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 -> 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 Dividing \\$(3000 + b) in a ratio 5: 6: 8, ... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 4300,
"question": "Dividing \\$(3000 + b) in a ratio 5: 6: 8, the smallest part is \\$c. Find c.",
"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 Use the Horner's Method to calculate the va... | math | {
"ground_truth": "320",
"style": "rule"
} | {
"answer": "320",
"index": 4301,
"question": "Use the Horner's Method to calculate the value of the polynomial $f(x) = x^6 - 5x^5 + 6x^4 + x^2 + 3x + 2$ when $x = -2$.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Mathematics 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 There are 7 parking spaces arranged in a ro... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 4302,
"question": "There are 7 parking spaces arranged in a row. Now, there are 3 different models of cars that need to be parked. If it is required that the remaining 4 parking spaces must be connected, find the number of distinct parking arrangements. Express your answer as a whole number.",
"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 How many \"simple\" ordered pairs (m, n) ar... | math | {
"ground_truth": "300",
"style": "rule"
} | {
"answer": "300",
"index": 4303,
"question": "How many \"simple\" ordered pairs (m, n) are there whose value is 1942, where m and n are non-negative integers and when adding m+n there is no carry in any digit? Express your answer as a whole number.",
"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 Holly needs to take 2 insulin pills per day... | math | {
"ground_truth": "106",
"style": "rule"
} | {
"answer": "106",
"index": 4304,
"question": "Holly needs to take 2 insulin pills per day, 3 blood pressure pills per day, and twice as many anticonvulsants as blood pressure pills each day. She takes calcium supplements every other day, consuming three times as many calcium pills as insulin pills. Also, she needs to take one multivitamin once every three days, and anxiety pills, which are taken once every four days. How many pills does Holly take in a week?",
"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 A tractor driver plowed three sections of l... | math | {
"ground_truth": "136",
"style": "rule"
} | {
"answer": "136",
"index": 4305,
"question": "A tractor driver plowed three sections of land. The area of the first section is equal to $\\frac{2}{5}$ of the total area of all three sections, and the area of the second section is related to the area of the third section as $\\frac{3}{2}: \\frac{4}{3}$. How many hectares were there in all three sections if the third section was 16 hectares less than the first section?",
"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 \"archer\" figure on a checkered board ... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"answer": "28",
"index": 4306,
"question": "The \"archer\" figure on a checkered board attacks in a line - across cells upwards, downwards, right, or left (exactly one direction out of four; directions for different archers do not depend on each other). What is the maximum number of non-attacking archers that can be placed on an $8 \\times 8$ chessboard?",
"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 In one step, it is possible to replace any ... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 4307,
"question": "In one step, it is possible to replace any letter in any of these words with any other letter (for example, in one step, the word ЗАНОЗА can be changed to the word ЗКНОЗА). What is the minimum number of steps needed to make all the words identical (even nonsensical words are allowed)?",
"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 A rubber band is 4 inches long. An ant begi... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 4308,
"question": "A rubber band is 4 inches long. An ant begins at the left end. Every minute, the ant walks one inch rightwards along the rubber band, but then the band is stretched uniformly by one inch. For what value of \\( n \\) will the ant reach the right end during the \\( n \\)-th minute?",
"split": "train"
} |
cn_k12 | [
"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 The polar equation of curve $C$ is $\\rho=2... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 4309,
"question": "The polar equation of curve $C$ is $\\rho=2\\sin\\theta$. What is the shortest distance from a point on curve $C$ to the line $l$: $\\begin{cases} x=\\sqrt{3}t+\\sqrt{3} \\\\ y=-3t+2 \\end{cases}$ (where $t$ is a parameter)?",
"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 In the set of natural numbers 0, 1, 2, 3, .... | math | {
"ground_truth": "246",
"style": "rule"
} | {
"answer": "246",
"index": 4310,
"question": "In the set of natural numbers 0, 1, 2, 3, ..., 9, any three distinct numbers are selected. The number of three-digit numbers that are multiples of 3 formed from these selected numbers 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 Last season, Jorge scored 156 goals playing... | math | {
"ground_truth": "546",
"style": "rule"
} | {
"answer": "546",
"index": 4311,
"question": "Last season, Jorge scored 156 goals playing soccer, which was 80% of his total goals for the season before. This season he scored 187 goals, which was a 25% increase compared to last season. Calculate the total number of goals he scored for the last three seasons.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> 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 a non-constant sequence {a_i} that sa... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 4312,
