prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present... | {
"ground_truth": "\\text{Dan}",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "John ran a total of $1732_7$ miles. Convert this distance from base seven to base ten.",
"role": "user"
}
] | {
"ground_truth": "709",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that the integers $0 \\leq a < 2^{2008}$ and $0 \\leq b < 8$ satisfy the equivalence $7(a+2^{2008}b) \\equiv 1 \\pmod{2^{2011}}$, determine the value of b.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "$10 \\cdot 17$ A bus ticket number is a six-digit number. If the sum of the first three digits equals the sum of the last three digits, the ticket is called a \"lucky ticket.\" How many consecutive ticket numbers must be bought from the ticket office to ensure that at least one of them is a \"luck... | {
"ground_truth": "1001",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In $\\bigtriangleup ABC$, $E$ is a point on side $\\overline{AB}$, and $D$ is a point on side $\\overline{BC}$ such that $BD=DE=EC$. Let $\\angle BDE$ be $90^{\\circ}$. Determine the degree measure of $\\angle AED$.",
"role": "user"
}
] | {
"ground_truth": "45^\\circ",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "18. There are 2012 students standing in a row, numbered from left to right as $1, 2, \\cdots \\cdots 2012$. In the first round, they report numbers from left to right as “1, 2”, and those who report 2 stay; from the second round onwards, each time the remaining students report numbers from left to... | {
"ground_truth": "1458",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. (10 points) In the equation below, $A, B, C, D, E, F, G, H, I$ each represent different digits from $1 \\sim 9$.\n$$\n\\overline{\\mathrm{ABCD}}+\\overline{\\mathrm{EF}} \\times \\overline{\\mathrm{GH}}-I=X\n$$\n\nThen the minimum value of $X$ is . $\\qquad$",
"role": "user"
}
] | {
"ground_truth": "2369",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "[Example 4.4.4] There is a tetrahedron $A-BCD$, where the sum of the dihedral angles at each vertex is $180^{\\circ}$, and it has three unequal edge lengths of $\\sqrt{34}$, $\\sqrt{58}$, and $\\sqrt{74}$. Find the volume of this tetrahedron.",
"role": "user"
}
] | {
"ground_truth": "35",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a$ be a positive real number, $n$ a positive integer, and define the *power tower* $a\\uparrow n$ recursively with $a\\uparrow 1=a$ , and $a\\uparrow(i+1)=a^{a\\uparrow i}$ for $i=1,2,3,\\ldots$ . For example, we have $4\\uparrow 3=4^{(4^4)}=4^{256}$ , a number which has $155$ d... | {
"ground_truth": " x_{42} ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## Task B-1.4.\n\nIn each cell of a $4 \\times 4$ table, a number is written. For each cell, the sum of the numbers in its adjacent cells is equal to the same natural number $x$ (two cells are adjacent if they share a side). Determine the number $x$ such that the sum of all numbers in the table is... | {
"ground_truth": "47",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Martin decided to spend all his savings on sweets. He found out that he could buy three lollipops and $3 \\mathrm{dl}$ of cola or $18 \\mathrm{dkg}$ of yogurt-covered raisins or $12 \\mathrm{dkg}$ of yogurt-covered raisins and half a liter of cola. In the end, he bought one lollipop and 6 dl of co... | {
"ground_truth": "60",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Vasya needs to write one digit on each face of several cubes in such a way that any ordered combination of three digits from 000 to 999 inclusive can be obtained by selecting some three different cubes and placing them with suitable faces up in the correct order. Note that the digits 6 and 9 are n... | {
"ground_truth": "5",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct trees with exactly 7 vertices are there? A tree in graph theory refers to a connected graph without cycles, which can be simply understood as connecting n vertices with n-1 edges. Provide your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "11",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 6.8. There are exactly 120 ways to color five cells in a $5 \\times 5$ table so that each column and each row contains exactly one colored cell.\n\nThere are exactly 96 ways to color five cells in a $5 \\times 5$ table without a corner cell so that each column and each row contains exactly... | {
"ground_truth": "78",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Numbers \\(1, 2, \\ldots, 2010\\) are placed on the circumference of a circle in some order. The numbers \\(i\\) and \\(j\\), where \\(i \\neq j\\) and \\(i, j \\in \\{1, 2, \\ldots, 2010\\}\\), form a friendly pair if:\n(i) \\(i\\) and \\(j\\) are not neighbors to each other, and\n(ii) on one or ... | {
