prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Each hotel room can accommodate no more than 3 people. The hotel manager knows that a group of 100 football fans, who support three different teams, will soon arrive. A room can only house either men or women; and fans of different teams cannot be housed together. How many rooms need to be booked ... | {
"ground_truth": "37",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Hiram's algebra notes are $50$ pages long and are printed on $25$ sheets of paper; the first sheet contains pages $1$ and $2$, the second sheet contains pages $3$ and $4$, and so on. One day he leaves his notes on the table before leaving for lunch, and his roommate decides to borrow some pages fr... | {
"ground_truth": "13",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Determination of Temperature 3 points\n\nTOTAL: 10 points\n\n## TASK 8\n\n## SOLUTION\n\nThe degree of ionization will be calculated using the formula:\n\n$$\n\\alpha=\\sqrt{ } K_{\\mathrm{HCN}} \\mathrm{C}\n$$\n\n$\\alpha_{\\text {ion }}=\\sqrt{ }\\left(7.2 \\cdot 10^{-10}\\right) / 0.1=\\sqrt... | {
"ground_truth": "0.0085",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "49th Kürschák 1948 Problem 1 Knowing that 23 October 1948 was a Saturday, which is more frequent for New Year's Day, Sunday or Monday?",
"role": "user"
}
] | {
"ground_truth": "Sunday",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Every day at noon, a scheduled ship departs from Moscow to Astrakhan and from Astrakhan to Moscow. The ship traveling from Moscow takes exactly four days to reach Astrakhan, then stays there for two days, and at noon two days after its arrival in Astrakhan, it departs back to Moscow. The ship trav... | {
"ground_truth": "13",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Let $S=\\{1,2, \\cdots, 50\\}$. Find the smallest positive integer $k$, such that in any $k$-element subset of $S$, there exist two distinct numbers $a$ and $b$ satisfying $(a+b) \\mid a b$.\n$(1996$, China Mathematical Olympiad)",
"role": "user"
}
] | {
"ground_truth": "39",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A motorcyclist left point A for point B, and at the same time, a pedestrian left point B for point A. When they met, the motorcyclist took the pedestrian on his motorcycle to point A and then immediately went back to point B. As a result, the pedestrian reached point A 4 times faster than if he ha... | {
"ground_truth": "2.75",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "<span style=\"color:darkred\"> Let $m$ and $n$ be two nonzero natural numbers. Determine the minimum number of distinct complex roots of the polynomial $\\prod_{k=1}^m\\, (f+k)$ , when $f$ covers the set of $n^{\\text{th}}$ - degree polynomials with complex coefficients.\n</span>",
"... | {
"ground_truth": "n(m-1) + 1",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Begueutzæ. V.\n\nTo each member of a certain finite sequence of consecutive natural numbers, two digits were appended on the right, and as a result, a sequence of squares of consecutive natural numbers was obtained. What is the maximum number of terms this sequence could have had?",
"role": "u... | {
"ground_truth": "19",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An equilateral triangle of side $n$ is divided into equilateral triangles of side $1$ . Find the greatest possible number of unit segments with endpoints at vertices of the small triangles that can be chosen so that no three of them are sides of a single triangle.",
"role": "user"
}
] | {
"ground_truth": " n(n+1) ",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the smallest value of the expression $|3 \\cdot 5^m - 11 \\cdot 13^n|$ for all $m,n \\in N$ . \n\n(Folklore)",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The expression $25x^2 - 130x - 120$ can be written as $(5x + a)(5x + b),$ where $a$ and $b$ are integers. What is $a + 3b$?",
"role": "user"
}
] | {
"ground_truth": "-86",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is a solution of table salt in a flask. From the flask, $\\frac{1}{5}$ of the solution is poured into a test tube and evaporated until the salt concentration in the test tube doubles. After that, the evaporated solution is poured back into the flask. As a result, the salt concentration in th... | {
"ground_truth": "27",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "King Arthur's bodyguards held a knightly tournament. At the end of the tournament, it turned out that the king could find a third one for any two bodyguards who participated, who had defeated both of them. What is the minimum number of bodyguards who participated in the tournament?",
