prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "$$\n\\begin{array}{l}\n\\text { Find } \\angle A+\\angle B \\\\\n+\\angle C+\\angle D \\\\\n+\\angle E+\\angle F \\\\\n=\n\\end{array}\n$$",
"role": "user"
}
] | {
"ground_truth": "360^\\circ",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Xiaojun's mother sells fish at the market. By the end, there are still 5 fish left in the basin. One large fish can be sold for 10 yuan, one medium fish for 5 yuan, and the other 3 small fish can each be sold for 3 yuan. Later, a customer bought the fish, and the amount this customer should pay... | {
"ground_truth": "15",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An ambitious young woman named Aisha grew up in the small town of Allipur and recently moved to a large city to attend university. In Allipur, Aisha used to walk 2 kilometers to her local library every week. Now, in the city, the university library is 5 kilometers from her apartment, but she can u... | {
"ground_truth": "64",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sandy's daughter has a playhouse in the backyard, which includes one shaded exterior wall and two identical sloped roof faces. The exterior wall is 10 feet wide and 7 feet high, and each of the roof sections is 10 feet wide and 6 feet high at the peak. The special siding used to cover these areas ... | {
"ground_truth": "\\$70",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The line \\(y = c - x\\) with \\(0 < c < 6\\) intersects the \\(y\\)-axis at point \\(P\\) and the line \\(x = 6\\) at point \\(S\\). If the ratio of the area of triangle \\(QRS\\) to the area of triangle \\(QOP\\) is 4:16, what is the value of \\(c\\)? Express the answer as a decimal to the neare... | {
"ground_truth": "4.0",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "299. When dividing the polynomial $x^{1051}-1$ by $x^{4}+x^{3}+2 x^{2}+x+1$, a quotient and a remainder are obtained. Find the coefficient of $x^{14}$ in the quotient.",
"role": "user"
}
] | {
"ground_truth": "-1",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. How many five-digit numbers of the form $\\overline{37 a b c}$ are there such that each of the numbers $\\overline{37 a b c}, \\overline{37 b c a}$, and $\\overline{37 c a b}$ is divisible by 37?",
"role": "user"
}
] | {
"ground_truth": "28",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The 26 letters of the alphabet are written in order, clockwise around a circle. A message is encrypted by replacing each letter with the letter that is 4 positions clockwise from the original letter. What is the ciphertext of the message \"WIN\"? Express your answer as a sequence of letters.",
... | {
"ground_truth": "AMR",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the last non-zero digit of \\(50! = 1 \\times 2 \\times \\cdots \\times 50\\).",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$7 \\cdot 32$ Find the smallest natural number $n$, such that every convex 100-gon can be represented as the intersection of $n$ triangles.",
"role": "user"
}
] | {
"ground_truth": "50",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": " $\\textbf{Problem C.1}$ There are two piles of coins, each containing $2010$ pieces. Two players $A$ and $B$ play a game taking turns ( $A$ plays first). At each turn, the player on play has to take one or more coins from one pile or exactly one coin from each pile. Whoever takes the last ... | {
"ground_truth": " B ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a motivated software engineer who is knowledgeable in mobile application development languages like Swift for iOS and Kotlin for Android. Alex is working on a new mobile app project that requires developing both iOS and Android versions. For the iOS version, Alex estimates it will take 120... | {
"ground_truth": "47",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From the set of three-digit numbers that do not contain the digits $0,1,2,3,4,5$, several numbers were written down in such a way that no two numbers could be obtained from each other by swapping two adjacent digits. What is the maximum number of such numbers that could have been written?",
"r... | {
"ground_truth": "40",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On the board, the number \\( x = 9999 \\) is written in a numeral system with an even base \\( r \\). Vasya found out that the \\( r \\)-ary representation of \\( x^2 \\) is an eight-digit palindrome, in which the sum of the second and third digits is 24. (A palindrome is a number that reads the s... | {