"question": "Given a non-constant sequence {a_i} that satisfies the recurrence relation a_{i+1}^2 - a_i a_{i+1} + a_i^2 = 0 and a_{i+1}!= a_{i-1} for i = 1, 2, 3,..., n, and the boundary conditions a_1 = a_{n+1} = 1, find the sum of the sequence from i = 1 to n. Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"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 If a^2 - b^2 = 10 and a * b = 8, find a^4 +... | math | {
"ground_truth": "548",
"style": "rule"
} | {
"answer": "548",
"index": 4313,
"question": "If a^2 - b^2 = 10 and a * b = 8, find a^4 + b^4.",
"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 Barney's grocery store sold out all of its ... | math | {
"ground_truth": "5608",
"style": "rule"
} | {
"answer": "5608",
"index": 4314,
"question": "Barney's grocery store sold out all of its items at the beginning of the pandemic, so they ordered extra items to restock the shelves. They sold another 1561 items that day, and have 575 items in the storeroom. They have 3,472 items left in the whole store. How many items did they order to restock the shelves?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> 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 Ada rolls a standard $4$ -sided die $5$ ... | math | {
"ground_truth": "23128",
"style": "rule"
} | {
"answer": "23128",
"index": 4315,
"question": "Ada rolls a standard $4$ -sided die $5$ times. The probability that the die lands on at most two distinct sides can be written as $ \\frac{A}{B}$ for relatively prime positive integers $A$ and $B$ . Find $1000A +B$ ",
"split": "train"
} |
omnimath | [
"Mathematics -> Discrete Mathematics -> 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 Let the sequence $a_{i}$ be defined as $a_{... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"answer": "50",
"index": 4316,
"question": "Let the sequence $a_{i}$ be defined as $a_{i+1}=2^{a_{i}}$. Find the number of integers $1 \\leq n \\leq 1000$ such that if $a_{0}=n$, then 100 divides $a_{1000}-a_{1}$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> 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 You have 6 identical balls and 4 distinct b... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 4317,
"question": "You have 6 identical balls and 4 distinct boxes. You want to place the balls in the boxes such that no box remains empty. How many different ways can you do this? (Answer with a number)",
"split": "train"
} |
omnimath | [
"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 Compute the number of ways to tile a $3 \\t... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 4318,
"question": "Compute the number of ways to tile a $3 \\times 5$ rectangle with one $1 \\times 1$ tile, one $1 \\times 2$ tile, one $1 \\times 3$ tile, one $1 \\times 4$ tile, and one $1 \\times 5$ tile. (The tiles can be rotated, and tilings that differ by rotation or reflection are considered distinct.)",
"split": "train"
} |
cn_k12 | [
"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 Given the set $A = \\{a+2, (a+1)^2, a^2+3a+... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 4319,
"question": "Given the set $A = \\{a+2, (a+1)^2, a^2+3a+3\\}$, and $1 \\in A$, find the value of the real number $a$.",
"split": "train"
} |
olympiads | [
"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 \\(\\boldsymbol{a} = \\left(\\cos \\f... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 4320,
"question": "Given \\(\\boldsymbol{a} = \\left(\\cos \\frac{2}{3} \\pi, \\sin \\frac{2}{3} \\pi\\right), \\overrightarrow{O A} = \\boldsymbol{a} - \\boldsymbol{b}, \\overrightarrow{O B} = \\boldsymbol{a} + \\boldsymbol{b},\\) if \\(\\triangle O A B\\) is an isosceles right triangle with \\(O\\) as the right-angle vertex, then the area of \\(\\triangle O A B\\) is _____",
"split": "train"
} |
math | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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 $A$ and $B$ be the endpoints of a semic... | math | {
"ground_truth": "28672",
"style": "rule"
} | {
"answer": "28672",
"index": 4321,
"question": "Let $A$ and $B$ be the endpoints of a semicircular arc of radius $2$. The arc is divided into seven congruent arcs by six equally spaced points $C_1$, $C_2$, $\\dots$, $C_6$. All chords of the form $\\overline {AC_i}$ or $\\overline {BC_i}$ are drawn. Find the product of the lengths of these twelve chords.",
"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 an average of 117 jellybeans in e... | math | {
"ground_truth": "47",
"style": "rule"
} | {
"answer": "47",
"index": 4322,
"question": "There are an average of 117 jellybeans in each of 34 bags of various sizes. In every bag, there are 5 different colors of jellybeans. After adding another bag, the average number of jellybeans per bag increases by 7. If the new bag contains twice the number of a specific color of jellybeans than the average of that color in the 34 original bags, how many jellybeans of that specific color are in the new bag?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 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 $m$ and $n$ be positive integers sa... | math | {
"ground_truth": "407",
"style": "rule"
} | {
"answer": "407",
"index": 4323,
"question": "Let $m$ and $n$ be positive integers satisfying the conditions\n\n\n- $\\gcd(m+n,210) = 1,$\n- $m^m$ is a multiple of $n^n,$ and\n- $m$ is not a multiple of $n$ .\n\nFind the least possible value of $m+n$ .",
"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 According to national regulations, only adu... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"answer": "35",
"index": 4324,
"question": "According to national regulations, only adults aged between 18 and 70 are eligible to apply for a motor vehicle driver's license. A sixth-grade student, Li Ming, says, \"My dad has a driver's license. His age equals the product of the month and day of his birth, and that product is 2975.\" How old is Li Ming's father?",
