prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Restore the digits. On the board, the product of three consecutive even numbers was written. During the break, Vasya erased some of the digits. As a result, the board shows $87*****8$. Help Petya find the missing digits in the product.",
"role": "user"
}
] | {
"ground_truth": "87526608",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Problem 6. (3 points)\n\nThree runners are moving along a circular track at constant equal speeds. When two runners meet, they instantly turn around and start running in opposite directions.\n\nAt some point, the first runner meets the second. After 15 minutes, the second runner meets the third ... | {
"ground_truth": "80",
"mean_reward": 0.25
} | 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: Job, Movie-Genre, Music-Genre, Nationality, Sport, Transport.\nThe attributes have the following possible values:\n- Job: analyst, doctor, scientist, writer\n- Movie-Gen... | {
"ground_truth": "scientist",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the value of $\\frac{2468_{10}}{111_{3}} - 3471_{9} + 1234_{7}$. Express your answer in base 10.",
"role": "user"
}
] | {
"ground_truth": "-1919",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A pot can hold 2 cakes at a time, and it takes 5 minutes to cook both sides of a cake. What is the minimum time required to cook 3 cakes thoroughly? Express your answer in minutes as a whole number.",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the amount of personal income tax (НДФЛ) paid by Sergey over the past year if he is a resident of the Russian Federation and had a stable income of 30,000 rubles per month and a one-time vacation bonus of 20,000 rubles during this period. Last year, Sergey sold his car, which he inherite... | {
"ground_truth": "10400",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the minimum kinetic energy of a proton to be scattered from a fixed proton target to produce an antiproton in MeV.",
"role": "user"
}
] | {
"ground_truth": "5630.0",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": " $ABC$ is triangle. $l_1$ - line passes through $A$ and parallel to $BC$ , $l_2$ - line passes through $C$ and parallel to $AB$ . Bisector of $\\angle B$ intersect $l_1$ and $l_2$ at $X,Y$ . $XY=AC$ . What value can take $\\angle A- \\angle C$ ?",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The numbers $1,2, \\ldots, 2002$ are written in order on a blackboard. Then the 1st, 4th, 7th, $\\ldots$, $3k+1$th, $\\ldots$ numbers in the list are erased. Then the 1st, 4th, 7th, $\\ldots$, $3k+1$th numbers in the remaining list are erased (leaving $3,5,8,9,12, \\ldots$ ). This process is carri... | {
"ground_truth": "1598",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A strip of paper that is 5 cm wide is wound around a cylindrical tube with a diameter of 2 cm for 600 turns, forming a cylindrical shape with a diameter of 10 cm. Assuming the paper strip forms 600 concentric cylindrical layers, with their diameters uniformly increasing from 2 cm to 10 cm, determi... | {
"ground_truth": "36 \\pi",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. For any positive integers $m, n$, define $r(m, n)$ as the remainder of $m \\div n$ (for example, $r(8,3)$ represents the remainder of $8 \\div 3$, so $r(8,3)=2$). The smallest positive integer solution that satisfies the equation $r(m, 1)+r(m, 2)+r(m, 3)+\\cdots+r(m, 10)=4$ is $\\qquad$",
... | {
"ground_truth": "120",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Simplify: $$\\sqrt[3]{5488000}$$",
"role": "user"
}
] | {
"ground_truth": "176.4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the smallest number of $1 \\Omega$ resistors needed such that when arranged in a certain arrangement involving only series and parallel connections, that the equivalent resistance is $\\frac{7}{6} \\Omega$ ?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sector has a central angle of 1 radian and a circumference of 6. Find the area of this sector. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a convex quadrilateral ABCD, where AB is parallel to CD and AB + BC = CD + AD, determine the relationship between AD and BC. Express your answer using standard mathematical notation for relationships (e.g., =, <, >, cannot be determined).",
"role": "user"
}
] | {
