prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "A rook has traversed the chessboard, visiting each square at least once. What is the minimum number of turns it could have made\n\n#",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "24.3.5 $\\star$ * 64 points arranged in an 8 by 8 grid, how many lines are needed at minimum to separate them?",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jamie is an avid reader and a big fan of the author Mark Edwards. Last month, Jamie read 3 of Mark Edwards' books. The first book had 320 pages, the second book had 450 pages, and the third book had 280 pages. If Jamie reads an average of 40 pages per day, how many days did it take Jamie to read a... | {
"ground_truth": "27",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Triangle $ABC$ lies entirely in the first quadrant of the Cartesian plane, and its sides have slopes $63$ , $73$ , $97$ . Suppose the curve $\\mathcal V$ with equation $y=(x+3)(x^2+3)$ passes through the vertices of $ABC$ . Find the sum of the slopes of the three tangents to $\\mathcal ... | {
"ground_truth": "237",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the diagram, the circle is inscribed in the square. This means that the circle and the square share points \\(S, T, U,\\) and \\(V\\), and the width of the square is exactly equal to the diameter of the circle. Rounded to the nearest tenth, what percentage of line segment \\(XY\\) is outside th... | {
"ground_truth": "29.3",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "33 Find the largest positive integer that cannot be expressed as the sum of a positive multiple of 42 and a composite number.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "215",
"mean_reward": 0
} | 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\nIf $n$ and $k$ are positive integers such that $5<\\frac nk<6$, then what is the smallest possible value of $\\frac{\\mathop{\\text{lcm}}[n,k]}{\\gcd(n,k)}$?\n\n[Solu... | {
"ground_truth": "-1",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "38. As shown in the figure, it is known that $D M$ bisects $\\angle A D C$, $B M$ bisects $\\angle A B C$, and $\\angle A=27^{\\circ}, \\angle M=33^{\\circ}$, then the degree measure of $\\angle C$ is ${ }^{\\circ}$. $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "39",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Let $[x]$ denote the greatest integer not exceeding the real number $x$. If\n$$\n\\begin{array}{l}\na=\\frac{\\sqrt{6+\\sqrt{6+\\cdots+\\sqrt{6}}},}{2016 \\text { nested radicals }}, \\\\\nb=\\frac{\\sqrt[3]{6+\\sqrt[3]{6+\\cdots+\\sqrt[3]{6}}},}{2 \\text { 2017 nested radicals }},\n\\end{array... | {
"ground_truth": "4",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.3. Perpendiculars $B E$ and $D F$, dropped from vertices $B$ and $D$ of parallelogram $A B C D$ to sides $A D$ and $B C$ respectively, divide the parallelogram into three parts of equal area. On the extension of diagonal $B D$ beyond vertex $D$, segment $D G$ is laid off, equal to segment $B D$.... | {
"ground_truth": "1:1",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A podcast host records an episode with Dave Franco, which lasts for 90 minutes. During the first 30 minutes, they discuss Dave's early career, followed by a 15-minute segment about his creative process. The remaining time is dedicated to discussing his recent projects. If the host wants to include... | {
"ground_truth": "5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Factorize the expression $27x^6 - 512y^6$ and find the sum of all integer coefficients in its factorized form.",
"role": "user"
}
] | {
"ground_truth": "92",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How can you cut a 5 × 5 square with straight lines so that the resulting pieces can be assembled into 50 equal squares? It is not allowed to leave unused pieces or to overlap them.",
"role": "user"
}
] | {
"ground_truth": "50",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3.200 to 220 has a unique prime number, it is $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "211",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 2 pizzerias in a town, with 2010 pizzas each. Two scientists $A$ and $B$ are taking turns ( $A$ is first), where on each turn one can eat as many pizzas as he likes from one of the pizzerias or exactly one pizza from each of the two. The one that has eaten the last pizza is the winn... | {
