prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Let \\( n \\) be any positive integer. Consider a sequence containing only the letters \\( \\mathrm{A} \\) and \\( \\mathrm{B} \\), where at most three consecutive \\( \\mathrm{A} \\)s and at most three consecutive \\( \\mathrm{B} \\)s are allowed. Let \\( S(n) \\) represent the number of such seq... | {
"ground_truth": "8",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A pedestrian is moving in a straight line towards a crosswalk at a constant speed of 3.6 km/h. Initially, the distance from the pedestrian to the crosswalk is 40 meters. The length of the crosswalk is 6 meters. What distance from the crosswalk will the pedestrian be after two minutes?",
"role"... | {
"ground_truth": "74",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Masha looked at the drawing and said: \"There are seven rectangles here: one big one and six small ones.\" \"There are also various middle-sized rectangles here,\" said her mother. How many rectangles are there in total in this drawing? Explain your answer.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\triangle ABC$ be a triangle with $AB=85$ , $BC=125$ , $CA=140$ , and incircle $\\omega$ . Let $D$ , $E$ , $F$ be the points of tangency of $\\omega$ with $\\overline{BC}$ , $\\overline{CA}$ , $\\overline{AB}$ respectively, and furthermore denote by $X$ , $Y$ , and $Z$ ... | {
"ground_truth": "30",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. (10 points) Ningning, Leilei, and Fanfan rented a car together to go home from school (as shown in the figure). They agreed: the cost of the shared part of the ride would be equally shared by the passengers; the cost of the individual part of the ride would be borne by the individual passenger.... | {
"ground_truth": "48",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the largest positive integer that is not the sum of a positive integral multiple of 42 and a positive composite integer?",
"role": "user"
}
] | {
"ground_truth": "215",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8 、Using 2 colors to color 4 small squares on a $2 \\times 2$ chessboard, there are. $\\qquad$ different coloring schemes.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6・18 Let $N$ be the set of positive integers, and define the function $f$ on $N$ as follows:\n(i) $f(1)=1, f(3)=3$;\n(ii) For $n \\in N$, we have\n$$\\begin{array}{l}\nf(2 n)=f(n) \\\\\nf(4 n+1)=2 f(2 n+1)-f(n) \\\\\nf(4 n+3)=3 f(2 n+1)-2 f(n)\n\\end{array}$$\n\nFind all $n$ such that $n \\leqslan... | {
"ground_truth": "92",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A structural engineer is designing a minimalist penthouse that incorporates a series of identical triangular glass panels as part of the rooftop design. Each triangular panel has a base of 3 meters and a height of 4 meters. The engineer needs to install a total of 10 panels to complement the moder... | {
"ground_truth": "580",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In triangle \\( ABC \\), side \\( AB \\) is longer than side \\( BC \\), and angle \\( B \\) is \\( 40^\\circ \\). Point \\( P \\) is taken on side \\( AB \\) such that \\( BP = BC \\). The angle bisector \\( BM \\) intersects the circumcircle of triangle \\( ABC \\) at point \\( T \\). Find the a... | {
"ground_truth": "20^\\circ",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Triangle $ABC$ has side lengths $AB = 11, BC=24$, and $CA = 20$. The bisector of $\\angle{BAC}$ intersects $\\overline{BC}$ in point $D$, and intersects the circumcircle of $\\triangle{ABC}$ in point $E \\ne A$. The circumcircle of $\\triangle{BED}$ intersects the line $AB$ in points $B$ and $F \\... | {
"ground_truth": "30",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the vertices of a regular 300-gon, the numbers from 1 to 300 are arranged in some order, each number appearing exactly once. It turns out that for each number \\(a\\), there are as many numbers smaller than \\(a\\) among the 15 closest numbers to it clockwise as there are among the 15 closest n... | {
"ground_truth": "10",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two dice (each die has sides numbered from 1 to 6) are rolled sequentially and land on a horizontal surface, recording the numbers facing up as x and y. Let event A be “x+y is an even number”, and event B be “one of x or y is an even number, and x!= y”. Calculate the conditional probability P(B|A)... | {
