prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "11.17. How many roots does the equation $\\sin x=\\frac{x}{100}$ have?\n\n## 11.4. Sums of Sines and Cosines Related to Regular Polygons\n\nIn solving the problems of this section, the following geometric problem is useful.",
"role": "user"
}
] | {
"ground_truth": "63",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Define a new function $\\$N$ such that $\\$N = 0.75N + 2$. Calculate $\\$(\\$(\\$30))$.",
"role": "user"
}
] | {
"ground_truth": "17.28125",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $P(x)$ be a polynomial with integer coefficients satisfying\n$$(x^2+1)P(x-1)=(x^2-10x+26)P(x)$$\nfor all real $x$. Find the sum of all possible values of $P(0)$ between $1$ and $5000$, inclusive.",
"role": "user"
}
] | {
"ground_truth": "5100",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jennifer plans a profit of 20% on the selling price of an item, and her expenses are 10% of the selling price. There is also a sales tax of 5% on the selling price of the item. The item sells for $10.00. Calculate the rate of markup on cost of this item.",
"role": "user"
}
] | {
"ground_truth": "53.85\\%",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jackson begins at $1$ on the number line. At each step, he remains in place with probability $85\\%$ and increases his position on the number line by $1$ with probability $15\\%$ . Let $d_n$ be his position on the number line after $n$ steps, and let $E_n$ be the expected value of $\... | {
"ground_truth": "13446",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the city of Omsk, a metro line was built in a straight line. On this same line is the house where Nikita and Yegor live. Every morning, they simultaneously leave the house for their lessons, after which Yegor runs to the nearest metro station at a speed of 12 km/h, while Nikita walks along the ... | {
"ground_truth": "23",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. From 7:00 to 8:00 in the morning is the peak hour in a city, during which all vehicles travel at half their original speed. Every morning at 6:50, two people, A and B, start from points $A$ and $B$ respectively, heading towards each other, and meet at a point 24 kilometers from $A$. If A start... | {
"ground_truth": "42",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "IMO 1998 Problem B3 Consider all functions f from the set of all positive integers into itself satisfying f(t 2 f(s)) = s f(t) 2 for all s and t. Determine the least possible value of f(1998).",
"role": "user"
}
] | {
"ground_truth": "120",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a,$ $b,$ $c$ be distinct, nonzero real numbers such that\n\\[ a - \\frac{1}{b} = b - \\frac{1}{c} = c - \\frac{1}{a}. \\]\nFind $|abc|$.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Which of the following words has the largest value, given that the first five letters of the alphabet are assigned the values $A=1, B=2, C=3, D=4, E=5$?",
"role": "user"
}
] | {
"ground_truth": "BEE",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. Suppose there are 128 ones written on a blackboard. In each step, you can erase any two numbers \\(a\\) and \\(b\\) and write \\(ab + 1\\). After performing this operation 127 times, only one number remains. Let the maximum possible value of this remaining number be \\(A\\). Determine the last... | {
"ground_truth": "2",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An arithmetic sequence has the following properties:\n\n- When the first, third, fifth, and so on terms are added, up to and including the last term, the sum is 320.\n- When the first, fourth, seventh, and so on, terms are added, up to and including the last term, the sum is 224.\n\nFind the sum o... | {
"ground_truth": "608",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is $2:1$. The ratio of the rectangle's length to its width is $2:1$. What percent of the rectangle's area is inside the square?",
"role": "user"
}
] | {
"ground_truth": "12.5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ satisfying for all $x, y \\in \\mathbb{R}$ :\n\n$$\nf(x+y)+y \\leqslant f(f(f(x)))\n$$",
"role": "user"
}
] | {
"ground_truth": "f(x)=C-x",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "I live in a five-story building with four entrances, with four apartments on each landing. What is the minimum number of questions you can ask to determine which apartment I live in, if I answer all your questions truthfully, but only with \"yes\" or \"no\"?",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "XLVI OM - III - Problem 2\n\nThe diagonals of a convex pentagon divide this pentagon into a pentagon and ten triangles. What is the maximum possible number of triangles with equal areas?",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A two-player game is played on a grid of varying sizes (6x7, 6x8, 7x7, 7x8, and 8x8). The game starts with a piece at the bottom-left corner, and players take turns moving the piece up, right, or diagonally up-right. The game ends when a player cannot make a move. How many of these grid sizes allo... | {
