\(DE=28\\), \\(EF=30\\), and \\(FD=16\\), calculate the area of \\(\\triangle DEF\\).",
"role": "user"
}
] | {
"ground_truth": "221.25",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex wrote all natural divisors of a natural number \\( n \\) on the board in ascending order. Dima erased several of the first and several of the last numbers of the resulting sequence so that 151 numbers remained. What is the maximum number of these 151 divisors that could be fifth powers of nat... | {
"ground_truth": "31",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Call the Graph the set which composed of several vertices $P_1,\\ \\cdots P_2$ and several edges $($ segments $)$ connecting two points among these vertices. Now let $G$ be a graph with 9 vertices and satisfies the following condition.\n\nCondition: Even if we select any five points from the... | {
"ground_truth": "9",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. For any positive integers $m, n$, define $r(m, n)$ as the remainder of $m \\div n$ (for example, $r(8,3)$ represents the remainder of $8 \\div 3$, so $r(8,3)=2$). The smallest positive integer solution that satisfies the equation $r(m, 1)+r(m, 2)+r(m, 3)+\\cdots+r(m, 10)=4$ is $\\qquad$.",
... | {
"ground_truth": "120",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "By finding a certain sixth-degree polynomial \\( x^{6} + a_{1} x^{5} + \\ldots + a_{5} x + a_{6} \\) with integer coefficients, one of whose roots is \\( \\sqrt{2} + \\sqrt[3]{5} \\), write the sum of its coefficients \\( a_{1} + a_{2} + \\ldots + a_{6} \\) in the answer.",
"role": "user"
}
... | {
"ground_truth": "-47",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( x, y, z, w \\) be four consecutive vertices of a regular \\( A \\)-gon. If the length of the line segment \\( xy \\) is 2 and the area of the quadrilateral \\( xyzw \\) is \\( a + \\sqrt{b} \\), find the value of \\( B = 2^a \\cdot 3^b \\).",
"role": "user"
}
] | {
"ground_truth": "108",
"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\nIn a class of 28 students, the teacher selects four people at random to participate in a geography contest. What is the probability that this group of four students i... | {
"ground_truth": "11",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's construct the projections of a cylinder, which is tangent to two given planes and the first trace (circle) of the projection axis. (How many solutions are possible?)",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.3125
} | 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 \\) satisfying \\( k(ab + bc + ca) > 5(a^2 + b^2 + c^2) \\), there exists a triangle with side lengths \\( a, b, c \\).",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "100. There are 5 different lines on a plane, these 5 lines form $n$ intersection points, then $n$ has $\\qquad$ different values.",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A cup is filled with a salt solution at a concentration of 15%. There are three iron balls in large, medium, and small sizes, with their volume ratio being 10:5:3. First, the small ball is placed into the cup of salt solution, causing 10% of the salt solution to overflow. After removing the small ... | {
"ground_truth": "10 \\%",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a_{0} = 2$ , $a_{1} = 5$ , and $a_{2} = 8$ , and for $n > 2$ define $a_{n}$ recursively to be the remainder when $4(a_{n-1} + a_{n-2} + a_{n-3})$ is divided by $11$ . Find $a_{2018} \\cdot a_{2020} \\cdot a_{2022}$ .",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the $33$ rd number after the decimal point of $(\\sqrt{10} + 3)^{2001}$?",
"role": "user"
}
] | {
"ground_truth": "0",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If rose bushes are spaced about 2 feet apart, calculate the number of bushes needed to surround a circular patio whose radius is 15 feet.",
"role": "user"
}
] | {
"ground_truth": "47",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the smallest positive period of the function y = sin(x)(1 + tan(x)tan(x/2)). Express your answer in terms of pi.",
"role": "user"
}
] | {
"ground_truth": "2\\pi",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Given $x=1-\\sqrt{3}$. Then $x^{5}-2 x^{4}-2 x^{3}$ $+x^{2}-2 x-1$ is\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Authors: Dumanov I., Krotovsky R.\n\nDiscussing winter holidays in class, Sasha said: \"Now, after I flew to Addis Ababa, I have celebrated New Year's in all possible hemispheres of the Earth, except one!\"\n\nWhat is the minimum number of places where Sasha has celebrated New Year's?\n\nConsider ... | {