"ground_truth": " B ",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ellen wants to color some of the cells of a $4 \\times 4$ grid. She wants to do this so that each colored cell shares at least one side with an uncolored cell and each uncolored cell shares at least one side with a colored cell. What is the largest number of cells she can color?",
"role": "use... | {
"ground_truth": "12",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ati has $ 7$ pots of flower, ordered in $ P_1,P_2,P_3,P_4,P_5,P_6,P_7$. She wants to rearrange the position of those pots to $ B_1,B_2,B_2,B_3,B_4,B_5,B_6,B_7$ such that for every positive integer $ n<7$, $ B_1,B_2,\\dots,B_n$ is not the permutation of $ P_1,P_2,\\dots,P_7$. In how many ways can A... | {
"ground_truth": "3447",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Petya wrote a natural number \\( A \\) on the board. If you multiply it by 8, you get the square of a natural number. How many such three-digit numbers \\( B \\) exist for which \\( A \\cdot B \\) is also a square of a natural number?",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Point $A$ lies on the circumference of a circle $\\Omega$ with radius $78$ . Point $B$ is placed such that $AB$ is tangent to the circle and $AB=65$ , while point $C$ is located on $\\Omega$ such that $BC=25$ . Compute the length of $\\overline{AC}$ .",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mark has $\\frac{5}{6}$ of a dollar, Carolyn has $\\frac{3}{10}$ of a dollar, and Jim has $\\frac{1}{2}$ of a dollar. How many dollars do they have altogether? (Give your answer as a decimal.)",
"role": "user"
}
] | {
"ground_truth": "\\$1.63",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Ostrovsky $M$.\n\nA number from 1 to 144 is guessed. You are allowed to select one subset of the set of numbers from 1 to 144 and ask whether the guessed number belongs to it. You have to pay 2 rubles for a \"yes\" answer and 1 ruble for a \"no\" answer. What is the minimum amount of money needed ... | {
"ground_truth": "11",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $y(x)$ be the unique solution of the differential equation\n$$\n\\frac{\\mathrm{d} y}{\\mathrm{~d} x}=\\log _{e} \\frac{y}{x}, \\quad \\text { where } x>0 \\text { and } y>0,\n$$\nwith the initial condition $y(1)=2018$.\nHow many positive real numbers $x$ satisfy the equation $y(x)=2000$ ?",
... | {
"ground_truth": "1",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For which natural numbers $n$ is the value of the following expression a perfect square?\n\n$$\nn^{5}-n^{4}-2 n^{3}+2 n^{2}+n-1\n$$",
"role": "user"
}
] | {
"ground_truth": "k^{2}+1",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( M \\) be the point of intersection of the diagonals of a convex quadrilateral \\( A B C D \\), in which the sides \\( A B \\), \\( A D \\), and \\( B C \\) are equal to each other.\n\nFind the angle \\( \\angle C M D \\), given that \\( D M = M C \\) and \\( \\angle C A B \\neq \\angle D B... | {
"ground_truth": "120^\\circ",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Illustrate a semicircle with diameter $A G$. The arc of the semicircle is divided into six equal parts by points $B$, $C$, $D$, $E$, and $F$. $D F$ and $C G$ are both straight line segments. Given that the area of the semicircle is $60 \\mathrm{~cm}^{2}$, what is the area of the shaded part in $\\... | {
"ground_truth": "20",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. $V, W, X, Y, Z$ are 5 digits in base 5. The three three-digit numbers $(V Y Z)_{5},(V Y X)_{5},(V V W)_{5}$ in base 5 increase sequentially with a common difference of 1. What is the three-digit number $(X Y Z)_{5}$ in base 10?",
"role": "user"
}
] | {
"ground_truth": "108",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "444. Eight hockey teams play against each other in a round-robin tournament to determine the final four. What is the minimum number of points that guarantees a team's advancement to the final four?",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "16. At the quiz in the Museum of Entertaining Sciences of SFU, 10 schoolchildren are participating. In each round, the students are divided into pairs. Each participant meets every other participant exactly once. A win in a match earns 1 point, a draw earns 0.5 points, and a loss earns 0 points. W... | {
"ground_truth": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task B-4.5.\n\nIn triangle $A B C$, $\\varangle C A B=50^{\\circ}$ and $\\varangle A B C=60^{\\circ}$. On side $\\overline{A B}$ there is a point $D$, and on side $\\overline{B C}$ there is a point $E$ such that $\\varangle C A E=\\varangle A C D=30^{\\circ}$. Calculate the measure of angle $\\... | {
