prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "3. A point in a triangle is connected to the vertices by three segments. What is the maximum number of these segments that can equal the opposite side?\n\n#",
"role": "user"
}
] | {
"ground_truth": "1",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Evaluate the expression:\n\\[4(1+4(1+4(1+4(1+4(1+4(1+4(1+4(1))))))))\\]",
"role": "user"
}
] | {
"ground_truth": "87380",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Right isosceles triangles are constructed on the sides of a 3-4-5 right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true? [asy] /* AMC8 2002 #16 Problem */ draw((0,0)--(4,0)--(4,3)--cycle); draw((4,3)--(-4,4)--(0,0)); draw((-0.15,0.1)--(... | {
"ground_truth": "X+Y=Z",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. In a convex quadrilateral $ABCD$, angles $A$ and $C$ are both 100°. Points $X$ and $Y$ are chosen on sides $AB$ and $BC$ respectively such that $AX = CY$. It turns out that line $YD$ is parallel to the bisector of angle $ABC$. Find angle $AXY$. (A. Kuznetsov, S. Berlov)",
"role": "user"
}... | {
"ground_truth": "80",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. Let $\\left(x^{2}+2 x-2\\right)^{6}=a_{0}+a_{1}(x+2)+a_{2}(x+2)^{2}+\\cdots+a_{12}(x+2)^{12}$, where $a_{i}(i=$ $1,2, \\cdots, 12)$ are real constants. Then $a_{0}+a_{1}+2 a_{2}+3 a_{3}+\\cdots+12 a_{12}=$ $\\qquad$ .",
"role": "user"
}
] | {
"ground_truth": "64",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The focus of the parabola $y^{2}=7 x$ is crossed by a line which intersects the $Y$ axis at (-1). What is the area of the parabolic segment thus obtained?",
"role": "user"
}
] | {
"ground_truth": "66.87",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Pedrinho is playing with three triangular pieces with sides $(5,8,10),(5,10,12)$ and $(5,8,12)$ as shown in the drawing below. He can join two pieces by exactly gluing the sides of the same length. For example, he can join the side 10 of the first piece with the side 10 of the second, but he canno... | {
"ground_truth": "49",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A volunteer photojournalist, Alex, is recovering from an injury sustained while documenting a conflict zone. During the recovery period, Alex spends 3 hours each day editing photos and writing articles. After 2 weeks of this routine, Alex decides to gradually increase the time spent working by 30 ... | {
"ground_truth": "77",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $ABC$ be a triangle in which $\\angle ABC = 60^{\\circ}$. Let $I$ and $O$ be the incentre and circumcentre of $ABC$, respectively. Let $M$ be the midpoint of the arc $BC$ of the circumcircle of $ABC$, which does not contain the point $A$. Determine $\\angle BAC$ given that $MB = OI$.",
"ro... | {
"ground_truth": "30^\\circ",
"mean_reward": 0.25
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The product of three consecutive integers is 384. What is their sum?",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Determine a four-digit number that is a square of a natural number and where the first two digits and the last two digits are equal.",
"role": "user"
}
] | {
"ground_truth": "7744",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "24. Find the number of 7-digit integers formed by some or all of the five digits, namely, $0,1,2,3$, and 4 , such that these integers contain none of the three blocks 22,33 and 44 .",
"role": "user"
}
] | {
"ground_truth": "29776",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the parabola $y^2 = 8x$ and the point (2, 4) which lies on it, determine the number of lines that pass through the point (2, 4) and intersect the parabola at exactly one point. Provide your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A talented writer focusing on psychological horror is drafting a new story that combines eerie elements with futuristic technology. In the story, they introduce a haunted AI that sends messages to 5 people every 6 hours. Each message contains 9 words, and each word increases in complexity with eac... | {
"ground_truth": "648",
"mean_reward": 0.1875
} | 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 certain state issues license plates consisting of six digits (from 0 through 9). The state requires that any two plates differ in at least two places. (Thus the pla... | {
