prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "An adventurous solo hiker is planning an expedition to the Himalayas. Her journey involves hiking through 3 different trails. The first trail is 12 kilometers long, the second trail is 15 kilometers long, and the third trail is 9 kilometers long. She plans to rest for 1 hour after every 8 kilomete... | {
"ground_truth": "13",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nAll the cells of a \\(100 \\times 100\\) square table are numbered in some order from 1 to 10000. Petya colors the cells according to the following rules. First, he colors \\(k\\) cells at his discretion. Then, on each turn, Petya can color one yet-to-be-colored cell with number \\(a\\) if at le... | {
"ground_truth": "k = 1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A circle $k$ has its center at $O$, and points $A, B, C, D$ are consecutive points on the circumference of $k$, such that $\\angle AOB = \\angle BOC = \\angle COD = \\alpha < 60^{\\circ}$. The projection of $D$ onto the diameter $AO$ is $E$, and the point $F$ is the closer trisection point of segm... | {
"ground_truth": "60",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": " $1989$ equal circles are arbitrarily placed on the table without overlap. What is the least number of colors are needed such that all the circles can be painted with any two tangential circles colored differently.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A six-digit number begins with digit 1 and ends with digit 7. If the digit in the units place is decreased by 1 and moved to the first place, the resulting number is five times the original number. Find this number.",
"role": "user"
}
] | {
"ground_truth": "142857",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a,b,c,x,y,$ and $z$ be complex numbers such that \\[a=\\dfrac{b+c}{x-2},\\qquad b=\\dfrac{c+a}{y-2},\\qquad c=\\dfrac{a+b}{z-2}.\\] If $xy+yz+xz=67$ and $x+y+z=2010$ , find the value of $xyz$ .",
"role": "user"
}
] | {
"ground_truth": "-5892",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The two seven-digit numbers 74A52B1 and 326AB4C are both divisible by 3. Find the value of C. Express your answer as a single digit.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let the sequence $\\{x_n\\}$ be defined by $x_1 \\in \\{5, 7\\}$ and, for $k \\ge 1, x_{k+1} \\in \\{5^{x_k} , 7^{x_k} \\}$ . For example, the possible values of $x_3$ are $5^{5^5}, 5^{5^7}, 5^{7^5}, 5^{7^7}, 7^{5^5}, 7^{5^7}, 7^{7^5}$ , and $7^{7^7}$ . Determine the sum of all possible v... | {
"ground_truth": "75",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "During a school recess, \\( n \\) children are sitting in a circle, playing a game. A teacher walks clockwise around the circle, distributing candies to the children according to the following rule:\n\n1. Pick a child and give them and the next child (clockwise) one candy each.\n2. Skip the next c... | {
"ground_truth": "2^k",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $1 \\leq n \\leq 2021$ be a positive integer. Jack has $2021$ coins arranged in a line where each coin has an $H$ on one side and a $T$ on the other. At the beginning, all coins show $H$ except the nth coin. Jack can repeatedly perform the following operation: he chooses a coin showing $T$, an... | {
"ground_truth": "n = 1011",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many points does one have to place on a unit square to guarantee that two of them are strictly less than 1/2 unit apart?",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Let the odd function $f(x)$ have a domain of $[-2,2]$,\n\nand be decreasing in the interval $[-2,0]$, satisfying\n$$\nf(1-m)+f\\left(1-m^{2}\\right)<0 \\text {. }\n$$\n\nThen the range of real number $m$ is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "[-1,1)",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Katie writes a different positive integer on the top face of each of the fourteen cubes in the pyramid shown. The sum of the nine integers written on the cubes in the bottom layer is 50. The integer written on each of the cubes in the middle and top layers of the pyramid is equal to the sum of the... | {
"ground_truth": "118",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 8 Find the maximum value of the function\n$$\nf(x)=\\sqrt{-x^{2}+10 x-9}+\\sqrt{-x^{2}+68 x-256}\n$$",
"role": "user"
}
] | {
"ground_truth": "3\\sqrt{35}",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Define the sequence $a_1,a_2,a_3,\\ldots$ by $a_n=\\sum_{k=1}^n\\sin(k)$, where $k$ represents radian measure. Find the index of the $100$th term for which $a_n<0$.",
"role": "user"
}
] | {
