prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "On the board after the class, there was a note left:\n\n\"Calculate $t(0)-t(\\pi / 5)+t\\left((\\pi / 5)-t(3 \\pi / 5)+\\ldots+t\\left({ }^{8 \\pi} / 5\\right)-t(9 \\pi / 5)\\right.$, where $t(x)=\\cos 5 x+* \\cos 4 x+* \\cos 3 x+* \\cos 2 x+$ $*^{\\cos x}+* \"$.\n\nSeeing it, a math student told ... | {
"ground_truth": "10",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine all triples \\((p, q, n)\\) that simultaneously satisfy\n$$\n\\begin{array}{l}\nq^{n+2} \\equiv 3^{n+2}\\left(\\bmod p^{n}\\right), \\\\\np^{n+2} \\equiv 3^{n+2}\\left(\\bmod q^{n}\\right)\n\\end{array}\n$$\nwhere \\( p \\) and \\( q \\) are odd prime numbers, and \\( n \\) is an integer... | {
"ground_truth": "(3, 3, n)",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. In the country of Landia, which breeds an elite breed of horses, an annual festival is held to test their speed, in which only one-year-old, two-year-old, three-year-old, and four-year-old horses can participate. For each horse that meets the speed standard, the festival organizers pay a fixed ... | {
"ground_truth": "200",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "29. There are 4 cards, each with a different number written on it. The doctor first distributes these 4 cards to four children: Damao, Ermao, Sanmao, and Simaoyi, then collects them back and redistributes them. This process is repeated 3 times. If the sum of the numbers on the cards received by Da... | {
"ground_truth": "7",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A number is guessed from 1 to 144. You are allowed to select one subset of the set of numbers from 1 to 144 and ask whether the guessed number belongs to it. For an answer of \"yes,\" you have to pay 2 rubles, and for an answer of \"no\" - 1 ruble. What is the smallest amount of money needed to su... | {
"ground_truth": "11",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. An electronic clock displays time from 00.00.00 to 23.59.59. How much time during a day does the clock display exactly four digit 3s?",
"role": "user"
}
] | {
"ground_truth": "105",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. (10 points) In a deck of cards, $J, Q, K$ are considered as 11, 12, 13 points respectively. From the 13 cards numbered 1 to 13, what is the maximum number of cards you can pick such that there are no 2 pairs of cards where the sum of the points of one pair equals the sum of the points of the ot... | {
"ground_truth": "6",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 7 (CMO-11 Test) Let $S=\\{1,2, \\cdots, 50\\}$, find the smallest natural number $k$, such that in any $-k$ element subset of $S$ there exist two distinct numbers $a$ and $b$, satisfying $(a+b) \\mid a b$.",
"role": "user"
}
] | {
"ground_truth": "39",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that $x$ and $y$ are complex numbers such that $x+y=1$ and that $x^{20}+y^{20}=20$. Find the sum of all possible values of $x^{2}+y^{2}$.",
"role": "user"
}
] | {
"ground_truth": "-90",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A bottle of cola costs 2 yuan, and two empty bottles can be exchanged for one more bottle of cola. With 30 yuan, what is the maximum number of bottles of cola that you can drink?",
"role": "user"
}
] | {
"ground_truth": "29",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13.337. At a plant that manufactures instant coffee, a batch of coffee beans for processing was delivered in late May. One mechanism, which grinds the beans, was put into operation on Monday, June 1st, and ground $m$ kg daily. Starting from June 6th, a second mechanism was added, which ground $n$ ... | {
"ground_truth": "June17",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Triangle $ABC$ is isosceles with $AC = BC$ and $\\angle ACB = 106^\\circ.$ Point $M$ is in the interior of the triangle so that $\\angle MAC = 7^\\circ$ and $\\angle MCA = 23^\\circ.$ Find the number of degrees in $\\angle CMB.$",
"role": "user"
}
] | {
"ground_truth": "83",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A beam of light shines from point \\( S \\), reflects off a reflector at point \\( P \\), and reaches point \\( T \\) such that \\( P T \\) is perpendicular to \\( R S \\). Given that \\(\\angle PTS = 90^\\circ\\) and \\(\\angle TSR = 26^\\circ\\), find the measure of angle \\( x \\). Express your... | {
"ground_truth": "32^\\circ",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 5. Task 5\n\nThe Wolf and Ivan the Tsarevich are 20 versts away from the source of living water, and the Wolf is carrying Ivan the Tsarevich there at a speed of 3 versts per hour. To revive Ivan the Tsarevich, one liter of water is needed, which flows from the source at a rate of half a liter pe... | {