"ground_truth": "2",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "22. Find the number of triangles whose sides are formed by the sides and the diagonals of a regular heptagon (7-sided polygon). (Note: The vertices of triangles need not be the vertices of the heptagon.)",
"role": "user"
}
] | {
"ground_truth": "287",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Shaovalov A.V.\n\nAmong the angles of each lateral face of a pentagonal prism, there is an angle $\\varphi$. Find all possible values of $\\varphi$.",
"role": "user"
}
] | {
"ground_truth": "90",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find all the functions $f(x),$ continuous on the whole real axis, such that for every real $x$ \\[f(3x-2)\\leq f(x)\\leq f(2x-1).\\]\n\n*Proposed by A. Golovanov*",
"role": "user"
}
] | {
"ground_truth": " f(x) = c ",
"mean_reward": 0.234375
} | 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": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8,9\n\nPoint $K$ is located on edge $AD$ of tetrahedron $ABCD$, point $N$ is on the extension of edge $AB$ beyond point $B$, and point $M$ is on the extension of edge $AC$ beyond point $C$, such that $AK:KD=3:1$, $BN=AB$, and $CM:AC=1:3$. Construct the section of the tetrahedron by the plane passi... | {
"ground_truth": "2:33",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Determine the radius $r$ of a circle inscribed within three mutually externally tangent circles of radii $a = 5$, $b = 10$, and $c = 20$ using the formula:\n\\[\n\\frac{1}{r} = \\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c} + 2 \\sqrt{\\frac{1}{ab} + \\frac{1}{ac} + \\frac{1}{bc}}.\n\\]",
"role": ... | {
"ground_truth": "1.381",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "91. On a long strip of paper, consecutive natural numbers $1, 2, 3, \\cdots \\cdots n$ are written in sequence. The long strip is cut into five segments, each containing some numbers (the digits of a single number will not be cut into different segments). The average of the numbers in these five s... | {
"ground_truth": "2014",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 4. A rectangle is divided into six squares (see figure). What is the side of the larger square if the side of the smaller one is 2.\n\n",
"role": "user"
}
] | {
"ground_truth": "14",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "I live on a very short street with 14 small family houses. The odd-numbered houses from 1 are on one side of the street, and the even-numbered houses from 2 are on the opposite side (e.g., 1 and 2 are opposite each other). \n\nOn one side of the street, all families have surnames that are colors, ... | {
"ground_truth": "13",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Six pirates - a captain and five crew members - are sitting around a campfire facing the center. They need to divide a treasure of 180 gold coins. The captain proposes a way to divide the coins (i.e., how many coins each pirate should receive: each pirate must receive a whole non-negative number o... | {
"ground_truth": "59",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Vasya wrote consecutive natural numbers \\(N\\), \\(N+1\\), \\(N+2\\), and \\(N+3\\) in rectangular boxes. Below each rectangle, he wrote the sum of the digits of the corresponding number in a circle.\n\nThe sum of the numbers in the first and second circles equals 200, and the sum of the numbers ... | {
"ground_truth": "103",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Mady has an infinite number of balls and empty boxes available to her. The empty boxes, each capable of holding four balls, are arranged in a row from left to right. At the first step, she places a ball in the first box (the leftmost box) of the row. At each subsequent step, she places a ball in t... | {
"ground_truth": "6",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "24. Brother Bear and Little Bear went on an adventure to find treasure and obtained a treasure chest. This treasure chest requires a ten-digit password consisting only of the digits 0 and 1 to open. Brother Bear first entered “1000000000”, and the treasure chest indicated that 1 digit was incorrec... | {
"ground_truth": "3",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Bo, Coe, Flo, Jo, and Moe have different amounts of money. Neither Jo nor Bo has as much money as Flo. Both Bo and Coe have more than Moe. Jo has more than Moe, but less than Bo. Who has the least amount of money?",
"role": "user"
}
] | {
