source stringclasses 10 values | domain listlengths 1 3 | llama8b_solve_rate float64 0 0.09 ⌀ | data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|---|---|
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Inside a large triangle with a perimeter of... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 21700,
"question": "Inside a large triangle with a perimeter of 120, several segments were drawn, dividing it into nine smaller triangles as shown in the image. It turned out that the perimeters of all nine small triangles are equal. What can they be equal to? Indicate all possible options.\n\nPerimeter of a figure is the sum of the lengths of all its sides.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Jan's three-eyed lizard has 3 times more wr... | math | {
"ground_truth": "102",
"style": "rule"
} | {
"answer": "102",
"index": 21701,
"question": "Jan's three-eyed lizard has 3 times more wrinkles than eyes, and seven times more spots than wrinkles. The lizard's cousin has 2 times more wrinkles than eyes, and 5 times more spots than wrinkles. How many fewer eyes do both lizards have combined, compared to the combined total of spots and wrinkles on both lizards?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Henley bought 300 candies and shared them w... | math | {
"ground_truth": "47",
"style": "rule"
} | {
"answer": "47",
"index": 21702,
"question": "Henley bought 300 candies and shared them with her two brothers and a cousin. However, they realized that 37.5% of the candies were sour, and they had to separate those out. If they then shared the good candies equally, how many candies did each get?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Calculus -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If for any positive real number x, lnx - ae... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 21703,
"question": "If for any positive real number x, lnx - ae^x - b + 1 ≤ 0 (where e is the base of the natural logarithm) holds true, then the minimum value of a + b is ___.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $\\triangle ABC \\sim \\triangle A'B'... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 21704,
"question": "Given $\\triangle ABC \\sim \\triangle A'B'C'$, and the similarity ratio is $3:2$. If $A'B' = 10$, then $AB$ is ______.",
"split": "train"
} |
olympiads | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \\(\\frac{\\sin 7 \\alpha}{\\sin \\alpha} -... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 21705,
"question": "\\(\\frac{\\sin 7 \\alpha}{\\sin \\alpha} - 2(\\cos 2 \\alpha + \\cos 4 \\alpha + \\cos 6 \\alpha) - 1 = 0\\).",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Determine the number of lattice points on t... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21706,
"question": "Determine the number of lattice points on the line segment with endpoints (3, 17) and (48, 281), including the endpoints. Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Figure 1 is the upper left part of a $101 \... | math | {
"ground_truth": "5201",
"style": "rule"
} | {
"answer": "5201",
"index": 21707,
"question": "Figure 1 is the upper left part of a $101 \\times 101$ grid. In the manner shown in Figure 1, start coloring a chain of gray squares from the upper left square until you can no longer continue. How many squares in the original grid will be colored gray?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If a, b, c, d, e, f, g, h, and i are intege... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21708,
"question": "If a, b, c, d, e, f, g, h, and i are integers and (ab + cdef + ghi) < 0, with the constraints |a| ≤ 10, |b| ≤ 10, and |c| ≤ 30, then what is the maximum number of integers (out of a, b, c, d, e, f, g, h, and i) that can be negative while still satisfying the inequality?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find a positive integer \\( k \\) whose pro... | math | {
"ground_truth": "84",
"style": "rule"
} | {
"answer": "84",
"index": 21709,
"question": "Find a positive integer \\( k \\) whose product of digits is equal to \\( \\frac{11k}{4} - 199 \\).",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the smallest positive integer \\( n \\... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 21710,
"question": "Find the smallest positive integer \\( n \\) such that a cube with side length \\( n \\) can be divided into 1996 smaller cubes, each with side length a positive integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n An ice skating rink charges 5 dollars for a... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"answer": "29",
"index": 21711,
"question": "An ice skating rink charges 5 dollars for admission and 2.50 dollars to rent skates. Jill can purchase a new pair of skates for 65 dollars. However, she also needs to consider the sales tax that applies to the purchase of new skates, which is 9%. If she purchases skates, she can only expect them to remain in good condition for a period of two years. Taking into account the cost and life expectancy of new skates as well as the rental fees, how many times would she need to go to the rink to justify buying the skates rather than renting a pair over a period of two years?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In how many ways can you transfer milk from... | math | {
"ground_truth": "233",
"style": "rule"
} | {
"answer": "233",
"index": 21712,