"ground_truth": "628",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For a finite sequence $B = (b_1, b_2, \\dots, b_n)$ of numbers, the Cesaro sum is defined as\n\\[\\frac{T_1 + T_2 + \\cdots + T_n}{n},\\] \nwhere $T_k = b_1 + b_2 + \\cdots + b_k$ for $1 \\leq k \\leq n$.\n\nIf the Cesaro sum of the 100-term sequence $(b_1, b_2, \\dots, b_{100})$ is 1200, where $b... | {
"ground_truth": "1191",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a line, there are 2020 white stones and one black stone. A possible operation is as follows: choose a black stone that is not at the edge and change the color of its neighboring stones. Find all possible initial positions for the black stone such that it is possible to color all the stones blac... | {
"ground_truth": "1011",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At a physical education lesson, 29 seventh graders attended, some of whom brought one ball each. During the lesson, sometimes one seventh grader would give their ball to another seventh grader who did not have a ball.\n\nAt the end of the lesson, $N$ seventh graders said, \"I received balls less o... | {
"ground_truth": "14",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. 99 wise men sat at a round table. They know that fifty of them are wearing hats of one of two colors, and the other forty-nine are wearing hats of the other color (but it is not known in advance which of the two colors 50 hats are, and which 49 are). Each wise man can see the colors of all the ... | {
"ground_truth": "74",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Among the numbers between 4000 and 7000, there are $\\qquad$ numbers that are even and have four distinct digits.\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": "728",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a triangle, the points \\( a \\) (a > 0) denote the incenter, and also the points of tangency of the inscribed circle with the sides respectively. Using no more than three lines with a straightedge, construct a segment of length \\( a - c \\).",
"role": "user"
}
] | {
"ground_truth": "a - c",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. March 19, 2017 was a Sunday, based on this, calculate what day of the week September 1, 2017 was.\n\nTranslate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "Friday",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "John is about to receive a certain amount of change less than one dollar from a cashier. If he gets the maximum number of quarters possible and the rest in nickels, he would need to receive 2 nickels to meet the amount. If he gets the maximum number of dimes possible and the rest in nickels, he wo... | {
"ground_truth": "60",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. In one year, January 1 and April 1 fell on a Thursday. How many months in that year had 5 Fridays?",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. A runner and two cyclists and a motorcyclist are moving along a ring road, each at a constant speed, but in different directions. The runner and one of the cyclists are moving in the same direction, while the motorcyclist and the other cyclist are moving in the opposite direction. The runner m... | {
"ground_truth": "3",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. There are 10 cards, each card has two different numbers from $1,2,3,4,5$, and no two cards have the same pair of numbers. These 10 cards are to be placed into five boxes labeled $1,2,3,4,5$, with the rule that a card with numbers $i, j$ can only be placed in box $i$ or box $j$. A placement is c... | {
"ground_truth": "120",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. (10 points) The area of rectangle $A B C D$ is 416 square centimeters, and the vertex $F$ of trapezoid $A F G E$ is on $B C$, with $D$ being the midpoint of the waist $E G$. Try to find the area of trapezoid $A F G E$.\n\n",
"role": "user"
}
] | {
"ground_truth": "416",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 12. (6 points)\n\nVictor received a large sum of money as a birthday gift in the amount of 45 thousand rubles. The young man decided to save this part of his savings in dollars on a currency deposit. The term of the deposit agreement was 2 years, with an interest rate of 4.7% per annum, co... | {
"ground_truth": "873",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14.Workdays. Three workers are digging a pit. They work in turns, and each works as long as the other two need to dig half the pit. Working this way, they dug the pit. How many times faster would they have finished the work if they had worked simultaneously\n\n## 43 Languages of Mathematics",
... | {