"ground_truth": "\\text{Moe}",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose a ping pong ball of radius $R$, thickness $t$, made out of a material with density $\\rho_{b}$, and Young's modulus $Y$, is hit so that it resonates in mid-air with small amplitude oscillations. Assume $t \\ll R$. The density of air around (and inside) the ball is $\\rho_{a}$, and the air ... | {
"ground_truth": "19.75",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the digits 0, 1, 2, 3, 4, 5, how many unique six-digit numbers greater than 300,000 can be formed where the digit in the thousand's place is less than 3?",
"role": "user"
}
] | {
"ground_truth": "216",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "21. Each of the integers $1,2,3, \\ldots, 9$ is assigned to each vertex of a regular 9 -sided polygon (that is, every vertex receives exactly one integer from $\\{1,2, \\ldots, 9\\}$, and two vertices receive different integers) so that the sum of the integers assigned to any three consecutive ver... | {
"ground_truth": "16",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "19 In a carriage, any $m(m \\geqslant 3)$ passengers have a unique common friend (if A is a friend of B, then B is also a friend of A, and no one is a friend of themselves), how many friends does the person with the most friends have in this carriage?\n\n",
"role": "user"
}
] | {
"ground_truth": "m",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4-192 Find such a three-digit number, it equals the sum of the factorials of its digits.\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": "145",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The product underwent a price reduction from 25 yuan to 16 yuan. Calculate the average percentage reduction for each price reduction.",
"role": "user"
}
] | {
"ground_truth": "20\\%",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "What is the minimum number of sides of a regular polygon that approximates the area of its circumscribed circle with an error less than one thousandth?",
"role": "user"
}
] | {
"ground_truth": "82",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Marie changed her dice by replacing 1, 3, and 5 with -1, -3, and -5 respectively. She left the even numbers unchanged. If she throws two such dice, what is the total that cannot be achieved? Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "7",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given $x, y \\in \\mathbb{N}$, find the maximum value of $y$ such that there exists a unique value of $x$ satisfying the following inequality:\n$$\n\\frac{9}{17}<\\frac{x}{x+y}<\\frac{8}{15}.\n$$",
"role": "user"
}
] | {
"ground_truth": "112",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Suppose that $A$ and $B$ are digits in base $d > 7$ such that $\\overline{AB}_d + \\overline{BA}_d = 202_d$. Find $A_d - B_d$ in base $d$.",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A Pretti number is a seven-digit positive integer with the following properties:\n\n- The integer formed by its leftmost three digits is a perfect square.\n- The integer formed by its rightmost four digits is a perfect cube.\n- Its ten thousands digit and ones (units) digit are equal.\n- Its thous... | {
"ground_truth": "30",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Calculate how many positive integer divisors of $2310^{2310}$ are divisible by exactly 2310 positive integers.",
"role": "user"
}
] | {
"ground_truth": "120",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "At least how many passengers must occupy a seat in a metro car so that no more can sit down? (Assumptions: a) The \"width\" of each passenger is 1/6 of the seat width. b) Seated passengers cannot be forced to change their position.)",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "**Begin with the integer 1,000,000,000. The sequence is formed by repeatedly dividing the number by 3. What is the last integer in this sequence?**",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "1. Replace the letters A, B, V, G, D, E with digits (different letters correspond to different digits), so that the difference between the three-digit numbers ABV-GDE takes the smallest possible positive value. In your answer, specify the value of this difference.\n\nOTBET:3.",
"role": "user"
... | {
"ground_truth": "3",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the positive value of $k$ such that the equation $4x^3 + 9x^2 + kx + 4 = 0$ has exactly one real solution in $x$.",
