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 |
|---|---|---|---|---|---|---|---|
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 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 two circles with equations $x^{2}+y^{... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 18900,
"question": "Given two circles with equations $x^{2}+y^{2}=1$ and $x^{2}+y^{2}-4x+2y-4=0$, determine the number of common tangent lines between them. Express your answer as a single numerical value.",
"split": "train"
} |
omnimath | [
"Mathematics -> Number Theory -> Divisor Functions"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the number of positive integers less t... | math | {
"ground_truth": "247548",
"style": "rule"
} | {
"answer": "247548",
"index": 18901,
"question": "Find the number of positive integers less than 1000000 which are less than or equal to the sum of their proper divisors. If your answer is $X$ and the actual value is $Y$, your score will be $\\max \\left(0,20-80\\left|1-\\frac{X}{Y}\\right|\\right)$ rounded to the nearest integer.",
"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 Find the number of integer solutions that s... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18902,
"question": "Find the number of integer solutions that satisfy the inequality \\(x - 1 < (x - 1)^2 < 3x + 7\\). Express your answer as a single integer.",
"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 Find the amount in 2 years, with the rate o... | math | {
"ground_truth": "6160",
"style": "rule"
} | {
"answer": "6160",
"index": 18903,
"question": "Find the amount in 2 years, with the rate of interest being 10% for the first year and 12% for the second year, if the initial amount is Rs. 6160. What was the initial amount?",
"split": "train"
} |
olympiads | [
"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 A company has $n$ employees. It is known th... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 18904,
"question": "A company has $n$ employees. It is known that for every pair of these $n$ employees, it can be guaranteed that there are at least three days in a week when one of the employees is working while the other is not (these days do not necessarily involve the same employee working, and employees may choose not to work at all during the week). Determine the maximum value of $n$.",
"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 Kevin holds the world record for eating the... | math | {
"ground_truth": "58",
"style": "rule"
} | {
"answer": "58",
"index": 18905,
"question": "Kevin holds the world record for eating the biggest quantity of hot wings in 8 minutes by consuming 64 wings without stopping. Alan, a boy who loves hot wings, wants to beat Kevin's record. He is currently able to eat 5 hot wings per minute. However, due to fatigue, his eating rate decreases by 0.5 hot wings per minute, every minute. \n\nLisa, a third competitor, eats hot wings at a varying rate. For the first 4 minutes, she eats 7 hot wings per minute, but then she doubles her eating rate for the remaining 4 minutes. \n\nConsidering Alan's decreasing eating rate and Lisa's varying eating rate, how many additional wings has Alan to eat in the first minute to beat both Kevin's and Lisa's records?",
"split": "train"
} |
big_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 What is the smallest result that can be obt... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18906,
"question": "What is the smallest result that can be obtained by choosing three different numbers from the set {3,5,7,11,13,17}, adding two of these numbers, and then multiplying their sum by the third number? Express your answer as a single integer.",
"split": "train"
} |
big_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 Given the odd function f(x) that satisfies ... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 18907,
"question": "Given the odd function f(x) that satisfies f(x+2) = -f(x) and f(x) = 3^x + 1/2 for x in (0, 1), find the exact value of f(log_3 54). Express your answer as a single number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Analysis -> Sequences and Series"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a sequence $\\{a_n\\}$ that satisfies... | math | {
"ground_truth": "2018",
"style": "rule"
} | {
"answer": "2018",
"index": 18908,
"question": "Given a sequence $\\{a_n\\}$ that satisfies $a_0= \\frac{1}{2}$ and $a_{n+1}=a_n+ \\frac{a_n^2}{2018}$ for $n=0,1,2,\\ldots$, if $a_k < 1 < a_{k+1}$, what is the value of the positive integer $k$?",
"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 group of people, 40% of the total numb... | math | {
"ground_truth": "1200",
"style": "rule"
} | {
"answer": "1200",
"index": 18909,
"question": "In a group of people, 40% of the total number of people plus 60 more people constitutes the number of people wearing a specific type of hat. If 25% of the total number of people are wearing shoes of a specific brand, find the difference between the number of people wearing that specific type of hat and those wearing the specific brand of shoes, given that the number of people wearing both the hat and the shoes is 20% of the total population size. What is the total number of people in the group?",