"ground_truth": "2007",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "## PROBLEM 44. COWS AND SHEEP\n\nTwo men jointly owned $x$ cows, which they sold for $x$ dollars a head. With the money they received, they bought sheep at 12 dollars a head. Since the proceeds from the sale of the cows did not divide by 12, they used the remaining money to buy a lamb. Then they d... | {
"ground_truth": "4",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For each integer $n\\geq 1$ , let $S_n$ be the set of integers $k > n$ such that $k$ divides $30n-1$ . How many elements of the set \\[\\mathcal{S} = \\bigcup_{i\\geq 1}S_i = S_1\\cup S_2\\cup S_3\\cup\\ldots\\] are less than $2016$ ?",
"role": "user"
}
] | {
"ground_truth": "536",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let \\(\\triangle ABC\\) have side lengths \\(AB=17\\), \\(AC=\\frac{70}{3}\\), and \\(BC=19\\). With \\(I\\) as the incenter and \\(E\\) as the excenter opposite \\(A\\), the circle with diameter \\(IE\\) meets \\(AB\\) (extended beyond \\(B\\)) at \\(D\\). If \\(BD\\) simplifies to \\(\\frac{a}{... | {
"ground_truth": "22",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "400. Calculate the force of water pressure on a dam that has the shape of a trapezoid, where the upper base, coinciding with the water surface, is $10 \\mathrm{~m}$ long, the lower base is $20 \\mathrm{~m}$, and the height is $3 \\mathrm{m}$.",
"role": "user"
}
] | {
"ground_truth": "735750",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Using only the paths and the directions shown, count the number of different routes from M to N. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. There are two hollows in the cedar. The baby squirrel sitting in front of the second hollow said:\n1) there are no nuts in the other hollow,\n2) there are nuts in at least one hollow.\n\nRed baby squirrels always tell the truth, while gray ones always lie. What color is this baby squirrel?",
... | {
"ground_truth": "Red",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $a_1,a_2,a_3,\\dots$ be an infinite sequence where each $a_i$ is chosen uniformly at random from $\\{1,2,\\dots,2016\\}$. Define $S$ as the set of indices $k$ for which $a_k$ is distinct from all previous $a_j$ (for $j<k$). If the expected number of indices $m$ such that both $m$ and $m+1$ bel... | {
"ground_truth": "4030",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nIn the row of Pascal's triangle that starts with 1 and then 10, what is the next number?\n\n[Solution]\n\n<paragraph_0>\nLet \\( n \\) be the row number of Pascal's t... | {
"ground_truth": "-1",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A rectangle with integer dimensions has an area that is numerically five times the number of units in its perimeter. What is the number of units in the perimeter of this rectangle if one of its sides is greater than 10 units?",
"role": "user"
}
] | {
"ground_truth": "90",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. Circle $k$ is inscribed in trapezoid $A B C D, A B \\| C D$, touching side $A B$ at point $E$. If $A E=15, B E=10$ and $C D=8$, determine the radius of circle $k$.\n\n",
"role": "user"
}
] | {
"ground_truth": "4\\sqrt{3}",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The U.S. produces about 8 million tons of apples each year. Initially, $30\\%$ of the apples are mixed with other products. If the production increases by 1 million tons, the percentage mixed with other products increases by $5\\%$ for each additional million tons. Of the remaining apples, $60\\%$... | {
"ground_truth": "2.24",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 5 people standing in a line numbered 1 through 5 in a left to right order.\nEach person has the following attributes: Food, Hobby, Music-Genre, Transport.\nThe attributes have the following possible values:\n- Food: cherry, pepper, plum, radish, spinach\n- Hobby: baking, chess, dancing,... | {
"ground_truth": "baking",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A circular disk is divided by 2n equally spaced radii (n > 0) and one chord. Calculate the maximum number of non-overlapping regions into which the disk can be divided. Express your answer as a formula in terms of n.",
"role": "user"
}
] | {
"ground_truth": "3n + 1",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given a rectangle $A B C D$. Through point $A$ we draw a line that intersects segment $C D$ at point $X$ such that the areas of the resulting figures satisfy $S_{A X D}: S_{A B C X}=1: 2$. Through point $X$ we draw a line that intersects segment $A B$ at point $Y$ such that $S_{A X Y}: S_{Y B C X}... | {