"ground_truth": "r = 26",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A hotel has three types of rooms: a triple room, a double room, and a single room, each type having one room available. Three adults and two children come to stay, and the children cannot stay in a room by themselves (they must be accompanied by an adult). Find the total number of different ways t... | {
"ground_truth": "27",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 40. Find the best positive real constant $k$ such that the following inequality holds for all positive real numbers $a, b$ and $c$\n$$\\frac{(a+b)(b+c)(c+a)}{a b c}+\\frac{k(a b+b c+c a)}{a^{2}+b^{2}+c^{2}} \\geq 8+k$$",
"role": "user"
}
] | {
"ground_truth": "4 \\sqrt{2}",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( g(n) \\) denote the sum of all the positive divisors of the integer \\( n \\) including twice the greatest prime divisor of \\( n \\). How many integers \\( j \\) exist such that \\( 1 \\leq j \\leq 5000 \\) and \\( g(j) = j + 2\\sqrt{j} + 1 \\)?",
"role": "user"
}
] | {
"ground_truth": "19",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A grocer decides to create a larger display for a special event, stacking oranges in a pyramid-like structure whose new rectangular base measures $7$ oranges by $10$ oranges. Each layer above the first still follows the rule that each orange rests in a pocket formed by four below, reducing by one ... | {
"ground_truth": "227",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When a function $f(x)$ is differentiated $n$ times ,the function we get id denoted $f^n(x)$ .If $f(x)=\\dfrac {e^x}{x}$ .Find the value of\n\\[\\lim_{n \\to \\infty} \\dfrac {f^ {2n}(1)}{(2n)!}\\]",
"role": "user"
}
] | {
"ground_truth": " 1 ",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For how many integers n, where 0 <= n < 2013, is the polynomial n^4 + 2n^3 - 20n^2 + 2n - 21 congruent to 0 modulo 2013? Provide your answer as a single integer representing the count of integers n.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 6. On the board, there are five \"equations\" of the form $x^{2}+\\ldots x+\\ldots=0$. Two players take turns filling in the dots with natural numbers from 1 to 10, with each number being used only once. The game ends when all numbers are filled in. The player who makes the first move want... | {
"ground_truth": "3",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example $\\mathbf{5}$ Three $12 \\times 12$ squares are each divided into two pieces, $A$ and $B$, by a line connecting the midpoints of two adjacent sides, as shown in Figure 5. These six pieces are then attached to the outside of a regular hexagon and folded into a polyhedron. Find the volume of... | {
"ground_truth": "864",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of 9-digit numbers in which each digit from 1 to 9 occurs exactly once, the digits 1, 2, 3, 4, 5 are in ascending order, and the digit 6 is placed before the digit 1 (for example, 916238457).",
"role": "user"
}
] | {
"ground_truth": "504",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. Let $a=\\lg z+\\lg \\left[x(y z)^{-1}+1\\right], b=\\lg x^{-1}+\\lg (x y z+1), c=\\lg y+\\lg \\left[(x y z)^{-1}+1\\right]$, and let the maximum of $a, b, c$ be $M$. Then the minimum value of $M$ is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "\\lg2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $ABC$ be a triangle, and $K$ and $L$ be points on $AB$ such that $\\angle ACK = \\angle KCL = \\angle LCB$ . Let $M$ be a point in $BC$ such that $\\angle MKC = \\angle BKM$ . If $ML$ is the angle bisector of $\\angle KMB$ , find $\\angle MLC$ .",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 3. On the ceiling of a room, there are 15 lamps, numbered from 1 to 15. Initially, all the lamps are off. In another room, there are 15 switches: one switch for lamp 1 and 2, one switch for lamp 2 and 3, one switch for lamp 3 and 4, and so on, up to a switch for lamp 15 and 1. When the switch... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. [4] You start with a number. Every second, you can add or subtract any number of the form $n$ ! to your current number to get a new number. In how many ways can you get from 0 to 100 in 4 seconds? ( $n!$ is defined as $n \\times(n-1) \\times(n-2) \\times \\cdots \\times 2 \\times 1$, so $1!=1,2... | {
"ground_truth": "36",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a transaction, a store sells two types of goods, each priced at 960 yuan. If calculated based on cost, one type of goods makes a 20% profit, while the other incurs a 20% loss. Calculate the overall profit or loss in yuan.",
"role": "user"
}
] | {
