prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "6. (B. Frenkin) A rook has traversed an $n \\times n$ board, visiting each cell exactly once, with each move being exactly one cell. The cells are numbered from 1 to $n^{2}$ in the order of the rook's traversal. Let $M$ be the maximum difference between the numbers of adjacent (by side) cells. Wha... | {
"ground_truth": "2n-1",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 9.8. From the set $\\{1,2,3, \\ldots, n\\}$, 9 distinct numbers are chosen and written in the cells of a $3 \\times 3$ table such that the products of the numbers in each row, column, and diagonal are equal. Determine the smallest value of $n$ for which such a table exists.",
"role": "... | {
"ground_truth": "36",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all the real numbers $k$ that have the following property: For any non-zero real numbers $a$ and $b$ , it is true that at least one of the following numbers: $$ a, b,\\frac{5}{a^2}+\\frac{6}{b^3} $$ is less than or equal to $k$ .",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a professional bowling competition's final phase, the top five players compete in a sequence where the loser of each match is awarded a place from 5th to 2nd, and the winner of the final match is awarded 1st place. Given that each match has two possible outcomes (a win or a loss), calculate the... | {
"ground_truth": "16",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose $S_n$ is the set of positive divisors of $n$, and denote $|X|$ as the number of elements in a set $X$. Let $\\xi$ be the set of positive integers $n$ where $|S_n| = 2m$ is even, and $S_n$ can be partitioned evenly into pairs $\\{a_i, b_i\\}$ for integers $1 \\le i \\le m$ such that the fol... | {
"ground_truth": "64",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nProblem 3. Find the least positive integer $n$ such that there exists a group of $n$ people such that:\n\n1. There is no group of four every two of which are friends;\n2. For any choice of $k \\geq 1$ people among which there are no friends there exists a group of three among the remaining $n-k$... | {
"ground_truth": "7",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given points D and E on sides AB and AC of ∠CAB respectively, the angle bisectors of ∠BDE and ∠CED intersect at F. If ∠BAC = 38°, find the measure of ∠DFE. Express your answer in degrees as a whole number.",
"role": "user"
}
] | {
"ground_truth": "71^\\circ",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On semicircle, with diameter $|AB|=d$ , are given points $C$ and $D$ such that: $|BC|=|CD|=a$ and $|DA|=b$ where $a, b, d$ are different positive integers. Find minimum possible value of $d$ ",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7,8,9 |\n\nIn a deck of 16 cards, numbered from top to bottom. It is allowed to take a portion of the deck from the top, after which the removed and remaining parts of the deck, without flipping, are \"interleaved\" with each other. Can it happen that after several such operations, the cards end u... | {
"ground_truth": "4",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five children had dinner. Chris ate more than Max. Brandon ate less than Kayla. Kayla ate less than Max but more than Tanya. What is the name of the child who ate the second most?",
"role": "user"
}
] | {
"ground_truth": "Max",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Through point \\( A \\) located on a circle, a diameter \\( AB \\) and a chord \\( AC \\) are drawn, where \\( AC = 8 \\) and \\( \\angle BAC = 30^\\circ \\).\n\nFind the length of the chord \\( CM \\), which is perpendicular to \\( AB \\).",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A unit square is called \"colorful\" if three of its four sides are colored in three different colors. Consider the $1 \\times 3$ grid, which contains 10 unit length line segments. These 10 line segments are to be colored using red, yellow, or blue, such that all three unit squares are colorful. H... | {
"ground_truth": "5184",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $n$ and $k$ be positive integers. Find all monic polynomials $f\\in \\mathbb{Z}[X]$, of degree $n$, such that $f(a)$ divides $f(2a^k)$ for $a\\in \\mathbb{Z}$ with $f(a)\\neq 0$.",
"role": "user"
}
] | {