"ground_truth": "9:10",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A professional stunt performer named Alex is recovering from a complex fracture. As part of the rehabilitation process, Alex's physical therapist recommends a special exercise routine. The routine consists of 5 sets of exercises, where each set includes 8 repetitions. Each repetition takes 2 minut... | {
"ground_truth": "120",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the dream market, a Sphinx offered a traveler seven illusions, two naps, and one nightmare for four dreams. To another traveler, the same Sphinx offered four illusions, four naps, and two nightmares for seven dreams. The Sphinx measures equally for all travelers.\n\nHow many illusions did one d... | {
"ground_truth": "10",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13.1 A store has received large cans of milk. The salesperson has a scale lacking weights (milk bottles can be placed on the scale pans), and there are 3 identical milk bottles, two of which are empty, and the other contains 1 liter of milk. How can one bottle be filled with exactly 85 liters of m... | {
"ground_truth": "85",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the sum of the two smallest odd primes $p$ such that for some integers $a$ and $b$ , $p$ does not divide $b$ , $b$ is even, and $p^2=a^3+b^2$ .\n\n\n*2021 CCA Math Bonanza Individual Round #13*",
"role": "user"
}
] | {
"ground_truth": "122",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "16. In a Cartesian coordinate system, there are 10 different points $P_{1}\\left(x_{1}, y_{1}\\right), P_{2}\\left(x_{2}, y_{2}\\right), \\cdots, P_{10}\\left(x_{10}, y_{10}\\right)$. If $x_{i}=x_{j}$ or $y_{i}=y_{j}$, then $P_{i}$ and $P_{j}$ are called a \"coordinate pair\" (the order of $P_{i}$... | {
"ground_truth": "4",
"mean_reward": 0.15625
} | 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 $a@b=\\dfrac{a^3-b^3}{a-b}$, for how many real values of $a$ does $a@1=0$?\n\n[Solution]\n\n<paragraph_0>\nSince $a@1=\\dfrac{a^3-1}{a-1}$, we want to find all val... | {
"ground_truth": "-1",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A light ray falls at an angle $\\alpha=60^{\\circ}$ on the front surface of a plane-parallel glass plate. The refractive index of the glass is $n=1.6$. By what angle from the direction of the incident ray is the ray, reflected from the back surface of the plate and exiting back through the front s... | {
"ground_truth": "60^\\circ",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is the trusted second-in-command at a company that specializes in strategic planning and internal operations. She is planning a team-building event for the company's 48 employees. Alex decides to divide the employees into 6 equal groups for various team activities. Each group will rotate thro... | {
"ground_truth": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "When we unfold the side view of a cone, we are essentially spreading out the curved surface into a flat shape. What geometric shape is formed by this unfolded side view? Express your answer as the name of the shape.",
"role": "user"
}
] | {
"ground_truth": "sector",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The numbers $1978^{n}$ and $1978^{m}$ have the same last three digits. Find the positive integers $n$ and $m$ such that $m+n$ is minimized, given that $n > m \\geq 1$.",
"role": "user"
}
] | {
"ground_truth": "106",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. (20 points) Ten graduating classes have donated books to younger students, and the total number of books donated by any six of these classes is no less than 50% of the total number of donated books. What is the maximum percentage of the total number of books that the class which donated the mos... | {
"ground_truth": "25",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What percentage error do we make if we approximate the side of a regular heptagon by taking half of the chord corresponding to the $120^\\circ$ central angle?",
"role": "user"
}
] | {
"ground_truth": "0.2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $c_1,c_2,\\ldots,c_{6030}$ be 6030 real numbers. Suppose that for any 6030 real numbers $a_1,a_2,\\ldots,a_{6030}$, there exist 6030 real numbers $\\{b_1,b_2,\\ldots,b_{6030}\\}$ such that \\[a_n = \\sum_{k=1}^{n} b_{\\gcd(k,n)}\\] and \\[b_n = \\sum_{d\\mid n} c_d a_{n/d}\\] for $n=1,2,\\ldot... | {
"ground_truth": "528",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many distinct sets are there such that each set contains only non-negative powers of $2$ or $3$ and sum of its elements is $2014$ ?",
"role": "user"
}
] | {