"split": "train"
} |
cn_k12 | [
"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 The circle $x^2+y^2-4x+2y+c=0$ intersects w... | math | {
"ground_truth": "-11",
"style": "rule"
} | {
"answer": "-11",
"index": 4325,
"question": "The circle $x^2+y^2-4x+2y+c=0$ intersects with the y-axis at points A and B, with its center at point P. If $\\angle APB = 120^\\circ$, then the real number $c$ equals \\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Algebraic Expressions -> 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 expansion of \\((x+y+z)^{8}\\), find... | math | {
"ground_truth": "1792",
"style": "rule"
} | {
"answer": "1792",
"index": 4326,
"question": "In the expansion of \\((x+y+z)^{8}\\), find the sum of the coefficients for all terms of the form \\(x^{2} y^{a} z^{b}\\) where \\(a, b \\in \\mathbf{N}\\). Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"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 The average of 7 consecutive numbers a, b, ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 4327,
"question": "The average of 7 consecutive numbers a, b, c, d, e, f, and g is a certain value. The percent of g that is a is 50%. What is the average of these consecutive numbers?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 candy store, a salesperson placed 91 c... | math | {
"ground_truth": "46",
"style": "rule"
} | {
"answer": "46",
"index": 4328,
"question": "In a candy store, a salesperson placed 91 candies of several kinds in a row on the counter. It turned out that between any two candies of the same kind, there is an even number of candies. What is the minimum number of kinds of candies that could be?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Permutations"
] | 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 Six high-performing students from Class 1, ... | math | {
"ground_truth": "216",
"style": "rule"
} | {
"answer": "216",
"index": 4329,
"question": "Six high-performing students from Class 1, Grade 12 are lining up from left to right for a photo. The leftmost position can only be occupied by student A or B, and the rightmost position cannot be occupied by student A. Calculate the total number of different arrangements.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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 length of the chord intercepted on the ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 4330,
"question": "The length of the chord intercepted on the circle x^{2}+y^{2}-2x-4y=0 by the line x+2y-5+\\sqrt{5}=0 is to be calculated. Provide the exact length of the chord as a numerical value.",
"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 A positive integer is said to be a \"palind... | math | {
"ground_truth": "495000",
"style": "rule"
} | {
"answer": "495000",
"index": 4331,
"question": "A positive integer is said to be a \"palindrome\" if it reads the same from left to right as from right to left. For example, 2002 is a palindrome. Find the sum of all 4-digit palindromes.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 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 sum of the first $n$ terms o... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 4332,
"question": "Given that the sum of the first $n$ terms of a geometric sequence $\\{a\\_n\\}$ is $S\\_n$, if $S\\_2 = 2a\\_2 + 3$, $S\\_3 = 2a\\_3 + 3$, find the value of the common ratio $q$.",
"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 Vasya has thought of six natural numbers: \... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 4333,
"question": "Vasya has thought of six natural numbers: \\( a, b, c, d, e, f \\). For one ruble, it is possible to specify any two of them and find out their product. Petya knows that any two of the thought numbers are coprime (i.e., they have no common divisors greater than 1). For what minimum amount can he find out all the thought numbers?",
"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 For Halloween, Robin scored 23 pieces of ca... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"answer": "19",
"index": 4334,
"question": "For Halloween, Robin scored 23 pieces of candy. She ate 2/3 of the candy the first night, and then her sister gave her 50% more pieces of candy than she initially had. How many pieces of candy does Robin have now?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> 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 Consider the sequence \\( x_{0}, x_{1}, \\c... | math | {
"ground_truth": "-1001",
"style": "rule"
} | {
"answer": "-1001",
"index": 4335,
"question": "Consider the sequence \\( x_{0}, x_{1}, \\cdots, x_{2002} \\) which satisfies the conditions \\( x_{0} = 0 \\) and \\( \\left| x_{n} - x_{n-1} \\right| = 1 \\) for \\( n = 1, 2, \\cdots, 2002 \\). Find the minimum value of the expression \\( x_{1} + x_{2} + \\cdots + x_{2002} \\).",
"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 How many 5-digit numbers \\(\\overline{abcd... | math | {
"ground_truth": "330",
"style": "rule"
} | {
"answer": "330",
"index": 4336,
"question": "How many 5-digit numbers \\(\\overline{abcde}\\) exist such that digits \\(b\\) and \\(d\\) are each the sum of the digits to their immediate left and right? (That is, \\(b = a + c\\) and \\(d = c + e\\).)",
"split": "train"
} |
aops_forum | [
"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 Below is a diagram showing a $6 \\times 8$... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"answer": "48",
"index": 4337,