"ground_truth": "4",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex, a responsible older cousin, is a role model for his teenage cousin, Jamie. Alex spends quality time with Jamie by helping him with his studies and planning fun but educational activities. This weekend, Alex decided to mentor Jamie on budgeting and managing time. They started with a simple pr... | {
"ground_truth": "-5",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mia is designing a rectangular flower bed against her house on one side, using 450 feet of fencing to enclose the remaining three sides. If 150 feet of it is planned to be used along the house, what is the maximum area she can achieve for her garden?",
"role": "user"
}
] | {
"ground_truth": "22500",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Triangle $ABC$ satisfies $AB=104$ , $BC=112$ , and $CA=120$ . Let $\\omega$ and $\\omega_A$ denote the incircle and $A$ -excircle of $\\triangle ABC$ , respectively. There exists a unique circle $\\Omega$ passing through $A$ which is internally tangent to $\\omega$ and externall... | {
"ground_truth": "49",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "**polyhedral**\n\nwe call a $12$ -gon in plane good whenever:\nfirst, it should be regular, second, it's inner plane must be filled!!, third, it's center must be the origin of the coordinates, forth, it's vertices must have points $(0,1)$ , $(1,0)$ , $(-1,0)$ and $(0,-1)$ .\nfind the faces of ... | {
"ground_truth": "36",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For any positive integers \\( m \\) and \\( 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 \\)). What is the smallest positive integer solution satisfying the equation \\( r(m, 1) + r(m... | {
"ground_truth": "120",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three. (Full marks 20 points) For every pair of real numbers $x, y$, the function $f(t)$ satisfies $f(x+y)=f(x)+f(y)+xy+1$. If $f(-2)=-2$, find the number of integer solutions $a$ that satisfy $f(a)=a$.\n\nTranslate the above text into English, please retain the original text's line breaks and for... | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6.2. There are 7 safes and 7 codes for them, but it is unknown which code belongs to which safe. What is the minimum number of attempts required to guarantee matching the codes to the safes?",
"role": "user"
}
] | {
"ground_truth": "21",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A set $A$ of positive integers is called *uniform* if, after any of its elements removed, the remaining ones can be partitioned into two subsets with equal sum of their elements. Find the least positive integer $n>1$ such that there exist a uniform set $A$ with $n$ elements.",
"role": ... | {
"ground_truth": "7",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Tarek wants to shade two further squares on the diagram shown so that the resulting pattern has a single axis of symmetry. How many different ways can he complete his pattern symmetrically? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A person is waiting at the $A$ HÉV station. They get bored of waiting and start moving towards the next $B$ HÉV station. When they have traveled $1 / 3$ of the distance between $A$ and $B$, they see a train approaching $A$ station at a speed of $30 \\mathrm{~km/h}$. If they run at full speed eithe... | {
"ground_truth": "10",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Several irrational numbers are written on a blackboard. It is known that for every two numbers $ a$ and $ b$ on the blackboard, at least one of the numbers $ a\\over b\\plus{}1$ and $ b\\over a\\plus{}1$ is rational. What maximum number of irrational numbers can be on the blackboard? \r\n\... | {
"ground_truth": "3",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task B-1.4.\n\nPoints $F, G$, and $H$ lie on the side $\\overline{A B}$ of triangle $A B C$. Point $F$ is between points $A$ and $G$, and point $H$ is between points $G$ and $B$. The measure of angle $C A B$ is $5^{\\circ}$, and $|B H|=|B C|,|H G|=$ $|H C|,|G F|=|G C|,|F A|=|F C|$. What is the ... | {
"ground_truth": "100",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangle with perimeter $176$ is divided into five congruent rectangles as shown in the diagram. What is the perimeter of one of the five congruent rectangles? [asy] defaultpen(linewidth(.8pt)); draw(origin--(0,3)--(4,3)--(4,0)--cycle); draw((0,1)--(4,1)); draw((2,0)--midpoint((0,1)--(4,1))); r... | {