"ground_truth": " f = X^n ",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ms. Math's kindergarten class has $16$ registered students. The classroom has a very large number, $N$, of play blocks which satisfies the conditions:\n (a) If $16$, $15$, or $14$ students are present in the class, then in each case all the blocks can be distributed in equal numbers to each studen... | {
"ground_truth": "148",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. Determine the number of 8-digit positive integers such that after deleting any one digit, the remaining 7-digit number is divisible by 7 .",
"role": "user"
}
] | {
"ground_truth": "64",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Sarah is a university student who loves exploring Islamic history and literature, especially Hadith sciences. She is organizing her collection of Hadith books on her bookshelf. She has 15 books on the history of Hadith, 12 books on Hadith interpretation, and 8 books on Hadith narrators. She wants ... | {
"ground_truth": "8",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the double integral\n\n$$\n\\iint_{D} x \\, dx \\, dy\n$$\n\nwhere the region \\( D \\) is bounded by the lines\n\n$$\ny^{2} - 4y + x^{2} = 0, \\quad y^{2} - 8y + x^{2} = 0, \\quad y = \\frac{x}{\\sqrt{3}}, \\quad x = 0\n$$",
"role": "user"
}
] | {
"ground_truth": "35",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the parabola $y^2 = 8x$ and the point (2, 4) which lies on it, determine the number of lines that pass through the point (2, 4) and intersect the parabola at exactly one point. Provide your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the minimum area of a triangle that contains a unit square?",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The number $734{,}851{,}474{,}594{,}578{,}436{,}096$ is equal to $n^6$ for some positive integer $n$ . What is the value of $n$ ?",
"role": "user"
}
] | {
"ground_truth": "3004",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the right-angled triangle $LMN$, suppose $\\sin N = \\frac{3}{5}$. If the length of $LM$ is 15, calculate the length of $LN$.",
"role": "user"
}
] | {
"ground_truth": "25",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 14. Problem 14\n\nCalculate the cadastral value of a land plot with an area of 11 acres, if the amount of tax paid amounted to 3300 rubles (tax rate $0.3 \\%$)",
"role": "user"
}
] | {
"ground_truth": "11000",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $P$ be a point not on line $XZ$ and $Q$ a point on line $XZ$ such that $PQ \\perp XZ.$ Meanwhile, $R$ is a point on line $PZ$ such that $SR \\perp PZ.$ If $SR = 5,$ $PQ = 6,$ and $XZ = 7,$ then what is the length of $PZ?$",
"role": "user"
}
] | {
"ground_truth": "8.4",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example. Random variables $\\xi_{1}, \\xi_{2}, \\ldots$ are independent and distributed according to the Poisson law with parameter $a=1$. Let $S_{n}=$ $=\\xi_{1}+\\ldots+\\xi_{n}, n=1,2, \\ldots$ Find the probability $\\mathrm{P}\\left(2 S_{300}>S_{600}-30\\right)$.",
"role": "user"
}
] | {
"ground_truth": "0.8897",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the values of $a, b$, and $c$ that satisfy the equality $\\sqrt{a^2 - \\frac{b}{c}} = a - \\sqrt{\\frac{b}{c}}$, where $a, b$, and $c$ are positive integers.",
"role": "user"
}
] | {
"ground_truth": "b = a^2c",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 35 (1999 Shanghai High School Competition Question) Let $a, b, c, d$ be four distinct real numbers such that $\\frac{a}{b}+\\frac{b}{c}+\\frac{c}{d}+\\frac{d}{a}=4$, and $a c=b d$. Find the maximum value of $\\frac{a}{c}+\\frac{b}{d}+\\frac{c}{a}+\\frac{d}{b}$.",
"role": "user"
}
] | {
"ground_truth": "-12",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4 [\n\nOn a sphere of radius 11, points $A, A 1, B, B 1, C$ and $C 1$ are located. Lines $A A 1, B B 1$ and $C C 1$ are pairwise perpendicular and intersect at point $M$, which is at a distance of $\\sqrt{59}$ from the center of the sphere. Find $A A 1$, given that $B B 1=18$, and point $M$ divide... | {
"ground_truth": "20",
"mean_reward": 0.234375
} | 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, *Neymar* 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 *Neymar* will never be able to write on the... | {
"ground_truth": " 2033 ",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Construct a curve of constant width \\( h \\), composed of five, seven, or any odd number of arcs of circles with radius \\( h \\). What is the length of each of these curves?",
"role": "user"
}
] | {