"question": "Below is a diagram showing a $6 \\times 8$ rectangle divided into four $6 \\times 2$ rectangles and one diagonal line. Find the total perimeter of the four shaded trapezoids.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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 circle C: $x^2+y^2-4x-6y+3=0$, and ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 4338,
"question": "Given a circle C: $x^2+y^2-4x-6y+3=0$, and a line $l: mx+2y-4m-10=0$ ($m\\in\\mathbb{R}$). When the chord cut by $l$ from $C$ is the shortest, find the value of $m$.",
"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 how many 3 - digit even numbers are possibl... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 4339,
"question": "how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 1 ?",
"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 In the sequence $\\{a_n\\}$, $a_{n+1} = ca_... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 4340,
"question": "In the sequence $\\{a_n\\}$, $a_{n+1} = ca_n$ (where $c$ is a non-zero constant), and the sum of the first $n$ terms is $S_n = 3^n + k$. Calculate the value of the real number $k$. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 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 From a collection of $5$ pairs of shoes, th... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"answer": "120",
"index": 4341,
"question": "From a collection of $5$ pairs of shoes, the number of ways to select $4$ individual shoes such that exactly $1$ pair is among them is ________.",
"split": "train"
} |
olympiads | [
"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 Find the minimum value of the function \\((... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 4342,
"question": "Find the minimum value of the function \\((\\sqrt{2} \\sin x - 3 \\tan y)^{2} + (\\sqrt{2} \\cos x - 3 \\cot y)^{2}\\), where \\(x, y \\in \\left(0, \\frac{\\pi}{2}\\right)\\).",
"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 In $\\triangle ABC$, the sides opposite to ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 4343,
"question": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. It is given that $\\cos A= \\frac {3}{5}$, $\\sin C=2\\cos B$, and $a=4$. Find the area of $\\triangle ABC$.",
"split": "train"
} |
amc_aime | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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 Circles $\\omega_1$ and $\\omega_2$ with ra... | math | {
"ground_truth": "672",
"style": "rule"
} | {
"answer": "672",
"index": 4344,
"question": "Circles $\\omega_1$ and $\\omega_2$ with radii $961$ and $625$, respectively, intersect at distinct points $A$ and $B$. A third circle $\\omega$ is externally tangent to both $\\omega_1$ and $\\omega_2$. Suppose line $AB$ intersects $\\omega$ at two points $P$ and $Q$ such that the measure of minor arc $\\widehat{PQ}$ is $120^{\\circ}$. Find the distance between the centers of $\\omega_1$ and $\\omega_2$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> 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 Let $x^{6}+x^{4}=a_{0}+a_{1}(x+2)+\\cdots +... | math | {
"ground_truth": "-168",
"style": "rule"
} | {
"answer": "-168",
"index": 4345,
"question": "Let $x^{6}+x^{4}=a_{0}+a_{1}(x+2)+\\cdots +a_{6}(x+2)^{6}$, then $a_{3}=$ ?",
"split": "train"
} |
big_math | [
"Mathematics -> 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 Given that point P is any point on the hype... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 4346,
"question": "Given that point P is any point on the hyperbola x^2/4 - y^2 = 1, and A, B are the left and right vertices of the hyperbola respectively, find the minimum value of PA * PB. Express your answer as a single number.",
"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 a race, the ratio of the speeds of two c... | math | {
"ground_truth": "900",
"style": "rule"
} | {
"answer": "900",
"index": 4347,
"question": "In a race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 200 m. A wins by 100 m. What is the total distance of the race?",
"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 **Text**: There are 4 intern teachers of di... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 4348,
"question": "**Text**: There are 4 intern teachers of different subjects to be assigned to three classes, with at least one teacher in each class. The number of different ways to assign them is \\_\\_\\_\\_\\_\\_\\_\\_.",
"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 For certain real values of $a, b, c,$ and... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"answer": "26",
"index": 4349,
"question": "For certain real values of $a, b, c,$ and $d,$ the equation $x^4+ax^3+bx^2+cx+d=0$ has four non-real roots. The product of two of these roots is $13+i$ and the sum of the other two roots is $3+4i,$ where $i=\\sqrt{-1}.$ Find $b.$ ",
"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 Given $(1-x)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+\\... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"answer": "64",
"index": 4350,
"question": "Given $(1-x)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+\\ldots+a_{n}x^{n}$, if $5a_{1}+2a_{2}=0$, then $a_{0}-a_{1}+a_{2}-a_{3}+\\ldots+(-1)^{n}a_{n}=$ \\_\\_\\_\\_\\_\\_.",
"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 Find the smallest positive integer \\( n \\... | math | {
"ground_truth": "337",
"style": "rule"
} | {
"answer": "337",
"index": 4351,
"question": "Find the smallest positive integer \\( n \\) such that the mean of the squares of the first \\( n \\) natural numbers (\\( n > 1 \\)) is an integer.\n\n(Note: The mean of the squares of \\( n \\) numbers \\( a_1, a_2, \\cdots, a_n \\) is given by \\( \\sqrt{\\frac{a_{1}^2 + a_{2}^2 + \\cdots + a_{n}^2}{n}} \\).)\n\n(Note: Fifteenth American Mathematical Olympiad, 1986)",