"ground_truth": "80",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Martin decided to spend all his savings on sweets. He found out that he could buy three cream puffs and $3 \\mathrm{dl}$ of Kofola, or $18 \\mathrm{dkg}$ of yogurt raisins, or $12 \\mathrm{dkg}$ of yogurt raisins and half a liter of Kofola. In the end, he bought one cream puff and $6 \\mathrm{dl}$... | {
"ground_truth": "60",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Thirty identical toothpicks were used to create the figure below. There are over 25 triangles in the figure. What is the fewest number of toothpicks that could be removed so that no triangles remain?\n\n[asy]\ndraw((0,0)--(8,0), linewidth(1));\ndraw(2dir(60)--(2dir(60)+(6,0)), linewidth(1));\ndraw... | {
"ground_truth": "10",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $O$ be the origin. $y = c$ intersects the curve $y = 2x - 3x^3$ at $P$ and $Q$ in the first quadrant and cuts the y-axis at $R$ . Find $c$ so that the region $OPR$ bounded by the y-axis, the line $y = c$ and the curve has the same area as the region between $P$ and $Q$ und... | {
"ground_truth": "4/9",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the scores (out of 150) of 8 students in the first year of Shuren High School: 85, 90, 93, 99, 101, 103, 116, and 130, find the 75th percentile of these scores. Express your answer as a single numerical value.",
"role": "user"
}
] | {
"ground_truth": "109.5",
"mean_reward": 0.015625
} | 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, how many ways are there to do th... | {
"ground_truth": "60",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. A car left point A for point B, and a second car left with some delay. When the first car had traveled half the distance, the second car had traveled $26 \\frac{1}{4}$ km, and when the second car had traveled half the distance, the first car had traveled $31 \\frac{1}{5}$ km. After overtaking t... | {
"ground_truth": "58",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Today is Barbara's birthday, and Alberto wants to give her a gift playing the following game. The numbers 0,1,2,...,1024 are written on a blackboard. First Barbara erases $2^{9}$ numbers, then Alberto erases $2^{8}$ numbers, then Barbara $2^{7}$ and so on, until there are only two numbers a,... | {
"ground_truth": "32",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Bakayev E.V.\n\nIn a circle, there are boys and girls (both are present), a total of 20 children. It is known that for each boy, the neighbor in the clockwise direction is a child in a blue T-shirt, and for each girl, the neighbor in the counterclockwise direction is a child in a red T-shirt. Can ... | {
"ground_truth": "10",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. (3 points) On the Island of Misfortune, there live knights who always tell the truth, and liars who always lie. One day, $n$ islanders gathered in a room.\n\nThe first one said: \"Exactly every second person in this room is a liar.\"\n\nThe second one said: \"Exactly every third person in this ... | {
"ground_truth": "2",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "43. As shown in the figure, the degree measure of $\\angle A+\\angle B+\\angle C+\\angle D+\\angle E$ is $\\qquad$ degrees.",
"role": "user"
}
] | {
"ground_truth": "180",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $P$, $A$, $B$, $C$, $D$ be points on a plane such that $PA = 9$, $PB = 19$, $PC = 9$, $PD = 5$, $\\angle APB = 120^\\circ$, $\\angle BPC = 45^\\circ$, $\\angle CPD = 60^\\circ$, and $\\angle DPA = 135^\\circ$. Let $G_1$, $G_2$, $G_3$, and $G_4$ be the centroids of triangles $PAB$, $PBC$, $PCD$... | {
"ground_truth": "29",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The surface of a round table is divided into 9 equal sectors with numbers from 1 to 9 written clockwise. There are 9 players sitting around the table with numbers \\(1, 2, \\ldots, 9\\) seated clockwise. The table can rotate around its axis in both directions while the players remain fixed. The pl... | {
"ground_truth": "57",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a stalk of bamboo with nine sections, with three sections from the bottom holding 3.9 liters, and the four sections from the top holding three liters, determine the combined volume of the middle two sections.",
"role": "user"
}
] | {
"ground_truth": "2.1",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The doctoral student is studying the economic history of a small town during the Industrial Revolution. They are analyzing the growth of a local factory that started with 50 workers in the year 1850. Each year, the factory hired 10 more workers. By the year 1855, the factory also started producing... | {