"ground_truth": "\\pi h",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$\\underline{\\text { Folklore }}$Among 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 partici... | {
"ground_truth": "5",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The number $2024$ needs to be expressed in the form $\\frac{a_1!a_2!...a_m!}{b_1!b_2!...b_n!}$, where $a_1 \\ge a_2 \\ge \\cdots \\ge a_m$ and $b_1 \\ge b_2 \\ge \\cdots \\ge b_n$ are positive integers and $a_m + b_n$ is as small as possible. Find the value of $|a_m - b_n|$.",
"role": "user"
... | {
"ground_truth": "1",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Professor Smith, an esteemed professor of military history, is conducting a demonstration of a famous historical battle. He sets up a battlefield on a large table with miniature soldiers to recreate the scene. In his demonstration, he uses 75 red soldiers to represent one army and 120 blue soldier... | {
"ground_truth": "21",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that the sum of $n$ positive integers $x_{1}, x_{2}, \\cdots, x_{n}$ is 2016. If these $n$ numbers can be divided into 32 groups with equal sums as well as into 63 groups with equal sums, find the minimum value of $n$.",
"role": "user"
}
] | {
"ground_truth": "94",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The perimeter of the parallelogram \\(ABCD\\) is 20. The bisector of angle \\(B\\) intersects the lines \\(AD\\) and \\(CD\\) at points \\(K\\) and \\(L\\) respectively. Find \\(CL\\), given that \\(DK = 4\\).",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A train with cross-sectional area $S_{t}$ is moving with speed $v_{t}$ inside a long tunnel of cross-sectional area $S_{0}\\left(S_{0}=4 S_{t}\\right)$. Assume that almost all the air (density $\\rho$ ) in front of the train flows back between its sides and the walls of the tunnel. Also, the air f... | {
"ground_truth": "9",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If \\( z = 2 \\cos \\frac{\\pi}{8}\\left(\\sin \\frac{3 \\pi}{4} + i \\cos \\frac{3 \\pi}{4} + i\\right) \\), then \\( z^{12} = \\) ?",
"role": "user"
}
] | {
"ground_truth": "-64 i",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A driver is transporting milk in a cylindrical tank. The diameter of the base is $180 \\mathrm{~cm}$, and the length of the tank is $4 \\mathrm{~m}$. How many hectoliters of milk are in the tank if it is filled to three-quarters of the diameter?\n\n![](https://cdn.mathpix.com/cropped/2024_04_17_2a... | {
"ground_truth": "82",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The squadron of $10$ powerful destroyers and $20$ small boats is about to attack the island. All ships are positioned on the straight line, and are equally spaced. \n\nTwo torpedo boats with $10$ torpedoes each want to protect the island. However, the first torpedo boat can shoot only $10$ ... | {
"ground_truth": "3",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that there are $400$ adults in total in City Z, with $370$ adults owning bikes and $75$ adults owning scooters, determine the number of bike owners who do not own a scooter.",
"role": "user"
}
] | {
"ground_truth": "325",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "77. The number of numbers that are divisible by 2145 and have exactly 2145 divisors 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": "24",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the pyramid \\(ABCD\\), the dihedral angle at edge \\(AC\\) is \\(90^{\\circ}\\), \\(AB = BC = CD\\), and \\(BD = AC\\). Find the dihedral angle at edge \\(AD\\).",
"role": "user"
}
] | {
"ground_truth": "60^\\circ",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given real numbers $a, b, c, d$ satisfy $a^{4}+b^{4}=c^{4}+d^{4}=2011, a c+b d=0$. Find the value of $a b+c d$.\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": "0",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider a $(2m-1)\\times(2n-1)$ rectangular region, where $m$ and $n$ are integers such that $m,n\\ge 4.$ The region is to be tiled using tiles of the two types shown:\n\\[\n\\begin{picture}(140,40)\n\n\\put(0,0){\\line(0,1){40}}\n\\put(0,0){\\line(1,0){20}}\n\\put(0,40){\\line(1,0){40}}\... | {
"ground_truth": "mn",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ivan, a proud nationalist from Russia, is organizing a cultural festival to celebrate Russian history and achievements. He wants to include a display of Russian traditional crafts and plans to hand out small Russian flags to each visitor. Ivan orders 1500 mini flags in total. On the first day of t... | {