"ground_truth": "1/3",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Using $1,2, \\cdots, n$ to form an $n$-digit number without repeating digits, where 2 cannot be adjacent to 1 or 3, a total of 2400 different $n$-digit numbers are obtained. Then $n=$ $\\qquad$\n\nTranslate the above text into English, please retain the original text's line breaks and format, a... | {
"ground_truth": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A function $f$ is defined on the positive integers by \\[\\left\\{\\begin{array}{rcl}f(1) &=& 1, f(3) &=& 3, f(2n) &=& f(n), f(4n+1) &=& 2f(2n+1)-f(n), f(4n+3) &=& 3f(2n+1)-2f(n), \\end{array}\\right.\\] for all positive integers $n$ . Determine the number of positive integers $n$ , less ... | {
"ground_truth": "92",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The union of sets \\( A \\) and \\( B \\), \\( A \\cup B = \\{a_1, a_2, a_3\\} \\). When \\( A \\neq B \\), pairs \\((A, B)\\) and \\((B, A)\\) are considered different. How many such pairs \\((A, B)\\) are there?",
"role": "user"
}
] | {
"ground_truth": "27",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Draw the height BH. \\(\\angle BCH = \\angle CBH = 45^\\circ\\), \\(\\angle ABH = 60^\\circ\\). Let BH = HC = \\(x\\), then BC = \\(x \\sqrt{2}\\), AB = \\(2 x\\).\n\n\\(\\frac{AB}{BC} = \\frac{BC}{MB} = \\sqrt{2}\\), \\(\\angle ABC\\) is common. Therefore, \\(\\triangle MBC \\sim \\triangle CBA\\... | {
"ground_truth": "135^\\circ",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Angela has deposited $\\$8,\\!000$ into an account that pays $6\\%$ interest compounded annually.\n\nBob has deposited $\\$10,\\!000$ into an account that pays $7\\%$ simple annual interest.\n\nIn $20$ years Angela and Bob compare their respective balances. To the nearest dollar, what is the posit... | {
"ground_truth": "\\$1,\\!657",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The line $y = c-x$ where $0 < c < 6$ intersects the $y$-axis at $P$ and the line $x=6$ at $S$. If the ratio of the area of triangle $QRS$ to the area of triangle $QOP$ is 4:16, what is the value of $c$?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "19th CanMO 1987 Problem 2 Find all the ways in which the number 1987 can be written in another base as a three digit number with the digits having the same sum 25.",
"role": "user"
}
] | {
"ground_truth": "19",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Solve the quadratic equation $2x^2 - 7x + 1 = x + 31$. Find the positive difference between the solutions.",
"role": "user"
}
] | {
"ground_truth": "2\\sqrt{19}",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a square $A B C D$ with side length 2, moving points $E$ and $F$ are both on side $A D$, satisfying $A E=D F$. Connecting $C F$ intersects the diagonal $B D$ at point $Q$, and connecting $A Q$ and $B E$ intersect at point $P$. Find the minimum value of $D P$.\n\n---\n\nThe translation preserves... | {
"ground_truth": "\\sqrt{5}-1",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 11.5. In a chess tournament, a team of schoolchildren and a team of students, each consisting of 15 people, are competing against each other. During the tournament, each schoolchild must play against each student exactly once, and each person must play no more than one game per day. The nu... | {
"ground_truth": "120",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6.1. (12 points) Yura has unusual clocks with several minute hands moving in different directions. Yura calculated that the minute hands coincided in pairs exactly 54 times in one hour. What is the maximum number of minute hands that can be on Yura's clocks?\n\n#",
"role": "user"
}
] | {
"ground_truth": "28",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "92. 50 chess pieces are arranged in a circle, and numbers $1, 2, 3, \\cdots \\cdots$ 50 are sequentially marked on the chess pieces in a clockwise direction. Then, in a clockwise direction, every other chess piece is removed until only one chess piece remains. If the number of the remaining chess ... | {
"ground_truth": "7",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What percent of square $ABCD$ is shaded? All angles in the diagram are right angles. [asy]\nimport graph;\ndefaultpen(linewidth(0.7));\n\nxaxis(0,5,Ticks(1.0,NoZero));\nyaxis(0,5,Ticks(1.0,NoZero));\n\nfill((0,0)--(1,0)--(1,1)--(0,1)--cycle);\nfill((2,0)--(3,0)--(3,3)--(0,3)--(0,2)--(2,2)--cycle)... | {
"ground_truth": "60",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nFind the point \\( M' \\) that is symmetric to the point \\( M \\) with respect to the plane.\n\nGiven:\n\\( M(3, -3, -1) \\)\n\nPlane equation:\n\\( 2x - 4y - 4z - 13 = 0 \\)",
"role": "user"
}