"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 A certain meter records voltage between som... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18910,
"question": "A certain meter records voltage between some range. The average value of 3 recordings on the meter was 4 volts, and the smallest possible recording was 2 volts. What is the range of voltage the meter can record?",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are two different numbers: A and B. F... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18911,
"question": "There are two different numbers: A and B. Find A from the two-digit addition formula of A7+3B=73.",
"split": "train"
} |
math | [
"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 Let $S_i$ be the set of all integers $n$ su... | math | {
"ground_truth": "708",
"style": "rule"
} | {
"answer": "708",
"index": 18912,
"question": "Let $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$. For example, $S_4$ is the set ${400,401,402,\\ldots,499}$. How many of the sets $S_0, S_1, S_2, \\ldots, S_{999}$ do not contain a perfect square?",
"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 Write the digits from 0 to 9 in a line, in ... | math | {
"ground_truth": "494",
"style": "rule"
} | {
"answer": "494",
"index": 18913,
"question": "Write the digits from 0 to 9 in a line, in any order you choose. On the line below, combine the neighboring digits to form nine new numbers, and sum these numbers. What is the maximum sum that can be obtained in this way? Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the greatest number which leaves the s... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 18914,
"question": "Find the greatest number which leaves the same remainder when it divides 1260, 2310, 30030, and 72930, which are all divisible by the first five prime numbers (2, 3, 5, 7, and 11) and their respective combinations.",
"split": "train"
} |
olympiads | [
"Mathematics -> Calculus -> Multivariable Calculus -> Limits"
] | 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 limit of the function \\( f(x, y) ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 18915,
"question": "Find the limit of the function \\( f(x, y) = (x^2 + y^2)^2 x^2 y^2 \\) as \\( x \\rightarrow 0 \\) and \\( y \\rightarrow 0 \\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> 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 There are 4 pairs of different gloves. If 4... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"answer": "54",
"index": 18916,
"question": "There are 4 pairs of different gloves. If 4 gloves are randomly selected, the number of ways to select such that at least two of them form a pair is ______. (Answer with a number)",
"split": "train"
} |
big_math | [
"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 Eight classes in the first year of high sch... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18917,
"question": "Eight classes in the first year of high school negotiate to form a grade basketball team, which needs a total of 10 players. Each class must contribute at least 1 player. Calculate the total number of different composition methods to form the basketball team.",
"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 In a basketball season, John has a varying ... | math | {
"ground_truth": "155",
"style": "rule"
} | {
"answer": "155",
"index": 18918,
"question": "In a basketball season, John has a varying success rate for hitting his free throws. In 20% of the games, he hits 60% of his free throws, in another 50% of the games, he hits 70% of his free throws, and in the remaining 30% of the games, he hits 80% of his free throws. Additionally, the number of fouls he gets each game also varies. In 40% of the games, he gets 4 fouls, in 35% of the games, he gets 5 fouls, and in 25% of the games, he gets 6 fouls. In each foul, he gets 2 shots. Out of 20 games the team plays, John plays in 80% of them. Calculate the total number of free throws John gets in the season, considering the varying percentages and the number of fouls he gets in each game.",
"split": "train"
} |
cn_k12 | [
"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 The digit in the 60th position after the de... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18919,
"question": "The digit in the 60th position after the decimal point in the repeating decimal $6.2\\overset{\\cdot}{4}5\\overset{\\cdot}{3}$ 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 Worker A takes some hours to do a job. Work... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18920,
"question": "Worker A takes some hours to do a job. Worker B takes 10 hours to do the same job. Working together but independently, they can do the same job in 2.857142857142857 hours. How long does it take for Worker A to do the job alone?",
"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 A product was introduced into a shopping ma... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 18921,