"ground_truth": "40",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The owner of a freight shipping company has three cargo ships that specialize in the bulk transportation of raw materials. Each ship can carry a maximum of 1,200 tons of material. One day, the owner receives an order to transport 2,500 tons of iron ore and 1,500 tons of coal to a nearby port. \n\n... | {
"ground_truth": "4",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "33. A project is completed in whole days when worked on in the order of Jia, Yi, Bing each working for one day. If the work is done in the order of Bing, Jia, Yi each working for one day, it will take 0.5 days longer than the original plan; if the work is done in the order of Yi, Bing, Jia each wo... | {
"ground_truth": "7.5",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 2. Along the path between the houses of Nезнайка (Nезнayka) and Синеглазка (Sineglazka), there were 15 peonies and 15 tulips growing in a row, mixed together.\n\nSetting out from home to visit Nезнайка, Синеглазка watered all the flowers in a row. After the 10th tulip, the water ran out, a... | {
"ground_truth": "19",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "From all the numbers with a digit sum of 25, find the one whose product of digits is maximum. If there are several such numbers, provide the smallest one among them.",
"role": "user"
}
] | {
"ground_truth": "33333334",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Let $\\alpha, \\beta$ be acute angles. When\n$$\n-\\frac{1}{\\cos ^{2} \\alpha}+\\frac{1}{\\sin ^{2} \\alpha \\sin ^{2} \\beta \\cos ^{2} \\beta}\n$$\n\ntakes the minimum value, the value of $\\operatorname{tg}^{2} \\alpha+\\operatorname{tg}^{2} \\beta$ is",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The incircle $\\Gamma$ of a scalene triangle $ABC$ touches $BC$ at $D, CA$ at $E$ and $AB$ at $F$. Let $r_A$ be the radius of the circle inside $ABC$ which is tangent to $\\Gamma$ and the sides $AB$ and $AC$. Define $r_B$ and $r_C$ similarly. If $r_A = 16, r_B = 25$ and $r_C = 36$, determine the r... | {
"ground_truth": "74",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Task 4.\n\nYevgeny Petrovich decided to take a loan from a banking institution in the amount of 3,000,000 rubles to purchase a one-bedroom apartment in Andronovka. The loan terms are as follows: he returns the initial loan amount and 150,000 rubles in interest over 8 months. Determine the annual i... | {
"ground_truth": "7.5",
"mean_reward": 0.015625
} | 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\nA target consists of four concentric circles with radii 4 inches, 6 inches, 8 inches and 10 inches as shown. Given that a dart is thrown that hits the target at a ran... | {
"ground_truth": "-1",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A test consists of 6 multiple-choice questions. The grading rule is as follows: each person initially scores 6 points, each correct answer adds 4 points, each incorrect answer deducts 1 point, and no answer gets 0 points. If 51 students take the test, what is the minimum number of students that mu... | {
"ground_truth": "3",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $S$ be the sum of all integers $b$ for which the polynomial $x^2+bx+2008b$ can be factored over the integers. Compute $|S|$.\n",
"role": "user"
}
] | {
"ground_truth": "88352",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 7.2. (15 points) Given an isosceles triangle $A B C(A B=B C)$. On the sides $A B, B C, A C$ points $K, L, M$ are marked respectively such that $\\angle A K M=90^{\\circ}, \\angle B L K=90^{\\circ}$ and $K M=K L$. What is the measure of angle $C M L ?$",
"role": "user"
}
] | {
"ground_truth": "90",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are $2022$ distinct integer points on the plane. Let $I$ be the number of pairs among these points with exactly $1$ unit apart. Find the maximum possible value of $I$ . \n(*Note. An integer point is a point with integer coordinates.*)\n\n*Proposed by CSJL.*",
"role": "user"
}
] | {
"ground_truth": "3954",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a warehouse, the inventory is stored in packages weighing no more than 1 ton each. We have a 1-ton and a 4-ton truck. What is the maximum load that we can definitely deliver in one trip?",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14.5. 14 ** A storybook contains 30 stories, with lengths of $1, 2, \\cdots, 30$ pages respectively. Starting from the first page of the book, stories are published, and each subsequent story begins on a new page. Question: What is the maximum number of stories that can start on an odd-numbered pa... | {