"ground_truth": "64",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Regular hexagon $XYZABC$ and regular octagon $AZHIJKLM$ are drawn on opposite sides of line segment $AZ$ such that they are coplanar. What is the degree measure of the exterior angle $ZAH$? [asy]\ndraw((0,2.5)--(0,7.5)--(4,10)--(8,7.5)--(8,2.5)--(4,0)--cycle,linewidth(1));\ndraw((8,2.5)--(11.5,-1)... | {
"ground_truth": "105^\\circ",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For each positive integer $n$ , let $S(n)$ be the sum of the digits of $n$ . Determines the smallest positive integer $a$ such that there are infinite positive integers $n$ for which you have $S (n) -S (n + a) = 2018$ .",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "On sides \\( BC \\) and \\( AC \\) of triangle \\( ABC \\), points \\( D \\) and \\( E \\) are chosen respectively such that \\( \\angle BAD = 50^\\circ \\) and \\( \\angle ABE = 30^\\circ \\). Find \\( \\angle BED \\) if \\( \\angle ABC = \\angle ACB = 50^\\circ \\).",
"role": "user"
}
] | {
"ground_truth": "40",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. consider seven different straight lines in the plane. A point is called good if it lies on at least three of these lines. Determine the largest possible number of good points.\n\n## 1st solution",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. In the tournament, 15 volleyball teams are playing, and each team plays against all other teams only once. Since there are no draws in volleyball, there is a winner in each match. A team is considered to have performed well if it loses no more than two matches. Find the maximum possible number ... | {
"ground_truth": "5",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The vertices of a $4 - 5 - 6$ right triangle are the centers of three mutually externally tangent circles. What is the sum of the areas of these circles?",
"role": "user"
}
] | {
"ground_truth": "20.75\\pi",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Fill the circles with the numbers $0, 1, 2, 3, 4, 5, 6$ in the grid, with each number appearing exactly once, to form an integer equation consisting of single-digit and two-digit numbers. What number is filled in the grid?\n$$\nO \\times O=\\square=O \\div O\n$$",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Unlocking the communicator is done by entering a 4-digit numerical code on the touch screen. The arrangement of digits on the keyboard changes after entering the code depending on a random prime number $k$ from 7 to 2017, and the digit $i$ is displayed as $a_{i}$, which is the last digit of the... | {
"ground_truth": "3212",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Given that the sum of 2008 consecutive positive integers is a perfect square. Then the minimum value of the largest number is $\\qquad$\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "... | {
"ground_truth": "2133",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the largest positive integer $n$ that divides $p^{6}-1$ for all primes $p>7$.\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": "504",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $N$ be a positive integer. Suppose given any real $x\\in (0,1)$ with decimal representation $0.a_1a_2a_3a_4\\cdots$, one can color the digits $a_1,a_2,\\cdots$ with $N$ colors so that the following hold:\n 1. each color is used at least once;\n 2. for any color, if we delete all the digi... | {
"ground_truth": "10",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. If $x^{2}-13 x+1=0$, then the unit digit of $x^{4}+x^{-4}$ is\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": "7",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A convex quadrilateral \\(EFGH\\) has vertices \\(E, F, G, H\\) lying respectively on the sides \\(AB, BC, CD,\\) and \\(DA\\) of another quadrilateral \\(ABCD\\). It satisfies the equation \\(\\frac{AE}{EB} \\cdot \\frac{BF}{FC} \\cdot \\frac{CG}{GD} \\cdot \\frac{DH}{HA} = 1\\). Given that point... | {
"ground_truth": "\\lambda",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. How many polynomials $P$ with integer coefficients and degree at most 5 satisfy $0 \\leq P(x)<120$ for all $x \\in\\{0,1,2,3,4,5\\} ?$",
"role": "user"
}
] | {
"ground_truth": "86400000",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. $\\left[\\left(\\frac{1+\\sqrt{5}}{2}\\right)^{2009}\\right]$ when divided by 7 leaves a remainder of\n\nThe above text is translated into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | {
"ground_truth": "6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1.6.5 ** Find all functions \\( f: \\mathbf{N}^{*} \\rightarrow \\mathbf{N}^{*} \\), such that for any \\( x, y \\in \\mathbf{N}^{*} \\), we have\n$$\nf(x+f(y))=f(x)+y .\n$$",