"ground_truth": "4",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For each positive integer $n$ , let $s(n)$ be the sum of the digits of $n$ . Find the smallest positive integer $k$ such that\n\\[s(k) = s(2k) = s(3k) = \\cdots = s(2013k) = s(2014k).\\]",
"role": "user"
}
] | {
"ground_truth": "9999",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that the range of the function $t=f(x)$ is $(0,8]$, determine the range of $y=t^{2}-10t-4$. Express your answer in interval notation.",
"role": "user"
}
] | {
"ground_truth": "(-29,-4)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three, try to find all positive integers $k$, such that for any positive numbers $a, b, c$ satisfying the inequality\n$$\nk(a b+b c+c a)>5\\left(a^{2}+b^{2}+c^{2}\\right)\n$$\n\nthere must exist a triangle with side lengths $a, b, c$.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "John has $25$ dollars and $45$ cents. He wants to buy as many notebooks as possible, where each notebook costs $2$ dollars and $35$ cents. However, for every $5$ notebooks he buys, he gets a $15$ cents discount on each notebook. How many notebooks can John buy?",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "54. There are 100 identical-looking coins. It is known that exactly 4 of them are counterfeit and weigh the same, but are lighter than the genuine ones. How can you find at least 13 genuine coins in 2 weighings using a balance scale without weights?",
"role": "user"
}
] | {
"ground_truth": "13",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the figure, ∆ABC is a right-angled triangle with ∠ACB = 90°, AC = AE, and BC = BF. Find the measure of angle ∠ECF in degrees.",
"role": "user"
}
] | {
"ground_truth": "45",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of permutations of $1, 2, 3, 4, 5, 6$ such that for each $k$ with $1$ $\\leq$ $k$ $\\leq$ $5$, at least one of the first $k$ terms of the permutation is greater than $k$.",
"role": "user"
}
] | {
"ground_truth": "461",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "34. In a triangular prism $A B C A_{1} B_{1} C_{1}{ }^{*}$, two planes are drawn: one passes through the vertices $A, B$ and $C_{1}$, and the other through the vertices $A_{1}, B_{1}$ and $C$. These planes divide the prism into four parts. The volume of the smallest of these parts is $V$. Find the... | {
"ground_truth": "12V",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\mathbf{F 1 7}$ (39-6, Bulgaria) Let $\\mathbf{N}^{*}$ be the set of all positive integers, and the function $f: \\mathbf{N}^{*} \\rightarrow \\mathbf{N}^{*}$ satisfies: for any $s$ and $t$ in $\\mathbf{N}^{*}$, we have\n$$\nf\\left(t^{2} f(s)\\right)=s(f(t))^{2},\n$$\n\nDetermine the smallest p... | {
"ground_truth": "120",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Car A and Car B start simultaneously from locations A and B, respectively, and they travel between these two locations at constant speeds. After the first time they meet, Car A takes 4 hours to reach B, while Car B takes 1 hour to reach A. How many hours have both cars traveled by the 15th time th... | {
"ground_truth": "86",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If \\(x\\) is real, compute the maximum integer value of\n\\[\n\\frac{4x^2 + 12x + 19}{4x^2 + 12x + 9}.\n\\]",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A person moves in the $x-y$ plane moving along points with integer co-ordinates $x$ and $y$ only. When she is at a point $(x,y)$, she takes a step based on the following rules:\n(a) if $x+y$ is even she moves to either $(x+1,y)$ or $(x+1,y+1)$;\n(b) if $x+y$ is odd she moves to either $(x,y+1)$ or... | {
"ground_truth": "462",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nLet \\( N \\) be the total number of students in the school before the New Year, among which \\( M \\) are boys, making up \\( k \\) percent of the total. This means \\( M = \\frac{k}{100} N \\), or \\( 100M = kN \\).\n\nAfter the New Year, the number of boys became \\( M+1 \\), and the total nu... | {
"ground_truth": "197",
"mean_reward": 0.328125
} | 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 maximum degree of a polynomial of the form $\\sum_{i=0}^n a_i x^{n-i}$ with $a_i = \\pm 1$ for $0 \\leq i \\leq n, 1 \\leq n$, such that all the zeros are... | {