"ground_truth": "2.5",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. For what value of $a$ does the inequality $\\log \\frac{1}{\\div}\\left(\\sqrt{x^{2}+a x+5}+1\\right) \\cdot \\log _{5}\\left(x^{2}+a x+6\\right)+\\log _{a} 3 \\geqslant 0$ have exactly one solution?",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. Let $a_{1}, a_{2}, \\cdots, a_{6}$ be any permutation of $\\{1,2, \\cdots, 6\\}$. If the sum of any three consecutive numbers cannot be divisible by 3, then the number of such permutations is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "96",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the maximal possible value of $n$ such that there exist points $P_1,P_2,P_3,\\ldots,P_n$ in the plane and real numbers $r_1,r_2,\\ldots,r_n$ such that the distance between any two different points $P_i$ and $P_j$ is $r_i+r_j$ .",
"role": "user"
}
] | {
"ground_truth": " n = 4 ",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The area of the floor in a rectangular room is 360 square feet. The length of the room is twice its width. The homeowners plan to cover the floor with 8-inch by 8-inch tiles. How many tiles will be in each row along the length of the room?",
"role": "user"
}
] | {
"ground_truth": "18\\sqrt{5}",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The 2020 members of the society of game theorists are holding the annual election for their leadership board. All members are initially on the board, and are ranked based on their qualifications. They start off by voting on whether to keep the board the same size; if they fail to get a strict majo... | {
"ground_truth": "1023",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. For a natural number ending not in zero, one of its digits (not the most significant) was erased. As a result, the number decreased by 9 times. How many numbers exist for which this is possible?",
"role": "user"
}
] | {
"ground_truth": "28",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B2. Given is a quadrilateral $A B C D$\n\nwith sides $A B=16, B C=21, C D=2$ and $D A=28$.\n\nFurthermore, $A B$ is parallel to $C D$. Two lines that are parallel to $A B$ and $C D$ divide quadrilateral $A B C D$ into three similar quadrilaterals. Calculate the perimeter of the smallest of these t... | {
"ground_truth": "13",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 1. The year 2009 has the following property: by swapping the digits of the number 2009, it is impossible to obtain a smaller four-digit number (numbers do not start with zero). In which year will this property reoccur for the first time?",
"role": "user"
}
] | {
"ground_truth": "2022",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two circles are given. Their common internal tangents are mutually perpendicular. The chords connecting the points of tangency are 3 and 5. Find the distance between the centers of the circles.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many triangles are in this figure? (Some triangles may overlap other triangles.) [asy] draw((0,0)--(42,0)--(14,21)--cycle); draw((14,21)--(18,0)--(30,9)); [/asy]",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Students have taken a test paper in each of $n \\ge 3$ subjects. It is known that in any subject exactly three students got the best score, and for any two subjects exactly one student got the best scores in both subjects. Find the smallest $n$ for which the above conditions imply that exactly one... | {
"ground_truth": " n = 7 ",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. $N$ is the set of positive integers. Define the function $f$ on $N$ as follows:\n$f(1)=1, f(3)=3$, and for $n \\in N$ we have $f(2 n)=f(n)$,\n$f(4 n+1)=2 f(2 n+1)-f(n)$,\n$f(4 n+3)=3 f(2 n+1)-2 f(n)$.\n\nQuestion: How many $n \\in N$, and $n \\leqslant 1988$ such that $f(n) = n$?",
"role": ... | {
"ground_truth": "92",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Among the keys below, the ones that are exactly the same are $\\qquad$ pairs.\n\n",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## SUBIECTUL I\n\na) Demonstrați că $\\frac{n}{k(k+n)}=\\frac{1}{k}-\\frac{1}{k+n}$, pentru orice $\\mathrm{k}$ și $\\mathrm{n}$ numere naturale.\n\nb) Determinați numărul natural nenul $n$ pentru care\n\n$$\n\\frac{1}{56 \\cdot 57}+\\frac{2}{57 \\cdot 59}+\\frac{3}{59 \\cdot 62}+\\cdots+\\frac{62... | {
"ground_truth": "2009",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The user has three computer disks from companies $\\mathrm{K}$, $\\mathrm{L}$, and $\\mathrm{M}$, one disk from each of these companies, but the company stamps on the disks are absent. Two out of the three disks are defective. What is the probability that the defective disks are from companies $\\... | {
