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 |
|---|---|---|---|---|---|---|---|
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> 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 a set of data: $24$, $30$, $40$, $44$... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 20800,
"question": "Given a set of data: $24$, $30$, $40$, $44$, $48$, $52$. The average of the $30$th percentile and the $50$th percentile of this data set is ______.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 \\(\\left(x_{1}, x_{2}, \\cdots, x_{2004}\\... | math | {
"ground_truth": "2004",
"style": "rule"
} | {
"answer": "2004",
"index": 20801,
"question": "\\(\\left(x_{1}, x_{2}, \\cdots, x_{2004}\\right)\\) is a permutation of \\(1, 2, 3, \\ldots, 2004\\). Define \\( M = \\left|x_{1}-x_{2}\\right| + \\left|x_{3}-x_{4}\\right| + \\cdots + \\left|x_{2003}-x_{2004}\\right| \\). What is the maximum value of \\(M\\)?",
"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 Given that $x > 0$ and $y > 0$, and they sa... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 20802,
"question": "Given that $x > 0$ and $y > 0$, and they satisfy the equation $x + \\frac{y}{2} + \\frac{1}{x} + \\frac{8}{y} = 10$, find the maximum value of $2x + y$.",
"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 On an island, there are chameleons of five ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 20803,
"question": "On an island, there are chameleons of five colors. When one chameleon bites another, the color of the bitten chameleon changes according to some rule, where the new color depends only on the color of the biting and the bitten chameleon. It is known that \\$ 2023 \\$ red chameleons can agree on a sequence of bites such that they all become blue. What is the smallest \\$ \\mathrm{k} \\$ that guarantees that \\$ \\mathrm{k} \\$ red chameleons can agree on a sequence of bites to become blue?\n\nFor example, the rules could be: if a red chameleon bites a green one, the bitten changes color to blue; if a green bites a red, the bitten remains red; if a red chameleon bites a red one, the bitten changes to yellow, and so on. (The specific color change rules may vary.)",
"split": "train"
} |
math | [
"Mathematics -> Number Theory -> 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 How many of the numbers from the set $\\{1,... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"answer": "19",
"index": 20804,
"question": "How many of the numbers from the set $\\{1,\\ 2,\\ 3,\\ldots,\\ 50\\}$ have a perfect square factor other than one?",
"split": "train"
} |
olympiads | [
"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 A teacher made 50 cards for their class of ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 20805,
"question": "A teacher made 50 cards for their class of 50 students, each card labeled with a number from 1 to 50. Each card has one red side and one blue side, with the same number printed on both sides. The teacher initially places all 50 cards blue side up on the table and tells the students: \"Each of you will take turns flipping cards following this rule: If any card has a number that is a multiple of your own student number, flip it. If it's blue, flip it to red; if it's red, flip it to blue.\"\n\nHow many cards are having their red side up after all students have followed the flipping rule?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid 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 In a cube, a line determined by two vertice... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 20806,
"question": "In a cube, a line determined by two vertices and a plane containing four vertices can form an \"orthogonal line-plane pair\". How many such pairs are possible in the cube? Express your answer as a whole number.",
"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 If \\( R = 1 \\times 2 + 2 \\times 2^2 + 3 ... | math | {
"ground_truth": "18434",
"style": "rule"
} | {
"answer": "18434",
"index": 20807,
"question": "If \\( R = 1 \\times 2 + 2 \\times 2^2 + 3 \\times 2^3 + \\ldots + 10 \\times 2^{10} \\), find the value of \\( R \\).",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> 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 Admit 4 students into 3 universities, with ... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 20808,
"question": "Admit 4 students into 3 universities, with each university admitting at least one student. Find the total number of different admission methods. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> 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 real numbers $x,y$ satisfy $... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 20809,
"question": "Given that the real numbers $x,y$ satisfy $3\\leqslant xy^{2}\\leqslant 8,4\\leqslant \\frac{x^{2}}{y}\\leqslant 9$, find the maximum value of $\\frac{x^{3}}{y^{4}}$.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other",
"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 Given a 20-sided regular polygon inscribed ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20810,
"question": "Given a 20-sided regular polygon inscribed in the unit circle on the complex plane, the complex numbers corresponding to its 20 vertices are $Z_{1}, Z_{2}, \\cdots, Z_{20}$. Determine the number of distinct points corresponding to the complex numbers $Z_{1}^{1995}, Z_{2}^{1995}, \\cdots, Z_{20}^{1995}$. Express your answer as a single integer.",
"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 In a plane, several points are marked, each... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 20811,
"question": "In a plane, several points are marked, each colored blue, yellow, or green. On any segment connecting points of the same color, there are no points of that same color, but there is at least one point of a different color. What is the maximum possible number of all points?",