"ground_truth": "-80",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In how many ways can 3 bottles of ketchup and 7 bottles of mustard be arranged in a row so that no bottle of ketchup is immediately between two bottles of mustard? (The bottles of ketchup are mutually indistinguishable, as are the bottles of mustard.)",
"role": "user"
}
] | {
"ground_truth": "22",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. The equation about $x$\n$$\n\\frac{x-a}{b c}+\\frac{x-b}{a c}+\\frac{x-c}{a b}=2\\left(\\frac{1}{a}+\\frac{1}{b}+\\frac{1}{c}\\right) \\text {, }\n$$\n\nwhere $a+b+c \\neq 0$, the solution of the equation is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "x=a+b+c",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The base of isosceles $\\triangle XYZ$ is 30 units and its area is 60 square units.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{241}",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Given that the three sides of $\\triangle A B C$ are $10$, $12$, and $14$, respectively, and that $\\triangle A B C$ is folded into a tetrahedron along its three midlines. Then the diameter of the circumscribed sphere of the tetrahedron is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{55}",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that \\(b\\) and \\(c\\) are both integers and \\(c < 2000\\). If the quadratic equation \\(x^{2} - bx + c = 0\\) has roots whose real parts are both greater than 1, how many pairs \\((b, c)\\) satisfy this condition?",
"role": "user"
}
] | {
"ground_truth": "1995003",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 15. Three $12 \\mathrm{~cm} \\times 12 \\mathrm{~cm}$ squares are each divided into two pieces, $A$ and $B$, by a line connecting the midpoints of two adjacent sides, as shown in the first figure. The six pieces are then attached to the outside of a regular hexagon, as shown in the second... | {
"ground_truth": "864",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nProblem 3. Let $A$ be a set with 8 elements. Find the maximal number of 3 -element subsets of $A$, such that the intersection of any two of them is not a 2-element set.\n",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "97. Write 100 consecutive integers starting from 1, and write $\\qquad$ number 1.",
"role": "user"
}
] | {
"ground_truth": "21",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In space, there are $n(n \\geqslant 3)$ planes, among which any three planes do not have a common perpendicular plane. There are the following four conclusions:\n(1) No two planes are parallel to each other;\n(2) No three planes intersect in a single line;\n(3) Any two lines of intersection bet... | {
"ground_truth": "4",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The score of a math test for a class of students, denoted as ξ (full marks: 100 points), follows a normal distribution: ξ ~ N(85, σ^2), and P(83 < ξ < 87) = 0.3, P(78 < ξ < 83) = 0.13. Calculate the probability P(ξ < 78). Express your answer as a decimal value between 0 and 1, rounded to 2 decimal... | {
"ground_truth": "0.22",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "104. The centers of three spheres, with radii of 3, 4, and 6, are located at the vertices of an equilateral triangle with a side length of 11. How many planes exist that are tangent to all three spheres simultaneously?",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Solve the rebus UHA = LCM(UX, UA, HA). Here U, X, A are three different digits. Two-digit and three-digit numbers cannot start with zero. Recall that the LCM of several natural numbers is the smallest natural number that is divisible by each of them.",
"role": "user"
}
] | {
"ground_truth": "150",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the largest number $N$ for which there exist $N$ consecutive positive integers such that the sum of the digits in the $k$ -th integer is divisible by $k$ for $1 \\le k \\le N$ ?\t\n\n(S Tokarev)",
"role": "user"
}
] | {
"ground_truth": " N = 21 ",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A $5 \\times 5$ square is to be cut into rectangles of two types: $1 \\times 4$ and $1 \\times 3$. How many rectangles can be obtained after the cutting? Justify your answer.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Light travel from water n=1.33 to diamond n=2.42. If the angle of incidence was 13 degree, determine the angle of refraction.",
"role": "user"
}
] | {