"ground_truth": "0.4821",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nProblem 2. For any set $A=\\left\\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\\right\\}$ of five distinct positive integers denote by $S_{A}$ the sum of its elements, and denote by $T_{A}$ the number of triples $(i, j, k)$ with $1 \\leqslant i<j<k \\leqslant 5$ for which $x_{i}+x_{j}+x_{k}$ divides $S_{A... | {
"ground_truth": "4",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three cyclists started simultaneously: the first and second from point A, and the third towards them from point B. After 1.5 hours, the first cyclist was equidistant from the other two, and 2 hours after departure, the third cyclist was equidistant from the first and second. How many hours after d... | {
"ground_truth": "3",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "IMO 1976 Problem A1 A plane convex quadrilateral has area 32, and the sum of two opposite sides and a diagonal is 16. Determine all possible lengths for the other diagonal.",
"role": "user"
}
] | {
"ground_truth": "8\\sqrt{2}",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.5. The numbers from 1 to 10 were written in some order and resulted in the numbers \\(a_{1}, a_{2}, a_{3}, \\ldots, a_{10}\\), and then the sums \\(S_{1}=a_{1}\\), \\(S_{2}=a_{1}+a_{2}\\), \\(S_{3}=a_{1}+a_{2}+a_{3}\\), \\ldots, \\(S_{10}=a_{1}+a_{2}+a_{3}+\\ldots+a_{10}\\) were calculated. What... | {
"ground_truth": "7",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given $0 \\leqslant x, y, z \\leqslant 1$, solve the equation:\n$$\\frac{x}{1+y+z x}+\\frac{y}{1+z+x y}+\\frac{z}{1+x+y z}=\\frac{3}{x+y+z} .$$",
"role": "user"
}
] | {
"ground_truth": "x=y=z=1",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the last non-zero digit of the product of the first hundred natural numbers?\n\n\n\n\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": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the sequence $2001$, $2002$, $2003$, $\\ldots$ , each term after the third is found by subtracting the previous term from the sum of the two terms that precede that term. For example, the fourth term is $2001 + 2002 - 2003 = 2000$. What is the $2004^\\textrm{th}$ term in this sequence?",
"r... | {
"ground_truth": "0",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangular grazing area is fenced on three sides using part of a 150 meter rock wall as the fourth side. The area needs to be 50 m by 70 m. Calculate the fewest number of fence posts required.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\n3. For a rational number $r$, its period is the length of the smallest repeating block in its decimal expansion. For example, the number $r=0.123123123 \\cdots$ has period 3 . If $S$ denotes the set of all rational numbers $r$ of the form $r=0 . \\overline{a b c d e f g h}$ having period 8 , fin... | {
"ground_truth": "49995000",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. In $\\triangle A B C$, $A B=\\sqrt{30}, A C=\\sqrt{6}, B C$ $=\\sqrt{15}$, there is a point $D$ such that $A D$ bisects $B C$ and $\\angle A D B$ is a right angle, the ratio $\\frac{S_{\\triangle A D B}}{S_{\\triangle A B C}}$ can be written as $\\frac{m}{n}$. ($m, n$ are coprime positive inte... | {
"ground_truth": "65",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the non-convex quadrilateral $ABCD$ shown below, $\\angle BCD$ is a right angle, $AB=12$, $BC=4$, $CD=3$, and $AD=13$. What is the area of quadrilateral $ABCD$? [asy]draw((0,0)--(2.4,3.6)--(0,5)--(12,0)--(0,0)); label(\"$B$\", (0, 0), SW); label(\"$A$\", (12, 0), ESE); label(\"$C$\", (2.4, 3.6)... | {
"ground_truth": "24",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task B-2.3.\n\nOne year, January 1 and April 1 were both on a Thursday. How many months in that year have five Fridays? Justify your answer.",
"role": "user"
}
] | {
"ground_truth": "5",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10. A key can only open one lock. Now there are 10 keys and 10 locks, but it is unknown which key opens which lock. At most how many attempts are needed to successfully match all the keys and locks.",
"role": "user"
}
] | {
"ground_truth": "45",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. A student participates in military training and must shoot 10 times. In the 6th, 7th, 8th, and 9th shots, he scored 9.0, 8.4, 8.1, and 9.3 points, respectively. The average score of his first 9 shots is higher than the average score of his first 5 shots. If he wants the average score of 10 sho... | {