"role": "user"
}
] | {
"ground_truth": "6.75",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In the pond, 30 pikes were released, which gradually eat each other. A pike is considered full if it has eaten no less than three pikes (full or hungry). What is the maximum number of pikes that can become full?",
"role": "user"
}
] | {
"ground_truth": "9",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Marvin had a birthday on Tuesday, May 27 in the leap year 2008. Calculate the next year when his birthday will fall on a Saturday.",
"role": "user"
}
] | {
"ground_truth": "2017",
"mean_reward": 0.109375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2. What day of the week was January 1, 2000?",
"role": "user"
}
] | {
"ground_truth": "Saturday",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. A project was originally planned to be completed by 100 workers in several days. If 20 workers are reduced, the construction period will be delayed by 5 days. If the average daily wage for each worker is 200 yuan, then the total wages paid after completion will be $\\qquad$ million yuan.",
... | {
"ground_truth": "40",
"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\nFind all positive integers $n < 10^{100}$ for which simultaneously $n$ divides $2^n$, $n-1$ divides $2^n-1$, and $n-2$ divides $2^n - 2$.\n\n[Solution]\n\n<paragraph_... | {
"ground_truth": "2",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For which integers $n>1$ does there exist a rectangle that can be subdivided into $n$ pairwise noncongruent rectangles similar to the original rectangle?",
"role": "user"
}
] | {
"ground_truth": " n \\ge 3 ",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Marvin had a birthday on Tuesday, May 27 in the leap year $2008$. In what year will his birthday next fall on a Saturday?",
"role": "user"
}
] | {
"ground_truth": "2017",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "An old clock's minute and hour hands overlap every 66 minutes of standard time. Calculate how much the old clock's 24 hours differ from the standard 24 hours.",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "13. As shown in the figure, natural numbers starting from 1 are arranged according to a certain rule. What is the number in the 3rd row and 51st column?\n$\\qquad$\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}\n\\hline 3 & & 7 & 9 & 12 & & 16 & 18 & 21 & $\\ldots$ \\\\\n\\hline 2 & 4 & 6 & & 11 & 13 & ... | {
"ground_truth": "113",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Points $A,B,Q,D$, and $C$ lie on the circle shown and the measures of arcs $\\widehat{BQ}$ and $\\widehat{QD}$ are $42^\\circ$ and $38^\\circ$ respectively. The sum of the measures of angles $P$ and $Q$ is [asy] size(3inch); draw(Circle((1,0),1)); pair A, B, C, D, P, Q; P = (-2,0); B=(sqrt(2)/2+1,... | {
"ground_truth": "40^\\circ",
"mean_reward": 0.140625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. Jure drew a regular 9-sided polygon. He wanted to arrange the numbers from 1 to 9 at its vertices such that the sum of the numbers in any three consecutive vertices would not exceed a natural number $n$. For what smallest number $n$ would he have succeeded?\n\n## 53rd Mathematical Competition f... | {
"ground_truth": "16",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Tommy’s Taco Town offers tacos with the following optional toppings: avocado, salsa, jalapeños, onions, cheese, beans, sour cream, and cilantro. A customer can choose to add double meat or triple meat to their taco, and they can select between a soft shell and a hard shell. How many different kind... | {
"ground_truth": "1536",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Consider a scenario where you have two regular polygons, one above the other, as shown in the diagram. One polygon is a regular pentagon and the other is a rectangle. Points $A$, $B$, $C$, and $D$ are as described in the diagram with $A$ connected to the vertices of both. Calculate the sum of the ... | {
"ground_truth": "198^\\circ",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A right triangle XYZ has legs XY = YZ = 8 cm. In each step of an iterative process, the triangle is divided into four smaller right triangles by joining the midpoints of the sides. However, for this problem, the area of the shaded triangle in each iteration is reduced by a factor of 3 rather than ... | {
"ground_truth": "16",