"ground_truth": "500",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The altitudes $A D$ and $B E$ of an acute-angled triangle $A B C$ intersect at point $H$. The circumcircle of triangle $A B H$ intersects sides $A C$ and $B C$ at points $F$ and $G$ respectively. Find $F G$, if $D E=5$ cm.",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The year 2009 has a unique property: by rearranging the digits of the number 2009, it is impossible to form a smaller four-digit number (numbers do not start with zero). In which future year will this property first repeat again?",
"role": "user"
}
] | {
"ground_truth": "2022",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that a scout troop buys 800 candy bars at a price of six for $3 dollars and incurs an additional expense of $50 on transportation, and they sell all the candy bars at the price of three for $2 dollars, calculate their profit.",
"role": "user"
}
] | {
"ground_truth": "83.33",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that $\\sqrt{23.6}=4.858$ and $\\sqrt{2.36}=1.536$, calculate the value of $\\sqrt{0.00236}$. Express your answer as a decimal value.",
"role": "user"
}
] | {
"ground_truth": "0.04858",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $P(x) = x^3 + 8x^2 - x + 3$ and let the roots of $P$ be $a, b,$ and $c.$ The roots of a monic polynomial $Q(x)$ are $ab - c^2, ac - b^2, bc - a^2.$ Find $Q(-1).$",
"role": "user"
}
] | {
"ground_truth": "1536",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Znayka told Neznayka that to convert kilolunes to kilograms, one needs to divide the mass in kilolunes by 4 and then decrease the obtained number by $4 \\%$. Neznayka decided that to convert from kilograms to kilolunes, one should multiply the mass in kilograms by 4 and then increase the obtain... | {
"ground_truth": "0.16",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B6. Sixteen counters, which are black on one side and white on the other, are arranged in a 4 by 4 square. Initially all the counters are facing black side up. In one 'move', you must choose a 2 by 2 square within the square and turn all four counters over once.\nDescribe a sequence of 'moves' of ... | {
"ground_truth": "6",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. The right figure is composed of 4 regular hexagons, each with an area of 6. Using the vertices of these 4 hexagons as vertices, the number of equilateral triangles that can be formed with an area of 4 is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 6 In 45 km away from city $A$, there is a metal mine at location $B$. It is known that there is a straight railway $A X$ from $A$ to a certain direction, and the distance from $B$ to this railway is 27 km. To transport materials between $A$ and $B$, it is planned to build a road from a poi... | {
"ground_truth": "20.41",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 4 As shown in Figure 4, in $\\triangle A B C$, $A B=A C, \\angle A$ $=100^{\\circ}, I$ is the incenter, and $D$ is a point on side $A B$ such that $B D=B I$. Find the measure of $\\angle B C D$.\n\nTranslate the above text into English, please keep the original text's line breaks and forma... | {
"ground_truth": "30",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let the elements of set $A$ be positive integers, and for any $x, y \\in A, x>y$, it holds that $x-y \\geq \\frac{x y}{25}$. What is the maximum number of elements that set $A$ can have?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n5. The side-lengths $a, b, c$ of a triangle $A B C$ are positive integers. Let\n\n$$\nT_{n}=(a+b+c)^{2 n}-(a-b+c)^{2 n}-(a+b-c)^{2 n}+(a-b-c)^{2 n}\n$$\n\nfor any positive integer $n$. If $\\frac{T_{2}}{2 T_{1}}=2023$ and $a>b>c$, determine all possible perimeters of the triangle $A B C$.\n\n",
... | {
"ground_truth": "49",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nFind all functions $f:\\mathbb Z_{>0}\\to \\mathbb Z_{>0}$ such that $a+f(b)$ divides $a^2+bf(a)$ for all positive integers $a$ and $b$ with $a+b>2019$.\n\n[Solution]... | {
"ground_truth": "1",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An official from the national human rights commission is organizing a project to distribute reports to different universities. They have a total of 480 reports to distribute. Each university needs to receive a set of 4 different reports. If the official is assisting 12 graduate students, and each ... | {