"ground_truth": "9.9",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "46th Putnam 1985 Problem B1 p(x) is a polynomial of degree 5 with 5 distinct integral roots. What is the smallest number of non-zero coefficients it can have? Give a possible set of roots for a polynomial achieving this minimum. Solution",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. Let $T=\\left\\{9^{4} \\mid k\\right.$ be an integer, $0 \\leqslant k$ $\\leqslant 4000\\}$. It is known that $9^{1000}$ has 3817 digits, and its most significant digit is 9. How many elements in $T$ have 9 as their most significant digit?",
"role": "user"
}
] | {
"ground_truth": "184",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Hamilton Avenue has eight houses. On one side of the street are the houses\nnumbered 1,3,5,7 and directly opposite are houses 2,4,6,8 respectively. An\neccentric postman starts deliveries at house 1 and delivers letters to each of\nthe houses, finally returning to house 1 for a cup of tea. Through... | {
"ground_truth": "12",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. The left figure below is a strange black box. This black box has one input port and one output port. When we input a number into the input port, a number result will be produced at the output port, following these rules:\n(1) If the input is an odd number $\\mathrm{k}$, the output is $4 \\math... | {
"ground_truth": "680",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alice writes differents real numbers in the board, if $a,b,c$ are three numbers in this board, least one of this numbers $a + b, b + c, a + c$ also is a number in the board. What's the largest quantity of numbers written in the board???",
"role": "user"
}
] | {
"ground_truth": " 7 ",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Six horizontal lines and five vertical lines are drawn in a plane. If a specific point, say (3, 4), exists in the coordinate plane, in how many ways can four lines be chosen such that a rectangular region enclosing the point (3, 4) is formed?",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If $f''(x_{0})=2$, find the value of $\\lim\\limits_{k\\to 0} \\frac{f(x_{0}-k)-f(x_{0})}{2k}$. Express your answer as a single numerical value.",
"role": "user"
}
] | {
"ground_truth": "-1",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5 By Fermat's Little Theorem, for any odd prime $p$, we have $2^{p-1} \\equiv 1(\\bmod p)$. Question: Does there exist a composite number $n$ such that $2^{n-1} \\equiv 1(\\bmod n)$ holds?",
"role": "user"
}
] | {
"ground_truth": "341",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Shapovalov A.V.\n\nThieves Hapok and Glazok are dividing a pile of 100 coins. Hapok grabs a handful of coins from the pile, and Glazok, looking at the handful, decides who of the two will get it. This continues until one of them receives nine handfuls, after which the other takes all the remaining... | {
"ground_truth": "46",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Zan has created this iterative rule for generating sequences of whole numbers:\n\n1) If a number is 25 or less, double the number.\n\n2) If a number is greater than 25, subtract 12 from it.\n\nLet $F$ be the first number in a sequence generated by the rule above. $F$ is a \"sweet number\" if 16 is... | {
"ground_truth": "16",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "B5. A sawtooth number is a positive integer with the following property: of each triplet of adjacent digits, the middle digit is either greater than its two neighboring digits or smaller than its two neighboring digits. The numbers 352723 and 314 are, for example, sawtooth numbers, but 3422 and 12... | {
"ground_truth": "110",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. There is a five-digit positive odd number $x$. Replace all 2s in $x$ with 5s, and all 5s with 2s, keeping other digits unchanged, to get a new five-digit number, denoted as $y$. If $x$ and $y$ satisfy the equation $y=2(x+1)$, then $x$ is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "29995",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From point \\( O \\), three rays \\( OA, OB, OC \\) are drawn, with the angles between each pair of rays being \\( 60^{\\circ}, 90^{\\circ}, \\) and \\( 120^{\\circ} \\) respectively. What is the minimum angle between the angle bisectors of these three angles?",
"role": "user"
}
] | {
"ground_truth": "45^\\circ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. A bear walks one mile south, one mile east, and one mile north, only to find itself where it started. Another bear, more energetic than the first, walks two miles south, two miles east, and two miles north, only to find itself where it started. However, the bears are not white and did not start... | {
"ground_truth": "3.477",
"mean_reward": 0.015625
