prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "The diagram shows three rectangles and three straight lines. What is the value of \\( p + q + r \\) in degrees?",
"role": "user"
}
] | {
"ground_truth": "180",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\{a_k\\}_{k=1}^{2011}$ be the sequence of real numbers defined by $a_1=0.201,$ $a_2=(0.2011)^{a_1},$ $a_3=(0.20101)^{a_2},$ $a_4=(0.201011)^{a_3}$, and in general,\n\\[a_k=\\begin{cases}(0.\\underbrace{20101\\cdots 0101}_{k+2\\text{ digits}})^{a_{k-1}}\\qquad\\text{if }k\\text{ is odd,}\\\\(... | {
"ground_truth": "1341",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. A rectangle is divided into four smaller rectangles by two straight lines. The areas of three of these rectangles are 20 mu, 25 mu, and 30 mu. What is the area of the other rectangle in mu?",
"role": "user"
}
] | {
"ground_truth": "37.5",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose we have $10$ balls and $10$ colors. For each ball, we (independently) color it one of the $10$ colors, then group the balls together by color at the end. If $S$ is the expected value of the square of the number of distinct colors used on the balls, find the sum of the digits of $S... | {
"ground_truth": "55",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose a stock has the following information. It is listed on the London stock exchange and operates throughout Europe. The yield on a UK 10 year treasury is 2.8%. The stock in question will earn 8.6% as per historical data. The Beta for the stock is 1.4, i.e., it is 140% volatile to the changes ... | {
"ground_truth": "10.92",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In the coordinate plane $x O y$, an integer coordinate grid is drawn. The segment ( $p$ ) in this plane is defined by\n\n$$\n(p) \\quad 7 x-3 y-5=0, \\quad 0 \\leq x \\leq 100\n$$\n\nDetermine the number of squares of this grid that contain points of the segment ( p).",
"role": "user"
}
] | {
"ground_truth": "301",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct sequences of four letters can be made from the letters in FREEDOM if each letter can be used only once and each sequence must begin with F and not end with M?",
"role": "user"
}
] | {
"ground_truth": "48",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When three planes divide the space into 7 parts, how many intersection lines are formed? Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.3125
} | 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\nAn arrangement of chips in the squares of $ n\\times n$ table is called [i]sparse[/i] if every $ 2\\times 2$ square contains at most 3 chips. Serge put chips in some ... | {
"ground_truth": "3",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 5 distinct lines on a plane, and these 5 lines form \\( n \\) intersections. How many different values can \\( n \\) have?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An elderly local historian from Zavidovići is creating a timeline of significant events in the town's history. They plan to display this timeline in the local museum. The timeline consists of 5 panels. Each panel can display 12 events. The historian has already gathered information about 38 histor... | {
"ground_truth": "0",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Leon has cards with digits from 1 to 7. How many ways are there to glue two three-digit numbers (one card will not be used) so that their product is divisible by 81, and their sum is divisible by 9?",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "First, select $n$ numbers from the set $ \\{1, 2, \\cdots, 2020\\} $. Then, from these $n$ numbers, choose any two numbers $a$ and $b$, such that $a$ does not divide $b$. Find the maximum value of $n$.",
"role": "user"
}
] | {
"ground_truth": "1010",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. In a commercial football tournament, five teams participated. Each was supposed to play exactly one match against each other. Due to financial difficulties, the organizers canceled some games. In the end, it turned out that all teams had scored a different number of points, and no team had a ze... | {
"ground_truth": "6",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Xiaoming has 4 identical coins, each with a head and a tail. He wants to stack the 4 coins in such a way that the heads of adjacent coins do not face each other. Find the number of different stacking methods. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 10 Let $x>y>0, xy=1$, find the minimum value of $\\frac{3x^3+125y^3}{x-y}$.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly. \n\nExample 10 Let $x>y>0, xy=1$, find the minimum value of $\\frac{3x^3... | {