"ground_truth": "23",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Misha has accepted a job in the mines and will produce one ore each day. At the market, he is able to buy or sell one ore for \\ $3, buy or sell bundles of three wheat for \\$ 12 each, or $\\textit{sell}$ one wheat for one ore. His ultimate goal is to build a city, which requires three ore and t... | {
"ground_truth": "9",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. In the equation $\\overline{A B C} \\times \\overline{A B C}=\\overline{D E F E D}$, the same letter represents the same digit, and different letters represent different digits, then the six-digit number $\\overline{A B C D E F}=$ $\\qquad$.\n\n",
"role": "user"
}
] | {
"ground_truth": "307942",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 Add three digits after 764 to make the resulting six-digit number divisible by 8, 9, and 11.",
"role": "user"
}
] | {
"ground_truth": "764280",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For how many positive integral values of \\( a \\) is it true that \\( x = 3 \\) is the only positive integer solution of the system of inequalities:\n$$\n\\begin{cases}\n2x + 1 > 3x - 2 \\\\\n4x - a > -11\n\\end{cases}\n$$",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The residents of the village of Razumeyevo, which is 3 km away from the river, like to visit the village of Vkusnoteevo, located 3.25 km downstream on the opposite bank of the river and 1 km away from the riverbank. The river width is 500 meters, and the current speed is 1 km/hour, with the banks ... | {
"ground_truth": "1.5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are \\(n\\) lilypads in a row labeled \\(1,2,\\dots,n\\). Fareniss the Frog picks a lilypad at random to start on and jumps every second to an adjacent lilypad; if there are two choices, she is twice as likely to jump to the right. After some time, there exist two lilypads \\(A\\) and \\(B\\... | {
"ground_truth": "12",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At an exchange point, there are two types of transactions:\n1) Give 2 euros - receive 3 dollars and a candy as a gift.\n2) Give 5 dollars - receive 3 euros and a candy as a gift.\n\nWhen the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he di... | {
"ground_truth": "10",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. (20 points) Given triangle $K L M$. A circle is drawn passing through point $M$, touching segment $L K$ at point $A$, which is its midpoint, and intersecting sides $M L$ and $M K$ at points $C$ and $B$, respectively, such that $C B=4$, point $C$ is equidistant from points $A$ and $L$, and $\\co... | {
"ground_truth": "\\sqrt{6}",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Jamie, a knowledgeable local and vegan enthusiast, loves taking visitors on a tour of the best vegan-friendly spots in their city. On a sunny Saturday, Jamie decides to take a group of 5 friends on a vegan food tour. They start the day at a vegan bakery, where each person buys 2 vegan pastries cos... | {
"ground_truth": "102",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alan, Beth, and Chris went on a camping trip and decided to share the expenses equally. Alan paid $110, Beth paid $140, and Chris paid $190. To equalize the cost, Alan gave Chris $a$ dollars and Beth gave Chris $b$ dollars after realizing they had forgotten to split the cost of a $60 picnic they a... | {
"ground_truth": "30",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two congruent squares, $ABCD$ and $PQRS$, have side length $15$. They overlap to form the $15$ by $25$ rectangle $AQRD$ shown. What percent of the area of rectangle $AQRD$ is shaded? [asy] filldraw((0,0)--(25,0)--(25,15)--(0,15)--cycle,white,black); label(\"D\",(0,0),S); label(\"R\",(25,0),S); lab... | {
"ground_truth": "20",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Divide the set \\( M = \\{1, 2, \\ldots, 12\\} \\) of the first 12 positive integers into four subsets each containing three elements, such that in each subset, one number is the sum of the other two. Find the number of different ways to do this.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "G6.3 Let $R$ be a point on the curve such that $O M R N$ is a square. If $r$ is the $x$-coordinate of $R$, find the value of $r$",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The graph of the function $y=g(x)$ is shown below. For all $x > 5$, it is true that $g(x) > 0.5$. If $g(x) = \\frac{x^2}{Dx^2 + Ex + F}$, where $D, E,$ and $F$ are integers, then find $D+E+F$. Assume the function has vertical asymptotes at $x = -3$ and $x = 4$ and a horizontal asymptote below 1 bu... | {