"mean_reward": 0.203125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Monica tosses a fair 8-sided die. If the roll is a prime number, she wins that amount in dollars. If the roll is composite, she wins nothing. If the roll is a multiple of 3, she loses that amount in dollars. Calculate the expected value of her winnings on one die toss.",
"role": "user"
}
] | {
"ground_truth": "\\$1.00",
"mean_reward": 0.28125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "60. Find the equation of the line passing through the point $(1 ; 3)$ and having a tangent with a slope equal to $2 x-3$ (see problem 19).",
"role": "user"
}
] | {
"ground_truth": "x^{2}-3x+5",
"mean_reward": 0.09375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A graduate student named Alex is conducting research on the impact of instant messaging on social interactions. As part of their research, Alex decides to observe the number of instant messages exchanged among a group of friends over a week. On Monday, the group exchanged 45 messages. On Tuesday, ... | {
"ground_truth": "391.5",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the points $(2, 3)$, $(10, 9)$, and $(6, m)$, where $m$ is an integer, determine the sum of all possible values of $m$ for which the area of the triangle formed by these points is a maximum.",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sequence of positive integers is defined by $a_0=1$ and $a_{n+1}=a_n^2+1$ for each $n\\ge0$ . Find $\\text{gcd}(a_{999},a_{2004})$ .",
"role": "user"
}
] | {
"ground_truth": "677",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "6. In convex quadrilateral $A B C D$ we have $A B=15, B C=16, C D=12, D A=25$, and $B D=20$. Let $M$ and $\\gamma$ denote the circumcenter and circumcircle of $\\triangle A B D$. Line $C B$ meets $\\gamma$ again at $F$, line $A F$ meets $M C$ at $G$, and line $G D$ meets $\\gamma$ again at $E$. De... | {
"ground_truth": "396",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The density of a body is defined as the ratio of its mass to the volume it occupies. There is a homogeneous cube with a volume of $V=8 \\, m^{3}$. As a result of heating, each of its edges increased by 4 mm. By what percentage did the density of this cube change?",
"role": "user"
}
] | {
"ground_truth": "0.6",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "How many integers \\( b \\) exist for which the equation \\( x^2 + b x - 9600 = 0 \\) has an integer solution that is divisible by both 10 and 12? Indicate the largest possible \\( b \\).",
"role": "user"
}
] | {
"ground_truth": "9599",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The bases \\(AB\\) and \\(CD\\) of trapezoid \\(ABCD\\) are 155 and 13 respectively, and its lateral sides are mutually perpendicular. Find the scalar product of the vectors \\(\\overrightarrow{AC}\\) and \\(\\overrightarrow{BD}\\).",
"role": "user"
}
] | {
"ground_truth": "-2015",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex and Bobette are playing on a $20 \\times 20$ grid where the cells are square and have a side length of 1. The distance between two cells is the distance between their centers. They take turns playing as follows: Alex places a red stone on a cell, ensuring that the distance between any two cel... | {
"ground_truth": "100",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $A B C$ be a triangle in which $\\angle A B C=60^{\\circ}$. Let $I$ and $O$ be the incentre and circumcentre of $A B C$, respectively. Let $M$ be the midpoint of the arc $B C$ of the circumcircle of $A B C$, which does not contain the point $A$. Determine $\\angle B A C$ given that $M B=O I$."... | {
"ground_truth": "30^{\\circ}",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 2 Find all positive integer solutions $(x, y, z)$ for $8^{x}+15^{y}=17^{x}$.",
"role": "user"
}
] | {
"ground_truth": "(2,2,2)",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The numbers \\(1, 2, 3, \\ldots, 400\\) are written on 400 cards. Two players, \\(A\\) and \\(B\\), play the following game:\n\n1. In the first step, \\(A\\) takes 200 cards for themselves.\n2. \\(B\\) then takes 100 cards from both the remaining 200 cards and the 200 cards that \\(A\\) has, total... | {
"ground_truth": "20000",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 11.1. Twelve different natural numbers are written in a circle, one of which is 1. Any two adjacent numbers differ by either 10 or 7. What is the greatest value that the largest written number can take?",