"ground_truth": "25",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Each of the points $A,B,C,D,E,$ and $F$ in the figure below represents a different digit from $1$ to $6.$ Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is $47.$ What is the ... | {
"ground_truth": "5",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n87.3. Let $f$ be a strictly increasing function defined in the set of natural numbers satisfying the conditions $f(2)=a>2$ and $f(m n)=f(m) f(n)$ for all natural numbers $m$ and $n$. Determine the smallest possible value of $a$.\n",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In each cell of a table $8\\times 8$ lives a knight or a liar. By the tradition, the knights always say the truth and the liars always lie. All the inhabitants of the table say the following statement \"The number of liars in my column is (strictly) greater than the number of liars in my row\". De... | {
"ground_truth": "255",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. $1991^{2000}$ divided by $10^{6}$, the remainder is",
"role": "user"
}
] | {
"ground_truth": "880001",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. A polyhedron, except for one vertex, the sum of the angles at the vertices of each face of the other vertices is $5160^{\\circ}$, then the sum of the angles at the vertices of all faces of the polyhedron is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "5400",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Initially, a natural number $n$ is written on the blackboard. Then, at each minute, [i]Neymar[/i] chooses a divisor $d>1$ of $n$, erases $n$, and writes $n+d$. If the initial number on the board is $2022$, what is the largest composite number that [i]Neymar[/i] will never be able to write on the b... | {
"ground_truth": " 2033 ",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 1000 rooms in a row along a long corridor. Initially, the first room contains 1000 people, and the remaining rooms are empty. Each minute, the following happens: for each room containing more than one person, someone in that room decides it is too crowded and moves to the next room. All ... | {
"ground_truth": "61",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "350. Among 18 coins, one is counterfeit. Genuine coins weigh the same, while the counterfeit coin differs in weight from the genuine ones. What is the minimum number of weighings on correct balance scales without weights needed to determine whether the counterfeit coin is lighter or heavier than t... | {
"ground_truth": "2",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If the sets of real numbers\n$$\nA=\\{2x, 3y\\} \\text{ and } B=\\{6, xy\\}\n$$\nhave exactly one common element, then the product of all elements in $A \\cup B$ is ____.",
"role": "user"
}
] | {
"ground_truth": "0",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $N=10^6$. For which integer $a$ with $0 \\leq a \\leq N-1$ is the value of \\[\\binom{N}{a+1}-\\binom{N}{a}\\] maximized?\n\n[i]Proposed by Lewis Chen[/i]",
"role": "user"
}
] | {
"ground_truth": "499499",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Use the Trapezoidal Rule with to approximate $\\int_0^{\\pi} sin^2(x)dx$. Return the approximated demical value.",
"role": "user"
}
] | {
"ground_truth": "1.570796",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Fifteen students numbered $1, 2, 3, \\ldots, 15$ stand in a circle facing inward. On the first turn, the student with number 1 turns around to face outward. On the second turn, the students numbered 2 and 3 turn around. On the third turn, the students numbered $4, 5, 6$ turn around, and so on. On ... | {
"ground_truth": "12",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 6 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(2005, China Western Mathematical Olympiad)",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "X rays scattered from rock salt (NaCl) are observed to have an intense maximum at an angle of 20° from the incident direction. Assuming n = 1 (from the intensity), what must be the Wavelength of the incident radiation in nm?",
"role": "user"
}
] | {