"role": "... | {
"ground_truth": "7",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2.1. Once, in a company, the following conversation took place:\n\n- We must call Misha immediately! - exclaimed Vanya.\n\nHowever, no one remembered Misha's phone number.\n\n- I remember for sure that the last three digits of the phone number are consecutive natural numbers, - said Nastya.\n- And... | {
"ground_truth": "7111765",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is an oak tree growing by the road from Yolkino to Palkino, and it is twice as close to Yolkino as it is to Palkino. Fedya, traveling at a constant (and positive) speed from Yolkino to Palkino, was twice as close to the oak tree as he was to Yolkino at 12:00. At 12:40, it turned out again th... | {
"ground_truth": "13:10 ",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( c \\) be a positive real number. If \\( x^{2} + 2 \\sqrt{c} x + b = 0 \\) has one real root only, find the value of \\( c \\).",
"role": "user"
}
] | {
"ground_truth": "c = b",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Five, in a rectangle $A B C D$ with an area of 1 (including the boundary), there are five points, no three of which are collinear. Find the minimum number of triangles, with these five points as vertices, whose area is not greater than $\\frac{1}{4}$.\n(Cold Gangsong, Contributed)",
"role": "u... | {
"ground_truth": "2",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The integers $1, 2, \\dots, n$ are written in order on a long slip of paper. The slip is then cut into five pieces, so that each piece consists of some (nonempty) consecutive set of integers. The averages of the numbers on the five slips are $1234$ , $345$ , $128$ , $19$ , and $9.5$ in so... | {
"ground_truth": "2014",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "96. There is a magical tree with 58 fruits on it. On the first day, 1 fruit will fall from the tree. Starting from the second day, the number of fruits that fall each day is 1 more than the previous day. However, if the number of fruits on the tree is less than the number that should fall on a cer... | {
"ground_truth": "12",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A cuckoo clock is on the wall. At the beginning of every hour, the cuckoo makes a number of \"cuckoo\" sounds equal to the hour displayed by the hour hand (for example, at 19:00 the cuckoo makes 7 sounds). One morning, Maxim approached the clock when it showed 9:05. He started turning the minute h... | {
"ground_truth": "43",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A is traveling at 50 mph and needs to pass B, who is traveling at 40 mph, by gaining 30 feet. Meanwhile, C is 210 feet away from A and is headed towards A at 50 mph. If B and C maintain their speeds, what is the minimum speed increase required for A to pass safely? Express your answer in mph.",
... | {
"ground_truth": "5",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Liam is an avid follower of Northern Irish politics and enjoys learning about the history of Irish nationalism. He recently read about the Good Friday Agreement, which was signed in 1998, marking an important moment in the peace process. To celebrate this anniversary, Liam decides to make a timeli... | {
"ground_truth": "12",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. As shown in Figure 1, calculate: If the input $x=5$, then the operation will end after $\\qquad$ times.",
"role": "user"
}
] | {
"ground_truth": "3",
"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": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On the lateral side $CD$ of trapezoid $ABCD (AD \\parallel BC)$, a point $M$ is marked. From vertex $A$, a perpendicular $AH$ is dropped to the segment $BM$. It is found that $AD = HD$. Find the length of segment $AD$ if it is known that $BC = 16$, $CM = 8$, $MD = 9$.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Today's date is written as: 22.11.2015. Name the last past date that is written with the same set of digits.",
"role": "user"
}
] | {
"ground_truth": "15.12.2012",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $t$ be TNYWR.\n\nArmen paid $\\$ 190$ to buy movie tickets for a group of $t$ people, consisting of some adults and some children. Movie tickets cost $\\$ 5$ for children and $\\$ 9$ for adults. How many children's tickets did he buy?",
"role": "user"
}
] | {