"ground_truth": "40",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A hexagon is created by joining, in order, the points $(0,0)$, $(2,1)$, $(3,3)$, $(2,4)$, $(0,3)$, $(1,1)$, and back to $(0,0)$. The perimeter of this hexagon can be written in the form $p+q\\sqrt{2}+r\\sqrt{10}$, where $p$, $q$, and $r$ are integers. Find $p+q+r$.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Tim has a working analog 12 -hour clock with two hands that run continuously (instead of, say, jumping on the minute). He also has a clock that runs really slow-at half the correct rate, to be exact. At noon one day, both clocks happen to show the exact time. At any given instant, the hands on ... | {
"ground_truth": "33",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the least number of colors needed to shade the tessellation shown, such that no two tiles sharing a side or overlapping vertically are the same color? The tessellation consists of a base layer of rectangles uniformly placed and a top layer consisting of circles, where each circle overlaps ... | {
"ground_truth": "3",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Bob has five airplane tickets with prices $\\$ 100, \\$ 120, \\$ 140, \\$ 160$, and $\\$ 180$. Bob gives an offer to Aerith: she can distribute his tickets among two bags, after which, without looking inside, Bob will randomly choose a bag and a ticket from it for Aerith to keep. What strategy sho... | {
"ground_truth": "155",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Without using any measuring tools or other auxiliary means, how can you cut exactly half a meter from a piece of cloth that is $\\frac{8}{15}$ meters long?",
"role": "user"
}
] | {
"ground_truth": "1/2",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a data scientist who loves exploring the city and taking street photographs. On a sunny Saturday, Alex decides to visit 5 different neighborhoods. In each neighborhood, Alex plans to take 24 photos. After visiting 3 neighborhoods, Alex realizes that they have filled up one of their camera'... | {
"ground_truth": "48",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When the integer $ {\\left(\\sqrt{3} \\plus{} 5\\right)}^{103} \\minus{} {\\left(\\sqrt{3} \\minus{} 5\\right)}^{103}$ is divided by 9, what is the remainder?",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangular barn with a roof is 12 yd. wide, 15 yd. long and 7 yd. high. Calculate the total number of sq. yd. to be painted inside and outside on the walls and the ceiling, and only on the outside of the roof but not on the floor.",
"role": "user"
}
] | {
"ground_truth": "1116",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose $a$, $b$ and $c$ are positive integers with $a+b+c=2006$, and $a!b!c!=m\\cdot 10^n$, where $m$ and $n$ are integers and $m$ is not divisible by $10$. What is the smallest possible value of $n$?",
"role": "user"
}
] | {
"ground_truth": "492",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Problem 3.\n\nIn triangle $A B C$, the bisector $B E$ and the median $A D$ are equal and perpendicular. Find the area of triangle $A B C$, if $A B=\\sqrt{13}$.",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide? [asy] draw((0,0)-... | {
"ground_truth": "5",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Represent the number 36 as the product of three whole number factors, the sum of which is equal to 4. What is the smallest of these factors?",
"role": "user"
}
] | {
"ground_truth": "-4",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex, a politically conservative book editor, is organizing a book drive in support of her community's local library. She has 120 books to donate, which she believes reflect her values and can encourage thoughtful discussion. During a bipartisan event, she decides to divide the books equally among... | {
"ground_truth": "6",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Each face of a $6 \\times 6 \\times 6$ cube is divided into $1 \\times 1$ cells. The cube is covered with $2 \\times 2$ squares such that each square covers exactly four cells, no squares overlap, and each cell is covered by an equal number of squares. What is the maximum value of this equal numbe... | {