"ground_truth": "180",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A comic book blogger is creating a new superhero comic series and receives artistic guidance from their parent, who is a professional artist. The parent suggests that the blogger use a color palette consisting of 8 different shades. The blogger decides to use these shades to color in the first 3 p... | {
"ground_truth": "8",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$7.295 A=\\frac{\\left(\\lg b \\cdot 2^{\\log _{2}(\\lg b)}\\right)^{\\frac{1}{2}} \\cdot \\lg ^{-\\frac{1}{2}} b^{2}}{\\left.\\sqrt{\\frac{\\lg ^{2} b+1}{2 \\lg b}+1}-10^{0.5 \\lg \\left(\\lg b^{\\frac{1}{2}}\\right.}\\right)}$.",
"role": "user"
}
] | {
"ground_truth": "\\lgb",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The focus of a vertically oriented, rotational paraboloid-shaped tall vessel is at a distance of 0.05 meters above the vertex. If a small amount of water is poured into the vessel, what angular velocity $\\omega$ is needed to rotate the vessel around its axis so that the water overflows from the t... | {
"ground_truth": "9.9",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. As shown in the figure, $M, N$ are points on the sides $AD, BC$ of the spatial quadrilateral $ABCD$. $AB=1, \\frac{AM}{AD}=\\frac{BN}{BC}=\\frac{1}{3}$, the angle between $MN$ and $AB$ is equal to the angle between $MN$ and $CD$, then $CD$ equals $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. In each cell of a $75 \\times 75$ table, a natural number is written. In each row, there are at least 15 different numbers, and in any three consecutive rows, there are no more than 25 different numbers. What is the maximum number of different numbers that can be in the table?",
"role": "us... | {
"ground_truth": "385",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Using $5,6,7,8$, 12 two-digit numbers without repeated digits can be formed. Arrange them in ascending order, the 11th number is larger than the 3rd number. $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "28",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. (5 points) Fill in the eight boxes below with the numbers $2,3,4,5,6,7,8,9$ (without repetition) to form many different subtraction expressions. To make the calculation result the smallest and a natural number, then this calculation result is . $\\qquad$\n\nFill in the eight boxes below with th... | {
"ground_truth": "247",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The number \\( N \\) has the smallest positive divisor 1, the second largest positive divisor \\( k \\), and the third largest positive divisor \\( m \\). Moreover, \\( k^k + m^m = N \\). What is \\( N \\)?",
"role": "user"
}
] | {
"ground_truth": "260",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that \\(\\mathrm{G}\\) is the centroid of \\(\\triangle \\mathrm{ABC}\\), and the equation \\(\\sqrt{7 \\mathrm{GA}} \\sin A + 3 \\overrightarrow{\\mathrm{GB}} \\sin B + 3 \\sqrt{7 \\mathrm{GC}} \\sin C = \\mathbf{0}\\) holds, find \\(\\angle \\mathrm{ABC}\\).",
"role": "user"
}
] | {
"ground_truth": "60^\\circ",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine all positive integers $n{}$ which can be expressed as $d_1+d_2+d_3$ where $d_1,d_2,d_3$ are distinct positive divisors of $n{}$ .",
"role": "user"
}
] | {
"ground_truth": "6k",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The length of a rectangular yard exceeds twice its width by 30 feet, and the perimeter of the yard is 700 feet. What is the area of the yard in square feet?",
"role": "user"
}
] | {
"ground_truth": "25955.56",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of permutations $( p_1, p_2, p_3 , p_4 , p_5 , p_6)$ of $1, 2 ,3,4,5,6$ such that for any $k, 1 \\leq k \\leq 5$ , $(p_1, \\ldots, p_k)$ does not form a permutation of $1 , 2, \\ldots, k$ .",
"role": "user"
}
] | {
"ground_truth": "461",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Find all eight-digit numbers with this property: if we strike out the first two and the last two digits of the number, we get a four-digit number that is 2019 times smaller than the original number.\n\n(Pavel Calábek)",
"role": "user"
}
] | {
"ground_truth": "19990119",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5 Calculate $\\left[\\frac{23 \\times 1}{101}\\right]+\\left[\\frac{23 \\times 2}{101}\\right]+\\cdots+$ $\\left[\\frac{23 \\times 100}{101}\\right]$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result direc... | {
"ground_truth": "1100",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "One day, School A bought 56 kilograms of fruit candy at 8.06 yuan per kilogram. A few days later, School B also needed to buy the same 56 kilograms of fruit candy, but it happened that there was a promotional event, and the price of fruit candy was reduced by 0.56 yuan per kilogram. Additionally, ... | {