"ground_truth": "20",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On an island, there are magical sheep. There are 22 blue ones, 18 red ones, and 15 green ones. When two sheep of different colors meet, they both turn the third color. Is it possible that after a finite number of encounters, all the sheep will be the same color? If so, what could this color be?",
... | {
"ground_truth": "blue",
"mean_reward": 0.125
} | 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": "A PhD student specializing in Islamic History is studying the timeline of various caliphates. She notices that the Umayyad Caliphate lasted from the year 661 to 750, and the Abbasid Caliphate lasted from 750 to 1258. If she spends 2 hours studying each year of the Umayyad Caliphate and 1 hour for ... | {
"ground_truth": "689",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ten, $1447, 1005, 1231$ have many things in common: they are all four-digit numbers, their highest digit is 1, and they each have exactly two identical digits. How many such numbers are there?",
"role": "user"
}
] | {
"ground_truth": "432",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "16. Consider the following propositions:\n(1) If $x^{2}=1998 \\times 2000+1$, then $x=1959$;\n(2) Removing the denominator to solve the equation $\\frac{x-3}{x-2}=\\frac{n}{x-2}$ for $x$ produces an extraneous root, then $m=-1$;\n(3) If $x y-1$;\n(4) Given that $\\alpha$ is an acute angle, and $\\... | {
"ground_truth": "(2), (3)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 2. There are 22 batteries, 15 of which are charged and 7 are discharged. The camera works with three charged batteries. You can insert any three batteries into it and check if it works. How can you guarantee to turn on the camera in 10 such attempts?",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $M$ be a set consisting of $n$ points in the plane, satisfying:\ni) there exist $7$ points in $M$ which constitute the vertices of a convex heptagon; \nii) if for any $5$ points in $M$ which constitute the vertices of a convex pentagon, then there is a point in $M$ which lies in the interior o... | {
"ground_truth": "11",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Using only pennies, nickels, dimes, quarters, and half-dollars, determine the smallest number of coins needed to pay any amount of money less than a dollar and a half.",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The set $X$ of $N$ four-digit numbers formed from the digits $1,2,3,4,5,6,7,8$ satisfies the following condition:\n\n\n*for any two different digits from $1,2,3,4,,6,7,8$ there exists a number in $X$ which contains both of them.*\n\nDetermine the smallest possible value of $N$ .",
"... | {
"ground_truth": "6",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Fix an integer $n \\geq 2$. An $n\\times n$ sieve is an $n\\times n$ array with $n$ cells removed so that exactly one cell is removed from every row and every column. A stick is a $1\\times k$ or $k\\times 1$ array for any positive integer $k$. For any sieve $A$, let $m(A)$ be the minimal number o... | {
"ground_truth": " 2n - 2 ",
"mean_reward": 0.1875
} | 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, Food, Movie-Genre, Beverage, Pet, Sport.\nThe attributes have the following possible values:\n- Nationality: indonesian, italian, japanese, spanish\n- Food:... | {
"ground_truth": "spinach",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. In $\\triangle A B C$, $A B=c, B C=a, C A=b, a^{4}+b^{4}+c^{4}=2 c^{2}\\left(a^{2}+b^{2}\\right)$, if $\\angle A=72^{\\circ}$, then $\\angle B=$ $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "63",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A researcher named Alex is working on a documentary about historical battles and needs to find shooting locations that are both historically accurate and visually captivating. Alex has identified three potential sites: Site A, Site B, and Site C. \n\n- Site A is 15 miles from the production studio... | {
"ground_truth": "600",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "28.2.9 * Find the smallest positive integer $n(n \\geqslant 3)$, such that in any set of $n$ points in the plane with no three points collinear, there are two points that are vertices of a non-isosceles triangle.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Flea Kuzya can make jumps along a line \\(L\\). The starting point for the jumps is point \\(A\\) on line \\(L\\), the length of each jump is \\(h\\), and the direction of each jump is chosen randomly and equally likely. Find the probability that after making between two and five random jumps, Kuz... | {