"question": "In how many ways can you transfer milk from a 12-liter can, filled with milk, to another empty 12-liter can using two empty jars with volumes of 1 liter and 2 liters? Pouring from jar to jar is not allowed.",
"split": "train"
} |
big_math | [
"Mathematics -> Calculus -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the function $f(x)=\\frac{x^{3}+\\sin... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21713,
"question": "Given the function $f(x)=\\frac{x^{3}+\\sin x}{1+x^{2}}+3$, let $M$ and $n$ be the maximum and minimum values of $f(x)$ respectively. Find the value of $M+n$. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A rectangle is composed of six squares. Fin... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21714,
"question": "A rectangle is composed of six squares. Find the side length of the largest square if the side length of the smallest square is 1. \n\nThe side length of the largest square is equal to the sum of the side lengths of the square next to it in a clockwise direction and the smallest square.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the expansion of $(x+1)(x^3+\\frac{1}{\\... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21715,
"question": "In the expansion of $(x+1)(x^3+\\frac{1}{\\sqrt{x}})^n$, the sum of the coefficients is 256. What is the coefficient of the $x$ term? (Answer with a number)",
"split": "train"
} |
math | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n For $1 \\le n \\le 100$, how many integers ... | math | {
"ground_truth": "86",
"style": "rule"
} | {
"answer": "86",
"index": 21716,
"question": "For $1 \\le n \\le 100$, how many integers are there such that $\\frac{n}{n+1}$ is a repeating decimal?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The average age of 10 men is increased by y... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"answer": "23",
"index": 21717,
"question": "The average age of 10 men is increased by years when one of them, whose age is 21 years, and another man are replaced by two new men with an average age of 32. What is the age of the other man who was replaced?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Nine children, numbered 1 to 9, each have a... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21718,
"question": "Nine children, numbered 1 to 9, each have a character pinned on their chest. The characters are: 惠 (Hui), 州 (Zhou), 西 (Xi), 湖 (Hu), 丰 (Feng), 鳄 (E), 平 (Ping), 菱 (Ling), 南 (Nan). They are standing in five circles, with the sum of the numbers of children in each circle being 13. What is the highest possible number for the child with the character \"丰\" (Feng) on their chest?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> Surface Area"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The diagram shows a cuboid in which the are... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 21719,
"question": "The diagram shows a cuboid in which the area of the shaded face is one-quarter of the area of each of the two visible unshaded faces. The total surface area of the cuboid is 72 cm². Find the area of one of the visible unshaded faces of the cuboid. Express your answer in square centimeters (cm²).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Permutations"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n 5 people are standing in a row for a photo,... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 21720,
"question": "5 people are standing in a row for a photo, among them one person must stand in the middle. There are ways to arrange them.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a 3x3 grid where all rows, columns, and ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 21721,
"question": "In a 3x3 grid where all rows, columns, and diagonals sum to 12, calculate the sum of the four corner numbers. Express your answer as a single integer.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Algebra -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $\\displaystyle\\prod_{i=6}^{2021} (1-\... | math | {
"ground_truth": "2018",
"style": "rule"
} | {
"answer": "2018",
"index": 21722,
"question": "If $\\displaystyle\\prod_{i=6}^{2021} (1-\\tan^2((2^i)^\\circ))$ can be written in the form $a^b$ for positive integers $a,b$ with $a$ squarefree, find $a+b$ .",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Non-Euclidean Geometry -> Hyperbolic Geometry"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a line $l$ intersects the hyperbola $... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21723,
"question": "Given a line $l$ intersects the hyperbola $x^2-y^2=1$ at points $A$ and $B$. If the midpoint of segment $AB$ is $C(2, 1)$, calculate the slope of line $l$. Express your answer as a single number.",
"split": "train"
} |
omnimath | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n For each positive integer $n$, let $k(n)$ b... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 21724,
"question": "For each positive integer $n$, let $k(n)$ be the number of ones in the binary representation of $2023 \\cdot n$. What is the minimum value of $k(n)$?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Arrange four identical red balls and four i... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"answer": "35",
"index": 21725,
"question": "Arrange four identical red balls and four identical black balls in a row, and then number them from left to right as 1, 2, …, 8. How many arrangements are there such that the sum of the numbers on the red balls is less than the sum of the numbers on the black balls?",