"ground_truth": "4",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Li Jiang, a student, buys a piece of sportswear at a sports counter in a mall and receives a 100 yuan voucher. This voucher can be used to purchase one of three different types of sports socks, priced at 18 yuan, 30 yuan, and 39 yuan respectively. It is required that the entire amount of the vouch... | {
"ground_truth": "3",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For sets $A, B, X$ satisfying: $A \\cap X = B \\cap X = A \\cap B, A \\cup B \\cup X = A \\cup B$. If $A, B$ are known sets, find the set $X$.\n\nIf sets $A, B$ are known, determine the set $X$ based on the conditions provided.",
"role": "user"
}
] | {
"ground_truth": "A\\capB",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Your tech-savvy cousin recently ran a successful crowdfunding campaign to launch a new gadget. They set an initial funding goal of $10,000, and they surpassed their goal by raising 150% of the target. During the campaign, they received contributions from 200 backers. Your cousin also provided tips... | {
"ground_truth": "17000",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The area of the closed shape formed by the graph of the function $y=2\\sin x$, where $x \\in \\left[\\frac{\\pi}{2}, \\frac{5\\pi}{2}\\right]$, and the lines $y=\\pm2$ is what?",
"role": "user"
}
] | {
"ground_truth": "4\\pi",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. If $a-b=3, a^{2}+b^{2}=11$, then $a^{5}-b^{5}=$\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": "393",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a special event, the five Vietnamese famous dishes including Phở, (Vietnamese noodle), Nem (spring roll), Bún Chả (grilled pork noodle), Bánh cuốn (stuffed pancake), and Xôi gà (chicken sticky rice) are the options for the main courses for the dinner of Monday, Tuesday, and Wednesday. Every d... | {
"ground_truth": "150",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A function f(x) defined on R satisfies f(0)=0, f(x)+f(1-x)=1, f(x/5)=1/2f(x), and f(x1) <= f(x2) when 0 <= x1 < x2 <= 1. Find the value of f(1/2007). Express your answer as a fraction in simplest form.",
"role": "user"
}
] | {
"ground_truth": "1/32",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the functions $ f:\\mathbb{N}\\longrightarrow\\mathbb{N} $ that satisfy the following relation: $$ \\gcd\\left( x,f(y)\\right)\\cdot\\text{lcm}\\left(f(x), y\\right) = \\gcd (x,y)\\cdot\\text{lcm}\\left( f(x), f(y)\\right) ,\\quad\\forall x,y\\in\\mathbb{N} . $$ ",
"role": "user"
... | {
"ground_truth": " f(x) = x ",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[level. $B$. .\n\nThere are 1000 candies lined up. First, Vasya ate the ninth candy from the left, and then he ate every seventh candy, moving to the right. After that, Petya ate the seventh candy from the left among the remaining candies, and then he ate every ninth candy, also moving to the righ... | {
"ground_truth": "763",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate the volumes of solids formed by the rotation of regions bounded by the graphs of the functions around the y-axis.\n\n$$\ny=\\arcsin \\frac{x}{5}, y=\\arcsin x, y=\\frac{\\pi}{2}\n$$",
"role": "user"
}
] | {
"ground_truth": "6 \\pi^2",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are $N{}$ points marked on the plane. Any three of them form a triangle, the values of the angles of which in are expressed in natural numbers (in degrees). What is the maximum $N{}$ for which this is possible?\n\n[i]Proposed by E. Bakaev[/i]",
"role": "user"
}
] | {
"ground_truth": "180",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.1. Let $a_{1}, a_{2}, \\cdots, a_{50}, b_{1}, b_{2}, \\cdots, b_{50}$ be distinct numbers such that the equation\n$$\n\\begin{array}{l}\n\\left|x-a_{1}\\right|+\\left|x-a_{2}\\right|+\\cdots+\\left|x-a_{50}\\right| \\\\\n=\\left|x-b_{1}\\right|+\\left|x-b_{2}\\right|+\\cdots+\\left|x-b_{50}\\ri... | {
"ground_truth": "49",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Nathan has discovered a new way to construct chocolate bars, but it’s expensive! He starts with a single $1\\times1$ square of chocolate and then adds more rows and columns from there. If his current bar has dimensions $w\\times h$ ($w$ columns and $h$ rows), then it costs $w^2$ dollars to add ano... | {