"ground_truth": "AD = BC",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the diagram, square \\(PQRS\\) has side length 40. Points \\(J, K, L,\\) and \\(M\\) are on the sides of \\(PQRS\\), so that \\(JQ = KR = LS = MP = 10\\). Line segments \\(JZ, KW, LX,\\) and \\(MY\\) are drawn parallel to the diagonals of the square so that \\(W\\) is on \\(JZ\\), \\(X\\) is on... | {
"ground_truth": "200",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Placing no more than one $\\text{X}$ in each small square, what is the greatest number of $\\text{X}$'s that can be put on the grid shown without getting three $\\text{X}$'s in a row vertically, horizontally, or diagonally? [asy] for(int a=0; a<4; ++a) { draw((a,0)--(a,3)); } for(int b=0; b<4; ++b... | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the function f(x) = ax + sin(x), find the range of the real number a that allows f(x) to have extreme points. Express your answer as an inequality.",
"role": "user"
}
] | {
"ground_truth": "-1 < a < 1",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given an integer $n\\geq 2$ and a closed unit disc, evaluate the maximum of the product of the lengths of all $\\frac{n(n-1)}{2}$ segments determined by $n$ points in that disc.",
"role": "user"
}
] | {
"ground_truth": "n^{n/2}",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If $\\frac{720}{2^6 \\cdot 3^5}$ is expressed as a decimal, how many non-zero digits are to the right of the decimal point?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. A function $g: \\mathbb{N} \\rightarrow \\mathbb{N}$ satisfies the following:\n(a) If $m$ is a proper divisor of $n$, then $g(m)<g(n)$.\n(b) If $m$ and $n$ are relatively prime and greater than 1 , then\n$$\ng(m n)=g(m) g(n)+(n+1) g(m)+(m+1) g(n)+m+n \\text {. }\n$$\n\nFind the least possible v... | {
"ground_truth": "3053",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a single-round-robin tournament, 10 chess players are participating. After what minimum number of rounds can it happen that a sole winner has already been determined prematurely? (In each round, the participants are divided into pairs. Win - 1 point, draw - 0.5 points, loss - 0).",
"role": ... | {
"ground_truth": "7",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. $P$ is a point inside $\\triangle A B C$, and line segments $A P D, B P E$, and $C P F$ are drawn such that $D$ is on $B C$, $E$ is on $A C$, and $F$ is on $A B$. Given that $A P=6, B P=9, P D=6, P E=3, C F=20$, find the area of $\\triangle A B C$.\n(7th AIME Problem)",
"role": "user"
}
] | {
"ground_truth": "108",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Out of 8 circular disks with radius \\( r \\), 7 are fixed on a table such that their centers are at the vertices and center of a regular hexagon with side length \\( 2r \\), and the 8th disk touches one of the 6 outer disks. The 8th disk is rolled around the 7 fixed disks once without slipping, u... | {
"ground_truth": "4",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The side lengths $a,b,c$ of a triangle $ABC$ are positive integers. Let:\n\n\\[T_{n}=(a+b+c)^{2n}-(a-b+c)^{2n}-(a+b-c)^{2n}+(a-b-c)^{2n}\\]\n\nfor any positive integer $n$ . If $\\frac{T_{2}}{2T_{1}}=2023$ and $a>b>c$ , determine all possible perimeters of the triangle $ABC$ .",
"rol... | {
"ground_truth": "49",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Problem 4. (3 points)\n\nThree runners are moving along a circular track at constant equal speeds. When two runners meet, they instantly turn around and start running in opposite directions.\n\nAt some point, the first runner meets the second. Twenty minutes later, the second runner meets the th... | {
"ground_truth": "100",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$5 \\cdot 61$ A group of young people went to dance disco. Each dance costs 1 yuan, and each boy danced with each girl exactly once, then they went to another place to dance. Here, they paid with subsidiary coins, and they spent the same amount of money as before. The entry fee for each person is ... | {