"role": "user"
}
] | {
"ground_truth": "f(x)=x",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "17th Iberoamerican 2002 Problem A1 The numbers 1, 2, ... , 2002 are written in order on a blackboard. Then the 1st, 4th, 7th, ... , 3k+1th, ... numbers in the list are erased. Then the 1st, 4th, 7th, ... 3k+1th numbers in the remaining list are erased (leaving 3, 5, 8, 9, 12, ... ). This process i... | {
"ground_truth": "1598",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the sum of the first 1234 terms of the sequence where the number of 2s between consecutive 1s increases by 1 each time?",
"role": "user"
}
] | {
"ground_truth": "2419",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The cross section for a 2.0-MeV neutron (a typical energy for a neutron released in fission) being absorbed by a U-238 nucleus and producing fission is 0.68 barn. For a pure U-238 sample of thickness 3.2 cm, what is the probability of a 2.0-MeV neutron producing fission?",
"role": "user"
}
] | {
"ground_truth": "0.1",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given that point B is the vertex of three angles $\\angle \\text{ABC}$, $\\angle \\text{ABD}$, and $\\angle \\text{CBD}$, where $\\angle \\text{CBD}$ is a right angle and the total sum of angles around point B is $180^\\circ$, and $\\angle \\text{ABD} = 30^\\circ$, find the measure of $\\angle \\t... | {
"ground_truth": "60^\\circ",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The complete graph of $y=f(x)$, 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 $f(x) = x+1$?",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "ABCD is a square. BDEF is a rhombus with A, E, and F collinear. Find ∠ADE.",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A bot is held in orbit by the gravitational force of attraction to the planet, which creates a centripetal acceleration equal to $4 \\pi^{2}(2 R) / T^{2}$, where $R$ is the radius of the planet and $T$ is the period of revolution of the bot. From Newton's second law, we have:\n\n$$\nm \\frac{4 \\p... | {
"ground_truth": "6000",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 5. At the city market, $3 \\mathrm{~kg}$ of apples cost the same as $2 \\mathrm{~kg}$ of pears, and $2 \\mathrm{~kg}$ of pears cost the same as $1 \\mathrm{~kg}$ of cherries. Georgi bought $5 \\mathrm{~kg}$ of apples, Ivan bought $3 \\mathrm{~kg}$ of cherries, and Filip bought $3 \\mathrm{... | {
"ground_truth": "Ivan",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Compute the number of subsets $S$ of $\\{0,1,\\dots,14\\}$ with the property that for each $n=0,1,\\dots,\n6$ , either $n$ is in $S$ or both of $2n+1$ and $2n+2$ are in $S$ .\n\n*Proposed by Evan Chen*",
"role": "user"
}
] | {
"ground_truth": "2306",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "19. Pleasant Goat is sitting around a round table with 6 of his friends, discussing strategies to catch Big Bad Wolf. At this moment, Slow Goat and Lazy Goat, who are late, also want to join the discussion. There are $\\qquad$ different ways to arrange the seats for Slow Goat and Lazy Goat.",
... | {
"ground_truth": "56",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the rectangle $ABCD, M, N, P$ and $Q$ are the midpoints of the sides. If the area of the shaded triangle is $1$ , calculate the area of the rectangle $ABCD$ .\n![Image](https://2.bp.blogspot.com/-9iyKT7WP5fc/XNYuXirLXSI/AAAAAAAAKK4/10nQuSAYypoFBWGS0cZ5j4vn_hkYr8rcwCK4BGAYYCw/s400/may3.gif... | {
"ground_truth": "8",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 5 In a competition consisting of $n$ true/false questions, 8 contestants participate. It is known that for any pair of true/false questions $(A, B)$ (referred to as an ordered pair), exactly two people's answers are (true, true); exactly two people's answers are (true, false); exactly two ... | {
"ground_truth": "7",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The score on a certain 150-point test varies directly with the square of the time a student spends preparing for the test. If a student receives 90 points on a test for which she spent 2 hours preparing, what score would she receive on the next test if she spent 3 hours preparing?",
"role": "u... | {
"ground_truth": "202.5",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "2. The Dao sequence $\\left\\{\\begin{array}{l}x_{1}=x_{2}=1, \\\\ x_{n+2}=a x_{n+1}+b x_{n}(n \\in N) .\\end{array}\\right.$\n\nIf $T=1996$ is the smallest natural number such that $x_{T+1}=x_{T+2}=1$, then $\\sum_{i=1}^{1006} x_{i}=$ $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "0",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Given $a_{1}, a_{2}, \\cdots, a_{100}$ are 100 distinct positive integers. For any positive integer $i \\in\\{1,2, \\cdots, 100\\}, d_{i}$ represents the greatest common divisor of the 99 numbers $a_{j}(j \\neq i)$, and $b_{i}=a_{i}+$ $d_{i}$. Question: How many different positive integers are ... | {