"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 At the arcade, Tom won some tickets playing... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 20812,
"question": "At the arcade, Tom won some tickets playing 'whack a mole' and 25 tickets playing 'skee ball'. He spent 7 of his tickets on a hat. Tom has 50 tickets left. How many tickets did Tom win playing 'whack a mole'?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> 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 In a class of 50 students, 12 enrolled for ... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 20813,
"question": "In a class of 50 students, 12 enrolled for both English and German, 22 enrolled for German, and 18 enrolled for French. Ten students enrolled for both English and French, while 8 enrolled for both German and French. Four students enrolled for all three languages. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German or French?",
"split": "train"
} |
omnimath | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 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 An up-right path between two lattice points... | math | {
"ground_truth": "175",
"style": "rule"
} | {
"answer": "175",
"index": 20814,
"question": "An up-right path between two lattice points $P$ and $Q$ is a path from $P$ to $Q$ that takes steps of 1 unit either up or to the right. A lattice point $(x, y)$ with $0 \\leq x, y \\leq 5$ is chosen uniformly at random. Compute the expected number of up-right paths from $(0,0)$ to $(5,5)$ not passing through $(x, y)$",
"split": "train"
} |
omnimath | [
"Mathematics -> Number Theory -> 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 A positive integer $n$ is known as an [i]in... | math | {
"ground_truth": "999989991",
"style": "rule"
} | {
"answer": "999989991",
"index": 20815,
"question": "A positive integer $n$ is known as an [i]interesting[/i] number if $n$ satisfies\n\\[{\\ \\{\\frac{n}{10^k}} \\} > \\frac{n}{10^{10}} \\] \nfor all $k=1,2,\\ldots 9$.\nFind the number of interesting numbers.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 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 Non-zero vectors $\\overrightarrow{a}$ and ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20816,
"question": "Non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{b}|=2$, $\\angle(\\overrightarrow{a}, \\overrightarrow{b}) = 30^{\\circ}$, and for all $\\lambda > 0$, $|\\overrightarrow{a}-\\lambda \\overrightarrow{b}|\\geqslant |\\overrightarrow{a}- \\overrightarrow{b}|$ always holds. Calculate the value of $\\overrightarrow{a}\\cdot \\overrightarrow{b}$.",
"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 An engineer undertakes a project to build a... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 20817,
"question": "An engineer undertakes a project to build a road 10 km long in 300 days and employs 30 men for the purpose. After 100 days, he finds only 2 km of the road has been completed. How many extra men must he employ to finish the work in time?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> 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 A school recommends 5 students to three uni... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"answer": "150",
"index": 20818,
"question": "A school recommends 5 students to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University for independent enrollment examinations. Each university should have at least one recommended student. Calculate the total number of different recommendation methods possible.",
"split": "train"
} |
orca_math | [
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 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 Three metal cubes with edges of 3 dm, 4 dm,... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 20819,
"question": "Three metal cubes with edges of 3 dm, 4 dm, and 5 dm, along with a metal cylinder of height 7 dm and a base diameter of 4 dm, and a metal rectangular prism of dimensions 2 dm x 3 dm x 6 dm, are melted and formed into a single cube. Find the edge of the new cube.",
"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 The little league stadium has 92 seats. 47 ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 20820,
"question": "The little league stadium has 92 seats. 47 people came to the game today, and there were 45 empty seats. How many people were holding banners?",
"split": "train"
} |
aops_forum | [
"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 In each cell of the table $4 \\times 4$ ,... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 20821,
"question": " In each cell of the table $4 \\times 4$ , in which the lines are labeled with numbers $1,2,3,4$ , and columns with letters $a,b,c,d$ , one number is written: $0$ or $1$ . Such a table is called *valid* if there are exactly two units in each of its rows and in each column. Determine the number of *valid* tables.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 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 $(x+2)^n = x^n + \\ldots + ax^3 + bx^2 +... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 20822,
"question": "If $(x+2)^n = x^n + \\ldots + ax^3 + bx^2 + cx + 2^n$ (where $n \\in \\mathbb{N}$, and $n \\geq 3$), and the ratio of $a$ to $b$ is $3:2$, then $n = \\_\\_\\_\\_\\_\\_$.",
"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 Using the 0.618 method to find the optimal ... | math | {
"ground_truth": "684",
"style": "rule"
} | {
"answer": "684",
"index": 20823,
"question": "Using the 0.618 method to find the optimal addition amount for an experiment, if the current optimal range is $[628, 774]$ and the better point is 718, then the value of the addition point for the experiment at this time is ___.",