"ground_truth": "5",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$[\\quad$ Evaluation + example $\\quad]$\n\nThe hostess baked a pie for her guests. She may have either 10 or 11 guests. Into what smallest number of slices should she cut the pie in advance so that it can be evenly divided among either 10 or 11 guests?",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $P_0 = (3,1)$ and define $P_{n+1} = (x_n, y_n)$ for $n \\ge 0$ by $$x_{n+1} = - \\frac{3x_n - y_n}{2}, y_{n+1} = - \\frac{x_n + y_n}{2}$$Find the area of the quadrilateral formed by the points $P_{96}, P_{97}, P_{98}, P_{99}$.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Winnie-the-Pooh eats 3 cans of condensed milk and a jar of honey in 25 minutes, while Piglet eats them in 55 minutes. Pooh eats one can of condensed milk and 3 jars of honey in 35 minutes, while Piglet eats them in 1 hour 25 minutes. How long will it take for them to eat 6 cans of condensed milk t... | {
"ground_truth": "20",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $S(n)$ be the sum of the digits of an integer $n$. For example, $S(327)=3+2+7=12$. Find the value of\n\n$$\nA=S(1)-S(2)+S(3)-S(4)+\\ldots-S(2016)+S(2017)\n$$",
"role": "user"
}
] | {
"ground_truth": "1009",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given natural numbers \\( m \\) and \\( n \\). There are two piles on the table: the first pile contains \\( n \\) stones, and the second pile contains \\( m \\) stones. Petya and Vasya play the following game. Petya starts. In one move, a player can break one of the available piles on the table i... | {
"ground_truth": "m \\neq n",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that the function\n\n$$\ny = ax^3 + bx^2 + cx + d\n$$\n\nhas both extrema. What is the relationship among the coefficients if the straight line connecting the points of the curve corresponding to the extrema passes through the origin?",
"role": "user"
}
] | {
"ground_truth": "9ad = bc",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Shapovalov A.V.\n\nIn a $10 \\times 10$ grid, the centers of all unit squares are marked (a total of 100 points). What is the minimum number of lines, not parallel to the sides of the square, needed to cross out all the marked points?",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( T = \\left\\{ |9^k| \\mid k \\in \\mathbf{Z}, 0 \\leqslant k \\leqslant 4000 \\right\\} \\). It is known that \\( 9^{4000} \\) is a 3817-digit number, and its first digit is 9. How many numbers in \\( T \\) have 9 as their first digit?",
"role": "user"
}
] | {
"ground_truth": "184",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\\section*{Exercise 2 - \\(331012=330912\\)}\n\nIs there a six-digit natural number that has exactly fourteen different natural numbers as divisors, including the number 14?",
"role": "user"
}
] | {
"ground_truth": "235298",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13.427 After passing through the filter, the liquid is evenly poured into a 40-bucket barrel and can be drained through a tap at the bottom of the barrel. If this tap is open, the inflow and outflow of the liquid are such that every 4 minutes, one bucket is reduced in the barrel. How long will it ... | {
"ground_truth": "96",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. In an acute triangle $\\triangle A B C$, $M$ is the midpoint of side $A C$. The circle $\\Gamma$ passing through points $B$ and $M$ intersects sides $A B$ and $B C$ at the second points $P$ and $Q$, respectively. Point $T$ satisfies that quadrilateral $B P T Q$ is a parallelogram. If $T$ lies o... | {
"ground_truth": "\\sqrt{2}",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. 2 (IMO 18) In a planar convex quadrilateral with an area of $32 \\mathrm{~cm}^{2}$, the sum of one diagonal and two opposite sides is $16 \\mathrm{~cm}$. Determine all possible lengths of the other diagonal.\n\nTranslate the above text into English, please keep the original text's line breaks a... | {
"ground_truth": "8\\sqrt{2}",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the parabola $y^{2}=4x$ with focus $F$ and directrix $l$, which intersects the hyperbola $\\frac {x^{2}}{a^{2}}-y^{2}=1$ ($a > 0$) at points $A$ and $B$, and $\\triangle FAB$ is a right-angled triangle, calculate the eccentricity of the hyperbola. Express your answer as a single value.",
... | {
"ground_truth": "\\sqrt{6}",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given \\( f: A_{3} \\rightarrow A_{3} \\), find the number of functions \\( f \\) that satisfy \\( f^{(3)} = f \\), and list all such functions.",
"role": "user"
}
] | {
"ground_truth": "19",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Symmetric Strategy ]\n\nOn the board, two numbers are written: 2014 and 2015. Petya and Vasya take turns, with Petya starting first. In one move, they can\n\n- either decrease one of the numbers by its non-zero digit or by a non-zero digit of the other number;\n- or divide one of the numbers by ... | {