} | 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": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A language scholar is studying ancient literature and discovers a fascinating pattern in a collection of ancient scrolls. Each scroll contains a number of chapters, and the scholar notices that the number of chapters in each scroll is related to a modern book by a certain factor. The scholar has f... | {
"ground_truth": "285",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "155 birds $ P_1, \\ldots, P_{155}$ are sitting down on the boundary of a circle $ C.$ Two birds $ P_i, P_j$ are mutually visible if the angle at centre $ m(\\cdot)$ of their positions $ m(P_iP_j) \\leq 10^{\\circ}.$ Find the smallest number of mutually visible pairs of birds, i.e. minimal set of ... | {
"ground_truth": "270",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Each rational number is painted with one of two colors, white and red. Such a coloring is called sanferminera when for any two rational numbers $x, y$, with $x \\neq y$, if one of the following three conditions is met:\na) $x y=1$,\nb) $x+y=0$,\nc) $x+y=1$,\n\nthen $x$ and $y$ are painted in di... | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "15. On a long strip of paper, the numbers 1, 2, 3, .... n are written in sequence. The long strip is cut into five segments, each containing some consecutive natural numbers (the digits of a single number are not split between different segments). We calculated the average of these five segments, ... | {
"ground_truth": "2014",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. (10 points) As shown in the figure, Ruru's vegetable garden is a large rectangle composed of 4 square plots and 1 small rectangular pond. If the area of each plot is 20 square meters and the length of the garden is 9 meters, then the perimeter of the pond (the shaded part in the figure) is $\\q... | {
"ground_truth": "18",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two differentiable real functions \\( f(x) \\) and \\( g(x) \\) satisfy\n\\[ \\frac{f^{\\prime}(x)}{g^{\\prime}(x)} = e^{f(x) - g(x)} \\]\nfor all \\( x \\), and \\( f(0) = g(2003) = 1 \\). Find the largest constant \\( c \\) such that \\( f(2003) > c \\) for all such functions \\( f, g \\).",
... | {
"ground_truth": "1 - \\ln 2",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14. Teacher $D$ placed cards with the numbers $1, 2, \\cdots, 13$ in a clockwise order on a circle. Initially, all cards are face up. Each time, one card can be flipped to face down (once a card is face down, it cannot be flipped again). Teacher $D$'s rule for flipping cards is: if a face-up card ... | {
"ground_truth": "26624",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "17. A courier company undertakes courier services between 13 cities in a certain area. If each courier can take on the courier services for at most four cities, to ensure that there is at least one courier between every two cities, the courier company needs at least $\\qquad$ couriers.",
"role... | {
"ground_truth": "13",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. There are two solutions of wine spirit in water ${ }^{1}$ ): The first solution weighs 4002 and contains $30 \\%$ spirit, the second solution weighs 6002 and contains $80 \\%$ spirit.\n\nFrom these two solutions, one solution is made. What percentage of spirit will it contain? (O. 117, U. 126, ... | {
"ground_truth": "60",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Every day at noon, a mail steamer leaves from Le Havre to New York, and at the same time, another steamer from the same company leaves New York for Le Havre. Each of these steamers takes exactly seven days to complete their journey, and they travel the same route.\n\nHow many steamers from the sam... | {
"ground_truth": "15",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "【Question 12】A and B take turns marking numbers from 1 to 17, with the rules: you cannot mark a number that has already been marked; you cannot mark a number that is twice a marked number; you cannot mark a number that is half of a marked number; the player who cannot mark a number loses. Now A ma... | {
"ground_truth": "6",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. On one website, there is a poll to determine the best hockey player of the last decade. The number of votes for each player is given as a percentage, rounded to the nearest whole number. After Mirek voted for Jaromír Jágr, his share of $7 \\%$ did not change. What is the minimum number of peopl... | {