"role": "user"
}
] | {
"ground_truth": "58",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "5. The Great Sage Equal to Heaven is immensely powerful; he can use his hairs to transform into many magical monkeys. Each hair of the Great Sage can split into 3 magical monkeys, and each magical monkey will split into 3 more every second. The Great Sage pulls out a handful of 10 hairs, blows imm... | {
"ground_truth": "7291",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A state issues a 15 year $1000 bond that pays $25 every six months. If the current market interest rate is 4%, what is the fair market value of the bond?",
"role": "user"
}
] | {
"ground_truth": "1111.97",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9.2. Seryozha chose two different natural numbers $a$ and $b$. He wrote down four numbers in his notebook: $a, a+2, b$ and $b+2$. Then he wrote on the board all six pairwise products of the numbers from the notebook. What is the maximum number of perfect squares that can be among the numbers on th... | {
"ground_truth": "2",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 12. Find the inverse function of $y=\\sqrt{x+5}(x \\geqslant-5)$.\n\n",
"role": "user"
}
] | {
"ground_truth": "y=x^{2}-5",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Square $AXYZ$ is inscribed in equiangular hexagon $ABCDEF$ with $X$ on $\\overline{BC}$, $Y$ on $\\overline{DE}$, and $Z$ on $\\overline{EF}$. Suppose that $AB=40$, and $EF=41(\\sqrt{3}-1)$. What is the side-length of the square?",
"role": "user"
}
] | {
"ground_truth": "29\\sqrt{3}",
"mean_reward": 0.15625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the conditions in the diagram, what is the ratio of the angles \\(\\frac{\\alpha}{\\beta}\\)?",
"role": "user"
}
] | {
"ground_truth": "2",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. The fox builds \"pyramids\" from 5 cubes in the following way: each \"pyramid\" consists of one or several levels; on each level, the number of cubes is strictly less than on the previous one; each new level consists of one or several consecutive cubes. You can see an example of a \"pyramid\" m... | {
"ground_truth": "7",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "58. Determine the measure of angle $\\hat{A}$ of triangle $ABC$, if it is known that the bisector of this angle is perpendicular to the line passing through the point of intersection of the altitudes and the center of the circumscribed circle of this triangle.",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a press conference before the All-Star Game, nine All-Stars are taking questions. Four are from the Cubs, three are from the Red Sox, and two are from the Yankees. Additionally, the coach of the Cubs insists on sitting with his team. If teammates and their coach insist on sitting together, how ... | {
"ground_truth": "8640",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "9. Revenues from 09.2019 to 12.2019 will be:\n\n$$\n(55000+45000+10000+17400) * 4=509600 \\text { rubles }\n$$\n\nExpenses from 09.2019 to 11.2019 will be:\n\n$$\n(40000+20000+5000+2000+2000) * 4=276000 \\text { rubles }\n$$\n\nBy 12.31.2019, the family will have saved $1147240+521600-276000=13408... | {
"ground_truth": "1340840",
"mean_reward": 0.046875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The eleventh question: A certain meeting has 30 participants, each of whom has at most 5 acquaintances among the others, and in any group of 5 people, there exist two who are not acquaintances. Find the maximum positive integer $\\mathrm{k}$, such that in the 30 people satisfying the above conditi... | {
"ground_truth": "6",
"mean_reward": 0.34375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In triangle $\\vartriangle ABC$ with orthocenter $H$, the internal angle bisector of $\\angle BAC$ intersects $\\overline{BC}$ at $Y$ . Given that $AH = 4$, $AY = 6$, and the distance from $Y$ to $\\overline{AC}$ is $\\sqrt{15}$, compute $BC$.",
"role": "user"
}
] | {
"ground_truth": "4\\sqrt{35}",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "It takes 18 men working steadily 3 days to build a wall. If 3 of the men work twice as efficiently as the others, how many days would it take 30 men to build the same wall, assuming 5 of them are twice as efficient as the others?",
"role": "user"
}
] | {