"ground_truth": "Petya",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A teacher wants to invest $30,000 into an account that compounds annually. The interest rate at this bank is 1.8%. How much money will be in the account after 6 years?",
"role": "user"
}
] | {
"ground_truth": "33389.35",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many numbers with less than four digits (from 0 to 9999) are neither divisible by 3, nor by 5, nor by 7?",
"role": "user"
}
] | {
"ground_truth": "4571",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A storm in Paris, France, caused €45 million in damage. At that time, 1.2 Euros were equivalent to 1 British pound. Determine the number of British pounds of damage the storm caused.",
"role": "user"
}
] | {
"ground_truth": "37,500,000",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. Real numbers $x, y$ satisfy $x^{2}+y^{2}=20$, then the maximum value of $x y+8 x+y$ is\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "42",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5 In a regular pentagon $A B C D E$, there is a point $P$ inside. It is known that $\\angle A B P=6^{\\circ}, \\angle A E P=12^{\\circ}$. Find the degree measure of $\\angle P A C$.",
"role": "user"
}
] | {
"ground_truth": "12^{\\circ}",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the largest constant $m$, so that for any positive real numbers $a, b, c, d,$ and $e$,\n\\[\\sqrt{\\frac{a}{b+c+d+e}} + \\sqrt{\\frac{b}{a+c+d+e}} + \\sqrt{\\frac{c}{a+b+d+e}} + \\sqrt{\\frac{d}{a+b+c+e}} > m.\\]",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the pyramid $A B C D$, the dihedral angle at edge $A C$ is $90^{\\circ}, A B=B C=C D, B D=A C$. Find the dihedral angle at edge $A D$.\n\n#",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a plane, 6 lines intersect pairwise, but only three pass through the same point. Find the number of non-overlapping line segments intercepted.",
"role": "user"
}
] | {
"ground_truth": "21",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task 2.\n\nLet $N$ be a natural number. We call a staircase a part of a square plate of dimensions $N \\times N$ that consists of the first $K$ fields in the $K$-th row for $K=1,2, \\ldots, N$. In how many ways can the staircase be cut into rectangles of different areas that consist of the fiel... | {
"ground_truth": "2^{N-1}",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For what value of \\(a\\) does the inequality \\(\\log \\frac{1}{\\div}\\left(\\sqrt{x^{2}+a x+5}+1\\right) \\cdot \\log _{5}\\left(x^{2}+a x+6\\right)+\\log _{a} 3 \\geqslant 0\\) have exactly one solution?",
"role": "user"
}
] | {
"ground_truth": "a = 2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\\(ABCD\\) is a square-based pyramid with base \\(ABCD\\) and apex \\(E\\). Point \\(E\\) is directly above point \\(A\\), with \\(AE = 1024\\) units and \\(AB = 640\\) units. The pyramid is sliced into two parts by a horizontal plane parallel to the base \\(ABCD\\), at a height \\(h\\) above the ... | {
"ground_truth": "85",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider a set $X$ with $|X| = n\\geq 1$ elements. A family $\\mathcal{F}$ of distinct subsets of $X$ is said to have property $\\mathcal{P}$ if there exist $A,B \\in \\mathcal{F}$ so that $A\\subset B$ and $|B\\setminus A| = 1$.\n\ni) Determine the least value $m$, so that any family $\\mathcal{F... | {
"ground_truth": "2^{n-1}",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2.4. The master's day shift lasts $40 \\%$ longer than the apprentice's shift. If the apprentice worked as long as the master, and the master worked as long as the apprentice, they would produce the same number of parts. By what percentage does the master produce more parts per day than the appren... | {
"ground_truth": "96",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that an isosceles triangle with legs of 1 kilometer each and a base length of 4.848 millimeters has a vertex angle of 1″, calculate the base length of a similar isosceles triangle with legs equal to the average distance from the sun to the earth (1.5×10^8 kilometers) and the same vertex angl... | {