"ground_truth": "5339",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. (40 points) In a store where all items cost a whole number of rubles, two special offers are in effect:\n1) A customer who buys at least three items can choose one item as a gift (free of charge), the cost of which does not exceed the minimum cost of the paid items;\n2) A customer who buys exa... | {
"ground_truth": "504",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Variant 1.\n\nA line parallel to the leg $A C$ of the right triangle $A B C$ intersects the leg $B C$ at point $K$, and the hypotenuse $A B$ at point $N$. On the leg $A C$, a point $M$ is chosen such that $M K=M N$. Find the ratio $\\frac{A M}{M C}$, if $\\frac{B K}{B C}=14$.",
"role": "use... | {
"ground_truth": "7",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A bicycle travels due north at $\\frac{1}{2}$ mile per minute on a straight path. Simultaneously, a circular fog bank with a radius of $40$ miles moves northeast at $\\frac{1}{3}\\sqrt{2}$ mile per minute. At time $t=0$, the center of the fog is $100$ miles due east of the bicycle. Determine $\\fr... | {
"ground_truth": "240",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Natural numbers are placed in an infinite grid. Such that the number in each cell is equal to the number of its adjacent cells having the same number. Find the most distinct numbers this infinite grid can have.\n\n(Two cells of the grid are adjacent if they have a common vertex)",
"role": "use... | {
"ground_truth": "5",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Approximate the increase in the volume of a cylinder with a height of \\( H = 40 \\) cm and a base radius of \\( R = 30 \\) cm when the radius is increased by \\( 0.5 \\) cm.",
"role": "user"
}
] | {
"ground_truth": "1200\\pi",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the largest number of integers that can be selected from the natural numbers from 1 to 3000 such that the difference between any two of them is different from 1, 4, and 5?",
"role": "user"
}
] | {
"ground_truth": "1000",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There is a tunnel between locations $A$ and $B$. A car departs from $B$ towards $A$ at 08:16, and a truck departs from $A$ towards $B$ at 09:00. It is known that the truck and the car arrive at the two ends of the tunnel simultaneously, but the truck leaves the tunnel 2 minutes later than the car.... | {
"ground_truth": "10:00",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex has a rare phobia of balloons popping, called globophobia. To overcome their fear, Alex decides to take small steps by gradually exposing themselves to balloons in a controlled setting. On the first day, Alex bravely handles 3 balloons. Each day, they increase the number of balloons by 2 more... | {
"ground_truth": "45",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B5. In a $5 \\times 5$ table, we place the numbers 1 through 5 such that each number appears exactly once in each row and each column. A number in a specific row and column of the table is correctly placed if the following two conditions are met:\n\n- In that row, all smaller numbers are to the le... | {
"ground_truth": "5",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path only allows moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture. ... | {
"ground_truth": "24",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For any positive integer $a,$ $\\sigma(a)$ denotes the sum of the positive integer divisors of $a$ . Let $n$ be the least positive integer such that $\\sigma(a^n)-1$ is divisible by $2021$ for all positive integers $a$ . Find the sum of the prime factors in the prime factorization of $n$ .",
"... | {
"ground_truth": "125",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Twenty-five percent of the audience listened to the entire 90-minute talk, and fifteen percent did not pay attention at all. Of the remainder, 40% caught half of the talk, and the rest heard only one fourth of it. Calculate the average time in minutes the talk was heard by the audience members.",
... | {
"ground_truth": "41.4",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A function $f: \\N\\rightarrow\\N$ is circular if for every $p\\in\\N$ there exists $n\\in\\N,\\ n\\leq{p}$ such that $f^n(p)=p$ ( $f$ composed with itself $n$ times) The function $f$ has repulsion degree $k>0$ if for every $p\\in\\N$ $f^i(p)\\neq{p}$ for every $i=1,2,\\dots,\\... | {