"question": "A product was introduced into a shopping mall for sale. In the first year, the mall did not charge a management fee, so the product was priced at 70 yuan per piece, with an annual sales volume of 11.8 thousand pieces. Starting from the second year, the mall charged a management fee of x% of the sales amount (i.e., for every 100 yuan of sales, x yuan was charged as a fee). As a result, the price per piece of the product increased by 70 * x% / (1 - x%) yuan compared to the first year, and the expected annual sales volume decreased by x thousand pieces. Find the maximum value of x such that the management fee collected by the mall from this product in the second year is not less than 140,000 yuan.",
"split": "train"
} |
olympiads | [
"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 On the coordinate plane, there are \\( T \\... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"answer": "25",
"index": 18922,
"question": "On the coordinate plane, there are \\( T \\) points \\((x, y)\\), where \\( x, y \\) are integers, satisfying \\( x^{2} + y^{2} < 10 \\). Find the value of \\( T \\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Positive integers $a$ and $b$ satisfy $1 < ... | math | {
"ground_truth": "4031",
"style": "rule"
} | {
"answer": "4031",
"index": 18923,
"question": "Positive integers $a$ and $b$ satisfy $1 < a < b$. If the system of equations about $x$ and $y$, $$ \\begin{cases} y=-2x+4033 \\\\ y=|x-1|+|x+a|+|x-b| \\end{cases} $$ has exactly one solution, then the maximum value of $a$ is $\\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Functions -> 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 that \\( y = f(x) + x^3 \\) is an eve... | math | {
"ground_truth": "-5",
"style": "rule"
} | {
"answer": "-5",
"index": 18924,
"question": "Given that \\( y = f(x) + x^3 \\) is an even function and \\( f(10) = 10 \\). If the function \\( g(x) = f(x) + 5 \\), find the value of \\( g(-10) \\).",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Intermediate Algebra -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $a = \\sqrt[3]{5 + 2 \\sqrt{13}}$ and $... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 18925,
"question": "Let $a = \\sqrt[3]{5 + 2 \\sqrt{13}}$ and $b = \\sqrt[3]{5 - 2 \\sqrt{13}}$. Calculate the value of $a + b$. Express your answer as a single number.",
"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 Anne, Bronwyn, and Carl ran a race at const... | math | {
"ground_truth": "165",
"style": "rule"
} | {
"answer": "165",
"index": 18926,
"question": "Anne, Bronwyn, and Carl ran a race at constant speeds. When Anne finished, Bronwyn had 15 meters left to run and Carl had 35 meters left to run. When Bronwyn finished, Carl had 22 meters left to run. Calculate the length of the race in meters.",
"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 In the expansion of $\\left(x-\\frac{1}{x}-... | math | {
"ground_truth": "-5",
"style": "rule"
} | {
"answer": "-5",
"index": 18927,
"question": "In the expansion of $\\left(x-\\frac{1}{x}-1\\right)^4$, the constant term is ______.",
"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 A middle school plans to use 4 monographs a... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18928,
"question": "A middle school plans to use 4 monographs as elective courses for the \"Mathematical Culture\" curriculum in high school. It is required to choose at least one monograph each academic year, and all 4 courses must be completed in three years. Calculate the different elective ways for Xiaonan. Express your answer as a single integer.",
"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 Place six balls numbered 1, 2, 3, 4, 5, 6 i... | math | {
"ground_truth": "135",
"style": "rule"
} | {
"answer": "135",
"index": 18929,
"question": "Place six balls numbered 1, 2, 3, 4, 5, 6 into six boxes also numbered 1, 2, 3, 4, 5, 6, with the requirement that each box contains one ball and exactly two balls have the same number as their boxes. Find the number of ways to place the balls. Express your answer as a numerical value.",
"split": "train"
} |
big_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 Given the alternating series \\( S_n = 1 - ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 18930,
"question": "Given the alternating series \\( S_n = 1 - 2 + 3 - 4 + \\cdots + (-1)^{n-1}n \\), calculate the sum \\( S_{17} + S_{33} + S_{50} \\). Express your answer as a single integer.",
"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 If a square is divided into parts by three ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 18931,
"question": "If a square is divided into parts by three lines, there is always a polygon among the resulting parts whose diameter is not less than $\\sqrt{13}$. What is the minimum side length of the square? (The diameter of a polygon is the distance between its two farthest vertices.)",
"split": "train"
} |
orca_math | [
"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 Find the simple interest on a certain amoun... | math | {
"ground_truth": "2000",
"style": "rule"
} | {
"answer": "2000",
"index": 18932,