"ground_truth": "99",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Under one of the squares of an $8 \\times 8$ board, there is a treasure buried. Under each of the remaining squares, there is a tag indicating the minimum number of steps it takes to reach the treasure from that square (one step consists of moving to an adjacent square along one of its sides). Wha... | {
"ground_truth": "3",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a regional athletics competition, $275$ sprinters participate in a $100-$meter dash. The track can accommodate $8$ runners at a time, and in each race, the top 2 runners qualify for the next round while the others are eliminated. Determine the number of races required to declare the overall win... | {
"ground_truth": "49",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A wooden cube has edges of length 3 meters. Square holes, of side one meter, centered in each face are cut through to the opposite face. The edges of the holes are parallel to the edges of the cube. Calculate the entire surface area of the cube, including the inside surfaces exposed by the holes. ... | {
"ground_truth": "72",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A department needs to arrange a duty schedule for the National Day holiday (a total of 8 days) for four people: A, B, C, and D. It is known that:\n\n- A and B each need to be on duty for 4 days.\n- A cannot be on duty on the first day, and A and B cannot be on duty on the same day.\n- C needs to b... | {
"ground_truth": "700",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Andrew, Boris, Svetlana, and Larisa are four people of different ages, forming two married couples. It is known that the oldest person is Larisa's husband, and Andrew is younger than Svetlana but older than Larisa. Who is Larisa married to?",
"role": "user"
}
] | {
"ground_truth": "Boris",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "11. From 30 people with distinct ages, select two groups, the first group consisting of 12 people and the second group consisting of 15 people, such that the oldest person in the first group is younger than the youngest person in the second group. How many different ways are there to do this?",
... | {
"ground_truth": "4060",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are three mathematics courses: algebra, geometry, and number theory. If any two courses cannot be scheduled consecutively, then how many different ways can a student schedule these courses in 6 periods in one day? Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. (10 points) The Spring Festival is approaching. Starting from January 17, 2011 (Monday), workers in the factory gradually return home for the New Year to reunite with their families. If the number of workers leaving the factory each day is the same, by January 31, there are still 121 workers le... | {
"ground_truth": "120",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 2. In a $3 \\times 3$ table, natural numbers (not necessarily distinct) are placed such that the sums in all rows and columns are different. What is the minimum value that the sum of the numbers in the table can take?",
"role": "user"
}
] | {
"ground_truth": "17",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let's assume that by removing a finite number of positive elements from the set of natural numbers, we obtained a set $S$ that is closed under addition. Let $k$ be an element of $S$. How many elements of $S$ are there such that subtracting $k$ from them results in a number that does not belong to ... | {
"ground_truth": "k",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $f : \\mathbb{R} \\to \\mathbb{R}$ be a function such that\n\\[f(f(x) + y) = f(x^2 - y) + 2cf(x)y\\]\nfor all real numbers $x$ and $y$, where $c$ is a constant. Determine all possible values of $f(2)$, find the sum of these values, and calculate the product of the number of possible values and... | {
"ground_truth": "8",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "10th Australian 1989 Problem B3 Let N be the positive integers. The function f : N → N satisfies f(1) = 5, f( f(n) ) = 4n + 9 and f(2 n ) = 2 n+1 + 3 for all n. Find f(1789). Solution",
"role": "user"
}
] | {
"ground_truth": "3581",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If a positive integer is equal to the sum of all its factors (including 1 but excluding the number itself), then this number is called a \"perfect number\". For example, 28 is a \"perfect number\" because $1 + 2 + 4 + 7 + 14 = 28$. If the sum of all factors of a positive integer (including 1 but e... | {