"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 At their respective rates, pump A can fulfi... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 4352,
"question": "At their respective rates, pump A can fulfill an empty tank, or pump-out the full tank in some hours. Pumps B and C can do the same in 3 and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, the tank will be empty in 0.75 hours. How many hours does it take for pump A to fulfill or pump-out the full tank?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 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 smallest number that must be ad... | math | {
"ground_truth": "176525",
"style": "rule"
} | {
"answer": "176525",
"index": 4353,
"question": "What is the smallest number that must be added to 956734 to make it exactly divisible by a combination of prime numbers, such as the product of 751 and 503?",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> 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 What is the minimum number of cells that ne... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 4354,
"question": "What is the minimum number of cells that need to be coloured in a 5x5 square grid so that every 1x4 or 4x1 rectangle in the grid has at least one coloured cell? Express your answer as a single integer.",
"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 In a right-angled triangle \\(ABC\\) (with ... | math | {
"ground_truth": "400",
"style": "rule"
} | {
"answer": "400",
"index": 4355,
"question": "In a right-angled triangle \\(ABC\\) (with right angle at \\(A\\)), the bisectors of the acute angles intersect at point \\(P\\). The distance from \\(P\\) to the hypotenuse is \\(\\sqrt{80000}\\). What is the distance from \\(P\\) to \\(A\\)?",
"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 Juvy has a garden that is divided into 60 e... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 4356,
"question": "Juvy has a garden that is divided into 60 equally spaced rows with 18 plants in each row. She plants parsley in 3/5 of the rows, rosemary in 1/4 of the rows, mint in 1/6 of the remaining rows, thyme in 7/12 of the remaining rows after mint, and basil in 2/3 of the remaining rows after thyme. The rest of the rows will be planted with chives. How many chives will Juvy plant?",
"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 Consider four parallel lines on the plane. ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 4357,
"question": "Consider four parallel lines on the plane. Let these be $a, b, c,$ and $d$ in order. It is known that the distance between $a$ and $b$ is 1, the distance between $b$ and $c$ is 3, and the distance between $c$ and $d$ is also 1. Consider all rectangles with vertices lying on exactly one of these lines. How can we obtain the rectangle with the smallest possible area, and what is this area?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series -> 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 sequence of numbers: 1, -5, 9, -13,... | math | {
"ground_truth": "-21",
"style": "rule"
} | {
"answer": "-21",
"index": 4358,
"question": "Given a sequence of numbers: 1, -5, 9, -13, 17, ..., according to its pattern, the next number should be ______.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Quadratic 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 Given the quadratic equation $x(kx+1)-x^{2}... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 4359,
"question": "Given the quadratic equation $x(kx+1)-x^{2}+3=0$, find the largest integer value of $k$ for which the equation has real roots.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> 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 the original arrangement \"abcd\", ho... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 4360,
"question": "Given the original arrangement \"abcd\", how many different rearrangements are there such that no two originally adjacent letters are adjacent in the new arrangement? Express your answer as a whole number.",
"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 At the store opening, Larry's grocery had 5... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 4361,
"question": "At the store opening, Larry's grocery had 50 lemons and 60 oranges. By closing, the store had some lemons and 40 oranges left. The ratio of lemons to oranges decreased by approximately 40% from opening to closing. How many lemons were left at the store closing?",
"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 \\( a \\) and \\( b \\) are positive intege... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 4362,
"question": "\\( a \\) and \\( b \\) are positive integers. After rounding to three decimal places, the expression \\(\\frac{a}{5} + \\frac{b}{7} = 1.51\\). Find \\( a + b \\).",
"split": "train"
} |
aops_forum | [
"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 Consider $9$ points in space, no four of ... | math | {
"ground_truth": " 33 ",
"style": "rule"
} | {
"answer": " 33 ",
"index": 4363,
"question": "Consider $9$ points in space, no four of which are coplanar. Each pair of points is joined by an edge (that is, a line segment) and each edge is either colored blue or red or left uncolored. Find the smallest value of $\\,n\\,$ such that whenever exactly $\\,n\\,$ edges are colored, the set of colored edges necessarily contains a triangle all of whose edges have the same color.",
"split": "train"
} |
omnimath | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 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 All subscripts in this problem are to be co... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 4364,