] | {
"ground_truth": "(2, -1, 1)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sequence is recursively defined as: \\( t_{1} = 1 \\). For \\( n > 1 \\), if \\( n \\) is even, \\( t_{n} = 1 + t_{\\frac{n}{2}} \\); if \\( n \\) is odd, \\( t_{n} = \\frac{1}{t_{n-1}} \\). Given that \\( t_{n} = \\frac{19}{87} \\), find the sum of the digits of \\( n \\). Express your answer a... | {
"ground_truth": "15",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "222 Find the smallest natural number $n$, such that for any $n$ points taken on a circle, among the central angles of the arcs connecting any two points, at least 2005 angles are not greater than $120^{\\circ}$.",
"role": "user"
}
] | {
"ground_truth": "91",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1st CIS 1992 Problem 20 Find all integers k > 1 such that for some distinct positive integers a, b, the number k a + 1 can be obtained from k b + 1 by reversing the order of its (decimal) digits.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the maximum real number $C$ such that\n$$\n\\sum_{i=1}^{n} \\frac{x_{i}}{x_{i-1}} \\geq n+C,\n$$\nfor all positive integers $n$ and all sequences of positive real numbers $x_{0}, x_{1}, \\ldots, x_{n}$ such that $x_{0}=1$ and $x_{n}=2$.",
"role": "user"
}
] | {
"ground_truth": "\\log2",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the least odd number $a > 5$ satisfying the following conditions: There are positive integers $m_1,m_2, n_1, n_2$ such that $a=m_1^2+n_1^2$ , $a^2=m_2^2+n_2^2$ , and $m_1-n_1=m_2-n_2.$ ",
"role": "user"
}
] | {
"ground_truth": "261",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Xiao Wang left home at 8:30 to visit a housing exhibition and returned home at 12:00, while his alarm clock at home was showing 11:46 when he got back. Calculate the time in minutes until the alarm clock will point to 12:00 exactly.",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The diagram shows a solid with six triangular faces and five vertices. Andrew wants to write an integer at each of the vertices so that the sum of the numbers at the three vertices of each face is the same. He has already written the numbers 1 and 5 as shown. What is the sum of the other three num... | {
"ground_truth": "11",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1.3. Replace the ellipsis with such a natural number $p$ so that the answer to the following question is unique: how many lines are drawn on the plane, if it is known that they intersect at ... different points?",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A community plans to invest 500 yuan to purchase three types of books, A, B, and C. Type A costs 30 yuan per book, type B costs 25 yuan per book, and type C costs 20 yuan per book. The community must buy at least 5 books of type A and at most 6 books of type A, and all three types of books must be... | {
"ground_truth": "6",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's determine the smallest natural number $n$ for which the inequality $\\left(x^{2}+y^{2}+z^{2}\\right)^{2} \\leq n\\left(x^{4}+y^{4}+z^{4}\\right)$ holds for all real values of $x, y, z$.\n\n---\n\nTranslate the above text into English, please keep the original text's line breaks and format, a... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A semicircular sponge with a diameter of $20 \\text{ cm}$ is used to wipe a corner of a room's floor such that the ends of the diameter continuously touch the two walls forming a right angle. What area does the sponge wipe?",
"role": "user"
}
] | {
"ground_truth": "100\\pi",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task 4 - 030514\n\n$\\cap \\bigcirc$\n$\\bigcirc \\Omega$ $\\bigcirc$\nb)\n\nTen pennies are arranged on the table as shown in figure a). Some pennies should be moved so that the arrangement shown in figure b) is achieved.\n\na) How many pennies must be moved at a minimum?\n\nb) Which pennies a... | {
"ground_truth": "3",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that July 1, 1997, was a Tuesday, determine the day of the week for June 9, 1898. Express your answer as the full day of the week (e.g., Monday, Tuesday, etc.).",
"role": "user"
}
] | {
"ground_truth": "Thursday",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## 94. An Irish Walk.\n\n- Once I needed to get from Boguly to Bollifoyne, where a friend was waiting for me. The only available transport was the old cart of Pat Doyle, which was pulled by a mare whose working life had clearly been extended too long.\n\nUnbearably slowly, but steadily, we moved f... | {