"ground_truth": "7.1",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find a constant $k$ such that for any chord $\\overline{AB}$ of the circle $x^2 + y^2 = 1$ passing through the point $P = (0, \\frac{1}{2})$, the value\n\\[ k = \\frac{1}{PA} + \\frac{1}{PB} \\]\nremains constant.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "30. [17] Find the number of unordered pairs $\\{a, b\\}$, where $a, b \\in\\{0,1,2, \\ldots, 108\\}$ such that 109 divides $a^{3}+b^{3}-a b$.",
"role": "user"
}
] | {
"ground_truth": "54",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\triangle ABC$ be an isosceles triangle with $\\angle A = 90^\\circ.$ There exists a point $P$ inside $\\triangle ABC$ such that $\\angle PAB = \\angle PBC = \\angle PCA$ and $AP = 10.$ Find the area of $\\triangle ABC.$",
"role": "user"
}
] | {
"ground_truth": "250",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "59. Petya and Vasya calculated that if they walk to the neighboring village, which is four kilometers away from them, at a speed of 4 km per hour, they will be 10 minutes late for the football match being held there for the district championship. How should they act to arrive at the match simultan... | {
"ground_truth": "10",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Solve for $x$: $0.05x + 0.07(30 + x) = 15.4$.",
"role": "user"
}
] | {
"ground_truth": "110.8333",
"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 as a whole number.",
"role": "user"
}
] | {
"ground_truth": "540",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Human explorers discover a solar system with 15 planets, 7 of which are Earth-like, and 8 are Mars-like. Each Earth-like planet requires 2 units of colonization effort, while each Mars-like planet requires only 1 unit. If the expedition has a total of 16 units of colonization effort available, how... | {
"ground_truth": "1141",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 4. A set of at least three positive integers is called uniform if removing any of its elements the remaining set can be disjoint into two subsets with equal sums of elements. Find the minimal cardinality of a uniform set.\n\nPeter Boyvalenkov, Emil Kolev",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the smallest natural $ k $ such that among any $ k $ distinct and pairwise coprime naturals smaller than $ 2018, $ a prime can be found.\n\n\n[i]Vlad Robu[/i]",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 22 black and 3 blue balls in a bag. Ahmet chooses an integer $ n$ in between 1 and 25. Betül draws $ n$ balls from the bag one by one such that no ball is put back to the bag after it is drawn. If exactly 2 of the $ n$ balls are blue and the second blue ball is drawn at $ n^{th}$ ... | {
"ground_truth": "13",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. At the parade of the royal musketeers, seeing that they could not be arranged in rows of 11 musketeers, D'Artagnan decided to arrange the musketeers in rows of 10 musketeers, but it turned out that there was one empty place in the last row. Then he tried to arrange them in rows of 9, 8, 7, 6, 5... | {
"ground_truth": "5039",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. $(\\mathbf{C H N} 3)^{\\mathrm{IMO}}$ Given nine points in space, no four of which are coplanar, find the minimal natural number $n$ such that for any coloring with red or blue of $n$ edges drawn between these nine points there always exists a triangle having all edges of the same color.",
... | {
"ground_truth": "33",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose there are 8,000 hours in a year (actually there are 8,760) and that an individual has a potential market wage of $5 per hour. Suppose a rich uncle dies and leaves the individual an annual income of $4,000 per year. If he or she devotes 75 percent of full income to leisure, how many hours w... | {
"ground_truth": "1400",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The function \\(g(x)\\) satisfies\n\\[xg(y) = 2yg(x)\\] for all real numbers \\(x\\) and \\(y.\\) If \\(g(10) = 15,\\) find \\(g(2).\\)",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A permutation of the set $\\{1, \\ldots, 2021\\}$ is a sequence $\\sigma=\\left(\\sigma_{1}, \\ldots, \\sigma_{2021}\\right)$ such that each element of the set $\\{1, \\ldots, 2021\\}$ is equal to exactly one term $\\sigma_{i}$. We define the weight of such a permutation $\\sigma$ as the sum\n\n$$... | {
"ground_truth": "2042219",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Billy and Bobby are located at points $A$ and $B$, respectively. They each walk directly toward the other point at a constant rate; once the opposite point is reached, they immediately turn around and walk back at the same rate. The first time they meet, they are located 3 units from point $A$; th... | {