"ground_truth": "1/2",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. The number of integers $n$ that satisfy $\\left(n^{2}-n-1\\right)^{n+2}=1$ is.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly. \n\nNote: The provided text is already in English, so no translation is n... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Given a six-digit decimal number composed of six positive integers, the digit in the units place is a multiple of 4, the digits in the tens and hundreds places are multiples of 3, and the sum of the digits of the six-digit number is 21. Then the number of six-digit numbers that satisfy the abov... | {
"ground_truth": "126",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose $a$ is a real number such that the equation \\[a\\cdot(\\sin{x}+\\sin{(2x)}) = \\sin{(3x)}\\] has more than one solution in the interval $(0, \\pi)$. The set of all such $a$ that can be written in the form \\[(p,q) \\cup (q,r),\\] where $p, q,$ and $r$ are real numbers with $p < q< r$. Wha... | {
"ground_truth": "{-}4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "It is known that 9 cups of tea cost less than 10 rubles, and 10 cups of tea cost more than 11 rubles. How much does one cup of tea cost?",
"role": "user"
}
] | {
"ground_truth": "111",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "25. There is an electronic clock using a 24-hour time system, and the current time displayed is $01: 23: 45$, where these 6 digits are consecutive and in ascending order. This is the first time, and after $\\qquad$ seconds, the fourth time will occur where 6 digits are consecutive and in ascending... | {
"ground_truth": "126671",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Vasya and Petya are participating in a school sports-entertainment game. They only have one pair of roller skates between the two of them, and need to traverse a distance of 3 km as quickly as possible. They start simultaneously, with one running and the other roller-skating. At any moment, the on... | {
"ground_truth": "0.5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a$ , $b$ , $c$ be positive integers and $p$ be a prime number. Assume that \\[ a^n(b+c)+b^n(a+c)+c^n(a+b)\\equiv 8\\pmod{p} \\] for each nonnegative integer $n$ . Let $m$ be the remainder when $a^p+b^p+c^p$ is divided by $p$ , and $k$ the remainder when $m^p$ is divided by $p... | {
"ground_truth": "399",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a developer who creates educational content for a poker training website. He wants to design a new course that includes 5 lessons on poker strategies. Each lesson requires 3 hours of video content and 2 hours of written content. If Alex records video content at a rate of 1 hour per day and... | {
"ground_truth": "15",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 6 people standing in a line numbered 1 through 6 in a left to right order.\nEach person has the following attributes: Job, Hobby, Food, Movie-Genre, Pet, Sport.\nThe attributes have the following possible values:\n- Job: architect, bartender, chef, nurse, social-worker, teacher\n- Hobby... | {
"ground_truth": "hamster",
"mean_reward": 0.03125
} | 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 $(x,y)$ of nonnegative integers that satisfy \\[x^3y+x+y=xy+2xy^2.\\]\n\n[Solution]\n\n<paragraph_0>\nTo find all pairs \\((x, y)\\) of nonnegative int... | {
"ground_truth": "-1",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11.8. In an alphabet of $n>1$ letters; a word is any finite sequence of letters in which any two adjacent letters are different. A word is called good if it is impossible to erase all letters from it, except for four, so that the remaining sequence is of the form $a a b b$, where $a$ and $b$ are d... | {
"ground_truth": "2n+1",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the interval within which the real number $\\sqrt{10}$ lies. Express your answer as an interval in the format (lower bound, upper bound).",
"role": "user"
}
] | {
"ground_truth": "(3, 4)",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. There are 2015 coins on the table. Two players play the following game: they take turns; on a turn, the first player can take any odd number of coins from 1 to 99, and the second player can take any even number of coins from 2 to 100. The player who cannot make a move loses. How many coins shou... | {
"ground_truth": "95",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $A$ be a subset of $\\{1, 2, 3, \\ldots, 50\\}$ with the property: for every $x,y\\in A$ with $x\\neq y$ , it holds that\n\\[\\left| \\frac{1}{x}- \\frac{1}{y}\\right|>\\frac{1}{1000}.\\]\nDetermine the largest possible number of elements that the set $A$ can have.",
"role": "user... | {