"split": "train"
} |
gsm8k | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A group of bedbugs infested an old mattress... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 21726,
"question": "A group of bedbugs infested an old mattress. Every day, the number of bedbugs would triple. After four days, there were 810 bedbugs burrowing into the mattress. How many bedbugs did the group start with?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a point \\( P \\) inside an equilater... | math | {
"ground_truth": "630",
"style": "rule"
} | {
"answer": "630",
"index": 21727,
"question": "Given a point \\( P \\) inside an equilateral triangle \\( ABC \\), perpendiculars are drawn from \\( P \\) to the three sides, with feet of the perpendiculars denoted as \\( D, E, F \\) respectively. Lines \\( AP, BP, \\) and \\( CP \\) are connected. If the area of the equilateral triangle \\( ABC \\) is 2028 square centimeters and the areas of triangles \\( PAD \\) and \\( PBE \\) are each 192 square centimeters, then the area of triangle \\( PCF \\) is \\( \\quad \\) square centimeters.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the function f(x) = x^3 + 3x^2 + 6x +... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 21728,
"question": "Given the function f(x) = x^3 + 3x^2 + 6x + 14, and f(a) = 1, f(b) = 19, calculate the value of a + b. Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( a \\) be a positive integer such th... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21729,
"question": "Let \\( a \\) be a positive integer such that \\( a < 100 \\). Given that \\( a^{3} + 23 \\) is divisible by 24, determine how many such values of \\( a \\) exist. Express your answer as a whole number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If p and t are positive integers such that ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21730,
"question": "If p and t are positive integers such that p > t > 1, what is the remainder when 92p × 5p + t + 11t × 6pt is divided by 10?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the ellipse $\\dfrac{x^{2}}{6}+ \\dfr... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21731,
"question": "Given the ellipse $\\dfrac{x^{2}}{6}+ \\dfrac{y^{2}}{2}=1$ with its left and right foci as $F_{1}$ and $F_{2}$ respectively, and the line $l$: $y=kx+m$ is tangent to the ellipse. Calculate the product of the distances from $F_{1}$ and $F_{2}$ to the line $l$, denoted as $d_{1}d_{2}$. Express your answer as a single numerical value.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the geometric sequence $\\\\{a_{n}\\\\}$... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21732,
"question": "In the geometric sequence $\\\\{a_{n}\\\\}$, $a_{3}=5$ and $a_{8}=2$. Calculate the sum of the first 10 terms of the sequence $\\\\{ \\log a_{n} \\\\}$. Express your answer as a single number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Distribute 5 volunteers into 4 groups, with... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"answer": "240",
"index": 21733,
"question": "Distribute 5 volunteers into 4 groups, with one group consisting of 2 individuals and the other three groups each having 1 individual. They are to be assigned to 4 different intersections to assist the traffic police. Calculate the number of different distribution methods.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \"Palindrome\" is a rhetorical device that ... | math | {
"ground_truth": "225",
"style": "rule"
} | {
"answer": "225",
"index": 21734,
"question": "\"Palindrome\" is a rhetorical device that exists in ancient and modern times both at home and abroad, such as \"I am for everyone, everyone is for me,\" etc. In mathematics, a class of numbers with this characteristic is called \"palindrome numbers.\" A \"palindrome number\" refers to a positive integer that reads the same from left to right and from right to left, such as $121$, $241142$, etc. Among all five-digit positive integers, the number of \"palindrome numbers\" with exactly two odd digits is ______. (Provide your answer in digits)",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a T-shaped figure made of four square... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21735,
"question": "Given a T-shaped figure made of four squares and eight identical lettered squares, determine how many of the resulting figures can be folded into a topless cubical box after adding one of the lettered squares. Provide your answer as a single integer.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A $4$ -dimensional hypercube of edge lengt... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21736,
"question": "A $4$ -dimensional hypercube of edge length $1$ is constructed in $4$ -space with its edges parallel to\nthe coordinate axes and one vertex at the origin. The coordinates of its sixteen vertices are given\nby $(a, b, c, d)$ , where each of $a, b, c,$ and $d$ is either $0$ or $1$ . The $3$ -dimensional hyperplane given\nby $x + y + z + w = 2$ intersects the hypercube at $6$ of its vertices. Compute the $3$ -dimensional\nvolume of the solid formed by the intersection.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Marta chose a number with 3 different non-z... | math | {
"ground_truth": "148",
"style": "rule"
} | {
"answer": "148",
"index": 21737,