"ground_truth": "10",
"mean_reward": 0.265625
} | 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\nA square grid on the Euclidean plane consists of all points $(m,n)$, where $m$ and $n$ are integers. Is it possible to cover all grid points by an infinite family of ... | {
"ground_truth": "2",
"mean_reward": 0.015625
} | 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\nHow many of the factorials from 1! to 100! are divisible by 9?\n\n[Solution]\n\n<paragraph_0>\nWe know that $9! = 362880$ is divisible by $9$, so all factorials after... | {
"ground_truth": "2",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. (10 points) In one of the regions on the planet, seismic activity was studied. 80 percent of all days were quiet. The instrument predictions promised a calm situation in 64 out of 100 cases; moreover, in 70 percent of all cases when the day was quiet, the instrument predictions came true. What ... | {
"ground_truth": "40",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 66, Given $x, y>0, x^{2}+y \\geq x^{3}+y^{2}$, find the maximum value of $x^{2}+y^{2$.\n\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\nNote: The note about the format and the trans... | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A model rocket follows the trajectory c(t) = (80t, 200t - 4.9t^2) until it hits the ground, with t in seconds and distance in meters. Find the rocket's maximum height in meters.",
"role": "user"
}
] | {
"ground_truth": "2041",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the village, there are 100 houses. What is the maximum number of closed, non-intersecting fences that can be built so that each fence encloses at least one house and no two fences enclose the same set of houses?\n\n#",
"role": "user"
}
] | {
"ground_truth": "199",
"mean_reward": 0.1875
} | 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\nFor $\\pi\\leq\\theta<2\\pi$, let\n\\[ P=\\dfrac12\\cos\\theta-\\dfrac14\\sin2\\theta-\\dfrac18\\cos3\\theta+\\dfrac1{16}\\sin4\\theta+\\dfrac1{32}\\cos5\\theta-\\dfr... | {
"ground_truth": "2",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Riddles ]\n\nThree syllables in a word\n\nThe first syllable -\n\nA large piece of a snowman.\n\nThe second syllable is carried out\n\nBy elephants coming to the waterhole.\n\nAnd the third syllable is called\n\nWhat the hard sign used to be called.\n\nCombine all three as needed -\n\nYou'll get... | {
"ground_truth": "COMPUTER",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mrs. Riley revised her data after realizing that there was an additional score bracket and a special bonus score for one of the brackets. Recalculate the average percent score for the $100$ students given the updated table:\n\n\\begin{tabular}{|c|c|}\n\\multicolumn{2}{c}{}\\\\\\hline\n\\textbf{$\\... | {
"ground_truth": "80.2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 10 different balls that need to be placed into 8 different empty boxes, with each box containing at least one ball. How many ways are there to do this?",
"role": "user"
}
] | {
"ground_truth": "30240000",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Find all possible values of the sum $x+y$, where real numbers $x$, $y$ satisfy the equation $x^{3}+y^{3}=3 x y$.",
"role": "user"
}
] | {
"ground_truth": "(-1,3)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a vintage collector who specializes in finding unique antique locks. During a weekend flea market visit, Alex finds three stalls selling antique locks. The first stall offers 5 locks for $20 each, the second stall offers 8 locks for $15 each, and the third stall offers 6 locks for $25 each... | {
"ground_truth": "16",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\triangle ABC$ have side lengths $AB=13$, $AC=14$, and $BC=15$. There are two circles located inside $\\angle BAC$ which are tangent to rays $\\overline{AB}$, $\\overline{AC}$, and segment $\\overline{BC}$. Compute the distance between the centers of these two circles.",
"role": "user"... | {
"ground_truth": "5\\sqrt{13}",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "61st Putnam 2000 Problem A3 An octagon is incribed in a circle. One set of alternate vertices forms a square area 5. The other set forms a rectangle area 4. What is the maximum possible area for the octagon? Solution",
"role": "user"
}
] | {
"ground_truth": "3\\sqrt{5}",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides as shown. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?\n[asy] draw((0,0)--(4,0)--(4,4)--(0,4)--cycle); draw(circle((2,2... | {