"ground_truth": "-24",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Triangle $ABC$ is isosceles with $AC = BC$ and $\\angle ACB = 106^\\circ.$ Point $M$ is in the interior of the triangle so that $\\angle MAC = 7^\\circ$ and $\\angle MCA = 23^\\circ.$ Find the number of degrees in $\\angle CMB.$",
"role": "user"
}
] | {
"ground_truth": "83",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$$\na=19911991 \\cdots \\cdots 1991\n$$\n3. Given: , Question: What is the remainder when $a$ is divided by 13?",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "19. Sesame Street has 100 households, and their house numbers are not consecutive, but are arranged according to the following pattern:\n$$\n1,2,4,5,7,9,10,12,14,16,17,19,21,23,25, \\cdots \\cdots\n$$\n\nAmong these 100 house numbers, there are $\\qquad$ odd numbers.",
"role": "user"
}
] | {
"ground_truth": "49",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Matchsticks can be used to form the digits 0 and 9, as shown in the figure below:\nUsing 9 matchsticks, the smallest two-digit number that can be formed is $\\qquad$.",
"role": "user"
}
] | {
"ground_truth": "18",
"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": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Water stands 12.0 m deep in a storage tank whose top is open to the atmosphere. What are the gauge pressures at the bottom of the tank? (Unit: 10 ^ 5 Pa)",
"role": "user"
}
] | {
"ground_truth": "1.18",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mrs. Thompson recorded the following scores from a recent test taken by all of her students. Calculate the average percent score for these $100$ students.\n\n\\begin{tabular}{|c|c|}\n\\multicolumn{2}{c}{}\\\\\\hline\n\\textbf{$\\%$ Score}&\\textbf{Number of Students}\\\\\\hline\n95&10\\\\\\hline\n... | {
"ground_truth": "68",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the $xy$ -coordinate plane, the $x$ -axis and the line $y=x$ are mirrors. If you shoot a laser beam from the point $(126, 21)$ toward a point on the positive $x$ -axis, there are $3$ places you can aim at where the beam will bounce off the mirrors and eventually return to $(126, 21)$... | {
"ground_truth": "111",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the production of a certain item, its weight \\( X \\) is subject to random fluctuations. The standard weight of the item is 30 g, its standard deviation is 0.7, and the random variable \\( X \\) follows a normal distribution. Find the probability that the weight of a randomly selected item is ... | {
"ground_truth": "0.9215",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8.1. Two mountain goats, Gennady and Nikolai, arranged a competition. Gennady makes two jumps of 6 meters each in the same time it takes Nikolai to make 3 jumps of 4 meters each. The goats agreed to jump along a straight line, not to turn around until they have traveled at least 2 kilometers, and ... | {
"ground_truth": "Nikolai",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For every integers $ a,b,c$ whose greatest common divisor is $n$ , if\n\\[ \\begin{array}{l} {x \\plus{} 2y \\plus{} 3z \\equal{} a} \n{2x \\plus{} y \\minus{} 2z \\equal{} b} \n{3x \\plus{} y \\plus{} 5z \\equal{} c} \\end{array}\n\\]\nhas a solution in integers, what is the smallest possible ... | {
"ground_truth": "28",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a sequence of $n$ positive integers $x_{1}, x_{2}, \\cdots, x_{n}$ whose sum is 2009, and which can be partitioned into 41 groups with equal sums as well as 49 groups with equal sums, find the smallest value of $n$.",
"role": "user"
}
] | {
"ground_truth": "89",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$2021$ points are given on a circle. Each point is colored by one of the $1,2, \\cdots ,k$ colors. For all points and colors $1\\leq r \\leq k$ , there exist an arc such that at least half of the points on it are colored with $r$ . Find the maximum possible value of $k$ .",
"role": "user... | {
"ground_truth": "k = 2",
"mean_reward": 0.09375
} | 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": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Among the 8 vertices, the midpoints of the 12 edges, the centers of the 6 faces, and the center of a cube (totaling 27 points), how many groups of three collinear points are there?",
"role": "user"
}
] | {