"ground_truth": "40",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# Task 3. Maximum 20 points\n\nAt the \"Economics and Law\" congress, a \"Tournament of the Best\" was held, in which more than 220 but fewer than 254 delegates—economists and lawyers—participated. Within one match, participants had to ask each other questions within a limited time and record the ... | {
"ground_truth": "105",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. (3 points) 60 adventure team members need to cross a river. There is only one rubber boat on the river that can carry 6 people (a round trip counts as two times), and it takes 3 minutes to cross the river once. The total time required for all team members to cross to the other side of the rive... | {
"ground_truth": "69",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Does there exist a six-digit natural number which, when multiplied by 9, results in the same digits but in reverse order?",
"role": "user"
}
] | {
"ground_truth": "109989",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A castle has a number of halls and \\( n \\) doors. Every door leads into another hall or outside. Every hall has at least two doors. A knight enters the castle. In any hall, he can choose any door for exit except the one he just used to enter that hall. Find a strategy allowing the knight to get ... | {
"ground_truth": "2n",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A young researcher is analyzing the impact of social media on populist rhetoric. She decides to study the number of times certain keywords appear in social media posts over a week. On Monday, she finds 15 posts containing the keywords. On Tuesday, she finds 12 more posts than on Monday. On Wednesd... | {
"ground_truth": "110.5",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. (2 points) Anya was making pancakes, planning for each of the three members of her family to get an equal number of pancakes. But something went wrong: every third pancake Anya couldn't flip; $40 \\%$ of the pancakes that Anya managed to flip burned; and $\\frac{1}{5}$ of the edible pancakes An... | {
"ground_truth": "32",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the equations:\n\\[\n\\log_{2}\\left[\\log_{\\frac{1}{2}}\\left(\\log_{2} x\\right)\\right]=\\log_{3}\\left[\\log_{\\frac{1}{3}}\\left(\\log_{3} y\\right)\\right]=\\log_{5}\\left[\\log_{\\frac{1}{5}}\\left(\\log_{5} z\\right)\\right]=0\n\\]\nDetermine the relationship among x, y, and z. Expr... | {
"ground_truth": "z < x < y",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[Example 5.6.1] If numbers $a_{1}, a_{2}, a_{3}$ are taken in ascending order from the set $1,2, \\cdots, 14$, such that both $a_{2}-a_{1} \\geqslant 3$ and $a_{1}-a_{2} \\geqslant 3$ are satisfied, how many different ways of selection are there?",
"role": "user"
}
] | {
"ground_truth": "120",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $m \\ge 3$ be an integer and let $S = \\{3,4,5,\\ldots,m\\}$. Find the smallest value of $m$ such that for every partition of $S$ into two subsets, at least one of the subsets contains integers $a$, $b$, and $c$ (not necessarily distinct) such that $ab = c$.\nNote: a partition of $S$ is a pair... | {
"ground_truth": "243",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Through how many squares does the diagonal of a 1983 × 999 chessboard pass?",
"role": "user"
}
] | {
"ground_truth": "2979",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On a long straight section of a two-lane highway where cars travel in both directions, cars all travel at the same speed and obey the safety rule: the distance from the back of the car ahead to the front of the car behind is exactly one car length for every 10 kilometers per hour of speed or fract... | {
"ground_truth": "200",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A soccer team has 23 players in total. 12 players start the game, while the remaining 11 are available as substitutes. The coach is allowed to make up to 5 substitutions during the game. Any one of the players in the game can be replaced by one of the substitutes, but substituting players cannot r... | {
"ground_truth": "93",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sequence of positive integers $a_0, a_1, a_2, . . .$ is defined by $a_0 = 3$ and $$ a_{n+1} - a_n = n(a_n - 1) $$ for all $n \\ge 0$ . Determine all integers $m \\ge 2$ for which $gcd (m, a_n) = 1$ for all $n \\ge 0$ .",
"role": "user"
}
] | {
"ground_truth": " m = 2^k ",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.9. On a plane, $N$ points are marked. Any three of them form a triangle, the angles of which in degrees are expressed by natural numbers. For what largest $N$ is this possible\n\n$$\n\\text { (E. Bakayev) }\n$$",