"ground_truth": "4",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\(ABCD\\) be a trapezoid with \\(AB\\parallel CD\\). Given \\(AB=21\\), \\(CD=7\\), \\(AD=13\\), and area \\(168\\), let \\(P=AC\\cap BD\\). A line through \\(P\\) parallel to \\(AB\\) meets the circumcircle of \\(\\triangle BCP\\) at \\(X\\). The circumcircles of \\(\\triangle BCP\\) and \\(... | {
"ground_truth": "17",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let 7 be the first term and the common difference of an arithmetic sequence both be non-negative integers, the number of terms is no less than 3, and the sum of all terms is $97^{2}$. How many such sequences are there?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. Let $f(x)=x^{2}+p x+q$. If the inequality $|f(x)|>2$ has no solution in the interval $[1,5]$. Try to find all real pairs $(p, q)$.\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 provid... | {
"ground_truth": "(-6,7)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In this problem, we explore how fast an iceberg can melt, through the dominant mode of forced convection. For simplicity, consider a very thin iceberg in the form of a square with side lengths $L=100 \\mathrm{~m}$ and a height of $1 \\mathrm{~m}$, moving in the arctic ocean at a speed of $0.2 \\ma... | {
"ground_truth": "60",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4、In the Fibonacci sequence, the first term and the second term are both 1, starting from the 3rd term, each term is equal to the sum of the two preceding ones. Numbers that appear in the Fibonacci sequence are called Fibonacci numbers. Express 121 as the sum of several different Fibonacci numbers... | {
"ground_truth": "8",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If $a,b,c$ are non-zero real numbers such that \\[\\frac{a+b-c}{c}=\\frac{a-b+c}{b}=\\frac{-a+b+c}{a},\\] and \\[x=\\frac{(a+b)(b+c)(c+a)}{abc},\\] and $x<0,$ then $x$ equals",
"role": "user"
}
] | {
"ground_truth": "{-}1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The roots of \\(f(x)=x^8+x^7-x^5-x^4-x^3+x+1\\) are all roots of unity. A real number \\(r\\in[0,1)\\) is called nice if \\(e^{2\\pi i r}\\) is a root of \\(f(x)\\) and has positive imaginary part. Let \\(S\\) be the sum of all nice \\(r\\). If \\(S=\\frac{p}{q}\\) in lowest terms, find \\(p+q\\).... | {
"ground_truth": "31",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of $1234_6$, $654_6$, and $12_6$ in base $6$.",
"role": "user"
}
] | {
"ground_truth": "2344_6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many integers (positive and negative) greater than 1 are divisors of 30?",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( A \\) be a set containing only positive integers, and for any elements \\( x \\) and \\( y \\) in \\( A \\), \\(|x-y| \\geq \\frac{x y}{30}\\). Determine at most how many elements \\( A \\) may contain.",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5. Find the extremum of $y=\\frac{\\sqrt{3} x+1}{\\sqrt{x^{2}+1}}+2$.\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": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. (Easy) Among all victims of zombie bites, $10 \\%$ are prescribed the experimental drug Undetenin to treat them. Overall, $4 \\%$ of the human population suffer an adverse reaction to Undetenin. Out of all the patients being treated with Undetenin, $2 \\%$ suffer an adverse reaction to the drug... | {
"ground_truth": "5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "41. Given that the two-digit number $\\overline{a b}$ and $\\overline{b a}$ differ by 45, find the number of $\\overline{a b}$ that satisfy the condition.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3 There are 155 birds on a circle $C$. If the arc $P_{i} P_{j} \\leqslant 10^{\\circ}$, then the birds are said to be mutually visible. If several birds are allowed to be at the same position, find the minimum number of visible bird pairs. (30th IMO)",
"role": "user"
}
] | {
"ground_truth": "270",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. The equation of the hyperbola $C$ is $x^{2}-\\frac{y^{2}}{3}=1$, with the left and right foci being $F_{1}$ and $F_{2}$, respectively. A line is drawn through point $F_{2}$ intersecting the right branch of the hyperbola $C$ at points $P$ and $Q$, such that $\\angle F_{1} P Q=90^{\\circ}$. Then,... | {
"ground_truth": "\\sqrt{7}-1",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 4 balls of different masses. How many weighings on a balance scale without weights are needed to arrange these balls in descending order of mass?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Express the quotient $1121_5 \\div 12_5$ in base $5$.",