"ground_truth": "49",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Express $52403_7 - 20345_5$ in base 10.",
"role": "user"
}
] | {
"ground_truth": "11540",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\( A = \\{1, 2, \\ldots, 2002\\} \\) and \\( M = \\{1001, 2003, 3005\\} \\). For any non-empty subset \\( B \\) of \\( A \\), \\( B \\) is called an \\( M \\)-free set if the sum of any two elements in \\( B \\) does not belong to \\( M \\). If \\( A = A_1 \\cup A_2 \\), \\( A_1 \\cap A_2 = \... | {
"ground_truth": "2^{501}",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $ABC$ be a triangle inscribed in circle $\\Gamma$, centered at $O$ with radius $333.$ Let $M$ be the midpoint of $AB$, $N$ be the midpoint of $AC$, and $D$ be the point where line $AO$ intersects $BC$. Given that lines $MN$ and $BO$ concur on $\\Gamma$ and that $BC = 665$, find the length of s... | {
"ground_truth": "444",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the difference between the sum of the first 1000 even counting numbers including 0, and the sum of the first 1000 odd counting numbers?",
"role": "user"
}
] | {
"ground_truth": "-1000",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "19. The documentary \"Chinese History\" has a total of 100 episodes. Xiao Ming only watched 47 consecutive episodes; his father only watched 65 consecutive episodes; his grandmother missed only 18 episodes, and there were no more than 3 consecutive episodes among them. How many episodes have Xiao ... | {
"ground_truth": "3",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given \\( a, b > 0 \\), determine the solutions \\( f: \\mathbb{R}^{+} \\rightarrow \\mathbb{R}^{+} \\) such that \\( f(f(x)) + a f(x) = b(a + b) x \\).",
"role": "user"
}
] | {
"ground_truth": "f(x) = bx",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mr. Carter is a construction company owner who believes that installing solar panels is too costly and impractical. He is currently working on a project to build 10 houses. If he decides to incorporate solar panels into each house, the cost of solar panels per house is $12,000. Additionally, the i... | {
"ground_truth": "70000",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The sides of rectangle $ABCD$ have lengths $10$ and $11$. An equilateral triangle is drawn so that no point of the triangle lies outside $ABCD$. The maximum possible area of such a triangle can be written in the form $p\\sqrt{q}-r$, where $p$, $q$, and $r$ are positive integers, and $q$ is not div... | {
"ground_truth": "554",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the smallest number of points that can be chosen on a circle of length 1956 so that for each of these points there is exactly one chosen point at a distance of 1 and exactly one at a distance of 2 (distances are measured along the circumference)?\n\n#",
"role": "user"
}
] | {
"ground_truth": "1304",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. The numbers $1,2,3, \\ldots, 999,1000$ are written one after another in this order on a circle. We cross out the number 1, and then every 15th number $(1,16,31, \\ldots)$. When we complete one full circle, we count again, including the crossed-out numbers. How many numbers will remain uncrossed... | {
"ground_truth": "800",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## 2. Megacube\n\nFrom identical small cubes, one large cube is assembled. The length of the edge of the large cube is a hundred times larger than the length of the edge of each small cube. The large cube is placed on a table, and all its sides, except the one that touches the table, are painted r... | {
"ground_truth": "788",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 18 Find $(1111)_{2} \\div(101)_{2}=$ ?",
"role": "user"
}
] | {
"ground_truth": "(11)_{2}",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When a plane intersects a cube, what type of polygon cannot be formed as a result of the intersection? Express your answer as the name of the polygon.",
"role": "user"
}
] | {
"ground_truth": "Heptagon",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A town experiences four consecutive yearly changes in its population census: a 25% increase, a 25% increase, a 25% decrease, and a 25% decrease. Calculate the net percentage change over these four years. Express your answer as a percentage, rounded to the nearest percent.",
"role": "user"
}
... | {