"ground_truth": "0.098",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A frog is placed at the origin on the number line, and moves according to the following rule: in a given move, the frog advances to either the closest point with a greater integer coordinate that is a multiple of 3, or to the closest point with a greater integer coordinate that is a multiple of 13... | {
"ground_truth": "169",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The graph of the function $y = g(x)$ is displayed. For all $x > 3$, $g(x) > 0.5$. If $g(x) = \\frac{x^2}{Ax^2 + Bx + C}$, where $A$, $B$, and $C$ are integers, determine $A+B+C$. The vertical asymptotes of $g$ are at $x = -3$ and $x = 2$, and the horizontal asymptote is at $y = 1/A$ with $1/A < 1$... | {
"ground_truth": "-8",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many numbers are in the list $-50, -44, -38, \\ldots, 68, 74$?",
"role": "user"
}
] | {
"ground_truth": "22",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The area of the enclosed shape formed by the line $y=0$, $x=e$, $y=2x$, and the curve $y= \\frac {2}{x}$ is $\\int_{1}^{e} \\frac{2}{x} - 2x \\,dx$.",
"role": "user"
}
] | {
"ground_truth": "e^{2}-3",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Since $a^{2} \\cos ^{4} t+1 \\geqslant 2|a| \\cos ^{2} t$ (with equality when $|a| \\cos ^{2} t=1$, if $|a| \\geqslant 1$), then\n\n$$\n\\left(\\cos ^{4} x+1\\right)\\left(4 \\cos ^{4} y+1\\right) \\geqslant 8 \\cos ^{2} x \\cos ^{2} y \\geqslant 8 \\cos ^{3} x \\cos ^{2} y\n$$\n\nTherefore, eq... | {
"ground_truth": "3\\pi/4",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[The ratio of the areas of triangles with a common base or common height] Class\n\nThe diagonals $AC$ and $BD$ of trapezoid $ABCD$ with bases $AD$ and $BC$ intersect at point $O$. It is known that $AD=2BC$ and the area of triangle $AOB$ is 4. Find the area of the trapezoid.",
"role": "user"
... | {
"ground_truth": "18",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. If the remainder of $\\underbrace{11 \\cdots 1}_{n+1 \\uparrow} 1$ divided by 3102 is 1, then the smallest positive integer $n$ is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "138",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given three non-collinear points \\( A, B, C \\) on a plane, construct a line \\( l \\) such that the ratio of the distances from points \\( A, B, C \\) to line \\( l \\) is \\( 1: 1: 2 \\) or \\( 1: 2: 1 \\) or \\( 2: 1: 1 \\). Calculate the total number of such lines. Express your answer as a wh... | {
"ground_truth": "12",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 4 people standing in a line numbered 1 through 4 in a left to right order.\nEach person has the following attributes: Food, Movie-Genre, Music-Genre, Pet, Sport.\nThe attributes have the following possible values:\n- Food: avocado, mango, pear, potato\n- Movie-Genre: disaster, sports, s... | {
"ground_truth": "sports",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Given that $n$ is a positive integer. Then\n$$\n\\lg 12 、 \\lg 75 、 \\lg \\left(n^{2}-16 n+947\\right)\n$$\n\nThese three numbers can form $\\qquad$ different triangles.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. If 6 pieces of $1 \\times 2$ paper are used to cover a $3 \\times 4$ grid, the number of different ways to cover it is.",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "39th IMO 1998 shortlist Problem N8 The sequence 0 ≤ a 0 < a 1 < a 2 < ... is such that every non-negative integer can be uniquely expressed as a i + 2a j + 4a k (where i, j, k are not necessarily distinct). Find a 1998 . Solution",
"role": "user"
}
] | {
"ground_truth": "1227096648",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10.16 There is a five-digit positive odd number $x$. In $x$, all 2s are replaced with 5s, and all 5s are replaced with 2s, while other digits remain unchanged, resulting in a new five-digit number, denoted as $y$. If $x$ and $y$ satisfy the equation $y=2(x+1)$, what is the value of $x$?\n(China Ju... | {
"ground_truth": "29995",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Square $ABCD$ is inscribed in a circle. Square $EFGH$ has vertices $E$ and $F$ on $\\overline{CD}$ and vertices $G$ and $H$ on the circle. The ratio of the area of square $EFGH$ to the area of square $ABCD$ can be expressed as $\\frac {m}{n}$ where $m$ and $n$ are relatively prime positive integer... | {
"ground_truth": "251",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. At a birthday party, 5 girls and 5 boys gathered. They were playing a game where two teams compete, with each team consisting of 2 boys and 1 girl. In how many ways could the teams be formed for the game, ensuring that the opponents are different?\n\nEach task is scored out of 10 points.\n\nThe... | {