"question": "All subscripts in this problem are to be considered modulo 6 , that means for example that $\\omega_{7}$ is the same as $\\omega_{1}$. Let $\\omega_{1}, \\ldots \\omega_{6}$ be circles of radius $r$, whose centers lie on a regular hexagon of side length 1 . Let $P_{i}$ be the intersection of $\\omega_{i}$ and $\\omega_{i+1}$ that lies further from the center of the hexagon, for $i=1, \\ldots 6$. Let $Q_{i}, i=1 \\ldots 6$, lie on $\\omega_{i}$ such that $Q_{i}, P_{i}, Q_{i+1}$ are colinear. Find the number of possible values of $r$.",
"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 Let \\(\\mathcal{P}\\) be a regular 17-gon.... | math | {
"ground_truth": "544",
"style": "rule"
} | {
"answer": "544",
"index": 4365,
"question": "Let \\(\\mathcal{P}\\) be a regular 17-gon. We draw in the \\(\\binom{17}{2}\\) diagonals and sides of \\(\\mathcal{P}\\) and paint each side or diagonal one of eight different colors. Suppose that there is no triangle (with vertices among vertices of \\(\\mathcal{P}\\)) whose three edges all have the same color. What is the maximum possible number of triangles, all of whose edges have different colors?",
"split": "train"
} |
big_math | [
"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 Consider the functions \\( y = A x^{2} \\) ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 4366,
"question": "Consider the functions \\( y = A x^{2} \\) and \\( y^{2} + 3 = x^{2} + 4 y \\), where \\( A \\) is a positive constant and \\( x \\) and \\( y \\) are real variables. Determine the number of intersection points of these two curves. Express your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> 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 \\( 75^{x}=0.75^{y}=10^{-2} \\), calc... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 4367,
"question": "Given \\( 75^{x}=0.75^{y}=10^{-2} \\), calculate \\( \\frac{1}{x}-\\frac{1}{y} \\). Express your answer as a single number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> 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 parabola is defined by the equation $C:y^... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 4368,
"question": "A parabola is defined by the equation $C:y^{2}=8x$, with a focus at point $F$ and a directrix intersecting the $x$-axis at point $K$. Point $A$ lies on the parabola and satisfies the condition $|AK|=\\sqrt{2}|AF|$. Determine the area of $\\triangle AFK$.",
"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 Maxwell leaves his home and walks toward Br... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 4369,
"question": "Maxwell leaves his home and walks toward Brad's house at 4 km/h. One hour later, Brad leaves his home and runs toward Maxwell's house at a certain speed. The distance between their homes is 14 kilometers. It takes Maxwell 2 hours before he meets up with Brad. What is Brad's running speed?",
"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 that the sequence $\\{a_n\\}$ satisfi... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 4370,
"question": "Given that the sequence $\\{a_n\\}$ satisfies $\\frac{1}{a_{n+1}} - \\frac{1}{a_n} = d (n \\in \\mathbb{N}^*, d$ is a constant$)$, it is called a harmonic sequence. It is known that the positive term sequence $\\{\\frac{1}{b_n}\\}$ is a harmonic sequence, and $b_1 + b_2 + b_3 +... + b_9 = 90$. Calculate the value of $b_4 + b_6$. Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 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 cube is divided into 216 identical cubele... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"answer": "96",
"index": 4371,
"question": "A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of the cube. The cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one color?",
"split": "train"
} |
olympiads | [
"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 With square tiles of a side length of an ex... | math | {
"ground_truth": "2016",
"style": "rule"
} | {
"answer": "2016",
"index": 4372,
"question": "With square tiles of a side length of an exact number of units, a room with a surface area of 18,144 square units has been tiled in the following manner: on the first day one tile was placed, the second day two tiles, the third day three tiles, and so on. How many tiles were necessary?",
"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 line $l_{1}: 4x-3y+6=0$ and line $l_{... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 4373,
"question": "Given line $l_{1}: 4x-3y+6=0$ and line $l_{2}: x=0$, the minimum sum of distances from a moving point $P$ on the parabola $y^{2}=4x$ to lines $l_{1}$ and $l_{2}$ is __________.",
"split": "train"
} |
aops_forum | [
"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 Evaluate the product $$ \\prod_{n=3}^{\\in... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 4374,
"question": "Evaluate the product $$ \\prod_{n=3}^{\\infty} \\frac{(n^3+3n)^2}{n^6-64}. $$",
"split": "train"
} |
big_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 In a reservoir, there are 10 floodgates des... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 4375,
"question": "In a reservoir, there are 10 floodgates designed for discharging excess water. The water level in the reservoir has already surpassed the safe level and continues to increase at a constant rate. To prevent flooding, it is necessary to adjust the discharge rate. Assuming each floodgate discharges water at the same rate, calculations show that opening one floodgate will bring the water level back to the safe line after 30 hours; opening two floodgates simultaneously will achieve this in 10 hours. Based on the flood control situation, it is required to reduce the water level to below the safety line within 3 hours. Calculate the minimum number of floodgates that must be opened simultaneously to achieve this.",