"ground_truth": "1.8",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "3. Finding the Volume\n\n3.5 points\n\n3.5 points\n\n3 points\n\nTOTAL: 10 points\n\n## TASK 4\n\n## SOLUTION\n\nThe standard enthalpy of formation of a substance is the thermal effect of the reaction of forming 1 mole of the substance from simple substances in standard states (at a pressure of 1 ... | {
"ground_truth": "-82.9",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "II. Find the last four digits of $2^{1999}$.\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": "4688",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A sphere has two parallel cross-sectional areas of $9 \\pi$ and $16 \\pi$. The distance between the planes is infinite. What is the surface area of the sphere?",
"role": "user"
}
] | {
"ground_truth": "100\\pi",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Xiaopang, Xiaodingding, Xiaoya, and Xiaoqiao have a total of 8 parents and 4 children in their four families. They are going to an amusement park together. The ticket pricing is as follows: Adult tickets are 100 yuan per person, children's tickets are 50 yuan per person. If there are 10 or more pe... | {
"ground_truth": "800",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The following is a math problem and a solution (split into paragraphs, enclosed with tags and indexed from 0):\n\n[Math Problem]\n\nFind $AX$ in the diagram if $CX$ bisects $\\angle ACB$. [asy]\nimport markers;\n\nreal t=1-.32;\npair A=(-4.07,0);\npair B=(40.008,0);\npair C=(0,20.616);\npair X=t*A... | {
"ground_truth": "5",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Example 3 Find the largest positive integer $n$, such that in three-dimensional space there exist $n$ points $P_{1}, P_{2}, \\cdots, P_{n}$, where no three points are collinear, and for any $1 \\leqslant i<j<k \\leqslant n, \\triangle P_{i} P_{j} P_{k}$ is not an obtuse triangle.",
"role": "us... | {
"ground_truth": "8",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of 7-digit integers formed by some or all of the five digits, namely, 0, 1, 2, 3, and 4, such that these integers contain none of the three blocks 22, 33, and 44.",
"role": "user"
}
] | {
"ground_truth": "29776",
"mean_reward": 0.359375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the number of solutions to\n\\[\\cos 4x + \\cos^2 3x + \\cos^3 2x + \\cos^4 x = 0\\]for $-\\pi \\le x \\le \\pi.$",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Let $A=\\{1,2,3,\\ldots,40\\}$ . Find the least positive integer $k$ for which it is possible to partition $A$ into $k$ disjoint subsets with the property that if $a,b,c$ (not necessarily distinct) are in the same subset, then $a\\ne b+c$ .",
"role": "user"
}
] | {
"ground_truth": "4",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "For example. (Beauty Giant: 26th Y Students Mathematics Competition Questions) In $\\triangle A B C$, $\\angle A<\\angle C<90^{\\circ}<\\angle B$, construct the external angle bisectors of $\\angle A$ and $\\angle B$. If the lengths of these two external angle bisectors (from the vertex to the int... | {
"ground_truth": "12^{\\circ}",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Given the equation $\\dfrac{x-1}{x-4}=\\dfrac{m}{x-4}$, find the value of $m$ that makes the equation have a root. Express your answer as a single integer.",
"role": "user"
}
] | {
"ground_truth": "3",
"mean_reward": 0.234375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "7. A row of 100 coins is laid out. All the coins look the same, but somewhere among them are 50 counterfeit ones (and the rest are genuine). All genuine coins weigh the same, and the counterfeit ones may weigh differently, but each counterfeit is lighter than a genuine one. Can at least 34 genuine... | {
"ground_truth": "34",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "8. Let $S$ be the sum of all positive integers less than $10^{6}$ which can be expressed as $m!+n$ !, where $m$ and $n$ are nonnegative integers. Determine the last three digits of $S$.",
"role": "user"
}
] | {
"ground_truth": "130",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Anna is a loyal supporter of the political party \"Latvian Farmers' Union and Union of Greens and Farmers\". She decided to organize a community event to promote sustainable farming practices. She invited local farmers and supporters to join the event. Anna prepared 5 different types of seeds to g... | {
"ground_truth": "76",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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