"ground_truth": "300",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a set $T = \\{a, b, c, d, e, f\\}$, determine the number of ways to choose two subsets of $T$ such that their union is $T$ and their intersection contains exactly three elements.",
"role": "user"
}
] | {
"ground_truth": "80",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A vertical wooden pillar has a rope tied to its top. The part of the rope hanging down from the top of the pillar to the ground measures 4 feet. When pulling the rope, it runs out when 8 feet away from the base of the pillar. What is the length of the rope? Express your answer in feet as a whole n... | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We folded a rectangular piece of paper along one of its diagonals. After the fold, the four vertices ended up at the four vertices of a trapezoid, three sides of which are of equal length. What is the length of the shorter side of the original rectangle if the longer side is 12 cm?",
"role": "... | {
"ground_truth": "4\\sqrt{3}",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10.85 Let $T=\\left\\{9^{k} \\mid k\\right.$ is an integer, $\\left.0 \\leqslant k \\leqslant 4000\\right\\}$, given that $9^{4000}$ has 3817 digits, and its leftmost digit is 9, how many elements in $T$ have 9 as their leftmost digit?\n(8th American Mathematical Invitational, 1990)",
"role": ... | {
"ground_truth": "184",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In rectangle $JKLM$, $JL=2$, and $LM=4$. Points $N$, $O$, and $P$ are midpoints of $\\overline{LM}$, $\\overline{MJ}$, and $\\overline{JK}$, respectively. Point $Q$ is the midpoint of $\\overline{NP}$. Find the area of the triangle formed by points $Q$, $O$, and $P$.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Rational numbers $x, y, z$ satisfy $(|x+2|+|x-4|)(|y-2|+|y-5|)(|z-2|+|z+3|)=90$, then the maximum value of $x-2 y+3 z$ is $\\qquad$\n\nTranslate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user... | {
"ground_truth": "6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 1. The probability of event $A$ occurring in each of 484 independent trials is 0.75. Find the probability that the relative frequency of event $A$ deviates from its probability in absolute value by no more than 0.03.",
"role": "user"
}
] | {
"ground_truth": "0.872",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 There are ten birds on the ground pecking at food, and among any five birds, at least four birds are on the same circumference. Question: What is the minimum number of birds on the circumference that contains the most birds?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "59. (USS 6) On the circle with center $O$ and radius 1 the point $A_{0}$ is fixed and points $A_{1}, A_{2}, \\ldots, A_{999}, A_{1000}$ are distributed in such a way that $\\angle A_{0} O A_{k}=k$ (in radians). Cut the circle at points $A_{0}, A_{1}, \\ldots, A_{1000}$. How many arcs with differen... | {
"ground_truth": "3",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$1022 \\pi$ positive integers $a_{1}, a_{2}, \\cdots, a_{2006}$ (which can be the same) such that $\\frac{a_{1}}{a_{2}}, \\frac{a_{2}}{a_{3}}, \\cdots, \\frac{a_{2005}}{a_{2006}}$ are all distinct. How many different numbers are there at least among $a_{1}, a_{2}, \\cdots, a_{2006}$?",
"role":... | {
"ground_truth": "46",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. In a certain year, the month of August has 5 Mondays and 4 Tuesdays, then the 8th of August in that year is a\n\nKeep the original text's line breaks and format, output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "Saturday",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. (15 points) Every day, Ivan Ivanovich is taken to work by a company car. One day, Ivan Ivanovich decided to walk and left the house an hour earlier than usual. On the way, he met the company car and finished the journey in it. As a result, he arrived at work 10 minutes earlier than the usual ti... | {
"ground_truth": "55",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "27. Put 10 different balls into 8 different empty boxes, with each box containing at least 1 ball, then there are $\\qquad$ ways to do this.",
"role": "user"
}
] | {