"ground_truth": "5/8",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. The graphs of the functions $y=x^{2}$ and $y=a x^{2}+b x+c$ intersect at points $A$ and $B$, which lie on opposite sides of the y-axis. Point $O$ is the origin. It turns out that $\\angle A O B=90^{\\circ}$. Find all possible values of $c$. (20 points)\n\nInternational School Olympiad URFU \"Em... | {
"ground_truth": "\\neq0",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Answer. 000001111100000\n\n#",
"role": "user"
}
] | {
"ground_truth": "1111100000",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. A pedestrian is walking along a highway at a speed of 5 km/h. Buses are traveling in both directions on this highway at the same speed, meeting every 5 minutes. At 12 o'clock, the pedestrian noticed that the buses met near him and, continuing to walk, started counting the oncoming and overtakin... | {
"ground_truth": "30",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9、A、 、 、 $\\mathrm{C} 、 \\mathrm{D} 、 \\mathrm{E}$ are all single digits, and $\\overline{D E}=A+B+C$. Given that $\\overline{A B C}+\\overline{B C A}+\\overline{C A B}+\\overline{D E}=2016, \\overline{D E A B C}$ is maximized as $\\qquad$ -",
"role": "user"
}
] | {
"ground_truth": "18981",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3 Task 1. For which natural $n(n \\geqslant 2)$ is the equality\n\n$$\n-\\sqrt[2]{17 \\sqrt{5}+38}+\\sqrt[2]{17 \\sqrt{5}-38}=\\sqrt{20} ?\n$$",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a positive integer $n$ greater than 2004, fill the numbers $1, 2, \\cdots, n^2$ into the squares of an $n \\times n$ chessboard (consisting of $n$ rows and $n$ columns) such that each square contains exactly one number. If a number in a square is greater than the numbers in at least 2004 squ... | {
"ground_truth": "n(n-2004)",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Lines parallel to the sides of a square form a small square whose center coincides with the center of the original square. It is known that the area of the cross, formed by the small square, is 17 times larger than the area of the small square. By how many times is the area of the original square ... | {
"ground_truth": "81",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2. How to find out how many fish are in the pond?\n\nWe catch $n_{a}=20$ fish, mark them, and release them back into the pond. After some time, sufficient for the marked fish to disperse throughout the pond, we catch $m=50$ fish. Suppose that among them, $k_{1}=7$ are marked. Determine the... | {
"ground_truth": "142",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. The equation of the hyperbola $C$ is $x^{2}-\\frac{y^{2}}{3}=1$, with the left and right foci being $F_{1}$ and $F_{2}$, respectively. A line is drawn through point $F_{2}$ intersecting the right branch of the hyperbola $C$ at points $P$ and $Q$, such that $\\angle F_{1} P Q=90^{\\circ}$. Then ... | {
"ground_truth": "\\sqrt{7}-1",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the values of $a\\in [0,\\infty)$ for which there exist continuous functions $f:\\mathbb{R}\\rightarrow \\mathbb{R}$ , such that $f(f(x))=(x-a)^2,\\ (\\forall)x\\in \\mathbb{R}$ .",
"role": "user"
}
] | {
"ground_truth": " a = 0 ",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A certain commodity has a cost price of 200 yuan and a marked price of 400 yuan. What is the maximum discount that can be offered to ensure that the profit margin is not less than 40%?",
"role": "user"
}
] | {
"ground_truth": "30\\%",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is an agricultural business owner who grows a single type of crop, corn, on a large farm. This season, Alex has planted corn on 150 acres of land. Each acre of Alex's farm typically produces about 120 bushels of corn. \n\nThis year, due to favorable weather conditions, the yield increased by ... | {
"ground_truth": "19536",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Let's call a natural number special if one of its digits can be replaced by another digit so that all digits in the resulting number are distinct. Numbers in which all digits are already distinct are also considered special. How many special ten-digit numbers exist? (20 points)",
"role": "u... | {
"ground_truth": "414\\cdot9!",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a prime $p$, let $f(p)$ be the number of ordered tuples $(x_1,x_2,\\dots,x_p)$ of nonnegative integers satisfying $$x_1+x_2+\\cdots+x_p=2022,$$ with the extra condition that $x_i\\equiv i\\pmod{p}$ for $1\\le i\\le p$. Let $S$ be the set of all primes less than 2022. Find the remainder when $$... | {