"question": "Find the simple interest on a certain amount at 25/4% per annum for the period from 4th Feb 2005 to 18th April 2005, if the interest earned is Rs. 25. What is the principal amount?",
"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 Given any \\( n \\) points \\( p_{1}, p_{2}... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 18933,
"question": "Given any \\( n \\) points \\( p_{1}, p_{2}, \\cdots, p_{n} \\) in a plane, where no three points are collinear, each point \\( p_{i} \\) (for \\( 1 \\leqslant i \\leqslant n \\)) is colored either red or blue. Let \\( S \\) be the set of triangles with vertices \\(\\{ p_{1}, p_{2}, \\cdots, p_{n} \\} \\) such that for any two line segments \\( p_{i}p_{j} \\) and \\( p_{u}p_{v} \\), the number of triangles in \\( S \\) having \\( p_{i}p_{j} \\) as a side is the same as the number of triangles having \\( p_{u}p_{v} \\) as a side. Find the minimum value of \\( n \\) such that \\( S \\) always contains at least two triangles, each with vertices of the same color.",
"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 Mac is trying to fill 2012 barrels with app... | math | {
"ground_truth": "46",
"style": "rule"
} | {
"answer": "46",
"index": 18934,
"question": "Mac is trying to fill 2012 barrels with apple cider. He starts with 0 energy. Every minute, he may rest, gaining 1 energy, or if he has \\( n \\) energy, he may expend \\( k \\) energy \\((0 \\leq k \\leq n)\\) to fill up to \\( n(k+1) \\) barrels with cider. What is the minimal number of minutes he needs to fill all the barrels?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied 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 $S=\\{1,2,\\dots,3000\\}$ . Determine ... | math | {
"ground_truth": "6000000",
"style": "rule"
} | {
"answer": "6000000",
"index": 18935,
"question": "Let $S=\\{1,2,\\dots,3000\\}$ . Determine the maximum possible integer $X$ that satisfies the condition:\nFor all bijective function $f:S\\rightarrow S$ , there exists bijective function $g:S\\rightarrow S$ such that $$ \\displaystyle\\sum_{k=1}^{3000}\\left(\\max\\{f(f(k)),f(g(k)),g(f(k)),g(g(k))\\}-\\min\\{f(f(k)),f(g(k)),g(f(k)),g(g(k))\\}\\right)\\geq X $$ ",
"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 Arthur baked 115 muffins. James baked 12.5 ... | math | {
"ground_truth": "1438",
"style": "rule"
} | {
"answer": "1438",
"index": 18936,
"question": "Arthur baked 115 muffins. James baked 12.5 times as many. James baked _____ muffins.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n From 7 different pots of flowers, 5 are to ... | math | {
"ground_truth": "1800",
"style": "rule"
} | {
"answer": "1800",
"index": 18937,
"question": "From 7 different pots of flowers, 5 are to be selected and placed in front of the podium. Among them, two pots are not allowed to be placed in the very center. How many different arrangements are there? (Answer with a number).",
"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 Kiana has two older twin brothers. The prod... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 18938,
"question": "Kiana has two older twin brothers. The product of their three ages is 128. Find the sum of their three ages. Express your answer as a whole number.",
"split": "train"
} |
big_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 Find the number of monomials that satisfy t... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 18939,
"question": "Find the number of monomials that satisfy the following conditions simultaneously: (1) contains the letters x, y, z; (2) coefficient is -3; (3) degree is 5. Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Other",
"Mathematics -> Trigonometry -> Trigonometric Functions -> 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 three angles \\( x, y, z \\) form an ari... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 18940,
"question": "If three angles \\( x, y, z \\) form an arithmetic sequence with a common difference of \\( \\frac{\\pi}{3} \\), then \\( \\tan x \\tan y + \\tan y \\tan z + \\tan z \\tan x = \\) ",
"split": "train"
} |
cn_k12 | [
"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 Given that vectors $a$ and $b$ are not coll... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 18941,
"question": "Given that vectors $a$ and $b$ are not collinear, let vector $c=3a-2b$, $d=-2a+4b$, $e=-4a$, if $e=λc$, then the value of the real number $λ$ is _______.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let the sequence \\\\(\\{a_n\\}\\) have a s... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"answer": "17",
"index": 18942,
"question": "Let the sequence \\\\(\\{a_n\\}\\) have a sum of the first \\\\(n\\\\) terms denoted by \\\\(S_n\\\\), with \\\\(a_1=2\\\\), and \\\\(a_{n+1}=a_{n+1}a_n+1\\\\). Find the value of \\\\(S_{31}\\\\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the function $f(x)$ defined on $... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18943,
"question": "Given that the function $f(x)$ defined on $\\mathbb{R}$ is an odd function and satisfies $f(\\frac{3}{2}-x)=f(x),f(-2)=-3,$ and the sequence ${ {a_{n}} }$ satisfies ${{a_{1}}}=-1$, and $\\frac{{{S_{n}}}}{n}=2\\times \\frac{{{a_{n}}}}{n}+1$ (where ${{S_{{n}}}}$ is the sum of the first $n$ terms of ${ {a_{n}} }$), find $f({a_{5}})+f({a_{6}})=$\\_\\_\\_\\_\\_\\_\\_\\_.",