"ground_truth": "32",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the geoboard shown, the points are evenly spaced vertically and horizontally. Segment $AB$ is drawn using two points, as shown. Point $C$ is to be chosen from the remaining $23$ points. How many of these $23$ points will result in triangle $ABC$ being isosceles? [asy]\ndraw((0,0)--(0,6)--(6,6)-... | {
"ground_truth": "6",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The reclusive musician has agreed to give an exclusive interview to a journalist. The musician has composed a total of 24 albums over his career. In preparation for the interview, the journalist plans to listen to 3 albums per day. If the journalist starts listening to the albums on a Monday, on w... | {
"ground_truth": "Monday",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "14. Given sets $A, B$ are both sets composed of positive integers, and $|A|=20,|B|=16$, set $A$ satisfies the following condition: if $a, b, m, n \\in A$, and $a+b=m+n$, then it must be that $\\{a, b\\}=\\{m, n\\}$. Define $A+B=\\{a+b \\mid a \\in A, b \\in B\\}$, try to determine the minimum valu... | {
"ground_truth": "200",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A nine-digit number is formed by repeating a three-digit number three times; for example, $256256256$. Determine the common factor that divides any number of this form exactly.",
"role": "user"
}
] | {
"ground_truth": "1001001",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A cone has a vertex angle of 90°, and a cross-section is made at a 45° angle with the axis. What type of curve is formed by this cross-section? Provide your answer as the name of the curve.",
"role": "user"
}
] | {
"ground_truth": "Parabola",
"mean_reward": 0.1875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Piggy and Feifei each chose a number from the 10 natural numbers between 1 and 10 (they can choose the same number). The probability that the two chosen numbers are coprime is $\\qquad$ $\\%$ .",
"role": "user"
}
] | {
"ground_truth": "63",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider a set $X$ with $|X| = n\\geq 1$ elements. A family $\\mathcal{F}$ of distinct subsets of $X$ is said to have property $\\mathcal{P}$ if there exist $A,B \\in \\mathcal{F}$ so that $A\\subset B$ and $|B\\setminus A| = 1$ .\n\ni) Determine the least value $m$ , so that any f... | {
"ground_truth": "2^{n-1}",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The graph below shows the total accumulated dollars (in millions) spent by the Surf City government during $1988$. For example, about $.5$ million had been spent by the beginning of February and approximately $2$ million by the end of April. Approximately how many millions of dollars were spent du... | {
"ground_truth": "2.5",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 Given $\\frac{x^{2}}{9}+\\frac{y^{2}}{4}=1$, find the maximum value of $\\frac{x+y-1}{y+2}$.\n\n untranslated text is retained in its original format and directly output the translation result.",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given positive integers$ m,n$ such that $ m < n$. Integers $ 1,2,...,n^2$ are arranged in $ n \\times n$ board. In each row, $ m$ largest number colored red. In each column $ m$ largest number colored blue. Find the minimum number of cells such that colored both red and blue.",
"role": "user"
... | {
"ground_truth": " m^2 ",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 100 points on a circle that are about to be colored in two colors: red or blue. Find the largest number $k$ such that no matter how I select and color $k$ points, you can always color the remaining $100-k$ points such that you can connect 50 pairs of points of the same color with l... | {
"ground_truth": " k = 50 ",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled the gas tank with $6$ gallons of gasoline. During the trip, the driver filled his tank again with $12$ gallons of gasoline when the odometer read $56,560$. At the end of the trip, the driver filled his tank aga... | {
"ground_truth": "26.9",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Question 8: Let $n \\geq 2$ be a positive integer, and let real numbers $a_{1}, a_{2}, \\ldots, a_{n}, b_{1}, b_{2}, \\ldots, b_{n}$ satisfy: $\\sum_{i=1}^{n} a_{i}=\\sum_{i=1}^{n} b_{i}=1$. Find the smallest real number $\\lambda$ such that $\\lambda \\cdot \\Sigma_{1 \\leq i<j \\leq n}\\left(a_{... | {
"ground_truth": "n",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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