"role": "user"
}
] | {
"ground_truth": "180",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "23. Find the smallest positive integer $n(\\geqslant 3)$, such that in any set of $n$ points in the plane with no three points collinear, there must be three points that are the vertices of a non-isosceles triangle.\n(2005 China National Training Team Problem)",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B4. The infinite sequence of numbers\n\n$$\n0,1,2,2,1,-1,-2,-1,1,3, \\ldots\n$$\n\nsatisfies the following rule. For each quadruple of consecutive numbers $\\ldots, a, b, c, d, \\ldots$ in the sequence, it always holds that $d$ is equal to $c$ minus the smallest of the two numbers $a$ and $b$. Thu... | {
"ground_truth": "2187",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A coin is flipped multiple times until an odd number of heads followed by a tail is obtained. Given $n \\in \\mathbb{N}^{*}$, find the number of sequences of $n$ flips.",
"role": "user"
}
] | {
"ground_truth": "F_{n-1}",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Professor Thompson, a Medieval Studies scholar, is preparing a syllabus for her upcoming course. She needs to gather a set of resources for her class, which includes 12 books, 8 journal articles, and 5 manuscripts. Each book costs $25, each journal article costs $10, and each manuscript costs $15.... | {
"ground_truth": "1820",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An eager young acoustic engineering student is shadowing a seasoned consultant on a project to design a new concert hall. The student is tasked with calculating the optimal number of sound panels needed for a section of the hall to ensure the best acoustics. The hall section is rectangular and mea... | {
"ground_truth": "96",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the equation $2 b x+b=3 c x+c$, both $b$ and $c$ can take any of the values $1,2,3,4,5,6$. In how many cases will the solution of the equation be positive?\n\n---\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation resul... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "This was a highly dangerous car rally. It began with a small and very narrow bridge, where one out of five cars would fall into the water. Then followed a terrifying sharp turn, where three out of ten cars would go off the road. Next, there was a dark and winding tunnel where one out of ten cars w... | {
"ground_truth": "69.76",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Square \\(ABCD\\) with side length 2 is inscribed in a circle. Using each side of the square as a diameter, semicircular arcs are drawn. Calculate the area of the shaded region outside the circle and inside the semicircles. Express your answer as a single number.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a $9 \\times 9$ square table, 9 cells are marked at the intersections of the second, fifth, and eighth rows with the second, fifth, and eighth columns. How many ways are there to get from the bottom-left cell to the top-right cell, moving only through unmarked cells upwards or to the right?",
... | {
"ground_truth": "678",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A set of positive integers is said to be pilak if it can be partitioned into 2 disjoint subsets \\(F\\) and \\(T\\), each with at least 2 elements, such that the elements of \\(F\\) are consecutive Fibonacci numbers, and the elements of \\(T\\) are consecutive triangular numbers. Find all positive... | {
"ground_truth": "30",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate $\\frac{\\pi}{\\sqrt{2}}$ to three decimal places.",
"role": "user"
}
] | {
"ground_truth": "2.221",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of ways a series of $+$ and $-$ signs can be inserted between the numbers $0,1,2,\\cdots, 12$ such that the value of the resulting expression is divisible by 5.\n\n[i]Proposed by Matthew Lerner-Brecher[/i]",
"role": "user"
}
] | {
"ground_truth": "816",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The mathematician Gypsy. He shamelessly stole. Of course, he denied it all the way. The count could not figure out how the precious birds, which were fed inside his strictly guarded game preserve, were being reached. But he loved a trick: he wanted to outsmart the thief's mind.\n\n- You, Gypsy... ... | {