"question": "Marta chose a number with 3 different non-zero digits and multiplied it by 3. The result was a number with 3 identical digits, equal to the tens digit of the chosen number. What number did Marta choose?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the land of Oz, only one or two-letter w... | math | {
"ground_truth": "1170",
"style": "rule"
} | {
"answer": "1170",
"index": 21738,
"question": "In the land of Oz, only one or two-letter words are used. The local language has 100 different letters. The parliament decided to forbid the use of the 10th to the 15th letters. How many words have the people of Oz lost because of the prohibition?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \nThe sequence is defined by the recurrence... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21739,
"question": "\nThe sequence is defined by the recurrence relations \\( a_{1} = 1 \\),\n\n\\[ \na_{2n} = \\left\\{\n\\begin{array}{ll}\na_{n}, & \\text{if } n \\text{ is even,} \\\\\n2a_{n}, & \\text{if } n \\text{ is odd;}\n\\end{array}\n\\right. \\quad\na_{2n+1} = \\left\\{\n\\begin{array}{ll}\n2a_{n}+1, & \\text{if } n \\text{ is even,} \\\\\na_{n}, & \\text{if } n \\text{ is odd.}\n\\end{array}\n\\right.\n\\]\n\nFind the smallest natural number \\( n \\) for which \\( a_{n} = a_{2017} \\).",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let S_n be the sum of the first n terms of ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21740,
"question": "Let S_n be the sum of the first n terms of an increasing arithmetic sequence {a_n}. If the sequence {S_n/a_n} is also an arithmetic sequence, calculate the value of S_3/a_3.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the constant term in the expansion of ... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 21741,
"question": "Find the constant term in the expansion of \\\\((x+ \\frac {3}{x})(x- \\frac {2}{x})^{5}\\\\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The sum of the binomial coefficients in the... | math | {
"ground_truth": "-220",
"style": "rule"
} | {
"answer": "-220",
"index": 21742,
"question": "The sum of the binomial coefficients in the expansion of $(\\sqrt[3]{x}- \\frac{1}{x})^{n}$ is $4096$. Find the constant term.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The product of two of the four roots of the... | math | {
"ground_truth": "86",
"style": "rule"
} | {
"answer": "86",
"index": 21743,
"question": "The product of two of the four roots of the quartic equation $x^4 - 18x^3 + kx^2+200x-1984=0$ is $-32$ . Determine the value of $k$ .",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given \\((\\sqrt{3} + 1)x = \\sqrt{3} - 1\\... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 21744,
"question": "Given \\((\\sqrt{3} + 1)x = \\sqrt{3} - 1\\), find the value of \\(x^4 - 5x^3 + 6x^2 - 5x + 4\\).",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n b takes 12 more days than a to finish a tas... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 21745,
"question": "b takes 12 more days than a to finish a task. b and a start this task and a leaves the task 12 days before the task is finished. b completes 60% of the overall task. How long would b have taken to finish the task if he had worked independently?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the focus $F$ of the parabola $C... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21746,
"question": "Given that the focus $F$ of the parabola $C\\_1$: $y=ax^{2}(a > 0)$ is also a focus of the ellipse $C\\_2$: $\\frac{y^{2}}{4}+\\frac{x^{2}}{b^{2}}=1 (b > 0)$, and the point $M$, $P(\\frac{3}{2}, 1)$ are points on the curves $C\\_1$ and $C\\_2$ respectively. Find the minimum value of $(|MP|+|MF|)$.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A mason has bricks with dimensions $2\\tim... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 21747,
"question": "A mason has bricks with dimensions $2\\times5\\times8$ and other bricks with dimensions $2\\times3\\times7$ . She also has a box with dimensions $10\\times11\\times14$ . The bricks and the box are all rectangular parallelepipeds. The mason wants to pack bricks into the box filling its entire volume and with no bricks sticking out.\nFind all possible values of the total number of bricks that she can pack.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A broken line consists of $31$ segments. ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 21748,
"question": "A broken line consists of $31$ segments. It has no self intersections, and its start and end points are distinct. All segments are extended to become straight lines. Find the least possible number of straight lines.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the expansion of $(1+x+x^2)(x+\\... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21749,
"question": "Given that the expansion of $(1+x+x^2)(x+\\frac{1}{x^3})^n$ does not contain a constant term, where $n \\in \\mathbb{N}^*$ and $2 \\leq n \\leq 7$, find the value of $n$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the circle $(x+1)^{2}+y^{2}=4$ and th... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21750,
"question": "Given the circle $(x+1)^{2}+y^{2}=4$ and the parabola $y^{2}=mx(m\\neq 0)$ intersect the directrix at points $A$ and $B$, and $|AB|=2 \\sqrt {3}$, then the value of $m$ is \\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that \\(a, b, c\\) are distinct real ... | math | {
"ground_truth": "186",
"style": "rule"
} | {
"answer": "186",
"index": 21751,