"ground_truth": "3",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider the set $S$ of permutations of $1, 2, \\dots, 2022$ such that for all numbers $k$ in the\npermutation, the number of numbers less than $k$ that follow $k$ is even.\n\nFor example, for $n=4; S = \\{[3,4,1,2]; [3,1,2,4]; [1,2,3,4]; [1,4,2,3]\\}$ If $|S| = (a!)^b$ where $a, b \... | {
"ground_truth": "2022",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many different positions can appear on a chessboard if both players, starting from the initial position, make just one move each?",
"role": "user"
}
] | {
"ground_truth": "400",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Rectangle $EFGH$ has sides $\\overline {EF}$ of length 6 and $\\overline {FG}$ of length 8. Divide $\\overline {EF}$ into 200 congruent segments with points $E=P_0, P_1, \\ldots, P_{200}=F$, and divide $\\overline {FG}$ into 200 congruent segments with points $F=Q_0, Q_1, \\ldots, Q_{200}=G$. For ... | {
"ground_truth": "2000",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2. Using the parabola formula with an accuracy of 0.0001, calculate $\\int_{0}^{1} \\frac{d x}{1+x^{2}}$",
"role": "user"
}
] | {
"ground_truth": "0.785395",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the following sum, \\( O \\) represents the digit 0. \\( A, B, X, \\) and \\( Y \\) each represent distinct digits. How many possible digits can \\( A \\) be?\n$$\n\\begin{array}{r}\nA O O B A O O B \\\\\n+\\quad B O O A B O O A \\\\\n\\hline X X O X Y X O X X\n\\end{array}\n$$\nExpress your an... | {
"ground_truth": "6",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n5. Find all real $a$ for which there exists a function $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ such that $f(x-f(y))=f(x)+a[y]$ for every real $x$ и $y$ ( $[y]$ denotes the integral part of $y$ ).\n\nAnswer: $a=-n^{2}$ for arbitrary integer $n$.\n",
"role": "user"
}
] | {
"ground_truth": "-n^{2}",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sample is divided into 5 groups, with a total of 160 data points in the first, second, and third groups, and a total of 260 data points in the third, fourth, and fifth groups, and the frequency of the third group is 0.20. Calculate the frequency of the third group.",
"role": "user"
}
] | {
"ground_truth": "70",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Within a cube structure consisting of 8 vertices, the midpoints of the 12 edges, the centers of the 6 faces, and the center of the cube (totaling 27 points), determine the total number of groups of three collinear points.",
"role": "user"
}
] | {
"ground_truth": "49",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mary is preparing for a Sunday service at her Christian Science Church, where she plans to hand out special bookmarks with inspirational quotes. She has 120 bookmarks and wants to distribute them equally among the 8 Sunday school classes. Each class should also receive an extra bookmark for the te... | {
"ground_truth": "15",
"mean_reward": 0.03125
} | 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
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Shapovalov A.V.\n\n55 boxers participated in a tournament with a \"loser leaves\" system. The fights proceeded sequentially. It is known that in each match, the number of previous victories of the participants differed by no more than 1. What is the maximum number of fights the tournament winner c... | {
"ground_truth": "8",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the interest rate (between 0 and 1) for an account that started with $5,000 and now has $13,000 and has been compounded annually for the past 12 years. Answer with the numeric value.",
"role": "user"
}
] | {
"ground_truth": "0.0828",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. (6 points) As shown in the figure, the side length of square $A B C D$ is 8 cm, the length of $A E$ is 10 cm, and the length of $B E$ is 6 cm. Then the length of $D F$ is $\\qquad$ cm.",
"role": "user"
}
] | {
"ground_truth": "6.4",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "You and a friend play a dangerous game starting from some point \\((x,y)\\) with nonnegative integers \\(x\\) and \\(y\\). On your turn, you command your friend to move from \\((x,y)\\) to one of three positions: left to \\((x-1,y)\\), down to \\((x,y-1)\\), or diagonally to \\((x-1,y-1)\\) (moves... | {