"ground_truth": "107",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## 17. ILLUSTRATIVE EXERCISE\n\nLet $n$ be a positive integer. A train stops at $2 n$ stations, including the initial and final ones, numbered in order from the first to the $2 n$-th. It is known that in a certain carriage, for every pair of integers $i, j$ such that $1 \\leq i < j \\leq 2 n$, exa... | {
"ground_truth": "n^2",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. The sum of all solutions of the equation $\\cos 2x=0$ in the interval $[0,100]$ is\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "1024 \\pi",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "24. Let $A=\\{1,2,3, \\cdots, 4 n+2\\}, M=\\{2 n+1,4 n+3,6 n+5\\}$. For any non-empty subset $B$ of $A$, if the sum of any two numbers in $B$ does not belong to $M$, then $B$ is called an $M$-free set. If $A=A_{1} \\cup A_{2}, A_{1} \\cap A_{2}=$ $\\varnothing$, and $A_{1}, A_{2}$ are both $M$-fre... | {
"ground_truth": "2^{n+1}",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A caretaker is giving candy to his two babies. Every minute, he gives a candy to one of his two babies at random. The five possible moods for the babies to be in, from saddest to happiest, are \"upset,\" \"sad,\" \"okay,\" \"happy,\" and \"delighted.\" A baby gets happier by one mood when they get... | {
"ground_truth": "337",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sequence $ (a_n)$ satisfies $ a_0 \\equal{} 0$ and $ \\displaystyle a_{n \\plus{} 1} \\equal{} \\frac85a_n \\plus{} \\frac65\\sqrt {4^n \\minus{} a_n^2}$ for $ n\\ge0$. Find the greatest integer less than or equal to $ a_{10}$.",
"role": "user"
}
] | {
"ground_truth": "983",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Does there exist an integer \\( n \\) such that \\( 21n \\equiv 1 \\mod 74 \\)?",
"role": "user"
}
] | {
"ground_truth": "67",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task A-3.4.\n\nInside the triangle $ABC$ there is a point $T$ such that $|AT|=56,|BT|=40,|CT|=$ 35. The feet of the perpendiculars from point $T$ to the sides of triangle $ABC$ are the vertices of an equilateral triangle. Determine the angle $\\varangle ABC$.",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A3. We call a positive integer alternating if the digits of the number alternate between even and odd. Thus, 2381 and 3218 are alternating, but 2318 is not. We call a number completely alternating if the number itself is alternating and double the number is also alternating. Thus, 505 is completel... | {
"ground_truth": "70",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Joel selected two different acute angles $x$ and $y$ (both strictly between 0 and 90 degrees) and wrote the values of $\\sin x$, $\\cos x$, $\\tan x$, and $\\sec y$ on four different cards. Then he gave those cards to four students, Malvina, Paulina, Georgina, and Bella, one card to each. They sha... | {
"ground_truth": "2",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. (10 points) A four-digit number \"HaoShiChengShuang\" divided by a two-digit number \"ChengShuang\" has a remainder exactly equal to \"HaoShi\". If different Chinese characters represent different digits and \"HaoShi\" and \"ChengShuang\" are not coprime, then the largest four-digit number \"Ha... | {
"ground_truth": "7281",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose the graphs of $y=h(x)$ and $y=j(x)$ intersect at $(3,3)$, $(6,9)$, and $(9,18)$. Find one point where the graphs of $y=h(3x)$ and $y=3j(x)$ must intersect. What is the sum of the coordinates of that point?",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Let $a=\\lg z+\\lg \\left[x(y z)^{-1}+1\\right], b=\\lg x^{-1}+\\lg (x y z+1), c=\\lg y+\\lg \\left[(x y z)^{-1}+1\\right]$, and let the maximum of $a, b, c$ be $M$, then the minimum value of $M$ is $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "\\lg2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. On each of the lines $x=0$ and $x=2$, there are 62 points with ordinates $1, 2, 3, \\ldots, 62$. In how many ways can three points be chosen from the marked 124 points so that they form the vertices of a right triangle?",
"role": "user"
}
] | {
"ground_truth": "7908",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the hyperbola $E: \\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ and the circle $(x-4)^2 + y^2 = 16$, find the eccentricity of the hyperbola if a chord cut by the circle has a length of 4. Express your answer as a single number.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The average age of the four Smith children is 9 years. If the three younger children are 6 years old, 9 years old, and 12 years old, how many years old is the oldest child?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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