"ground_truth": "475",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "As shown in the diagram, two lines intersect with two circles at 9 points. Choose 4 points from these 9 points such that any 3 points among these 4 are neither collinear nor lie on the same circle. How many different selections can be made?",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If there are several heaps of stones on the table, it is said that there are $\\textit{many}$ stones on the table, if we can find $50$ piles and number them with the numbers from $1$ to $50$ so that the first pile contains at least one stone, the second - at least two stones,..., the $50$-th has a... | {
"ground_truth": "5099",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mom gave Vasya money for 30 pencils. It turned out that the pencil factory was running a promotional campaign in the store: in exchange for a receipt for a set of 20 pencils, they return $25\\%$ of the set's cost, and for a receipt for a set of 5 pencils, they return $10\\%$. What is the maximum n... | {
"ground_truth": "36",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two circles touch each other internally. It is known that two radii of the larger circle, which form an angle of $60^\\circ$ between them, are tangent to the smaller circle. Find the ratio of the radii of the circles.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The height of the cone is 20, and the radius of the base is 25. Find the area of the section passing through the vertex if its distance from the center of the base of the cone is 12.\n\n#",
"role": "user"
}
] | {
"ground_truth": "500",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jack drove 150 miles in 2.5 hours. His average speed during the first hour was 50 mph. After a 15-minute stop, he resumed travel for another hour at an average speed of 55 mph. Calculate his average speed, in mph, during the last 30 minutes.",
"role": "user"
}
] | {
"ground_truth": "90",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A thin diverging lens with an optical power of $D_{p} = -6$ diopters is illuminated by a beam of light with a diameter $d_{1} = 10$ cm. On a screen positioned parallel to the lens, a light spot with a diameter $d_{2} = 20$ cm is observed. After replacing the thin diverging lens with a thin converg... | {
"ground_truth": "18",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of lines that pass through the point P(-1,0) and have exactly one point in common with the parabola y^2 = x. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A collection of four positive integers has a mean of 6.5, a unique mode of 6, and a median of 7. If a 10 is added to the collection, what is the new median?",
"role": "user"
}
] | {
"ground_truth": "7.0",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ahmed is a Pakistani Muslim community leader living in New York City, and he is organizing an interfaith dinner to promote global harmony. He invites people from different cultural backgrounds, including 12 from the Pakistani community, 15 from the local mosque, 18 from a nearby church, and 20 fro... | {
"ground_truth": "4225",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A doctoral student is analyzing political communication strategies used by different leaders. She decides to study two leaders, Leader A and Leader B, over a month. Leader A gives 3 speeches per week, each containing an average of 2000 words. Leader B gives 2 speeches per week, each containing an ... | {
"ground_truth": "-4000",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is $56$. The area of the region bounded by the polygon is [asy] draw((0,0)--(1,0)--(1,-1)--(2,-1)--(2,-2)--(3,-2)--(3,-3)--(4,-3)--(4,-2)--(5,-2)--(5,-1)--(6,... | {
"ground_truth": "100",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The three different points \\(A(x_1, y_1)\\), \\(B\\left(4, \\frac{9}{5}\\right)\\), and \\(C(x_2, y_2)\\) on the ellipse \\(\\frac{x^{2}}{25} + \\frac{y^{2}}{9} = 1\\), along with the focus \\(F(4,0)\\) have distances that form an arithmetic sequence. If the perpendicular bisector of line segment... | {
"ground_truth": "5/4",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jamie owns a plumbing business and is passionate about training new apprentices. Each apprentice requires 3 hours of training per day. Jamie currently has 4 apprentices and wants to take on 2 more. If Jamie spends a total of 8 hours a day running the business and can work up to 14 hours a day, how... | {