"ground_truth": "15",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14. A construction company\n\nhas contracted two projects, each to be constructed by two different teams. According to the progress of the projects, the construction company can adjust the number of people in the two teams at any time. If 70 people are transferred from Team A to Team B, then the n... | {
"ground_truth": "130",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For any 2016 complex numbers \\( z_1, z_2, \\ldots, z_{2016} \\), it holds that\n\\[ \n\\sum_{k=1}^{2016} |z_k|^2 \\geq \\lambda \\min_{1 \\leq k \\leq 2016} \\{ |z_{k+1} - z_k|^2 \\}, \n\\]\nwhere \\( z_{2017} = z_1 \\). Find the maximum value of \\( \\lambda \\).",
"role": "user"
}
] | {
"ground_truth": "504",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Will claims to have a polynomial with integer coefficients in mind. Starting at minute 1, Lucas asks for \\(f(i)\\). If Will is honest he gives \\(f(i)\\); if he is lying he picks a random integer from \\([1,(i+1)!]\\). Lucas can immediately detect any inconsistency. Assuming Will is lying, let th... | {
"ground_truth": "289",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the height of Camille’s model water tower, given that the real water tower is 50 meters high and can contain 200,000 liters of water, while her model's version contains only 0.05 liters of water.",
"role": "user"
}
] | {
"ground_truth": "0.315",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Subject II. (30 points)\n\nIn triangle $\\triangle A B C$, the angle bisector $[A E, \\mathrm{E} \\in(B C)$ intersects the median $[B F], \\mathrm{F} \\in(A C)$, at point G.\n\na) Determine $a \\in \\mathrm{N}$, such that $\\frac{B G}{G F} \\cdot \\frac{C E}{B E}=2^{a}$.\n\nb) If triangles $\\t... | {
"ground_truth": "1,",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five, (15 points) Find the smallest positive integer $n$ such that $2^{2005}$ । $\\left(161^{n}-1\\right)$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly. \n\n---\n\nFive, (15 points) Find the smallest... | {
"ground_truth": "2^{2000}",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangular prism has a volume of 720 cubic units, where $a, b,$ and $c$ are integers and $1 < c < b < a$. Find the maximum possible value of $b$ if $c=3$, while ensuring $a$, $b$, and $c$ are distinct prime factors.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given constants $\\lambda \\neq 0$, $n$, and $m$ as positive integers with $m > n$ and $m \\neq 2n$, the function $f(x)$ defined by the equation\n$$\nf(x+\\lambda)+f(x-\\lambda)=2 \\cos \\frac{2n\\pi}{m} f(x)\n$$\nis a periodic function with period $m\\lambda$.",
"role": "user"
}
] | {
"ground_truth": "m\\lambda",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B3. Twelve balls are numbered with the numbers $1,2,3, \\ldots, 12$. Each ball is painted either red or green such that the following conditions are met:\n\n(a) if the balls labeled with different numbers $a$ and $b$ are painted red and $a+b<13$, then the ball labeled with the number $a+b$ is also... | {
"ground_truth": "6",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "18. The diagram shows a semicircle with diameter $P Q$ inscribed in a rhombus $A B C D$. The rhombus is tangent to the arc of the semicircle in two places. Points $P$ and $Q$ lie on sides $B C$ and $C D$ of the rhombus respectively. The line of symmetry of the semicircle is coincident with the dia... | {
"ground_truth": "603",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex, a non-religious skeptic living in Kansas, loves to explore unusual facts about the state. Recently, Alex discovered that Kansas has a curious number of counties: 105. Wanting to dig deeper into the state's history, Alex decides to visit 3 counties each weekend. If Alex also plans to take a 2... | {
"ground_truth": "37",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Is $ \\sqrt{2} $ the limit of a sequence of numbers of the form $ \\sqrt[3]{n} - \\sqrt[3]{m} $ , where $ n, m = 0, 1, 2, \\cdots $ .",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## 162. Math Puzzle $11 / 78$\n\nAssume that a fly lays 120 eggs at the beginning of summer, on June 21st, and after 20 days, fully developed insects emerge from these eggs, each of which then lays 120 eggs. How many \"descendants\" would this fly have in total by the beginning of autumn?",
"r... | {
"ground_truth": "209102520",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mekkora $B$ betétet kell öt éven át minden év elején a bankban elhelyeznünk, hogy évi $20 \\%$-os kamat mellett az ötödik év végén ugyanakkora legyen a követelésünk, mintha az első év elején egyszerre $100000 \\mathrm{Ft}$-ot tettünk volna a bankba?\n\nWhat amount $B$ must we deposit at the beginn... | {