"ground_truth": "51.36",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "I1.2 Let $x, y, z, w$ be four consecutive vertices of a regular $A$-gon. If the length of the line segment $x y$ is 2 and the area of the quadrilateral $x y z w$ is $a+\\sqrt{b}$, find the value of $B=2^{a} \\cdot 3^{b}$.",
"role": "user"
}
] | {
"ground_truth": "108",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In 1860, someone deposited 100,000 florins at 5% interest with the goal of building and maintaining an orphanage for 100 orphans from the accumulated amount. When can the orphanage be built and opened if the construction and furnishing costs are 100,000 florins, the yearly personnel cost is 3,960 ... | {
"ground_truth": "1896",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Arrange $1,2, \\cdots, n^{2}$ in a clockwise spiral pattern into an $n$ by $n$ table $T_{n}$, with the first row being $1,2, \\cdots, n$. For example: $T_{3}=\\left[\\begin{array}{lll}1 & 2 & 3 \\\\ 8 & 9 & 4 \\\\ 7 & 6 & 5\\end{array}\\right]$.\nLet 2018 be in the $i$-th row and $j$-th column ... | {
"ground_truth": "(34,95)",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nFind all sequences with distinct natural numbers as members such that \\( a_{n} \\) is divisible by \\( a_{a_{n}} \\) for all \\( n \\).",
"role": "user"
}
] | {
"ground_truth": "a_n = n",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. If we consider a pair of skew lines as one pair, then among the 12 lines formed by the edges of a regular hexagonal pyramid, the number of pairs of skew lines is $\\qquad$ pairs.",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a class with $23$ students, each pair of students have watched a movie together. Let the set of movies watched by a student be his [i]movie collection[/i]. If every student has watched every movie at most once, at least how many different movie collections can these students have?",
"role":... | {
"ground_truth": "23",
"mean_reward": 0.046875
} | 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 pairs $(n, p)$ of positive integers such that $p$ is prime and\n\\[ 1 + 2 + \\cdots + n = 3 \\cdot (1^2 + 2^2 + \\cdot + p^2). \\]\n\n[Solution]\n\n<paragrap... | {
"ground_truth": "-1",
"mean_reward": 0.375
} | 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": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. [60] Let $n$ be a fixed positive integer, and choose $n$ positive integers $a_{1}, \\ldots, a_{n}$. Given a permutation $\\pi$ on the first $n$ positive integers, let $S_{\\pi}=\\left\\{i \\left\\lvert\\, \\frac{a_{i}}{\\pi(i)}\\right.\\right.$ is an integer $\\}$. Let $N$ denote the number of... | {
"ground_truth": "2^{n}-n",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A regular tetrahedron has two vertices on the body diagonal of a cube with side length 12 . The other two vertices lie on one of the face diagonals not intersecting that body diagonal. Find the side length of the tetrahedron.",
"role": "user"
}
] | {
"ground_truth": "4\\sqrt{3}",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How can you weigh 1 kg of grain on a balance scale using two weights, one weighing 300 g and the other 650 g?",
"role": "user"
}
] | {
"ground_truth": "1000",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[b] Problem 5. [/b]Denote with $d(a,b)$ the numbers of the divisors of natural $a$, which are greater or equal to $b$. Find all natural $n$, for which\r\n$d(3n+1,1)+d(3n+2,2)+\\ldots+d(4n,n)=2006.$\r\n\r\n[i]Ivan Landgev[/i]",
"role": "user"
}
] | {
"ground_truth": "708",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Let $\\mathrm{ABC}$ be a triangle with sides $\\mathrm{AB}=7, \\mathrm{BC}=8$ and $\\mathrm{AC}=9$. $\\mathrm{A}$ unique circle can be drawn touching the side $\\mathrm{AC}$ and the lines BA produced and BC produced. Let D be the centre of this circle. Find the value of $\\mathrm{BD}^{2}$.",
... | {
"ground_truth": "224",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( S = \\{1, 2, \\cdots, 2005\\} \\). Find the minimum value of \\( n \\) such that any set of \\( n \\) pairwise coprime elements from \\( S \\) contains at least one prime number.",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8th Putnam 1948 Problem A4 Let D be a disk radius r. Given (x, y) ∈ D, and R > 0, let a(x, y, R) be the length of the arc of the circle center (x, y), radius R, which is outside D. Evaluate lim R→0 R -2 ∫ D a(x, y, R) dx dy. Solution",
"role": "user"
}
] | {