"ground_truth": "0",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n\nThe radius of the sphere that touches all the edges of a regular tetrahedron is 1. Find the edge of the tetrahedron.",
"role": "user"
}
] | {
"ground_truth": "2\\sqrt{2}",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Given $x \\cdot y \\in\\left[-\\frac{\\pi}{4} \\cdot \\frac{\\pi}{4}\\right], a \\in \\mathbf{R}$, and $\\left\\{\\begin{array}{l}x^{3}+\\sin x-2 a=0 \\\\ 4 y^{3}+\\frac{1}{2} \\sin 2 y-a=0\\end{array}\\right.$, then $\\cos (x+2 y)=$\n\nTranslate the above text into English, please retain the o... | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. Given\n$$\nS_{n}=|n-1|+2|n-2|+\\cdots+10|n-10| \\text {, }\n$$\n\nwhere, $n \\in \\mathbf{Z}_{4}$. Then the minimum value of $S_{n}$ is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. If $p$ is a prime number, and the two roots of $x^{2}+p x-23988 p=0$ are integers, then $p=$\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": "1999",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. Find the integer, given that the decimal representation of its sixth power consists of the digits $0,1,2,2,2,3,4,4$.\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": "18",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a_1 = a_2 = a_3 = 1.$ For $n > 3,$ let $a_n$ be the number of real numbers $x$ such that\n\\[x^4 - 2a_{n - 1} x^2 + a_{n - 2} a_{n - 3} = 0.\\]Compute the sum $a_1 + a_2 + a_3 + \\dots + a_{1000}.$",
"role": "user"
}
] | {
"ground_truth": "2329",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a linear arrangement, points $A$, $B$, $C$, $D$, $E$, and $F$ are aligned in a straight line such that the distances are $AB = 2$, $BC = 4$, $CD = 6$, $DE = 4$, and $EF = 2$. Semi-circles with diameters $AF$, $AB$, $BC$, $CD$, $DE$, and $EF$ form a shape as illustrated. Calculate the area of th... | {
"ground_truth": "48\\pi",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jacob wants to tile the floor of a 14-foot by 20-foot hallway. He plans to use 2-foot by 2-foot square tiles for a border along the edges of the hallway and fill in the rest of the floor with three-foot by three-foot square tiles. Calculate the total number of tiles he will use.",
"role": "use... | {
"ground_truth": "48",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Four. (20 points) Let the line $y=\\sqrt{3} x+b$ intersect the parabola $y^{2}=2 p x(p>0)$ at points $A$ and $B$. The circle passing through $A$ and $B$ intersects the parabola $y^{2}=2 p x(p>0)$ at two other distinct points $C$ and $D$. Find the size of the angle between the lines $AB$ and $CD$.\... | {
"ground_truth": "60^{\\circ}",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Marie changed her dice by replacing 1, 3, and 5 with -1, -3, and -5 respectively. She left the even numbers unchanged. If she throws two such dice, what is the total that cannot be achieved? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. The train is traveling at a speed of 60 kilometers per hour, making stops every 48 kilometers. The duration of each stop, except the fifth, is 10 minutes, and the fifth stop is half an hour. How far has the train traveled if it departed at noon on September 29 and arrived at its destination on ... | {
"ground_truth": "2870",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The bar graph shows the results of a survey on color preferences. What percent preferred blue? [asy] for (int a = 1; a <= 6; ++a) { draw((-1.5,4*a)--(1.5,4*a)); } draw((0,28)--(0,0)--(32,0)); draw((3,0)--(3,20)--(6,20)--(6,0)); draw((9,0)--(9,24)--(12,24)--(12,0)); draw((15,0)--(15,16)--(18,16)--(... | {
"ground_truth": "24\\%",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the smallest natural $ k $ such that among any $ k $ distinct and pairwise coprime naturals smaller than $ 2018, $ a prime can be found.\n\n\n*Vlad Robu*",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Find all functions from the positive integers to the positive integers such that for all $x, y$ we have:\n$$\n2 y f\\left(f\\left(x^{2}\\right)+x\\right)=f(x+1) f(2 x y) \\text {. }\n$$",
"role": "user"
}
] | {
"ground_truth": "f(x)=x",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $\\mathcal P$ denote the set of planes in three-dimensional space with positive $x$, $y$, and $z$ intercepts summing to one. A point $(x,y,z)$ with $\\min \\{x,y,z\\} > 0$ lies on exactly one plane in $\\mathcal P$. What is the maximum possible integer value of $\\left(\\frac{1}{4} x^2 + 2y^2 ... | {