"split": "train"
} |
big_math | [
"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 The numbers 1 to 8 are to be placed, one pe... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"answer": "17",
"index": 20824,
"question": "The numbers 1 to 8 are to be placed, one per circle, in the circles shown. The number next to each arrow shows what the product of the numbers in the circles on that straight line should be. Calculate the sum of the numbers in the three circles at the bottom of the diagram. Use each number from 1 to 8 exactly once.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 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 six-digit number starts with 1. If we mov... | math | {
"ground_truth": "142857",
"style": "rule"
} | {
"answer": "142857",
"index": 20825,
"question": "A six-digit number starts with 1. If we move this digit 1 from the first position to the last position on the right, we obtain a new six-digit number, which is three times the original number. What is this number?",
"split": "train"
} |
orca_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 What least number must be subtracted from 5... | math | {
"ground_truth": "668",
"style": "rule"
} | {
"answer": "668",
"index": 20826,
"question": "What least number must be subtracted from 50248 so that the remaining number is divisible by both 20 and 37?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 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 Find the minimum value of the function $y =... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20827,
"question": "Find the minimum value of the function $y = \\frac{\\cos^2 x}{\\cos x \\sin x - \\sin^2 x}$ when $0 < x < \\frac{\\pi}{4}$.",
"split": "train"
} |
olympiads | [
"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 Determine the smallest integer \\( n \\geq ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 20828,
"question": "Determine the smallest integer \\( n \\geq 4 \\) for which one can choose four different numbers \\( a, b, c \\), and \\( d \\) from any \\( n \\) distinct integers such that \\( a + b - c - d \\) is divisible by 20.",
"split": "train"
} |
omnimath | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> 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 Joe has written 5 questions of different di... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"answer": "25",
"index": 20829,
"question": "Joe has written 5 questions of different difficulties for a test with problems numbered 1 though 5. He wants to make sure that problem $i$ is harder than problem $j$ whenever $i-j \\geq 3$. In how many ways can he order the problems for his test?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 sequence ${a_n}$ with the sum of ... | math | {
"ground_truth": "210",
"style": "rule"
} | {
"answer": "210",
"index": 20830,
"question": "Given the sequence ${a_n}$ with the sum of its first $n$ terms denoted as $S_n$, and it is known that $a_1=1$, $2S_n=a_{n+1}a_n$, find the value of $S_{20}$. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 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 vectors $\\overrightarrow{OM}$ a... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 20831,
"question": "Given that vectors $\\overrightarrow{OM}$ and $\\overrightarrow{ON}$ are unit vectors with an angle of $60^{\\circ}$ between them, and vector $\\overrightarrow{OP} = x \\cdot \\overrightarrow{OM} + y \\cdot \\overrightarrow{ON}$, where $x$ and $y$ are real numbers. If $\\triangle PMN$ is a right triangle with right angle at point $M$, find the value of $x - y$.",
"split": "train"
} |
math | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 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 $x=\\frac{\\sum\\limits_{n=1}^{44} \\co... | math | {
"ground_truth": "241",
"style": "rule"
} | {
"answer": "241",
"index": 20832,
"question": "Let $x=\\frac{\\sum\\limits_{n=1}^{44} \\cos n^\\circ}{\\sum\\limits_{n=1}^{44} \\sin n^\\circ}$. What is the greatest integer that does not exceed $100x$?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> 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 Define the function $f(x) = \\frac{4^{x+1}}... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 20833,
"question": "Define the function $f(x) = \\frac{4^{x+1}}{4^x+2}$ on $\\mathbb{R}$. Let $S = f\\left(\\frac{1}{10}\\right) + f\\left(\\frac{2}{10}\\right) + \\ldots + f\\left(\\frac{9}{10}\\right)$. Find the value of $S$.",
"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 In a fort, there are 1200 soldiers. If each... | math | {
"ground_truth": "300",
"style": "rule"
} | {
"answer": "300",
"index": 20834,
"question": "In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for a certain number of days. If 528 more soldiers join and each soldier consumes 2.5 kg per day, the provisions available will last for 25 days. For how many days will the provisions last with the initial number of soldiers?",
"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 If $x^{2}+x-1=0$, then $x^{4}+2x^{3}-3x^{2}... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 20835,
"question": "If $x^{2}+x-1=0$, then $x^{4}+2x^{3}-3x^{2}-4x+5=\\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems",
"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 How many ways are there to arrange four 3's... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 20836,
"question": "How many ways are there to arrange four 3's and two 5's into a six-digit number divisible by 11?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> 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 Find all three-digit numbers $\\overline{\\... | math | {
"ground_truth": "156",
"style": "rule"
} | {