"ground_truth": "727.2",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The last three digits of \\( 1978^n \\) and \\( 1978^m \\) are the same. Find the positive integers \\( m \\) and \\( n \\) such that \\( m+n \\) is minimized (here \\( n > m \\geq 1 \\)).",
"role": "user"
}
] | {
"ground_truth": "106",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. For the numbers $x$ and $y, 0<x<y$, the equation $x^{2}+4 y^{2}=5 x y$ holds. Calculate the value of the expression $\\frac{x+2 y}{x-2 y}$.",
"role": "user"
}
] | {
"ground_truth": "-3",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Arrange the 5 numbers $2,0,1,9,2019$ in any order in a row, to form an 8-digit number (the first digit cannot be 0), then the number of different 8-digit numbers that can be produced is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "95",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. (16 points) Two vegetable bases, A and B, supply the same type of vegetables to three farmers' markets, $A$, $B$, and $C$. According to the signed contract, 45 t should be supplied to $A$, 75 t to $B$, and 40 t to $C$. Base A can arrange for 60 t, and Base B can arrange for 100 t. The distance ... | {
"ground_truth": "960",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. [6] A sphere is the set of points at a fixed positive distance $r$ from its center. Let $\\mathcal{S}$ be a set of 2010dimensional spheres. Suppose that the number of points lying on every element of $\\mathcal{S}$ is a finite number $n$. Find the maximum possible value of $n$.",
"role": "u... | {
"ground_truth": "2",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1614. 600 corn seeds are planted with a probability of 0.9 for each seed to germinate. Find the boundary of the absolute value of the deviation of the frequency of germinated seeds from the probability $p=0.9$, if this boundary is to be guaranteed with a probability $P=0.995$.",
"role": "user"... | {
"ground_truth": "0.034",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Given the function\n$$\nf(x)=A \\cos \\left(\\omega x+\\frac{\\pi}{4} \\omega\\right)(A>0)\n$$\n\nis decreasing on $\\left(0, \\frac{\\pi}{8}\\right)$. Then the maximum value of $\\omega$ is",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Parallelogram ABCD is made up of four equilateral triangles of side length 1. Calculate the length of diagonal AC. Express your answer as a radical if necessary.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{7}",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. Find $P_{4}^{\\neq}(16)$.\n\n untranslated text is preserved in the response, maintaining the original line breaks and format.",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. B. Given that the lengths of the two legs are integers $a$ and $b$ $(b<2011)$. Then the number of right triangles with the hypotenuse length $b+1$ is",
"role": "user"
}
] | {
"ground_truth": "31",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.7. Given a polynomial\n\n$$\nP(x)=a_{2 n} x^{2 n}+a_{2 n-1} x^{2 n-1}+\\ldots+a_{1} x+a_{0}\n$$\n\nwhere each coefficient $a_{i}$ belongs to the interval $[100,101]$. For what minimal $n$ can such a polynomial have a real root? (I. Bogdanov, K. Sukhov)",
"role": "user"
}
] | {
"ground_truth": "100",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A conveyor system produces on average 85% of first-class products. How many products need to be sampled so that, with a probability of 0.997, the deviation of the frequency of first-class products from 0.85 in absolute magnitude does not exceed 0.01?",
"role": "user"
}
] | {
"ground_truth": "11475",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a game, a strictly positive integer $n$ can be replaced by the integer $a b$ if $n=a+b$, with strictly positive integers $a$ and $b$. Can we obtain the number 2011 starting from $n=5$?",
"role": "user"
}
] | {
"ground_truth": "2011",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two vertices of a right triangle are located at \\((3, 3)\\) and \\((0,0)\\). The third vertex is on the positive branch of the \\(x\\)-axis. What are the coordinates of the third vertex if the area of the triangle is 18 square units?",
"role": "user"
}
] | {
"ground_truth": "(12,0)",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Find all real numbers $P$ such that the cubic equation $5 x^{3}-5(P+1) x^{2}+(71 P-1) x+1=66 P$ has three roots that are all natural numbers.",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.3125