"ground_truth": "31",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Select some numbers without repetition from $1,2, \\ldots 15$, such that the sum of any two numbers is not a perfect square of a natural number, then the maximum number of numbers that can be selected is ( ).",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3 Find all positive integers $k$ such that for any positive numbers $a$, $b$, and $c$ satisfying the inequality $k(ab + bc + ca) > 5(a^2 + b^2 + c^2)$, there must exist a triangle with side lengths $a$, $b$, and $c$.\n(Qian Zhanwang)",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. (2 points) In trapezoid $A B C D$ with bases $A D=16$ and $B C=10$, the circles constructed on sides $A B, B C$ and $C D$ as diameters intersect at one point. The length of diagonal $A C$ is 10. Find the length of $B D$.",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. Color the circles in the figure, requiring that two adjacent circles connected by a line be colored with different colors, then at least $\\qquad$ colors are needed.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. (3 points) Cars A and B start from locations $A$ and $B$ simultaneously and travel back and forth between $A$ and $B$ at a constant speed. If after the first meeting, Car A continues to drive for 4 hours to reach $B$, while Car B only drives for 1 hour to reach $A$, then when the two cars meet ... | {
"ground_truth": "86",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A coastal management officer is tasked with building a series of breakwaters to protect a 2-kilometer stretch of coastline. Each breakwater is 100 meters long and needs to be placed every 200 meters along the coast. If the officer has already placed 3 breakwaters, how many more breakwaters does th... | {
"ground_truth": "7",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the greatest positive integer $m$ with the following property:\nFor every permutation $a_1, a_2, \\cdots, a_n,\\cdots$ of the set of positive integers, there exists positive integers $i_1<i_2<\\cdots <i_m$ such that $a_{i_1}, a_{i_2}, \\cdots, a_{i_m}$ is an arithmetic progression wit... | {
"ground_truth": " 3 ",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given three points \\(A, B, C\\) forming a triangle with angles \\(30^{\\circ}\\), \\(45^{\\circ}\\), and \\(105^{\\circ}\\). Two of these points are chosen, and the perpendicular bisector of the segment connecting them is drawn. The third point is then reflected across this perpendicular bisector... | {
"ground_truth": "12",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. (12 points) In the animal kingdom, tigers always tell the truth, foxes always lie, and monkeys sometimes tell the truth and sometimes lie. There are 100 tigers, 100 foxes, and 100 monkeys, divided into 100 groups, with each group consisting of 3 animals, exactly 2 of one kind and 1 of another.... | {
"ground_truth": "76",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For example, what day of the week is January 1, 32000?",
"role": "user"
}
] | {
"ground_truth": "Saturday",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the addition problem, each digit has been replaced by a letter. If different letters represent different digits then what is the value of $C$?",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1.5. Ana, Biljana, Vesna, and Gordana crossed the river in a canoe as follows: There were three trips from the left to the right bank, each time with two girls in the canoe, one of whom was rowing. On both trips from the right bank to the left, there was only one girl in the canoe. It is known tha... | {
"ground_truth": "Vesna",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When $600_{10}$ is expressed in a certain base, it has four digits in the form ABBA, where A and B are different digits. What is this base?",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A glass contains 0.25 kg of Omni-Cola (mostly water) initially at 25°C. How much ice, initially at -20°C must you add to obtain a final temperature of 0°C with all the ice melted? Neglect the heat capacity of the glass. (Unit: g)",
"role": "user"
}
] | {
"ground_truth": "70",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Incompressible oil of density 850 kg/m^3 is pumped through a cylindrical pipe at a rate of 9.5 liters per second. The second section of the pipe has a diameter of 4.0 cm. What are the flow speed in that section? (Unit: m/s)",
"role": "user"
}
] | {
"ground_truth": "7.6",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[ Ratio of areas of similar triangles ]\n\nIn a right triangle, the sine of the smaller angle is $\\frac{1}{3}$. A line perpendicular to the hypotenuse divides the triangle into two equal areas. In what ratio does this line divide the hypotenuse?",
"role": "user"
}
] | {
"ground_truth": "2:1",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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