"ground_truth": "4\\pir",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.5. Varya and Miron are playing the following game. There are 10 piles of 10 stones each on the table. The players take turns, with Varya starting first. On their turn, a player divides any pile that has more than one stone into several equal piles. The player who cannot make a move (when there i... | {
"ground_truth": "Miron",
"mean_reward": 0.328125
} | 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\nDetermine all functions $f: \\mathbb{R} \\to \\mathbb{R}$ such that \n$$ f(x^3) + f(y)^3 + f(z)^3 = 3xyz $$\nfor all real numbers $x$, $y$ and $z$ with $x+y+z=0$.\n\n... | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Points \\(O\\) and \\(I\\) are the centers of the circumscribed and inscribed circles of triangle \\(ABC\\), \\(M\\) is the midpoint of the arc \\(AC\\) of the circumscribed circle (which does not contain \\(B\\)). It is known that \\(AB = 15\\), \\(BC = 7\\), and \\(MI = MO\\). Find \\(AC\\).",
... | {
"ground_truth": "13",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a professional athlete who has been training for another bodybuilding competition. As part of their daily routine, Alex does 4 sets of exercises, with each set consisting of 15 repetitions. Each repetition burns 12 calories. After the exercises, Alex drinks a protein shake that contains 18... | {
"ground_truth": "1600",
"mean_reward": 0.265625
} | 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?",
"role": "us... | {
"ground_truth": "5",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Define a function $g(n)$ as follows:\n\\[ g(n) =\n\\begin{cases}\nn^2 - 2n + 2 & \\text{if } n \\text{ is odd} \\\\\n2n & \\text{if } n \\text{ is even}\n\\end{cases}.\n\\]\nFor how many integers $n$ from 1 to 100, inclusive, does $g( g (\\dotsb g (n) \\dotsb )) = 2$ for some number of application... | {
"ground_truth": "1",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6.38 25 chess players participate in a chess competition, their strengths are all different, and in each match, the stronger one wins. How many matches are needed at least to determine the two strongest players?\n\nWill the above text be translated into English, please retain the original text's l... | {
"ground_truth": "28",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alisha wrote an integer in each square of a 4x4 grid. Integers in squares with a common edge differed by 1. She wrote a 3 in the top left corner, as shown. She also wrote a 9 somewhere in the grid. Calculate the number of different integers she wrote.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Altitudes $\\overline{AP}$ and $\\overline{BQ}$ of an acute triangle $\\triangle ABC$ intersect at point $H$. If $HP=8$ and $HQ=3$, then calculate $(BP)(PC)-(AQ)(QC)$.",
"role": "user"
}
] | {
"ground_truth": "55",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From a large grid paper, cut out 5 connected squares (two squares with only one common vertex are not considered connected), such that the resulting shape can be folded into an open-top cube. How many different shapes can be cut out, considering shapes that are the same after rotation or flipping ... | {
"ground_truth": "8",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "35. A group of workers went to two construction sites, Site A and Site B, for cleanup work. The workload at Site A is $1 \\frac{1}{2}$ times that of Site B. In the morning, the number of workers at Site A was 3 times the number at Site B. In the afternoon, $\\frac{7}{12}$ of the workers went to Si... | {
"ground_truth": "36",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "We define the ridiculous numbers recursively as follows:\n[list=a]\n[*]1 is a ridiculous number.\n[*]If $a$ is a ridiculous number, then $\\sqrt{a}$ and $1+\\sqrt{a}$ are also ridiculous numbers. \n[/list]\nA closed interval $I$ is ``boring'' if\n\n\n- $I$ contains no ridiculous numbers, ... | {
"ground_truth": "9",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nLet $D_n$ be the set of divisors of $n$. Find all natural $n$ such that it is possible to split $D_n$ into two disjoint sets $A$ and $G$, both containing at least thr... | {
"ground_truth": "6",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. Person A and Person B start from points $A$ and $B$ respectively (Person A starts from $A$), walking towards each other and continuously moving back and forth between the two points. Person A's speed is 4 times that of Person B. It is known that the distance between $A$ and $B$ is $S$ kilomete... | {