"ground_truth": "-12",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Bill buys a stock for $100. On the first day, the stock decreases by $25\\%$, on the second day it increases by $35\\%$ from its value at the end of the first day, and on the third day, it decreases again by $15\\%$. What is the overall percentage change in the stock's value over the three days?",... | {
"ground_truth": "-13.9375\\%",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$6 \\cdot 18$ Let $N$ be the set of positive integers, and define the function $f$ on $N$ as follows:\n(i) $f(1)=1, f(3)=3$;\n(ii) For $n \\in N$, we have\n$$\n\\begin{array}{l}\nf(2 n)=f(n), \\\\\nf(4 n+1)=2 f(2 n+1)-f(n), \\\\\nf(4 n+3)=3 f(2 n+1)-2 f(n) .\n\\end{array}\n$$\n\nFind all $n$ such ... | {
"ground_truth": "92",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many square units are in the area of the pentagon shown here with sides of length 15, 20, 27, 24 and 20 units?\n\n[asy]\npair a,b,c,d,e;\na=(0,0);\nb=(24,0);\nc=(24,27);\nd=(5.3,34);\ne=(0,20);\ndraw((0,0)--(24,0)--(24,27)--(5.3,34)--(0,20)--cycle);\ndraw((4.8,32.7)--(6.1,32.2)--(6.6,33.5));... | {
"ground_truth": "714",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Solve the following equation for $x, y, z \\in \\mathbb{N}$\n\n$$\n\\left(1+\\frac{x}{y+z}\\right)^{2}+\\left(1+\\frac{y}{z+x}\\right)^{2}+\\left(1+\\frac{z}{x+y}\\right)^{2}=\\frac{27}{4}\n$$",
"role": "user"
}
] | {
"ground_truth": "x=y=z",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7th Australian 1986 Problem A2 What is the smallest tower of 100s that exceeds a tower of 100 threes? In other words, let a 1 = 3, a 2 = 3 3 , and a n+1 = 3 a n . Similarly, b 1 = 100, b 2 = 100 100 etc. What is the smallest n for which b n > a 100 ?",
"role": "user"
}
] | {
"ground_truth": "99",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Points \\( M, N, \\) and \\( K \\) are located on the lateral edges \\( A A_{1}, B B_{1}, \\) and \\( C C_{1} \\) of the triangular prism \\( A B C A_{1} B_{1} C_{1} \\) such that \\( A M : A A_{1} = 1 : 2, B N : B B_{1} = 1 : 3, \\) and \\( C K : C C_{1} = 1 : 4 \\). Point \\( P \\) belongs to th... | {
"ground_truth": "4",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The complete graph of \\( y=g(x) \\), which consists of five line segments, is shown in red below. (On this graph, the distance between grid lines is \\( 1 \\)).\n\nWhat is the sum of the \\( x \\)-coordinates of all points where \\( g(x) = x+2 \\)?",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If Person B trades all their chairs for the same number of tables as Person A, Person B needs to pay an additional 320 yuan. If Person B does not pay the extra money, they would receive 5 fewer tables. It is known that the price of 3 tables is 48 yuan less than the price of 5 chairs. How many chai... | {
"ground_truth": "20",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2. Approximate the larger negative root of the equation $x^{3}-12 x-8=0$ using the tangent method with an accuracy of five decimal places after the decimal point.",
"role": "user"
}
] | {
"ground_truth": "-0.694593",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In this diagram, the first polygon is a regular pentagon, and the second is a regular triangle. What is the value, in degrees, of the sum of the measures of angles $ABC$ and $ABD$?\n\n[asy]\ndraw(10dir(18)--10dir(90)--10dir(162)--10dir(234)--10dir(306)--cycle,linewidth(2)); // Pentagon\ndraw(10di... | {
"ground_truth": "168^\\circ",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "\nIn three-dimensional space, let \\( S \\) be the region of points \\( (x, y, z) \\) satisfying \\( -1 \\leq z \\leq 1 \\). Let \\( S_{1}, S_{2}, \\ldots, S_{2022} \\) be 2022 independent random rotations of \\( S \\) about the origin \\( (0,0,0) \\). The expected volume of the region \\( S_{1} \... | {
"ground_truth": "271619",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a risk management specialist who helps poker players optimize their winnings and minimize their losses. One of his clients, Jamie, played three rounds of poker. In the first round, Jamie won $120. In the second round, Jamie lost $45. In the third round, Jamie won double the amount he lost ... | {
"ground_truth": "52.5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "IMO 1974 Problem A1 Three players play the following game. There are three cards each with a different positive integer. In each round the cards are randomly dealt to the players and each receives the number of counters on his card. After two or more rounds, one player has received 20, another 10 ... | {
"ground_truth": "9",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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