"answer": "156",
"index": 20837,
"question": "Find all three-digit numbers $\\overline{\\Pi В \\Gamma}$, consisting of the distinct digits $П$, $В$, and $\\Gamma$, for which the equality $\\overline{\\Pi В \\Gamma}=(П+В+\\Gamma) \\times (П+В+\\Gamma+1)$ holds.",
"split": "train"
} |
aops_forum | [
"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 Positive integers $x, y, z$ satisfy $xy ... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"answer": "64",
"index": 20838,
"question": "Positive integers $x, y, z$ satisfy $xy + z = 160$ . Compute the smallest possible value of $x + yz$ .",
"split": "train"
} |
cn_k12 | [
"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 In triangle ABC, a, b, and c are the sides ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 20839,
"question": "In triangle ABC, a, b, and c are the sides opposite to angles A, B, and C, respectively. Given that $$sin(2A+ \\frac {π}{6})= \\frac {1}{2}$$, b=1, and the area of triangle ABC is $$\\frac { \\sqrt {3}}{2}$$, find the value of $$\\frac {b+c}{sinB+sinC}$$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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^{2} + y^{2} = 9\\) wi... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 20840,
"question": "Given the circle \\(x^{2} + y^{2} = 9\\) with chord \\(AB\\) having its midpoint at \\((1,1)\\), and the line \\(AB\\) intersects the x-axis at point \\(P\\), find the value of \\(|PA| \\cdot |PB|\\).",
"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 How many pieces of 85 cm length can be cut ... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"answer": "34",
"index": 20841,
"question": "How many pieces of 85 cm length can be cut from a rod of 34 meters long?",
"split": "train"
} |
olympiads | [
"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 Masha left home for school. A few minutes l... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20842,
"question": "Masha left home for school. A few minutes later, Vanya ran out of the same house towards the school. He overtook Masha one-third of the way, and when he reached the school, Masha still had half of the way to go. How many times faster does Vanya run compared to Masha's walking speed?",
"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 Martha has 56 butterflies in her collection... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"answer": "34",
"index": 20843,
"question": "Martha has 56 butterflies in her collection. She has twice as many blue butterflies as yellow butterflies, three times as many red butterflies as yellow butterflies, and the rest of her butterflies are black. If Martha has 12 blue butterflies and 10 red butterflies, how many black butterflies does she have?",
"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 Let \\( S = \\{1, 2, 3, 4\\} \\), and a seq... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 20844,
"question": "Let \\( S = \\{1, 2, 3, 4\\} \\), and a sequence of \\( n \\) terms \\( a_1, a_2, \\ldots, a_n \\) has the following property: For any non-empty subset \\( B \\) of \\( S \\), there exist \\( |B| \\) consecutive elements in the sequence that exactly form the set \\( B \\). Find the minimum value of \\( n \\).",
"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 A man leaves point P at 6 a.m. and reaches ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 20845,
"question": "A man leaves point P at 6 a.m. and reaches point Q at 10 a.m. Another man leaves point Q at 8 a.m. and reaches point P at 12 noon. At what time do they meet?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 a sequence $\\{a_n\\}$ where $a_1=1$,... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 20846,
"question": "Given a sequence $\\{a_n\\}$ where $a_1=1$, $a_2=2$, and for any integer $n>1$, the equation $S_{n+1} + S_{n-1} = 2(S_n + S_1)$ holds, find the value of $S_5$.",
"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 In a 10-mile race, two runners are competin... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20847,
"question": "In a 10-mile race, two runners are competing. The first runs at a certain pace, while the second runs at an average pace of 7 minutes per mile. After 56 minutes, the second runner stops for a drink of water. The second runner could remain stopped for 8 minutes before the first runner catches up with him. What is the average pace of the first runner in minutes per mile?",
"split": "train"
} |
olympiads | [
"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 In an $8 \\times 12$ table, some $N$ cells ... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 20848,
"question": "In an $8 \\times 12$ table, some $N$ cells are black, while the rest are white. In one operation, it is allowed to paint three cells that form a three-cell corner to white (some of them might have been white before repainting). It turns out that it is impossible to make the entire table completely white in fewer than 25 such operations. Find the smallest possible value of $N$.",
"split": "train"
} |
olympiads | [
"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 The bottom of a box is a table of size $8 \... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"answer": "28",
"index": 20849,
"question": "The bottom of a box is a table of size $8 \\times 8$. What is the smallest non-zero number of $2 \\times 1$ or $1 \\times 2$ tiles that can be placed on the bottom of the box so that no tile can be moved either horizontally or vertically? Each tile must occupy exactly two cells that are not occupied by other tiles.",
"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 How many ways are there to arrange the numb... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 20850,