"question": "Given that \\(a, b, c\\) are distinct real roots of the polynomial equation \\(x^3 - 3x + 1 = 0\\), calculate the value of \\(a^8 + b^8 + c^8\\). Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Trigonometry -> Trigonometric Equations",
"Mathematics -> Calculus -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the equations \\( x + \\sin x \\cdot ... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 21752,
"question": "Given the equations \\( x + \\sin x \\cdot \\cos x - 1 = 0 \\) and \\( 2 \\cos y - 2 y + \\pi + 4 = 0 \\), find the value of \\( \\sin (2x - y) \\).",
"split": "train"
} |
math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Annie's soccer team is conducting a passing... | math | {
"ground_truth": "330",
"style": "rule"
} | {
"answer": "330",
"index": 21753,
"question": "Annie's soccer team is conducting a passing drill in which each of the 11 members of the soccer team must pass the ball to each of the other members exactly three times. How many times must the ball be passed before the passing drill is over?",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sets $A=\\{-1,0,1,2,3\\}$ and $B=... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21754,
"question": "Given the sets $A=\\{-1,0,1,2,3\\}$ and $B=\\{-1,0,1\\}$, let $f(x)$ be a function from $A$ to $B$. Find the number of possible value sets for the function $f(x)$. Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a race, the ratio of the speeds of two c... | math | {
"ground_truth": "600",
"style": "rule"
} | {
"answer": "600",
"index": 21755,
"question": "In a race, the ratio of the speeds of two contestants A and B is 5 : 4. A has a start of 100 m. A wins by 200 m. What is the total distance of the race?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $f(x)=x^{2}+ax+b$ where $a, b \\in \\ma... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 21756,
"question": "Let $f(x)=x^{2}+ax+b$ where $a, b \\in \\mathbb{R}$. If the solution set of the inequality $0 \\leq f(x) \\leq 6-x$ with respect to $x$ is $\\left[2,3\\right]\\cup \\{6\\}$, then $a+b=$____.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Sequences and Series -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The sequence \\( a_n \\) is defined as foll... | math | {
"ground_truth": "40200",
"style": "rule"
} | {
"answer": "40200",
"index": 21757,
"question": "The sequence \\( a_n \\) is defined as follows:\n\\( a_1 = 2, a_{n+1} = a_n + \\frac{2a_n}{n} \\) for \\( n \\geq 1 \\). Find \\( a_{200} \\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The minimum value of the function $y=\\cos^... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 21758,
"question": "The minimum value of the function $y=\\cos^2x-2\\sin x$ is ______.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence: \\(\\frac{2}{3}, \\frac... | math | {
"ground_truth": "1553",
"style": "rule"
} | {
"answer": "1553",
"index": 21759,
"question": "Given the sequence: \\(\\frac{2}{3}, \\frac{2}{9}, \\frac{4}{9}, \\frac{6}{9}, \\frac{8}{9}, \\frac{2}{27}, \\frac{4}{27}, \\cdots, \\frac{26}{27}, \\cdots, \\frac{2}{3^{n}}, \\frac{4}{3^{n}}, \\cdots, \\frac{3^{n}-1}{3^{n}}, \\cdots\\). Then, \\(\\frac{2020}{2187}\\) is the \\(n\\)-th term of this sequence.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Arrange the 5 natural numbers from 1 to 5 i... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21760,
"question": "Arrange the 5 natural numbers from 1 to 5 in a row from left to right, in such a way that starting from the third number, each number is either the sum or difference of the previous two numbers. How many valid arrangements are there? Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the average of the first 20 even nu... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"answer": "35",
"index": 21761,
"question": "What is the average of the first 20 even numbers that are not divisible by 3 or 5?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n From four classes, 28% of the students rece... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 21762,
"question": "From four classes, 28% of the students received a grade of \"5\" on the final math exam, 35% received a \"4\", 25% received a \"3\", and 12% received a \"2\". How many students took the exam if there are no more than 30 students in each class?",
"split": "train"
} |
omnimath | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $A B C$ be a triangle with $A B=13, B C... | math | {
"ground_truth": "69",
"style": "rule"
} | {
"answer": "69",
"index": 21763,
"question": "Let $A B C$ be a triangle with $A B=13, B C=14, C A=15$. Company XYZ wants to locate their base at the point $P$ in the plane minimizing the total distance to their workers, who are located at vertices $A, B$, and $C$. There are 1,5 , and 4 workers at $A, B$, and $C$, respectively. Find the minimum possible total distance Company XYZ's workers have to travel to get to $P$.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Consider the figure consisting of a square,... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 21764,
"question": "Consider the figure consisting of a square, its diagonals, and the segments joining the midpoints of opposite sides. What is the total number of triangles of any size in the figure? Express your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Mr. Zhang plans to purchase single-piece so... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21765,