"split": "train"
} |
olympiads | [
"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 Find the value of the function \\( f(x) \\)... | math | {
"ground_truth": "1499001",
"style": "rule"
} | {
"answer": "1499001",
"index": 4376,
"question": "Find the value of the function \\( f(x) \\) at the point \\( x_{0}=2000 \\), given \\( f(0)=1 \\) and for any \\( x \\) the equality \\( f(x+4)=f(x)+3x+4 \\) holds.",
"split": "train"
} |
orca_math | [
"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 If some number times a equals 7 b, and both... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 4377,
"question": "If some number times a equals 7 b, and both are equal to 20, then 84 ab = 800. What is the number that, when multiplied by a, equals 7 b?",
"split": "train"
} |
big_math | [
"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 the sequence $\\{n(n+4)\\left(\\frac{... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 4378,
"question": "Given the sequence $\\{n(n+4)\\left(\\frac{2}{3}\\right)^{n}\\}$, find the value of $k$ for which the $k$-th term is the largest. Express your answer as a single integer.",
"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 An apartment building consists of 20 rooms ... | math | {
"ground_truth": "257",
"style": "rule"
} | {
"answer": "257",
"index": 4379,
"question": "An apartment building consists of 20 rooms numbered \\(1, 2, \\ldots, 20\\) arranged clockwise in a circle. To move from one room to another, one can either walk to the next room clockwise (i.e. from room \\(i\\) to room \\((i+1) \\mod 20\\)) or walk across the center to the opposite room (i.e. from room \\(i\\) to room \\((i+10) \\mod 20\\)). Find the number of ways to move from room 10 to room 20 without visiting the same room twice.",
"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 For the walls of the house, John would use ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 4380,
"question": "For the walls of the house, John would use 12 large planks of wood and 10 small planks. If large planks together need 15 pieces of nails to be secured and small planks together need 5 nails, how many nails does John need for the house wall?",
"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 Five points are located on a line. When the... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 4381,
"question": "Five points are located on a line. When the ten distances between pairs of points are listed from smallest to largest, the list reads: 2, 4, 5, 7, 8, k, 13, 15, 17, 19. Calculate the value of the missing distance k.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 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 Consider the set \\( S = \\{1, 2, 3, \\cdot... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 4382,
"question": "Consider the set \\( S = \\{1, 2, 3, \\cdots, 2010, 2011\\} \\). A subset \\( T \\) of \\( S \\) is said to be a \\( k \\)-element RP-subset if \\( T \\) has exactly \\( k \\) elements and every pair of elements of \\( T \\) are relatively prime. Find the smallest positive integer \\( k \\) such that every \\( k \\)-element RP-subset of \\( S \\) contains at least one prime number.",
"split": "train"
} |
aops_forum | [
"Mathematics -> 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 Let $u, v$ be real numbers. The minimum v... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"answer": "80",
"index": 4383,
"question": "Let $u, v$ be real numbers. The minimum value of $\\sqrt{u^2+v^2} +\\sqrt{(u-1)^2+v^2}+\\sqrt {u^2+ (v-1)^2}+ \\sqrt{(u-1)^2+(v-1)^2}$ can be written as $\\sqrt{n}$ . Find the value of $10n$ .",
"split": "train"
} |
cn_k12 | [
"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 If $a$, $b$, $c$, and $d$ are positive numb... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 4384,
"question": "If $a$, $b$, $c$, and $d$ are positive numbers, and it is given that $a+b+c+d=4$, let $M$ represent the maximum among $a+b+c$, $a+b+d$, $a+c+d$, and $b+c+d$. Find the minimum value of $M$.",
"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 $S$ be the set of all 3-digit numbers w... | math | {
"ground_truth": "127",
"style": "rule"
} | {
"answer": "127",
"index": 4385,
"question": "Let $S$ be the set of all 3-digit numbers with all digits in the set $\\{1,2,3,4,5,6,7\\}$ (so in particular, all three digits are nonzero). For how many elements $\\overline{a b c}$ of $S$ is it true that at least one of the (not necessarily distinct) 'digit cycles' $\\overline{a b c}, \\overline{b c a}, \\overline{c a b}$ is divisible by 7? (Here, $\\overline{a b c}$ denotes the number whose base 10 digits are $a, b$, and $c$ in that order.)",
"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 Katie loves to travel. On her birthday, she... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"answer": "104",
"index": 4386,
"question": "Katie loves to travel. On her birthday, she decided to go on a trip on a mysterious continent. Her first destination was in an island of statues which is 436 miles from her place. She took a plane that made some stopovers, the 2nd stopover after covering 236 miles. The island is 68 miles farther from the 2nd stopover. How far was the 1st stopover from her place?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles",
"Mathematics -> Discrete Mathematics -> Combinatorics -> Counting Methods"
] | 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 Points R, S, and T are vertices of an equil... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 4387,
"question": "Points R, S, and T are vertices of an equilateral triangle, and points X, Y, and Z are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices? Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"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 Given $\\sin \\alpha - \\cos \\alpha = -\\f... | math | {