"ground_truth": "30240000",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3-4 Find the number of permutations of the 6 characters $a, b, c, d, e, f$ that do not contain the patterns $a c e$ and $d f$.\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": "582",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. The sequence is defined by the following conditions: $x_{0}=1, x_{n+1}=\\sin \\left(\\operatorname{arctg}\\left(x_{n}\\right)\\right)$. Find $x_{99} 999999$.",
"role": "user"
}
] | {
"ground_truth": "0.0001",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7 Find the maximum number of elements in a set $S$ that satisfies the following conditions:\n(1) Each element in $S$ is a positive integer not exceeding 100;\n(2) For any two different numbers $a, b$ in $S$, there exists a number $c$ in $S$ such that the greatest common divisor (gcd) of $a... | {
"ground_truth": "72",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. On the sides $\\mathrm{AB}$ and $\\mathrm{AC}$ of the right triangle $\\mathrm{ABC}\\left(\\angle B C A=90^{\\circ}\\right)$, right triangles АВТ and АСК are constructed externally such that $\\angle A T B=\\angle A K C=90^{\\circ}$, $\\angle A B T=\\angle A C K=60^{\\circ}$. On the side $\\mat... | {
"ground_truth": "120",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a line \\( l \\) and points \\( A \\) and \\( B \\) on opposite sides of it, use a compass and straightedge to construct a point \\( M \\) such that the angle between \\( AM \\) and \\( l \\) is half the angle between \\( BM \\) and \\( l \\), provided these angles do not share common sides.... | {
"ground_truth": "M",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two squares, each with side length 5 cm, overlap as shown. The shape of their overlap is a square, which has an area of 4 cm². Find the perimeter, in centimeters, of the shaded figure. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "32",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find $x$ if $x \\cdot x! + 2x! = 40320$, where $x! = x \\cdot (x-1) \\cdot (x-2)\\cdots 2 \\cdot 1$.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is a five-digit odd positive integer \\( x \\). By changing all 2s in \\( x \\) to 5s and all 5s in \\( x \\) to 2s, while keeping all other digits unchanged, we obtain a new five-digit number \\( y \\). If \\( x \\) and \\( y \\) satisfy the equation \\( y = 2(x+1) \\), then \\( x \\) is __... | {
"ground_truth": "29995",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $x,$ $y,$ $z$ be nonnegative real numbers. Let\n\\begin{align*}\nC &= \\sqrt{x + 3} + \\sqrt{y + 6} + \\sqrt{z + 11}, \\\\\nD &= \\sqrt{x + 2} + \\sqrt{y + 2} + \\sqrt{z + 2}.\n\\end{align*}\nFind the minimum value of $C^2 - D^2.$",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sergeev I.N.\n\nAt the base $A_{1} A_{2} \\ldots A_{n}$ of the pyramid $S A_{1} A_{2} \\ldots A_{n}$ lies a point $O$, such that $S A_{1}=S A_{2}=\\ldots=S A_{n}$ and $\\angle S A_{1} O=\\angle S A_{2} O=$ $\\ldots=\\angle S A_{n} O$.\n\nFor what least value of $n$ does it follow from this that $S... | {
"ground_truth": "5",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider the sequence of numbers defined recursively by $t_1=1$ and for $n>1$ by $t_n=1+t_{n/2}$ when $n$ is even and by $t_n=\\frac{1}{t_{n-1}}$ when $n$ is odd. Given that $t_n=\\frac{19}{87}$, find $n.$",
"role": "user"
}
] | {
"ground_truth": "1905",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[\n\nA circle inscribed in a right trapezoid divides its larger lateral side into segments of 1 and 4. Find the area of the trapezoid.\n\n#",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find \\(n\\) if \\(n \\cdot n! + 2 \\cdot n! = 5040\\), where \\(n! = n \\cdot (n-1) \\cdot (n-2) \\cdots 2 \\cdot 1\\).",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 12 Let $m, n$ be positive integers, and $n>1$. Find the minimum value of $\\left|2^{m}-5^{n}\\right|$.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly. \n\n(Note: The note is for you, the assistant... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Using only pennies, nickels, dimes, quarters, and half-dollars, find the smallest number of coins Freddie would need to pay any amount of money less than a dollar.",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 4 spheres in space with radii 2, 2, 3, and 3, respectively. Each sphere is externally tangent to the other 3 spheres. Additionally, there is a small sphere that is externally tangent to all 4 of these spheres. Find the radius of the small sphere.",
"role": "user"
}
] | {