"question": "Mr. Zhang plans to purchase single-piece software and boxed tapes with a budget of no more than 500 yuan. The unit prices of the software and tapes are 60 yuan and 70 yuan, respectively. According to his needs, he must buy at least 3 pieces of software and 2 boxes of tapes. How many different purchasing methods meet these requirements?",
"split": "train"
} |
big_math | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the function \\( f(n) = k \\), where ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21766,
"question": "Given the function \\( f(n) = k \\), where \\( k \\) is the \\( n \\)-th digit after the decimal point in the repeating decimal \\( 0.\\dot{9}1827364\\dot{5} \\), determine the value of \\( \\underbrace{f\\{f \\cdots f[f}_{1996 \\text{ times }}(1)]\\} \\). Express your answer as a single digit.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( S = \\{1, 2, 3, 4, \\ldots, 50\\} \... | math | {
"ground_truth": "6544",
"style": "rule"
} | {
"answer": "6544",
"index": 21767,
"question": "Let \\( S = \\{1, 2, 3, 4, \\ldots, 50\\} \\). A 3-element subset \\(\\{a, b, c\\}\\) of \\(S\\) is said to be good if \\(a + b + c\\) is divisible by 3. Determine the number of 3-element subsets of \\(S\\) which are good.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Each square of a $7 \\times 8$ board is p... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 21768,
"question": "Each square of a $7 \\times 8$ board is painted black or white, in such a way that each $3 \\times 3$ subboard has at least two black squares that are neighboring. What is the least number of black squares that can be on the entire board?\n\nClarification: Two squares are *neighbors* if they have a common side.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n How many pairs of integers $(m,n)$ satisfy ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21769,
"question": "How many pairs of integers $(m,n)$ satisfy the equation $mn+n+14=\\left (m-1 \\right)^2$? Express your answer as a single integer.",
"split": "train"
} |
math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Suppose that $*(n) = \\left\\{ n-2, n+2, 2n... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21770,
"question": "Suppose that $*(n) = \\left\\{ n-2, n+2, 2n, \\frac{n}{2} \\right\\}$. For example, $*(6) = \\{4, 8, 12, 3\\}$. For how many distinct integers $n$ does $*(n)$ have exactly three distinct elements?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the function $f(x)=\\frac{2^x}{2^x+3x... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21771,
"question": "Given the function $f(x)=\\frac{2^x}{2^x+3x}$, if real numbers $m$ and $n$ satisfy $2^{m+n}=3mn$, and $f(m)=-\\frac{1}{3}$, then $f\\left(n\\right)=\\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Calculus -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the function y=f(x) is an odd fu... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"answer": "45",
"index": 21772,
"question": "Given that the function y=f(x) is an odd function defined on the domain R and is a monotonic function on R, and the function g(x) = f(x-5), and the sequence {a_n} is an arithmetic sequence with a non-zero common difference, if g(a_1) + g(a_9) = 0, calculate the sum of the first 9 terms of the sequence {a_n}.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Select 3 numbers from the set $\\{0,1,2,3,4... | math | {
"ground_truth": "51",
"style": "rule"
} | {
"answer": "51",
"index": 21773,
"question": "Select 3 numbers from the set $\\{0,1,2,3,4,5,6,7,8,9\\}$ such that their sum is an even number not less than 10. How many different ways are there to achieve this?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Three generous friends, each of whom has ca... | math | {
"ground_truth": "252",
"style": "rule"
} | {
"answer": "252",
"index": 21774,
"question": "Three generous friends, each of whom has candies, redistribute them as follows: Vasya gives part of his candies to Petya and Kolya, thereby doubling the number of candies they have. After that, Petya gives part of his candies to Kolya and Vasya, thereby doubling the number of candies they have as well. Finally, Kolya gives part of his candies to Vasya and Petya, whose counts also double. It turned out that Kolya had 36 candies both at the beginning and at the end. How many candies do the boys have in total?",
"split": "train"
} |
big_math | [
"Mathematics -> Calculus -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the function f(x) = x^2 - 4x + 1, and... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21775,
"question": "Given the function f(x) = x^2 - 4x + 1, and suppose that 1 ≤ x_1 < x_2 < x_3 <... < x_n ≤ 4, find the minimum value of M such that |f(x_1) - f(x_2)| + |f(x_2) - f(x_3)| +... + |f(x_{n-1}) - f(x_n)| ≤ M. Express your answer as a single integer.",
"split": "train"
} |
omnimath | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A lame king is a chess piece that can move ... | math | {
"ground_truth": "43",
"style": "rule"
} | {
"answer": "43",
"index": 21776,
"question": "A lame king is a chess piece that can move from a cell to any cell that shares at least one vertex with it, except for the cells in the same column as the current cell. A lame king is placed in the top-left cell of a $7 \\times 7$ grid. Compute the maximum number of cells it can visit without visiting the same cell twice (including its starting cell).",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given triangle \\( ABC \\) with \\( AB = 12... | math | {
"ground_truth": "91",
"style": "rule"
} | {
"answer": "91",