"ground_truth": "-8",
"style": "rule"
} | {
"answer": "-8",
"index": 4388,
"question": "Given $\\sin \\alpha - \\cos \\alpha = -\\frac{\\sqrt{5}}{2}$, calculate the value of $\\tan \\alpha + \\frac{1}{\\tan \\alpha}$. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Combinations"
] | 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 five pairs of boots, each with differe... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"answer": "120",
"index": 4389,
"question": "From five pairs of boots, each with different numbers, find the number of ways to pick exactly four boots such that exactly one pair is included.",
"split": "train"
} |
aops_forum | [
"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 Let $M= \\{ 1, 2, \\cdots, 19 \\}$ and $... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 4390,
"question": "Let $M= \\{ 1, 2, \\cdots, 19 \\}$ and $A = \\{ a_{1}, a_{2}, \\cdots, a_{k}\\}\\subseteq M$ . Find the least $k$ so that for any $b \\in M$ , there exist $a_{i}, a_{j}\\in A$ , satisfying $b=a_{i}$ or $b=a_{i}\\pm a_{i}$ ( $a_{i}$ and $a_{j}$ do not have to be different) .",
"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 A school table tennis championship was held... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 4391,
"question": "A school table tennis championship was held using the Olympic system. The winner won 6 matches. How many participants in the championship won more matches than they lost? (In the first round of the championship, conducted using the Olympic system, participants are divided into pairs. Those who lost the first match are eliminated from the championship, and those who won in the first round are again divided into pairs for the second round. The losers are again eliminated, and winners are divided into pairs for the third round, and so on, until one champion remains. It is known that in each round of our championship, every participant had a pair.)",
"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 A bank teller has some stacks of bills. The... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 4392,
"question": "A bank teller has some stacks of bills. The total value of the bills in each stack is $1000. Every stack contains at least one $20 bill, at least one $50 bill, and no other types of bills. If no two stacks have the same number of $20 bills, what is the maximum possible number of stacks that the teller could have? Provide your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 What is the least number n such that any se... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 4393,
"question": "What is the least number n such that any set with n elements contains a subset of six elements whose sum is divisible by 6? Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> 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 the sum of all possible distinct two-d... | math | {
"ground_truth": "1375",
"style": "rule"
} | {
"answer": "1375",
"index": 4394,
"question": "Find the sum of all possible distinct two-digit numbers, all of whose digits are odd.",
"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 Mom made 32 chocolate chip cookies. It took... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 4395,
"question": "Mom made 32 chocolate chip cookies. It took 24 minutes to mix the ingredients and some time to bake. Julie and Matt ate 9 cookies after dinner. There were 23 cookies left. How many minutes did it take to bake the cookies?",
"split": "train"
} |
orca_math | [
"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 The area of a square is added to one of its... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 4396,
"question": "The area of a square is added to one of its sides, and the perimeter is then subtracted from this total. The result is 4. What is the area of the square if the length of one side is 4?",
"split": "train"
} |
aops_forum | [
"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 At a university dinner, there are 2017 math... | math | {
"ground_truth": "127009",
"style": "rule"
} | {
"answer": "127009",
"index": 4397,
"question": "At a university dinner, there are 2017 mathematicians who each order two distinct entrées, with no two mathematicians ordering the same pair of entrées. The cost of each entrée is equal to the number of mathematicians who ordered it, and the university pays for each mathematician's less expensive entrée (ties broken arbitrarily). Over all possible sets of orders, what is the maximum total amount the university could have paid?",
"split": "train"
} |
big_math | [
"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 Given the parabola y^2 = 2px (p > 0) and it... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 4398,
"question": "Given the parabola y^2 = 2px (p > 0) and its focus F, the minimum distance from any point P on the parabola to F is 1. Points A and B on the parabola satisfy |AF| + |BF| = 6. Find the distance from the midpoint of segment AB to the y-axis. Express your answer as a single number.",
"split": "train"
} |
aops_forum | [
"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 The cells of a $100 \\times 100$ table ar... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 4399,
"question": "The cells of a $100 \\times 100$ table are colored white. In one move, it is allowed to select some $99$ cells from the same row or column and recolor each of them with the opposite color. What is the smallest number of moves needed to get a table with a chessboard coloring?",
"split": "train"
} |
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