"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 Yanna bought 60 apples. She gave away 40% o... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 18944,
"question": "Yanna bought 60 apples. She gave away 40% of the apples to Zenny. After that, she gave 25% of the remaining apples to Andrea. Finally, she distributed half of the remaining apples among her three friends equally. How many apples did she keep?",
"split": "train"
} |
big_math | [
"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 Find the last three digits of the product \... | math | {
"ground_truth": "375",
"style": "rule"
} | {
"answer": "375",
"index": 18945,
"question": "Find the last three digits of the product \\(1 \\times 3 \\times 5 \\times 7 \\times \\cdots \\times 1997 \\times 1999 \\times 2001 \\times 2003 \\times 2005\\). Express your answer as a three-digit number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a triangle \\( \\triangle ABC \\) wit... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18946,
"question": "Given a triangle \\( \\triangle ABC \\) with \\( BC=a \\), \\( AC=b \\), and \\( AB=c \\), if \\( \\angle A + \\angle C = 2 \\angle B \\), find the largest positive integer \\( n \\) such that \\( a^n + c^n \\leq 2b^n \\) holds for any such triangle.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> 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 Using the digits 1, 2, and 3, form a four-d... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 18947,
"question": "Using the digits 1, 2, and 3, form a four-digit number with the condition that all three digits must be used and identical digits cannot be adjacent. How many such four-digit numbers can be formed? Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a military exercise, there is a defensiv... | math | {
"ground_truth": "69600",
"style": "rule"
} | {
"answer": "69600",
"index": 18948,
"question": "In a military exercise, there is a defensive line with 20 posts. Five different new weapons need to be distributed among the posts. The first and last posts should not be equipped with the new weapons. Additionally, among every set of 5 consecutive posts, at least one post should be equipped with a new weapon, and no two adjacent posts should be equipped simultaneously. How many possible arrangements are there to equip the posts with the new weapons?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence $\\{a_n\\}$, where $a_1=... | math | {
"ground_truth": "505",
"style": "rule"
} | {
"answer": "505",
"index": 18949,
"question": "Given the sequence $\\{a_n\\}$, where $a_1=1$, $a_2=2+3$, $a_3=4+5+6$, $a_4=7+8+9+10$,..., find the value of $a_{10}$. Express your answer as a single integer.",
"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 A store received fewer than 600 but more th... | math | {
"ground_truth": "547",
"style": "rule"
} | {
"answer": "547",
"index": 18950,
"question": "A store received fewer than 600 but more than 500 plates. When they tried to arrange the plates in groups of ten, three plates were missing to make complete groups of ten. When they tried to arrange them in dozens (12 plates), 7 plates remained. How many plates were there?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Angles"
] | 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 On a circle, fifteen points A₁, A₂, A₃, …, ... | math | {
"ground_truth": "108",
"style": "rule"
} | {
"answer": "108",
"index": 18951,
"question": "On a circle, fifteen points A₁, A₂, A₃, …, A₁₅ are equally spaced. Find the measure of angle ∠A₁A₃A₇. Express your answer in degrees as a whole number.",
"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 There are 11 consecutive natural numbers, a... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 18952,
"question": "There are 11 consecutive natural numbers, and the sum of the largest and smallest numbers is 90. Fill these 11 numbers into the circles in the figure below, with each circle containing one number, so that the sum of the numbers in each regular hexagon formed by six circles is equal. What is the minimum possible value of this sum?",
"split": "train"
} |
olympiads | [
"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 Divide a regular 2017-gon into 2015 triangu... | math | {
"ground_truth": "2010",
"style": "rule"
} | {
"answer": "2010",
"index": 18953,
"question": "Divide a regular 2017-gon into 2015 triangular regions using 2014 diagonals that do not intersect within the polygon. Find the maximum possible number of isosceles triangles among these 2015 triangles.",
"split": "train"
} |
big_math | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the number of positive integers n < 10... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 18954,
"question": "Find the number of positive integers n < 10^6 that are equal to twice the square of an integer and three times the cube of an integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $a+b+c+3=2(\\sqrt{a}+\\sqrt{b+1}+\\sq... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18955,