"ground_truth": "90133",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( n \\) be a natural number and \\( f(n) \\) be the sum of the digits of \\( n^2 + 1 \\) (in base 10),\n\\[ f^{(1)}(n) = f(n), \\quad f^{(2)}(n) = f(f(n)), \\quad \\ldots, \\quad f^{(k+1)}(n) = f(f^{(k)}(n)), \\]\nfor \\( k \\geq 1 \\). Find \\( f^{(100)}(1990) \\).",
"role": "user"
}
... | {
"ground_truth": "11",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a software developer who specializes in creating custom publishing software for independent authors. He recently developed a new software package that helps authors publish their books more efficiently. Alex has already sold this software to 15 authors at a price of $120 each.\n\nNow, Alex... | {
"ground_truth": "1500",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "31. [23] Let\n$$\nP=\\prod_{i=0}^{2016}\\left(i^{3}-i-1\\right)^{2} .\n$$\n\nThe remainder when $P$ is divided by the prime 2017 is not zero. Compute this remainder.",
"role": "user"
}
] | {
"ground_truth": "1994",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a rectangular storage with length 20 feet, width 15 feet, and height 10 feet, and with the floor and each of the four walls being two feet thick, calculate the total number of one-foot cubical blocks needed for the construction.",
"role": "user"
}
] | {
"ground_truth": "1592",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Properties and signs of tangents ] [ Rectangles and squares. Properties and signs ]\n\nTwo circles are given. Their common internal tangents are perpendicular to each other. The chords connecting the points of tangency are 3 and 5. Find the distance between the centers of the circles.",
"rol... | {
"ground_truth": "8",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\dots, a_{-1}, a_0, a_1, a_2, \\dots$ be a sequence of positive integers satisfying the folloring relations: $a_n = 0$ for $n < 0$ , $a_0 = 1$ , and for $n \\ge 1$ ,\n\\[a_n = a_{n - 1} + 2(n - 1)a_{n - 2} + 9(n - 1)(n - 2)a_{n - 3} + 8(n - 1)(n - 2)(n - 3)a_{n - 4}.\\]\nCompute\n\\[\... | {
"ground_truth": "e^{23110}",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What percent of the square $EFGH$ is shaded? All angles in the diagram are right angles, and the side length of the square is 8 units. In this square:\n- A smaller square in one corner measuring 2 units per side is shaded.\n- A larger square region, excluding a central square of side 3 units, occu... | {
"ground_truth": "17.1875\\%",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Evaluate the expression $(2(2(2(2(2(2(3+2)+2)+2)+2)+2)+2)+2)$.",
"role": "user"
}
] | {
"ground_truth": "446",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mason is seeking to ascertain the Fermat point \\(P\\) of \\(\\triangle ABC\\), where \\(A\\) is at the origin, \\(B\\) is at \\( (12, 0) \\), and \\(C\\) is at \\( (4, 6) \\). Thinking that \\(P = (5,3)\\) could be the Fermat point, he decides to compute the sum of the distances from \\(P\\) to t... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 7 balls of each of the three colors: red, blue, and yellow. Each set of 7 balls of the same color is numbered from 1 to 7. If we randomly pick 3 balls with different numbers, and these 3 balls are of different colors and their numbers are not consecutive, find the number of ways to do th... | {
"ground_truth": "60",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( p, q, r, s \\) be distinct real numbers such that the roots of \\( x^2 - 12px - 13q = 0 \\) are \\( r \\) and \\( s \\), and the roots of \\( x^2 - 12rx - 13s = 0 \\) are \\( p \\) and \\( q \\). Find the value of \\( p + q + r + s \\).",
"role": "user"
}
] | {
"ground_truth": "2028",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When $0.73\\overline{864}$ is expressed as a fraction in the form $\\frac{y}{999900}$, what is the value of $y$?",
"role": "user"
}
] | {
"ground_truth": "737910",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the least positive integer $n$ ( $n\\geq 3$ ), such that among any $n$ points (no three are collinear) in the plane, there exist three points which are the vertices of a non-isoscele triangle.",
"role": "user"
}
] | {
"ground_truth": " n = 7 ",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Given $f(x)=\\frac{\\left(2^{x}+1\\right)^{2}}{2^{x} \\cdot x}+1$ on $[-2018,0) \\cup(0,2018]$, the maximum value is $M$, and the minimum value is $N$, then $M+N$ ( )\n\n\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translati... | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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