"question": "How many ways are there to arrange the numbers \\(1, 2, 3, 4, 5, 6\\) on the vertices of a regular hexagon such that exactly 3 of the numbers are larger than both of their neighbors? Rotations and reflections are considered the same.",
"split": "train"
} |
big_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 The numbers from 0 to 9 can be represented ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 20851,
"question": "The numbers from 0 to 9 can be represented using matchsticks in the following way:\nRemoving the bottom left matchstick from the character “日” turns it into the number 1, which we refer to as \"马\" corresponding to 1; removing both the top and bottom matchsticks and the bottom left matchstick from the character “日” turns it into the number 3, which we refer to as \"他\" corresponding to 3. The character “日” itself corresponds to 0.\n\nHow many different numbers can be represented using this method? Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"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 We created a three-digit natural number amo... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 20852,
"question": "We created a three-digit natural number among the number cards 1 to 9 and overlaps were allowed. Find how many numbers there are whose sum of each digit is 7.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> 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 Simplify first, then evaluate: $\\left(a-b\... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 20853,
"question": "Simplify first, then evaluate: $\\left(a-b\\right)^{2}-2a\\left(a+3b\\right)+\\left(a+2b\\right)\\left(a-2b\\right)$, where $a=1$, $b=-3$.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 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 Find the number of ways to distribute 17 id... | math | {
"ground_truth": "5720",
"style": "rule"
} | {
"answer": "5720",
"index": 20854,
"question": "Find the number of ways to distribute 17 identical red balls and 10 identical white balls into 4 distinct boxes such that the number of red balls is greater than the number of white balls in each box.",
"split": "train"
} |
omnimath | [
"Mathematics -> Number Theory -> 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 Compute the number of positive integers $n ... | math | {
"ground_truth": "43",
"style": "rule"
} | {
"answer": "43",
"index": 20855,
"question": "Compute the number of positive integers $n \\leq 1000$ such that \\operatorname{lcm}(n, 9)$ is a perfect square.",
"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 There are approximately 11.9 numbers betwee... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20856,
"question": "There are approximately 11.9 numbers between 100 and 600 that are divisible by 2, a certain number, and 7 together. What is the second number by which the numbers in the range are divisible?",
"split": "train"
} |
cn_k12 | [
"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 Let $x, y$ be integers that satisfy the equ... | math | {
"ground_truth": "588",
"style": "rule"
} | {
"answer": "588",
"index": 20857,
"question": "Let $x, y$ be integers that satisfy the equation $y^2 + 3x^2y^2 = 30x^2 + 517$. Then, $3x^2y^2 =$ ?",
"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 working at a constant rate , p can finish a... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 20858,
"question": "working at a constant rate , p can finish a job in 4 hours . q , also working at a constant rate , can finish the same job in 15 hours . if they work together for 3 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?",
"split": "train"
} |
big_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 The distance from the top of the can on the... | math | {
"ground_truth": "130",
"style": "rule"
} | {
"answer": "130",
"index": 20859,
"question": "The distance from the top of the can on the floor to the top of the bottle on the table is $150 \\textrm{ cm}$. The distance from the top of the bottle on the floor to the top of the can on the table is $110 \\textrm{ cm}$. Find the height of the table. Express your answer in centimeters as a whole number.",
"split": "train"
} |
olympiads | [
"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 Given \\( x, y \\in \\left[-\\frac{\\pi}{4}... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 20860,
"question": "Given \\( x, y \\in \\left[-\\frac{\\pi}{4}, \\frac{\\pi}{4}\\right] \\), \\( a \\in \\mathbb{R} \\), and the equations:\n\\[ \n\\begin{cases} \nx^3 + \\sin x - 2a = 0, \\\\ \n4y^3 + \\sin y \\cdot \\cos y + a = 0 \n\\end{cases}\n\\]\nfind \\(\\cos(x + 2y) =\\).",
"split": "train"
} |
big_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 5 volunteers are to be distributed to 3 sch... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"answer": "150",
"index": 20861,
"question": "5 volunteers are to be distributed to 3 schools for teaching, with each school receiving at least one volunteer. Calculate the total number of different distribution methods. Provide your answer as a whole number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> 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 $abcd$ is a four-digit natural number. It i... | math | {
"ground_truth": "2243",
"style": "rule"
} | {
"answer": "2243",
"index": 20862,
"question": "$abcd$ is a four-digit natural number. It is known that $abcd - abc - ab - a = 1995$. Determine the four-digit number $abcd$.",
"split": "train"
} |
olympiads | [
"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 Identify a six-digit number \\( N \\) compo... | math | {
"ground_truth": "142857",
"style": "rule"
} | {
"answer": "142857",
"index": 20863,
"question": "Identify a six-digit number \\( N \\) composed of distinct digits such that the numbers \\( 2N, 3N, 4N, 5N, \\) and \\( 6N \\) are permutations of its digits.",