"role": "user"
}
] | {
"ground_truth": "43_5.",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The math teacher of the ninth grade teaches an average of 6 tutoring classes per month. If the classes are taught by female teachers, each female teacher should teach 15 classes per month. If the classes are taught only by male teachers, how many classes should each male teacher teach per month? E... | {
"ground_truth": "10",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. What time does she finish the third task? Express your answer in 12-hour clock format (e.g., 3:30 PM).",
"role": "user"
}
] | {
"ground_truth": "3:30 PM",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Rowena is able to mow 2/5 of a lawn in 18 minutes. If she began the job at 10:00 a.m., and mowed at this same constant rate, what time did she finish mowing the entire lawn? Express your answer in 12-hour time format (e.g., 10:45 a.m.).",
"role": "user"
}
] | {
"ground_truth": "10:45 a.m.",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. Given a regular tetrahedron $P-ABC$ with a volume of $9 \\sqrt{3}$, the dihedral angle between the side face $PAB$ and the base $ABC$ is $60^{\\circ}$. Point $D$ is a point on line segment $AB$ such that $AD=\\frac{1}{6} AB$, point $E$ is a point on line segment $AC$ such that $AE=\\frac{1}{6}... | {
"ground_truth": "\\sqrt{57}",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "131. If a certain number is multiplied by 5, subtract its third from the product, divide the remainder by 10 and add to this sequentially $1 / 3, 1 / 2$ and $1 / 4$ of the original number, the result is 68. What is the number?",
"role": "user"
}
] | {
"ground_truth": "48",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A pool is fitted with 5 pipes numbered (1), (2), (3), (4), and (5). The time required to fill the pool when two pipes are opened simultaneously is given in the table below:\n\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline Open Pipe Numbers & (1)(2) & (2)(3) & (3)(4) & (4)(3) & (5)(1) \\\\\n\\hline Time... | {
"ground_truth": "(4)",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.6. Thirty girls - 13 in red dresses and 17 in blue dresses - were dancing in a circle around a Christmas tree. Later, each of them was asked if their right neighbor was in a blue dress. It turned out that those who answered correctly were only the girls standing between girls in dresses of the s... | {
"ground_truth": "17",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The lock opens only if a specific three-digit number is entered. An attempt consists of randomly selecting three digits from a given set of five. The code was guessed correctly only on the last of all attempts. How many attempts preceded the successful one?",
"role": "user"
}
] | {
"ground_truth": "124",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $p$, $q$, and $r$ be real numbers, and let $A$, $B$, $C$ be points such that the midpoint of $\\overline{BC}$ is $(p,2,0)$, the midpoint of $\\overline{AC}$ is $(0,q,2)$, and the midpoint of $\\overline{AB}$ is $(0,0,r)$. Find\n\\[\n\\frac{AB^2 + AC^2 + BC^2}{p^2 + q^2 + r^2}.\n\\]",
"role... | {
"ground_truth": "8",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Rectangle ABCD with AB = 7 and AD = 10 is joined with right triangle DCE so that DC is common to both shapes. The areas of ABCD and DCE are equal. If both ABCD and DCE form a pentagon, find the length of DE.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{449}",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Processes and Operations ]\n\nBetween neighboring camps, it takes 1 day to travel. The expedition needs to transfer 1 can of food to the camp located 5 days away from the base camp and return. At the same time:\n\n- each member of the expedition can carry no more than 3 cans of food;\n- in 1 day... | {
"ground_truth": "243",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A target is a triangle divided by three sets of parallel lines into 100 equal equilateral triangles with unit sides. A sniper shoots at the target. He aims at a triangle and hits either it or one of the adjacent triangles sharing a side. He can see the results of his shots and can choose when to s... | {
"ground_truth": "25",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The shortest path from Atown to Cetown runs through Betown. Two signposts on this path are shown, but one of them is broken and a number is missing. Given that the distance from Atown to Betown is 4 km and the distance from Atown to the second signpost is 6 km, calculate the distance that was writ... | {