"ground_truth": "27864.98",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A king has eight sons, and they are all fools. Each night, the king sends three of them to guard the golden apples from the Firebird. The princes cannot catch the Firebird and blame each other, so no two of them agree to go on guard together a second time. What is the maximum number of nights this... | {
"ground_truth": "8",
"mean_reward": 0.203125
} | 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\nConvert the point $\\left( 6 \\sqrt{3}, \\frac{5 \\pi}{3}, -2 \\right)$ in cylindrical coordinates to rectangular coordinates.\n\n[Solution]\n\n<paragraph_0>\nTo conv... | {
"ground_truth": "-1",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$:$ Folkiore\n\nIt is known that among 63 coins there are 7 counterfeit ones. All counterfeit coins weigh the same, all genuine coins also weigh the same, and a counterfeit coin is lighter than a genuine one. How can you determine 7 genuine coins in three weighings using a balance scale without we... | {
"ground_truth": "7",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the greatest number of positive integers lesser than or equal to 2016 we can choose such that it doesn't have two of them differing by 1,2, or 6?",
"role": "user"
}
] | {
"ground_truth": "576",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nLet $a,$ $b,$ and $c$ be real numbers such that $a^2 + b^2 + c^2 = 1.$ Find the minimum value of\n\\[ab + ac + bc.\\]\n\n[Solution]\n\n<paragraph_0>\nTo find the min... | {
"ground_truth": "3",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In Yang's number theory class, Michael K, Michael M, and Michael R take a series of tests. Afterwards, Yang makes the following observations about the test scores:\n\n(a) Michael K had an average test score of $90$ , Michael M had an average test score of $91$ , and Michael R had an average test... | {
"ground_truth": "413",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Julia invested a certain amount of money in two types of assets: real estate and mutual funds. The total amount she invested was $\\$200,000$. If she invested 6 times as much in real estate as she did in mutual funds, what was her total investment in real estate?",
"role": "user"
}
] | {
"ground_truth": "171,428.58",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Convert the binary number (1101)_2 into a decimal number using the method of multiplying each digit by 2^(n-1) and summing the results. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "= 13",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Elmo makes $N$ sandwiches for a school event. For each sandwich, he uses $B$ dollops of peanut butter at $3$ cents each and $J$ spoonfuls of jelly at $7$ cents each. The total cost for the peanut butter and jelly to make all the sandwiches is $\\$3.78$. Assume that $B$, $J$, and $N$ are positive i... | {
"ground_truth": "\\$2.94",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose there are 128 ones written on a blackboard. At each step, you can erase any two numbers \\(a\\) and \\(b\\) from the blackboard and write \\(ab + 1\\). After performing this operation 127 times, only one number is left. Let \\(A\\) be the maximum possible value of this remaining number. Fi... | {
"ground_truth": "2",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a rectangular prism \\(ABCD - A'B'C'D'\\), how many pairs of skew lines are there among the following twelve lines: \\(AB', BA', CD', DC', AD', DA', BC', CB', AC, BD, A'C', B'D'\\)? Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of real solutions of the equation\n\\[\\frac{x}{150} = \\sin x.\\]",
"role": "user"
}
] | {
"ground_truth": "95",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jamie owns a small bakery and is looking for an efficient and flexible financial service platform to manage her transactions. In one week, Jamie made 45 sales, with each sale averaging $12. She found a platform that charges a fixed monthly fee of $30 and an additional fee of $0.50 per transaction.... | {
"ground_truth": "30.00",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A social justice advocate from another state is organizing online campaigns to raise awareness about a discriminatory ordinance. They manage to recruit 8 volunteers, each of whom reaches out to 50 people every week. If each of these people shares the campaign with 5 additional people, how many peo... | {