"split": "train"
} |
aops_forum | [
"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 Let $P_0 = (3,1)$ and define $P_{n+1} = ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 20864,
"question": "Let $P_0 = (3,1)$ and define $P_{n+1} = (x_n, y_n)$ for $n \\ge 0$ by $$ x_{n+1} = - \\frac{3x_n - y_n}{2}, y_{n+1} = - \\frac{x_n + y_n}{2} $$ Find the area of the quadrilateral formed by the points $P_{96}, P_{97}, P_{98}, P_{99}$ .",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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 As shown in the figure, the area of circle ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20865,
"question": "As shown in the figure, the area of circle \\(O\\) is \\(32\\). \\(OC \\perp AB\\), \\(\\angle AOE = \\angle EOD\\), and \\(\\angle COF = \\angle FOD\\). Find the area of the sector \\(EOF\\).",
"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 In the rectangular coordinate system $Oy$, ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 20866,
"question": "In the rectangular coordinate system $Oy$, establish a polar coordinate system with the origin as the pole and the positive semi-axis as the polar axis. Suppose points $A$ and $B$ are located on the curves $C_1$: $\\begin{cases} x=3+\\cos \\theta, \\\\ y=4+\\sin \\theta \\end{cases}$ ($\\theta$ is the parameter) and $C_2$: $\\rho=1$, respectively. The minimum value of $|AB|$ is ________.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> 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 Find all positive integers $x$ such that ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20867,
"question": "Find all positive integers $x$ such that $2x+1$ is a perfect square but none of the integers $2x+2, 2x+3, \\ldots, 3x+2$ are perfect squares.",
"split": "train"
} |
olympiads | [
"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 Neo has an infinite supply of red pills and... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 20868,
"question": "Neo has an infinite supply of red pills and blue pills. When he takes a red pill, his weight will double, and when he takes a blue pill, he will lose one pound. If Neo originally weighs one pound, what is the minimum number of pills he must take to make his weight 2015 pounds?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 sequence $\\{a_n\\}$, $a_1=1$, $a_2=... | math | {
"ground_truth": "2600",
"style": "rule"
} | {
"answer": "2600",
"index": 20869,
"question": "In the sequence $\\{a_n\\}$, $a_1=1$, $a_2=2$, and $a_{n+2}-a_{n}=1+(-1)^{n}$. Calculate the sum of the first 100 terms, $S_{100}$. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"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 Given an ellipse $C:\\frac{{x}^{2}}{{a}^{2}... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20870,
"question": "Given an ellipse $C:\\frac{{x}^{2}}{{a}^{2}}+\\frac{{y}^{2}}{96}=1(a＞4\\sqrt{6})$ with the left and right foci $F_{1}$ and $F_{2}$ respectively. Let $P$ be a point on the ellipse $C$ such that $|PF_{1}|:|PF_{2}|:|OF_{2}|=8:6:5$ (where $O$ is the origin). Find $|PF_{1}|-|PF_{2}|$.",
"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 There are 25 students in a class. The teach... | math | {
"ground_truth": "600",
"style": "rule"
} | {
"answer": "600",
"index": 20871,
"question": "There are 25 students in a class. The teacher wants to stockpile $N$ candies, conduct a competition, and distribute all $N$ candies based on the students' performance (students who solved the same number of problems should receive the same number of candies, students who solved fewer problems should receive fewer candies, including possibly zero candies). What is the minimum $N$ for which this will be possible regardless of the number of problems in the competition and the students' success?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane 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 In triangle \\(\\triangle ABC\\), point \\(... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 20872,
"question": "In triangle \\(\\triangle ABC\\), point \\(F\\) is on side \\(AC\\) such that \\(FC = 2AF\\). If \\(G\\) is the midpoint of segment \\(BF\\) and \\(E\\) is the intersection of the line passing through \\(A\\) and \\(G\\) with segment \\(BC\\), calculate the ratio \\(\\frac{EC}{EB}\\).",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 1, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 1, 2, 3... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 20873,
"question": "1, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 1, 2, 3, 4, 5, 4, 2, 1, 2, 3, 4, 5, 6, 5, 3, 1, 2, 3, 4, 5, 6, 7, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 7, 5, 3, 1, ___?",
"split": "train"
} |
cn_k12 | [
"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 Given the sequence $\\{a_n\\}$ that satisfi... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 20874,
"question": "Given the sequence $\\{a_n\\}$ that satisfies $3a_{n+1} + a_n = 4$, with $a_1 = 9$, and the sum of its first $n$ terms is denoted by $S_n$. Find the smallest natural number $n$ that satisfies the inequality $|\\begin{matrix} S_n - n - 6 \\end{matrix}| < \\frac{1}{125}$.",
"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 Given the expansion of $(5x-\\sqrt{x})^n$, ... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"answer": "150",
"index": 20875,
"question": "Given the expansion of $(5x-\\sqrt{x})^n$, let $M$ be the sum of the coefficients of all terms and $N$ be the sum of the binomial coefficients. If $M-N=240$, determine the coefficient of the ${x}^{3}$ term in the expansion.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> 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 Within a cube structure consisting of 8 ver... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"answer": "49",