"ground_truth": "6/11",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12. The diagram shows a 16 metre by 16 metre wall. Three grey squares are painted on the wall as shown.\n\nThe two smaller grey squares are equal in size and each makes an angle of $45^{\\circ}$ with the edge of the wall. The grey squares cover a total area of $B$ metres squared.\nWhat is the valu... | {
"ground_truth": "128",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nBaron Munchausen told a story. \"There were a whole crowd of us. We reached a crossroads. Then half of our group turned left, a third turned right, and a fifth went straight.\" \"But wait, the Duke remarked, the sum of half, a third, and a fifth isn't equal to one, so you are lying!\" The Baron ... | {
"ground_truth": "37",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. 100 999 in ascending order, forming a multi-digit number:\n$$\n100101102103104 \\cdots 997998999\n$$\n\nIn this multi-digit number, any two adjacent digits are considered a pair, and there are $\\qquad$ pairs where the sum of the two\n\ndigits is a multiple of 3. (Note: 0 is not considered a mu... | {
"ground_truth": "897",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $n \\in \\mathbb{N}_{\\geq 2}.$ For any real numbers $a_1,a_2,...,a_n$ denote $S_0=1$ and for $1 \\leq k \\leq n$ denote $$ S_k=\\sum_{1 \\leq i_1 < i_2 < ... <i_k \\leq n}a_{i_1}a_{i_2}...a_{i_k} $$ Find the number of $n-$ tuples $(a_1,a_2,...a_n)$ such that $$ (S_n-S_{n-2}+S_{... | {
"ground_truth": " 2^{n-1} ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. A smaller square was cut out from a larger square, one of its sides lying on the side of the original square. The perimeter of the resulting octagon is $40 \\%$ greater than the perimeter of the original square. By what percentage is its area less than the area of the original square?",
"ro... | {
"ground_truth": "64",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If the angle between the vectors $\\mathbf{a}$ and $\\mathbf{b}$ is $70^\\circ$, and the angle between $\\mathbf{b}$ and $\\mathbf{c}$ is $50^\\circ$, what is the angle between the vectors $-\\mathbf{a}$ and $\\mathbf{c}$?",
"role": "user"
}
] | {
"ground_truth": "60^\\circ",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the largest natural number $n$ for which the rectangular parallelepipeds $T_{1}, T_{2}, \\ldots, T_{n}$ can be specified such that their faces are parallel to one of the coordinate planes and for which it holds that for any subset $H$ of the set of the first $n$ natural numbers, there exis... | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In a square paper box, a cylinder with a volume of 628 cubic centimeters can fit perfectly. What is the volume of the paper box? (Pi = 3.14).",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Fill the numbers $1,2, \\cdots, 36$ into a $6 \\times 6$ grid, with each cell containing one number, such that the numbers in each row are in increasing order from left to right. The minimum value of the sum of the six numbers in the third column is $\\qquad$\n(2015, National Junior High School... | {
"ground_truth": "63",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "John learned that Lisa scored exactly 85 on the American High School Mathematics Examination (AHSME). Due to this information, John was able to determine exactly how many problems Lisa solved correctly. If Lisa's score had been any lower but still over 85, John would not have been able to determin... | {
"ground_truth": "85",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The keystone arch is an ancient architectural feature. It is composed of congruent isosceles trapezoids fitted together along the non-parallel sides, as shown. The bottom sides of the two end trapezoids are horizontal. In an arch made with 9 trapezoids, let x be the angle measure in degrees of the... | {
"ground_truth": "100",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 6.5. Cat Matroskin, Uncle Fyodor, Postman Pechkin, and Sharik sat down at a round table. In front of each of them was a plate with 15 sandwiches. Every minute, three of them ate a sandwich from their own plate, while the fourth ate a sandwich from their neighbor's plate. After 5 minutes of... | {
"ground_truth": "7",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task 1 - 090921\n\nAt a class party, the students present their math teacher with the following problem:\n\nThe students inform their teacher that they have secretly divided themselves into three groups such that every student in the class belongs to exactly one group. The students in the first... | {