"index": 21777,
"question": "Given triangle \\( ABC \\) with \\( AB = 12 \\), \\( BC = 10 \\), and \\( \\angle ABC = 120^\\circ \\), find \\( R^2 \\), where \\( R \\) is the radius of the smallest circle that can contain this triangle.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A middle school holds a sports meeting, wit... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21778,
"question": "A middle school holds a sports meeting, with participation by grade. There are three events: high jump, long jump, and 100m sprint, with the top three in each event receiving points: 5 points for first place, 3 points for second place, and 1 point for third place. It is known that the total scores of the seventh and eighth grades are equal, and they are tied for first place. Moreover, the number of students from the eighth grade who placed in the top three is twice that of the seventh grade. What is the total score of the ninth grade?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the equation concerning $x$, $(m-1)x^... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 21779,
"question": "Given the equation concerning $x$, $(m-1)x^{m^{2}+1}+2x-3=0$, the value of $m$ is ________.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combinations"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Using the digits 1 and 3 to form a four-dig... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 21780,
"question": "Using the digits 1 and 3 to form a four-digit number, and both digits 1 and 3 must appear at least once, there are a total of $\\_\\_\\_\\_\\_\\_\\_$ such four-digit numbers.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Quadratic Functions"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $m$ and $n$ be the two roots of the qua... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21781,
"question": "Let $m$ and $n$ be the two roots of the quadratic equation $x^{2}+2x-7=0$. Then, the value of $m^{2}+3m+n$ is __________.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Precalculus -> Functions"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a geometric sequence with positive te... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21782,
"question": "Given a geometric sequence with positive terms $\\{a_n\\}$ satisfying $\\log_{2}a_{1}+\\log_{2}a_{2}+\\ldots+\\log_{2}a_{2009}=2009$, find the minimum value of $\\log_{2}(a_{1}+a_{2009})$.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The organizing committee needs to select fo... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 21783,
"question": "The organizing committee needs to select four volunteers from Xiao Zhang, Xiao Zhao, Xiao Li, Xiao Luo, and Xiao Wang to undertake four different tasks: translation, tour guide, etiquette, and driver. If Xiao Zhang and Xiao Zhao can only work in the first two positions, while the other three can work in any of the four positions, calculate the total number of different assignment plans.",
"split": "train"
} |
math | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the greatest three-digit integer in... | math | {
"ground_truth": "611",
"style": "rule"
} | {
"answer": "611",
"index": 21784,
"question": "What is the greatest three-digit integer in which the product of the digits is 6?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Permutations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Petya has four cards with the digits $1, 2,... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 21785,
"question": "Petya has four cards with the digits $1, 2, 3, 4$. Each digit appears exactly once. How many natural numbers greater than 2222 can Petya form using these cards?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the function $f(x) = ax^2 + bx + c$ $... | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"answer": "-6",
"index": 21786,
"question": "Given the function $f(x) = ax^2 + bx + c$ $(a, b, c \\in \\mathbb{R})$, if there exists a real number $a \\in [1,2]$ such that for any $x \\in [1,2]$, $f(x) \\leqslant 1$, then the maximum value of $7b+5c$ is \\_\\_\\_\\_.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 4 students participating in the e... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 21787,
"question": "There are 4 students participating in the election for class monitor and entertainment committee member, with only 1 position available for each role. Among them, student A cannot be an entertainment committee member. Determine the total number of different outcomes (answer with a numerical value).",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the equation 3m + 3/(n + 1/p) = 17, w... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21788,
"question": "Given the equation 3m + 3/(n + 1/p) = 17, where m, n, and p are positive integers, find the value of p. Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the equation $x^{4}=a_{0}+a_{1}(x-2)+... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 21789,
"question": "Given the equation $x^{4}=a_{0}+a_{1}(x-2)+a_{2}(x-2)^{2}+a_{3}(x-2)^{3}+a_{4}(x-2)^{4}$, use the binomial theorem to calculate the value of $a_{2}$. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Calculus -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given positive numbers $a$ and $b$ that sat... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21790,
"question": "Given positive numbers $a$ and $b$ that satisfy the equation $3ab - 3 = a + 3b$, find the minimum value of $a + 3b$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \nThe rules of a game are as follows: A pla... | math | {