"index": 20876,
"question": "Within a cube structure consisting of 8 vertices, the midpoints of the 12 edges, the centers of the 6 faces, and the center of the cube (totaling 27 points), determine the total number of groups of three collinear points.",
"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 Layla, Nahima, Ramon, and Aria played a gam... | math | {
"ground_truth": "320",
"style": "rule"
} | {
"answer": "320",
"index": 20877,
"question": "Layla, Nahima, Ramon, and Aria played a game with complex scoring rules: each player scored double points in the first round, triple points in the second round, and normal points in the third round. Layla won with a total of 760 points and the sum of all the points scored by the players was 1,330. If Layla scored 120 in the first round and 90 in the second round, how many more points did Layla score than the combined points of Nahima, Ramon, and Aria in the third round?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> 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 Select 5 people from 3 orthopedic doctors, ... | math | {
"ground_truth": "590",
"style": "rule"
} | {
"answer": "590",
"index": 20878,
"question": "Select 5 people from 3 orthopedic doctors, 4 neurosurgeons, and 5 internists to form an earthquake relief medical team. The number of ways to select such that there is at least one doctor from each specialty is (answer in digits).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 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 order to investigate the number of stude... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 20879,
"question": "In order to investigate the number of students from various classes participating in the extracurricular calligraphy group in a school, 5 classes were randomly selected, and the number of students from each class participating in the group was taken as a sample. It is known that the sample mean is 7, the sample variance is 4, and the sample data are all different. What is the maximum value among the sample data?",
"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 In triangle $\\triangle ABC$ with internal ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 20880,
"question": "In triangle $\\triangle ABC$ with internal angles $A$, $B$, and $C$, if $$\\frac { \\sqrt {3}\\cos A+\\sin A}{ \\sqrt {3}\\sin A-\\cos A} = \\tan\\left(-\\frac {7}{12}\\pi\\right)$$, then $\\tan A = $ ______.",
"split": "train"
} |
cn_k12 | [
"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 Given two positive numbers $a$ and $b$ that... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 20881,
"question": "Given two positive numbers $a$ and $b$ that satisfy $\\frac{1}{a}+\\frac{1}{b}=1$, find the minimum value of $\\frac{1}{a-1}+\\frac{4}{b-1}$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> 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 When Seokjin was doing a division, he misre... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"answer": "81",
"index": 20882,
"question": "When Seokjin was doing a division, he misread the tens digit and units digit of the divisor 65 as the opposite to get the quotient of division 25, and the remainder also 25. Find the sum of the correctly calculated quotient and remainder.",
"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 A vegan restaurant serves four kinds of pro... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 20883,
"question": "A vegan restaurant serves four kinds of protein: seitan, beans, lentils, and tempeh. There are 20 dishes on their menu. Three dishes have beans and lentils, four have beans and seitan, and two have tempeh and lentils. The remaining dishes only have one kind of protein in them. Of the single protein dishes, twice as many dishes have only beans as those with only tempeh, and there are three times as many dishes with only seitan as those with only tempeh. How many dishes include lentils?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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 Through point \\( A \\) located on a circle... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 20884,
"question": "Through point \\( A \\) located on a circle, a diameter \\( AB \\) and a chord \\( AC \\) are drawn, where \\( AC = 8 \\) and \\( \\angle BAC = 30^\\circ \\).\n\nFind the length of the chord \\( CM \\), which is perpendicular to \\( AB \\).",
"split": "train"
} |
olympiads | [
"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 There are a batch of wooden strips with len... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 20885,
"question": "There are a batch of wooden strips with lengths of \\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10,\\) and 11 centimeters, with an adequate quantity of each length. If you select 3 strips appropriately to form a triangle with the requirement that the base is 11 centimeters long, how many different triangles can be formed?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 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 the Cartesian coordinate system $xOy$, t... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 20886,
"question": "In the Cartesian coordinate system $xOy$, the graph of the parabola $y=ax^2 - 3x + 3 \\ (a \\neq 0)$ is symmetric with the graph of the parabola $y^2 = 2px \\ (p > 0)$ with respect to the line $y = x + m$. Find the product of the real numbers $a$, $p$, and $m$.",
"split": "train"
} |
cn_k12 | [
"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 If $\\forall x\\geqslant 0$, the inequality... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 20887,