"ground_truth": "2",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Equilateral $\\triangle ABC$ has side length $1$, and squares $ABDE$, $BCHI$, $CAFG$ lie outside the triangle. What is the area of hexagon $DEFGHI$? [asy] import graph; size(6cm); pen dps = linewidth(0.7) + fontsize(8); defaultpen(dps); pair B = (0,0); pair C = (1,0); pair A = rotate(60,B)*C; pair... | {
"ground_truth": "3+\\sqrt3",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The diagram shows three triangles which are formed by the five line segments \\(A C D F, B C G, G D E, A B\\), and \\(E F\\) so that \\(A C = B C = C D = G D = D F = E F\\). Also, \\(\\angle C A B = \\angle E F D\\). What is the size, in degrees, of \\(\\angle C A B\\)?",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An infinite sequence of real numbers $a_1, a_2, \\dots$ satisfies the recurrence\n\\[ a_{n+3} = a_{n+2} - 2a_{n+1} + a_n \\]for every positive integer $n$. Given that $a_1 = a_3 = 1$ and $a_{98} = a_{99}$, compute $a_1 + a_2 + \\dots + a_{100}$.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Cut a square with a side of 4 into rectangles, the sum of the perimeters of which is 25.",
"role": "user"
}
] | {
"ground_truth": "25",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. (20 points) Ksyusha, Vanya, and Vasya decided to go to the cinema. They agreed to meet at the bus stop, but they don't know when each will arrive. Each of them can arrive at a random time between 15:00 and 16:00. Vasya is the most patient: if he arrives and there is neither Ksyusha nor Vanya at... | {
"ground_truth": "1",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5th Putnam 1942 Problem B4 A particle moves in a circle through the origin under the influence of a force a/r k towards the origin (where r is its distance from the origin). Find k.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct sequences of five letters can be made from the letters in EXAMPLE if each letter can be used only once and each sequence must begin with E and end with M?",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the smallest positive integer \\(n\\) such that \\(32^n \\equiv 2 \\pmod{167}\\).",
"role": "user"
}
] | {
"ground_truth": "50.",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that the roots of the quadratic $x^2 + ax + b$ are $\\alpha$ and $\\beta$ . Then $\\alpha^3$ and $\\beta^3$ are the roots of some quadratic $x^2 + cx + d$ . Find $c$ in terms of $a$ and $b$ .\n",
"role": "user"
}
] | {
"ground_truth": "a^3 - 3ab",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 4-19 The number of different schemes for dice in Example 4-15 of Section 4.6 can also be solved using the generating function type Pólya's theorem as follows:\n$$\n\\begin{aligned}\nP= & \\frac{1}{24} \\times\\left[\\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}\\right)^{6}\\right. \\\\\n& +6\\... | {
"ground_truth": "30",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\underline{\\text { Folklore }}$\n\nAmong the actors of Karabas Barabas theater, a chess tournament was held. Each participant played exactly one game with each of the others. One solido was given for a win, half a solido for a draw, and nothing for a loss. It turned out that among any three par... | {
"ground_truth": "5",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sequence of positive integers is defined by \\(a_{0}=1\\) and \\(a_{n+1}=a_{n}^{2}+1\\) for each \\(n \\geq 0\\). Find \\(\\operatorname{gcd}\\left(a_{999}, a_{2004}\\right)\\).",
"role": "user"
}
] | {
"ground_truth": "677",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Square $AXYZ$ is inscribed in equiangular hexagon $ABCDEF$ with $X$ on $\\overline{BC}$, $Y$ on $\\overline{DE}$, and $Z$ on $\\overline{EF}$. Suppose that $AB=40$, and $EF=41(\\sqrt{3}-1)$. What is the side-length of the square? [asy] size(200); defaultpen(linewidth(1)); pair A=origin,B=(2.5,0),C... | {
"ground_truth": "29\\sqrt{3}",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. (6 points) Using 24 matchsticks of the same length, first use some of them to form 6 triangles on a plane, with each side of the equilateral triangle being one matchstick. Then use the remaining matchsticks to form squares on the plane, with each side of the square being one matchstick. How ma... | {
"ground_truth": "4",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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