} | 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: Nationality, Hobby, Music-Genre, Beverage, Sport, Transport.\nThe attributes have the following possible values:\n- Nationality: argentine, canadian, mexican, thai\n- Ho... | {
"ground_truth": "water",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Using each of the nine digits exactly once, form prime numbers (numbers that are divisible only by 1 and themselves) such that their sum is minimized.",
"role": "user"
}
] | {
"ground_truth": "207",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. Let $a_{1}, a_{2}, \\cdots, a_{50}, b_{1}, b_{2}, \\cdots, b_{50}$ be distinct numbers, such that the following equation\n$$\n\\left|x-a_{1}\\right|+\\cdots+\\left|x-a_{50}\\right|=\\left|x-b_{1}\\right|+\\cdots+\\left|x-b_{50}\\right|\n$$\n\nhas a finite number of roots. How many roots can th... | {
"ground_truth": "49",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14. Teacher $D$ placed cards with the numbers $1, 2, \\cdots, 13$ in a clockwise order on a circle. Initially, all cards are face up. Each time, one card can be flipped to face down (once a card is face down, it cannot be flipped again). Teacher $D$'s rule for flipping cards is: if a face-up card ... | {
"ground_truth": "26624",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Find all real numbers $p$ such that the cubic equation $5 x^{3}-5(p+1) x^{2}+(71 p-1) x+1=66 p$ has three roots that are all natural numbers.",
"role": "user"
}
] | {
"ground_truth": "76",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two planes, $P$ and $Q$ , intersect along the line $p$ . The point $A$ is given in the plane $P$ , and the point $C$ in the plane $Q$ ; neither of these points lies on the straight line $p$ . Construct an isosceles trapezoid $ABCD$ (with $AB \\parallel CD$ ) in which a circle can be ... | {
"ground_truth": " ABCD ",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 15 Find the minimum value of $\\sqrt{x^{2}+1}+\\sqrt{(4-x)^{2}+4}$.\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": "5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( a, b, c, d \\) be 4 distinct nonzero integers such that \\( a + b + c + d = 0 \\) and the number \\( M = (bc - ad)(ac - bd)(ab - cd) \\) lies strictly between 96100 and 98000. Determine the value of \\( M \\).",
"role": "user"
}
] | {
"ground_truth": "97344",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "12 people attend two separate meetings. At the first meeting, 7 people attend and shake hands with each other. At the next meeting, 5 new people attend along with 2 people from the previous meeting, and everyone shakes hands with each other without anyone from the first meeting shaking hands again... | {
"ground_truth": "41",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A wooden cube has edges of length $3$ meters. Square holes, of side one meter, centered in each face are cut through to the opposite face. The edges of the holes are parallel to the edges of the cube. The entire surface area including the inside, in square meters, is",
"role": "user"
}
] | {
"ground_truth": "72",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "I1.1 Three cubes with volumes $1,8,27$ are glued together at their faces. If $a$ is the smallest possible surface area of the resulting polyhedron, find the value of $a$.",
"role": "user"
}
] | {
"ground_truth": "72",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the slope angle of the line passing through the points (-2,1) and (1,4). Express your answer in degrees, including the degree symbol (°).",
"role": "user"
}
] | {
"ground_truth": "45°",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nA sphere is inscribed in a dihedral angle.\n\nPoint \\( O \\) is located in the section \\( A A^{\\prime} C^{\\prime} C \\) of a rectangular parallelepiped \\( A B C D A^{\\prime} B^{\\prime} C^{\\prime} D^{\\prime} \\) with dimensions \\( 2 \\times 6 \\times 9 \\) such that \\( \\angle O A B + ... | {
"ground_truth": "3",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A cube has six faces, and each face has two diagonals. From these diagonals, choose two to form a pair. Among these pairs, how many form an angle of $60^\\circ$?",
"role": "user"
}
] | {