"ground_truth": "21",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## [ Algebraic inequalities (other).] Induction (other). $\\quad]$\n\nFor which natural numbers $n$ does the inequality $2^{n} \\geq n^{3}$ hold?\n\n#",
"role": "user"
}
] | {
"ground_truth": "n\\geq10",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $z_1 = 18 + 83i$ , $z_2 = 18 + 39i,$ and $z_3 = 78 + 99i,$ where $i = \\sqrt{-1}$ . Let $z$ be the unique complex number with the properties that $\\frac{z_3 - z_1}{z_2 - z_1} \\cdot \\frac{z - z_2}{z - z_3}$ is a real number and the imaginary part of $z$ is the greatest possible. Find the rea... | {
"ground_truth": "56",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "P, Q, R are adjacent vertices of a regular 9-gon with center O. M is the midpoint of the segment joining O to the midpoint of QR and N is the midpoint of PQ. Find the ∠ONM.",
"role": "user"
}
] | {
"ground_truth": "30^\\circ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A circle with center $O$ is tangent to the coordinate axes and to the hypotenuse of the $30^\\circ$-$60^\\circ$-$90^\\circ$ triangle $ABC$ as shown, where $AB=1$. To the nearest hundredth, what is the radius of the circle? [asy] defaultpen(linewidth(.8pt)); dotfactor=3; pair A = origin; pair B = (... | {
"ground_truth": "2.37",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A regular hexagon with side length $1$ is given. Using a ruler construct points in such a way that among the given and constructed points there are two such points that the distance between them is $\\sqrt7$ .\n\nNotes: ''Using a ruler construct points $\\ldots$ '' means: Newly constructed poi... | {
"ground_truth": "\\sqrt{7}",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Emma is a straight-A student who loves spending time in the library. She has 5 favorite books that she reads repeatedly. One day, she observes her friend Alex, a social butterfly, confidently talking to a group of 12 students about their favorite books. Inspired by Alex’s confidence, Emma decides ... | {
"ground_truth": "Tuesday",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13th Swedish 1973 Problem 1 log 8 2 = 0.2525 in base 8 (to 4 places of decimals). Find log 8 4 in base 8 (to 4 places of decimals).",
"role": "user"
}
] | {
"ground_truth": "0.5253",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": " $2019$ circles split a plane into a number of parts whose boundaries are arcs of those circles. How many colors are needed to color this geographic map if any two neighboring parts must be coloured with different colours?",
"role": "user"
}
] | {
"ground_truth": " 2 ",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "30th CanMO 1998 Problem 1 How many real x satisfy x = [x/2] + [x/3] + [x/5]? Solution",
"role": "user"
}
] | {
"ground_truth": "30",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Divide into two parts, each part containing an odd number of edges of $P$, then this diagonal is called a \"good edge\". It is stipulated that each edge of $P$ is a \"good edge\".\n\nGiven 2003 non-intersecting diagonals inside $P$ that partition $P$ into several triangles. How many isosceles tria... | {
"ground_truth": "1003",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "26. In the diagram below, $A B C D$ is a cyclic quadrilateral with $A B=A C$. The line $F G$ is tangent to the circle at the point $C$, and is parallel to $B D$. If $A B=6$ and $B C=4$, find the value of $3 A E$.",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a triangle with sides 6 cm, 10 cm, and 12 cm, an inscribed circle is tangent to the two longer sides. Find the perimeter of the resulting triangle formed by the tangent line and the two longer sides.",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a 7 by 7 grid, each of the 49 squares measures 1 cm by 1 cm and is shaded. Seven unshaded circles are placed on top of the grid as shown. The area of the visible shaded region can be written in the form $C-D\\pi$ square cm. What is the value of $C+D$?\n\n[asy]\nfor(int i = 0; i < 7; ++i)\n{\n ... | {
"ground_truth": "52.75",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the maximum number of points that can be placed on a segment of length 1 such that on any subsegment of length \\( d \\) contained in this segment, there are no more than \\( 1 + 1000 d^2 \\) points?",
"role": "user"
}
] | {
"ground_truth": "32",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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