"question": "If $\\forall x\\geqslant 0$, the inequality $xe^{x}+ae^{x}\\ln \\left(x+1\\right)+1\\geqslant e^{x}(x+1)^{a}$ always holds, then the minimum value of the real number $a$ is ______.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Permutations"
] | 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 There are three cards, each with different ... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"answer": "48",
"index": 20888,
"question": "There are three cards, each with different numbers written on their front and back sides: 1, 3, 5, and 2, 4, 6. When arranging the numbers on these three cards to form a three-digit number, calculate the total number of different three-digit numbers that can be formed. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"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 Six positive numbers, not exceeding 3, sati... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"answer": "72",
"index": 20889,
"question": "Six positive numbers, not exceeding 3, satisfy the equations \\(a + b + c + d = 6\\) and \\(e + f = 2\\). What is the minimum value of the expression\n\n$$\n\\left(\\sqrt{a^{2}+4}+\\sqrt{b^{2}+e^{2}}+\\sqrt{c^{2}+f^{2}}+\\sqrt{d^{2}+4}\\right)^{2}\n$$",
"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 Each week Carina puts 20 more seashells in ... | math | {
"ground_truth": "320",
"style": "rule"
} | {
"answer": "320",
"index": 20890,
"question": "Each week Carina puts 20 more seashells in a jar than she did the week before. If there are 50 seashells in the jar this week, how many will there be in a month?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 an arithmetic sequence {a_n} with a n... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"answer": "25",
"index": 20891,
"question": "Given an arithmetic sequence {a_n} with a non-zero common difference, let S_n denote the sum of its first n terms. If S_3 = 9, and a_2-1, a_3-1, a_5-1 form a geometric sequence, then find the value of S_5. Express your answer as a single numerical value.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> 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 From the natural numbers 1 to 100, each tim... | math | {
"ground_truth": "2500",
"style": "rule"
} | {
"answer": "2500",
"index": 20892,
"question": "From the natural numbers 1 to 100, each time we take out two different numbers so that their sum is greater than 100, how many different ways are there to do this?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> 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 For positive integer $n$ let $a_n$ be t... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 20893,
"question": "For positive integer $n$ let $a_n$ be the integer consisting of $n$ digits of $9$ followed by the digits $488$ . For example, $a_3 = 999,488$ and $a_7 = 9,999,999,488$ . Find the value of $n$ so that an is divisible by the highest power of $2$ .",
"split": "train"
} |
olympiads | [
"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 Let \\( S = \\{1, 2, 4, 8, 16, 32, 64, 128,... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 20894,
"question": "Let \\( S = \\{1, 2, 4, 8, 16, 32, 64, 128, 256\\} \\). A subset \\( P \\) of \\( S \\) is called squarely if it is nonempty and the sum of its elements is a perfect square. A squarely set \\( Q \\) is called super squarely if it is not a proper subset of any squarely set. Find the number of super squarely sets. (A set \\( A \\) is said to be a proper subset of a set \\( B \\) if \\( A \\) is a subset of \\( B \\) and \\( A \\neq B \\).)",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Polynomial Operations -> 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 Find the number of polynomials of the form ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 20895,
"question": "Find the number of polynomials of the form $a_0x^n+a_1x^{n-1}+\\cdots+a_{n-1}x+a_n$ that satisfy the condition $h=n+a_0+|a_1|+|a_2|+\\cdots+|a_n|=3$, where $n$ is a non-negative integer, $a_0$ is a positive integer, and the remaining $a_i$ are integers or zero.",
"split": "train"
} |
olympiads | [
"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 5 sheets of red cardboard can be exchanged ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 20896,
"question": "5 sheets of red cardboard can be exchanged for 2 sheets of gold cardboard, and 1 sheet of gold cardboard can be exchanged for 1 sheet of red cardboard and 1 sheet of silver cardboard. If person A has three sheets each of red and gold cardboard, how many sheets of silver cardboard can they get?",
"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 in a school with 604 students , the average... | math | {
"ground_truth": "151",
"style": "rule"
} | {
"answer": "151",
"index": 20897,
"question": "in a school with 604 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is",
"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 An oil pipe in the sea broke. Before engine... | math | {
"ground_truth": "6206",
"style": "rule"
} | {
"answer": "6206",
"index": 20898,
"question": "An oil pipe in the sea broke. Before engineers started to fix the pipe, 2475 gallons of oil leaked into the water. Some gallons of oil leaked before the pipe was fixed. 3731 gallons of oil leaked while the engineers were fixing the pipe. What was the total amount of oil that leaked before the pipe was fixed?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 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 function $y=x^2-1840x+2009$ inter... | math | {
"ground_truth": "2009",
"style": "rule"
} | {
"answer": "2009",
"index": 20899,
"question": "Given the function $y=x^2-1840x+2009$ intersects the x-axis at points $(m,0)$ and $(n,0)$, calculate the value of $(m^2-1841m+2009)(n^2-1841n+2009)$. Express your answer as a single integer.",
"split": "train"
} |
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