"ground_truth": "2",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many roots does the equation $\\sin x = \\frac{x}{100}$ have?",
"role": "user"
}
] | {
"ground_truth": "63",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jin, a quiet musician from South Korea, finds peace and comfort in playing the guitar. Each day, he spends 3 hours practicing new songs and 2 hours playing his favorite tunes for relaxation. Over the weekend, Jin dedicates 5 hours each day solely to learning new techniques on the guitar. \n\nIf Ji... | {
"ground_truth": "30",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4-4. 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 8. Find the sum of the distances from point $C$ to the sides of the angle, given that one of these distances is 30 less than the other.",
"role": "user"
}... | {
"ground_truth": "34",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. 12 friends agree to go out for a meal once a week, each time evenly divided into 3 tables. Each table seats 4 people, until any two people have eaten at the same table at least once. How many weeks are needed at minimum?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An engineer arrives at the train station every day at 8 AM. At exactly 8 AM, a car arrives at the station and takes the engineer to the factory. One day, the engineer arrived at the station at 7 AM and started walking towards the car. Upon meeting the car, he got in and arrived at the factory 20 m... | {
"ground_truth": "50",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The polygon enclosed by the solid lines in the figure consists of 4 congruent squares joined edge-to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can be folded to form a cube with one face missing?",
"rol... | {
"ground_truth": "6",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A flight from Toronto to Gander takes 2 hours and 50 minutes. When the time in Toronto is 1:00 p.m., the time in Gander is 2:30 p.m. If the flight departs from Toronto at 3:00 p.m. (Toronto time), what time will the flight land in Gander (Gander time)? Express your answer in 12-hour clock format w... | {
"ground_truth": "7:20 p.m.",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 1: Two vegetable bases, A and B, supply the same type of vegetables to three farmers' markets, A, B, and C, according to the signed contracts. They are to supply 45 tons to A, 75 tons to B, and 40 tons to C. Base A can arrange 60 tons, and Base B can arrange 100 tons. The distances in kilo... | {
"ground_truth": "960",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1st Swedish 1961 Problem 3 For which n is it possible to put n identical candles in a candlestick and to light them as follows. For i = 1, 2, ... , n, exactly i candles are lit on day i and burn for exactly one hour. At the end of day n, all n candles must be burnt out. State a possible rule for d... | {
"ground_truth": "n",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Find all values of the parameter $a$ for which the system\n\n$$\n\\left\\{\\begin{array}{l}\ny=\\frac{x+1}{|x|-1} \\\\\n|x+y+a|+|x-y-a|=1\n\\end{array}\\right.\n$$\n\nhas a unique solution. In your answer, specify the smallest of all the obtained values of the parameter $a$.",
"role": "user... | {
"ground_truth": "3.5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2 In a simple graph with eight vertices, what is the maximum number of edges in a graph without a quadrilateral?\n\nThe maximum number of edges in a graph without a quadrilateral in a simple graph with eight vertices is what?",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Finitely many polygons are placed in the plane. If for any two polygons of them, there exists a line through origin $O$ that cuts them both, then these polygons are called \"properly placed\". Find the least $m \\in \\mathbb{N}$ , such that for any group of properly placed polygons, $m$ lines... | {
"ground_truth": " m = 2 ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The radius of a sphere that touches all the edges of a regular tetrahedron is 1. Find the edge length of the tetrahedron.",
"role": "user"
}
] | {
"ground_truth": "2 \\sqrt{2}",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 4 In a class of 30 students, each student has the same number of friends within the class. After the final exam, any two students' scores can be compared, with no ties. A student who scores better than the majority of their friends is called a good student. What is the maximum number of go... | {