"ground_truth": "2",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was $A$ dollars. The cost of his movie ticket was $20\\%$ of the difference between $A$ and the cost of his soda, while the cost of his soda was $5\\%$ of the difference between $A$ and the cost ... | {
"ground_truth": "23\\%",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Task № 5.4\n\n## Condition:\n\nA Dog, a Cat, and a Mouse are running around a circular lake. They started simultaneously in the same direction from the same point and finished simultaneously, all running at constant speeds.\n\nThe Dog ran 12 laps, the Cat ran 5 laps, and the Mouse ran 2 laps. Ho... | {
"ground_truth": "17",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. What is the day of the week today, if it is known that \"when the day after tomorrow becomes yesterday, today will be as far from Sunday as the day that was today when yesterday was tomorrow\"?",
"role": "user"
}
] | {
"ground_truth": "Wednesday",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5.79 To guard a certain target, someone needs to be on duty day and night, so there are day shifts and night shifts. Personnel can be scheduled for a single day shift or a single night shift, or they can be scheduled for a continuous day and night shift. After working a day shift, a night shift, o... | {
"ground_truth": "4",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7. Find the integer part of $(\\sqrt{3}+1)^{6}$.\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": "415",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A circle with a circumscribed and an inscribed square centered at the origin of a rectangular coordinate system with positive $x$ and $y$ axes is shown in each figure I to IV below.\n\nThe inequalities\n\\(|x|+|y| \\leq \\sqrt{2(x^{2}+y^{2})} \\leq 2\\mbox{Max}(|x|, |y|)\\)\nare represented geomet... | {
"ground_truth": "II",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 9.8. On a plane, 36 points are marked, no three of which lie on the same line. Some pairs of marked points are connected by segments such that no more than 3 segments emanate from each marked point.\n\nWhat is the maximum number of different closed 4-segment broken lines that can result?\n... | {
"ground_truth": "54",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Identify a four-digit number $m$ which is the product of three distinct prime factors $x$, $y$, and $10x+y$. Moreover, introduce another prime factor $z$, such that $10z + x$ must also be a prime. Here $x$, $y$, and $z$ are distinct primes each less than 10. What is the maximum value of $m$ under ... | {
"ground_truth": "1533",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\\section*{Products and factorials $\\quad]$ Decimal number system $\\quad]$ Formulas for abbreviated multiplication (etc.).]\n\n\n\nThe product of four consecutive positi... | {
"ground_truth": "0",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A teacher teaches one class for each of three grades in a day, with a total of 8 periods in a day, 5 in the morning and 3 in the afternoon. The teacher cannot teach three consecutive classes (periods 5 and 6 do not count as consecutive). Calculate the total number of possible schedules for the tea... | {
"ground_truth": "312",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the enclosure dimensions are 15 feet long, 8 feet wide, and 7 feet tall, with each wall and floor being 1 foot thick, determine the total number of one-foot cubical blocks used to create the enclosure.",
"role": "user"
}
] | {
"ground_truth": "372",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider a modified sequence rule:\n1) If a number is 30 or less, triple the number.\n2) If a number is more than 30, subtract 15 from it.\n\nLet $G$ be the first number in a sequence generated by the new rule. $G$ is a \"magic number\" if 18 is not a term in the sequence that starts with $G$. Det... | {
"ground_truth": "12",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B5. Given is the sequence of numbers $a_{0}, a_{1}, a_{2}, \\ldots, a_{2020}$. It is given that $a_{0}=0$. Moreover, for every $k=1,2, \\ldots, 2020$ it holds that\n\n$$\na_{k}= \\begin{cases}a_{k-1} \\cdot k & \\text { if } k \\text { is divisible by } 8, \\\\ a_{k-1}+k & \\text { if } k \\text {... | {
"ground_truth": "2",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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