"ground_truth": "105",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that each cone can contain two ice cream balls, how many different ice cream cones can you make if you have 6 flavors of ice cream and 5 types of cones?",
"role": "user"
}
] | {
"ground_truth": "180",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. In this class, there are fewer girls than boys by $\\qquad$ people.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The War of 1812 started with a declaration of war on Thursday, June 18, 1812. The peace treaty to end the war was signed 919 days later. Calculate the day of the week on which the treaty was signed. Express your answer as a day of the week (e.g., Monday, Tuesday, etc.).",
"role": "user"
}
] | {
"ground_truth": "Saturday",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[The product of the lengths of the segments of chords and the lengths of the segments of secants] [Properties and characteristics of an isosceles triangle.] [Thales' theorem and the theorem of proportional segments]\n\nOn the extension of side $A D$ of rhombus $A B C D$ beyond point $D$, point $K$... | {
"ground_truth": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "One writes, initially, the numbers $1,2,3,\\dots,10$ in a board. An operation is to delete the numbers $a, b$ and write the number $a+b+\\frac{ab}{f(a,b)}$ , where $f(a, b)$ is the sum of all numbers in the board excluding $a$ and $b$ , one will make this until remain two numbers $x, y$... | {
"ground_truth": "1320",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( g(x) = x^3 + ax^2 + bx + c \\) be a polynomial whose roots are all positive odd integers. If \\( a + b + c = -11, \\) find \\( c \\).",
"role": "user"
}
] | {
"ground_truth": "-15",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Split a face of a regular tetrahedron into four congruent equilateral triangles. How many different ways can the seven triangles of the tetrahedron be colored using only the colors orange and black? (Two tetrahedra are considered to be colored the same way if you can rotate one so it looks like th... | {
"ground_truth": "48",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In triangle \\(ABC\\), angle bisectors \\(AA_{1}\\), \\(BB_{1}\\), and \\(CC_{1}\\) are drawn. \\(L\\) is the intersection point of segments \\(B_{1}C_{1}\\) and \\(AA_{1}\\), \\(K\\) is the intersection point of segments \\(B_{1}A_{1}\\) and \\(CC_{1}\\). Find the ratio \\(LM: MK\\) if \\(M\\) is... | {
"ground_truth": "11/12",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the points M(2,0) and N(a,b) in the Cartesian coordinate system, with the Manhattan distance between M and N defined as d(M,N) = |x₁ - x₂| + |y₁ - y₂|, and d(M,N) = 2, find the sum of the minimum and maximum values of a² + b² - 4a.",
"role": "user"
}
] | {
"ground_truth": "-2",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## 139. Math Puzzle $12 / 76$\n\nRalf and Marion had set their watches, real \"vintages,\" at the beginning of a longer hike. At the destination, Marion's watch shows 13:46 and Ralf's 14:13.\n\nWhat time is it really, if Marion's watch gains 2 minutes daily and Ralf's old alarm clock loses 4 minut... | {
"ground_truth": "13:55",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Krekov D:\n\nIn an acute scalene triangle $ABC$, the altitudes $AA'$ and $BB'$ intersect at point $H$, and the medians of triangle $AHB$ intersect at point $M$. The line $CM$ bisects the segment $A'B'$. Find the angle $C$.",
"role": "user"
}
] | {
"ground_truth": "45",
"mean_reward": 0.09375
} | 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\nIn a certain polynomial, all the coefficients are integers, and the constant coefficient is 42. All the roots are integers, and distinct. Find the largest possible ... | {
"ground_truth": "2",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. let \\(a, b, c, d\\) and \\(e\\) be positive real numbers. Determine the largest value that the following expression can take:\n\n\\[\n\\frac{a b + b c + c d + d e}{2 a^{2} + b^{2} + 2 c^{2} + d^{2} + 2 e^{2}}\n\\]",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{3/8}",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nC4. We have a group of $n$ kids. For each pair of kids, at least one has sent a message to the other one. For each kid $A$, among the kids to whom $A$ has sent a message, exactly $25 \\%$ have sent a message to $A$. How many possible two-digit values of $n$ are there?\n",
"role": "user"
}
... | {
"ground_truth": "26",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the $100$th digit after the decimal point when $\\frac{3}{26}$ is expressed as a decimal?",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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