"ground_truth": "68",
"style": "rule"
} | {
"answer": "68",
"index": 21791,
"question": "\nThe rules of a game are as follows: A player has four skills—water, fire, wind, and earth. Each skill requires a certain number of crystals to activate, and the specific effects are as follows:\n\n- Water: Consumes 4 crystals and reduces the enemy's health by 4 points (if the enemy’s health is less than 4 points, they are killed directly).\n- Fire: Consumes 10 crystals and reduces the enemy’s health by 11 points (if the enemy’s health is less than 11 points, they are killed directly).\n- Wind: Consumes 10 crystals and reduces the enemy’s health by 5 points (if the enemy’s health is less than 5 points, they are killed directly) and the next skill’s crystal cost is halved (e.g., using the water skill after using the wind skill will cost only 2 crystals).\n- Earth: Consumes 18 crystals and halves the enemy's health (if the enemy’s health is an odd number, 1 is added before halving).\n\nIf the enemy’s health is 120 points, how many crystals are needed at least to kill the enemy (reducing their health to 0)?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Polynomial Operations -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $(3x-1)^{5}=a_{0}+a_{1}x+a_{2}x^{2}+\... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"answer": "240",
"index": 21792,
"question": "Given $(3x-1)^{5}=a_{0}+a_{1}x+a_{2}x^{2}+\\ldots+a_{5}x^{5}$, find the value of $a_{1}+2a_{2}x+3a_{3}x^{2}+4a_{4}x^{3}+5a_{5}x^{4}$ when x=1. Express your answer as a single number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Zara bought 24 cows, 7 sheep, and 113 goats... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"answer": "144",
"index": 21793,
"question": "Zara bought 24 cows, 7 sheep, and 113 goats. Next week, she will transport all of them to a new farm in equally-sized groups. Each group will have the same number of animals. How many animals are in each group?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A and B start a business, with A investing ... | math | {
"ground_truth": "18750",
"style": "rule"
} | {
"answer": "18750",
"index": 21794,
"question": "A and B start a business, with A investing the total capital of Rs. 5000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs. 500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. What is the total profit for the year?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Suppose $a$ and $b$ are positive intege... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21795,
"question": "Suppose $a$ and $b$ are positive integers with a curious property: $(a^3 - 3ab +\\tfrac{1}{2})^n + (b^3 +\\tfrac{1}{2})^n$ is an integer for at least $3$ , but at most finitely many different choices of positive integers $n$ . What is the least possible value of $a+b$ ? ",
"split": "train"
} |
aops_forum | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Define a sequence of polynomials $F_n(x)$ ... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 21796,
"question": "Define a sequence of polynomials $F_n(x)$ by $F_0(x)=0, F_1(x)=x-1$ , and for $n\\geq 1$ , $$ F_{n+1}(x)=2xF_n(x)-F_{n-1}(x)+2F_1(x). $$ For each $n$ , $F_n(x)$ can be written in the form $$ F_n(x)=c_nP_1(x)P_2(x)\\cdots P_{g(n)}(x) $$ where $c_n$ is a constant and $P_1(x),P_2(x)\\cdots, P_{g(n)}(x)$ are non-constant polynomials with integer coefficients and $g(n)$ is as large as possible. For all $2< n< 101$ , let $t$ be the minimum possible value of $g(n)$ in the above expression; for how many $k$ in the specified range is $g(k)=t$ ?",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the greatest common divisor (GCD... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 21797,
"question": "Given that the greatest common divisor (GCD) of \\(a\\) and \\(b\\) is 4, the least common multiple (LCM) of \\(a\\) and \\(c\\) as well as the LCM of \\(b\\) and \\(c\\) are both 100, and \\(a \\leqslant b\\), how many sets of natural numbers \\(a\\), \\(b\\), and \\(c\\) satisfy these conditions?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A local elementary school has some students... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"answer": "23",
"index": 21798,
"question": "A local elementary school has some students and 9 teachers. To make sure each teacher has the same amount of students in their classroom, 4 students would have to be added to the school. How many students are currently in the school?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the \"U Temného Hvozdu\" inn, giant twin... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21799,
"question": "In the \"U Temného Hvozdu\" inn, giant twins Pravdoslav and Křivomil serve customers. Pravdoslav is honest and always charges the exact prices, whereas Křivomil is dishonest and adds two krejcars to the price of each pie and each jug of mead. \n\nOnce, seven dwarves visited the inn and sat at two tables. They paid the same amount for four pies served by one twin as they did for three jugs of mead served by the other. Another time, they paid 14 krejcars more for four jugs of mead served by Křivomil than for three pies served by Pravdoslav.\n\nDetermine the cost of one pie and one jug of mead at Pravdoslav's table. All prices are in whole krejcars, and the prices did not change between visits.",
"split": "train"
} |
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