"ground_truth": "48",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From the set {0,1,2,3,4,5,6}, two distinct numbers a and b are chosen to form the complex number a+bi. How many imaginary numbers can be formed? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "36",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's find a 6-digit number that is a perfect square and remains the same when the order of its digits is reversed.",
"role": "user"
}
] | {
"ground_truth": "698896",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Thompson, a parent who believes that teachers should focus solely on academic subjects, is organizing a math-focused weekend event for students. He decides to create a workbook with a series of math exercises. For every 5 math problems he writes, he takes a 10-minute break. If he spends a tota... | {
"ground_truth": "45",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Given that $a$, $b$, $c$, $d$ are the thousands, hundreds, tens, and units digits of a four-digit number, respectively, and the digits in lower positions are not less than those in higher positions. When $|a-b|+|b-c|+|c-d|+|d-a|$ takes the maximum value, the maximum value of this four-digit num... | {
"ground_truth": "1999",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 3, 7, and 7, as shown. What is the area of the shaded quadrilateral? [asy] unitsize(1.5cm); defaultpen(.8); pair A = (0,0), B = (3,0),... | {
"ground_truth": "18",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. The number of integers $n$ that make $n^{4}-3 n^{2}+9$ a prime number is $\\qquad$.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Pauline Bunyan can shovel snow at the rate of $20$ cubic yards for the first hour, $19$ cubic yards for the second, $18$ for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is $4$ yards wide, $10$ yards long, and covered with snow $3$ yards d... | {
"ground_truth": "7",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. A semicircle $\\Gamma$ has diameter $A B=25$. Point $P$ lies on $A B$ with $A P=16$ and $C$ is on the semicircle such that $P C \\perp A B$. A circle $\\omega$ is drawn so that it is tangent to segment $P C$, segment $P B$, and $\\Gamma$. What is the radius of $\\omega$ ?",
"role": "user"
... | {
"ground_truth": "4",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sequence of vertices $v_1,v_2,\\ldots,v_k$ in a graph, where $v_i=v_j$ only if $i=j$ and $k$ can be any positive integer, is called a $\\textit{cycle}$ if $v_1$ is attached by an edge to $v_2$ , $v_2$ to $v_3$ , and so on to $v_k$ connected to $v_1$ . Rotations and reflection... | {
"ground_truth": "1001",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A third-year student at Washington University is planning her class schedule for the semester. She wants to take a total of 5 classes. Each class has a different number of credit hours: 3, 4, 2, 5, and 3. She attends each class once a week, and each class session is 1.5 hours long. How many total ... | {
"ground_truth": "112.5",
"mean_reward": 0.375
} | 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 each integer $n\\ge 2$ , determine, with proof, which of the two positive real numbers $a$ and $b$ satisfying \\[a^n=a+1,\\qquad b^{2n}=b+3a\\] is larger.\n\n[Sol... | {
"ground_truth": "4",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. If $x^{4}+16 x=12$, then $(x+1)^{2}=$\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": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If \\( a \\) and \\( b \\) are prime numbers greater than 7, then the expression\n\n$$\n\\left(a^{2}-1\\right)\\left(b^{2}-1\\right)\\left(a^{6}-b^{6}\\right)\n$$\n\nis divisible by 290304.",
"role": "user"
}
] | {
"ground_truth": "290304",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the relationships between the number of days required by teams A, B, and C working alone and together, calculate the value of the expression \n\n\\[\n\\frac{1}{a+1} + \\frac{1}{b+1} + \\frac{1}{c+1}\n\\]\n\nwhere a, b, and c are defined as in the original problem. Express your answer as a si... | {
"ground_truth": "1",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.5. In the parliament of the island state of Promenade-and-Tornado, 2019 indigenous inhabitants were elected, who are divided into knights and liars: knights always tell the truth, liars always lie. At the first meeting, 2016 of them sat in the parliamentary seats arranged in the hall in a rectan... | {
"ground_truth": "227",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.