"ground_truth": "9600",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nFind all integers $\\,a,b,c\\,$ with $\\,1<a<b<c\\,$ such that \\[ (a-1)(b-1)(c-1) \\] is a divisor of $abc-1.$\n\n[Solution]\n\n<paragraph_0>\nTo find all integers ... | {
"ground_truth": "1",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A ball with diameter 4 inches starts at point A to roll along the track shown. The track is comprised of 3 semicircular arcs whose radii are $R_1 = 100$ inches, $R_2 = 60$ inches, and $R_3 = 80$ inches, respectively. The ball always remains in contact with the track and does not slip. What is the ... | {
"ground_truth": "238\\pi",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "【Question 6】\nA bottle contains 1001 blue balls, 1000 red balls, and 1000 green balls. At the same time, Xiaoming has enough balls of these three colors in his hand. Next, Xiaoming takes out two balls from the bottle each time, and then puts one or two balls back into the bottle according to the f... | {
"ground_truth": "red",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We have a homogeneous material, square-shaped, thin plate with a side length of $20 \\mathrm{~cm}$. Find a point on its perimeter such that when the plate is suspended from this point, the nearest corner will be the highest relative to the suspension point. Determine the distance between the suspe... | {
"ground_truth": "5.47",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7.5 There are 100 points distributed on a straight line. We mark the midpoints of all possible line segments with these points as endpoints. How many such midpoints can we get at least?\n\nWill the above text be translated into English, please keep the original text's line breaks and format, and o... | {
"ground_truth": "197",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 4. Let $n$ be a non-zero natural number; consider the set $M=\\{1,2, \\ldots, 2 n+1\\}$.\n\nDetermine in how many ways the set $M$ can be partitioned into three non-empty subsets $A, B, C$ $(A \\cup B \\cup C=M, A \\cap B=B \\cap C=C \\cap A=\\emptyset)$ such that the following conditions ... | {
"ground_truth": "n",
"mean_reward": 0.203125
} | 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 $P_1,P_2,\\dots,P_n$ be $n$ distinct points over a line in the plane ($n\\geq2$). Consider all the circumferences with diameters $P_iP_j$ ($1\\leq{i,j}\\leq{n}$) ... | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Professor Smith is an English literature professor who recently came across a collection of Islamic poetry while researching for her next lecture. She decides to include a few poems in her syllabus and plans to allocate a certain number of days for her students to study them. Professor Smith has 4... | {
"ground_truth": "Sunday",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the least positive integer \\( n \\) such that\n$$ \\frac{1}{\\sin 15^\\circ \\sin 16^\\circ} + \\frac{1}{\\sin 17^\\circ \\sin 18^\\circ} + \\cdots + \\frac{1}{\\sin 173^\\circ \\sin 174^\\circ} = \\frac{1}{\\sin n^\\circ}. $$",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nIn a football tournament, each team is supposed to play one match against each of the other teams. However, during the tournament, half of the teams were disqualified and did not participate further. As a result, a total of 77 matches were played, and the disqualified teams managed to play all t... | {
"ground_truth": "14",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sides of the base of a brick are 28 cm and 9 cm, and its height is 6 cm. A snail crawls rectilinearly along the faces of the brick from one vertex of the lower base to the opposite vertex of the upper base. The horizontal and vertical components of its speed $v_{x}$ and $v_{y}$ are related by ... | {
"ground_truth": "35",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Let $\\mathrm{K}=6$. This number has 4 divisors, so $\\mathrm{L}=4$. The number 4 has 3 divisors, which is exactly equal to $\\frac{K}{2}$. This also works.\n\nThus, there are two possibilities: $K=4, L=3$, and $K=6, L=4$. In the first case, the sum $K+2L$ is 10, and in the second case, it is 1... | {
"ground_truth": "4",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A *quadratic* number is a real root of the equations $ax^2 + bx + c = 0$ where $|a|,|b|,|c|\\in\\{1,2,\\ldots,10\\}$ . Find the smallest positive integer $n$ for which at least one of the intervals $$ \\left(n-\\dfrac{1}{3}, n\\right)\\quad \\text{and}\\quad\\left(n, n+\\dfrac{1}{3}\\right) ... | {
"ground_truth": "11",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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