"ground_truth": "25",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider the following molecules: $\\mathrm{Br}_{3} \\mathrm{O}_{8}, \\mathrm{~F}_{2} \\mathrm{O}, \\mathrm{H}_{2} \\mathrm{~S}_{4} \\mathrm{O}_{6}, \\mathrm{H}_{2} \\mathrm{~S}_{5} \\mathrm{O}_{6}$, and $\\mathrm{C}_{3} \\mathrm{O}_{2}$.\n\n\n\nCount the number of atoms existing in their zero oxi... | {
"ground_truth": "6",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "20. $P$ is a point inside $\\triangle ABC$, the extension of $AP$ intersects $BC$ at point $D$, the extension of $BP$ intersects $AC$ at point $E$, and the extension of $CP$ intersects $AB$ at point $F$. Let $x=\\frac{PD}{AD}, y=\\frac{PE}{BE}, z=\\frac{PF}{CF}$, then the minimum value of $58 \\ti... | {
"ground_truth": "2",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $O$ be the set of odd numbers between 0 and 100. Let $T$ be the set of subsets of $O$ of size $25$. For any finite subset of integers $S$, let $P(S)$ be the product of the elements of $S$. Define $n=\\textstyle{\\sum_{S \\in T}} P(S)$. If you divide $n$ by 17, what is the remainder?",
... | {
"ground_truth": "15",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Find the sum of all integer values of c for which the equation $15|p-1|+|3 p-| p+c||=4$ has at least one root with respect to p\n\n#",
"role": "user"
}
] | {
"ground_truth": "-15",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 6. The center of square $ABCD$ is $O$, and its area is $1989 \\mathrm{~cm}^{2} . P$ is a point inside the square, and $\\angle O P B=45^{\\circ}, P A : P B=5 : 14$. Then $P B=$ $\\qquad$ . (1989, National Junior High School League)",
"role": "user"
}
] | {
"ground_truth": "42",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Each number in the list $1,2,3,\\ldots,10$ is either colored red or blue. Numbers are colored independently, and both colors are equally probable. The expected value of the number of positive integers expressible as a sum of a red integer and a blue integer can be written as $\\frac{m}{n}$ for... | {
"ground_truth": "455",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8,9}\n\nIn triangle $A B C$, angle $A$ is equal to $\\arccos \\frac{5}{13}$, side $B C$ is equal to 12. On the extension of $C B$ beyond point $C$, a point $M$ is taken such that $C M=6$. Find the radius of the circle passing through vertex $A$, tangent to line $B C$ at point $M$, and tangent to t... | {
"ground_truth": "6",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the number of ways to serve $n$ foods in the cafeteria, knowing that apples are taken in groups of 3, yogurts come in pairs, and one is allowed at most 2 pieces of bread and one bowl of cereal due to a change in provider.",
"role": "user"
}
] | {
"ground_truth": "n+1",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sandy is updating her backyard playhouse. She wants to replace siding on one exterior wall measuring 10 feet wide by 8 feet high and on two inclined roof sections, each inclined at a 30-degree angle with a base of 10 feet and an average height of 7 feet. The siding is only available in 10-foot by ... | {
"ground_truth": "\\$90",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a 14 team baseball league, each team played each of the other teams 10 times. At the end of the season, the number of games won by each team differed from those won by the team that immediately followed it by the same amount. Determine the greatest number of games the last place team could have... | {
"ground_truth": "52",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of $453_6$, $436_6$, and $42_6$ in base 6.",
"role": "user"
}
] | {
"ground_truth": "1415_6",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.35 Find the largest positive integer $n$, such that there exists a unique integer $k$ satisfying\n$$\\frac{8}{15}<\\frac{n}{n+k}<\\frac{7}{13}$$",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Points \\(A, A_1, B, B_1, C,\\) and \\(C_1\\) are located on a sphere of radius 11. Lines \\(AA_1, BB_1,\\) and \\(CC_1\\) are pairwise perpendicular and intersect at point \\(M\\), which is at a distance of \\(\\sqrt{59}\\) from the center of the sphere. Find the length of \\(AA_1\\), given that ... | {
"ground_truth": "20",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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