"question": "Given $a+b+c+3=2(\\sqrt{a}+\\sqrt{b+1}+\\sqrt{c-1})$, find the value of $a^{2}+b^{2}+c^{2}$.",
"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 6 barrels of water have an average capacity... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 18956,
"question": "6 barrels of water have an average capacity of 12 gallons. The capacities of the barrels must be between 8 and 16 gallons, inclusive. What is the maximum possible capacity of the smallest barrel if the median is 14 gallons and the capacity of the largest barrel is a prime number?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 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 picture, there is a grid consisting ... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 18957,
"question": "In the picture, there is a grid consisting of 25 small equilateral triangles. How many rhombuses can be made from two adjacent small triangles?",
"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 One ton has some pounds, and one pound has ... | math | {
"ground_truth": "2000",
"style": "rule"
} | {
"answer": "2000",
"index": 18958,
"question": "One ton has some pounds, and one pound has 16 ounces. 1840 packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons. How many pounds are there in one ton?",
"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 The monthly incomes of A, B, C, and D are i... | math | {
"ground_truth": "255000",
"style": "rule"
} | {
"answer": "255000",
"index": 18959,
"question": "The monthly incomes of A, B, C, and D are in the ratio 5 : 2 : 4 : 3, respectively. B's monthly income is 12% more than C's monthly income. C's monthly income is 15% less than D's monthly income. If D's monthly income after paying an income tax of 10% is Rs. 18000, then find the annual income of A before tax?",
"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 Two trains of different lengths are running... | math | {
"ground_truth": "153",
"style": "rule"
} | {
"answer": "153",
"index": 18960,
"question": "Two trains of different lengths are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. The first train is 121 meters long. They will be completely clear of each other in 6.802214443534172 seconds from the moment they meet. What is the length of the second train?",
"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 In a kilometer race, A can give B a 50 mete... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 18961,
"question": "In a kilometer race, A can give B a 50 meters start and C a certain amount of meters start. B can give C a 52.63157894736844 meters start in a kilometer race. How much start can A give C in a kilometer race?",
"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 Given the set\n$$\nM=\\{1,2, \\cdots, 2020\... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 18962,
"question": "Given the set\n$$\nM=\\{1,2, \\cdots, 2020\\} \\text{.}\n$$\n\nEach number in $M$ is colored with one of three colors: red, yellow, or blue, ensuring that each color is used at least once. Define\n$$\n\\begin{aligned}\nS_{1}= & \\left\\{(x, y, z) \\in M^{3} \\mid x, y, z \\text{ are the same color and } 2020 \\mid(x+y+z)\\right\\}, \\\\\nS_{2}= & \\left\\{(x, y, z) \\in М^{3} \\mid x, y, z \\text{ are all different colors and } 2020 \\mid(x+y+z)\\right\\}.\n\\end{aligned}\n$$\n\nFind the minimum value of $2\\left|S_{1}\\right|-\\left|S_{2}\\right|$.",
"split": "train"
} |
big_math | [
"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 Let \\( f(n) \\) be the sum of the squares ... | math | {
"ground_truth": "145",
"style": "rule"
} | {
"answer": "145",
"index": 18963,
"question": "Let \\( f(n) \\) be the sum of the squares of the digits of positive integer \\( n \\) (in decimal). For example, \\( f(123) = 1^{2} + 2^{2} + 3^{2} = 14 \\). Define \\( f_{1}(n) = f(n) \\), and \\( f_{k+1}(n) = f\\left(f_{k}(n)\\right) \\) for \\( k = 1, 2, 3, \\ldots \\). Calculate the value of \\( f_{2005}(2006) \\). Express your answer as a single integer value.",
"split": "train"
} |
cn_k12 | [
"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 Given an arithmetic sequence $a_n$ with a c... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"answer": "49",
"index": 18964,
"question": "Given an arithmetic sequence $a_n$ with a common difference $d < 0$, if $a_3a_7 = 9$ and $a_1 + a_9 = 10$, then the maximum value of the sum of the first $n$ terms of this sequence, $S_n$, is.",
"split": "train"
} |
olympiads | [
"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 rectangle \\(ABCD\\), where \\(AB = 3\\)... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18965,
"question": "In rectangle \\(ABCD\\), where \\(AB = 3\\) and \\(BC = 1\\), point \\(P\\) moves along side \\(CD\\). Let \\(\\angle PAB = \\alpha\\) and \\(\\angle PBA = \\beta\\). Find the maximum value of \\(\\frac{\\overrightarrow{PA} \\cdot \\overrightarrow{PB}}{\\cos (\\alpha + \\beta)}\\).",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( A \\) be a \\( k \\)-element subset... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18966,
"question": "Let \\( A \\) be a \\( k \\)-element subset of the set \\(\\{1, 2, 3, \\cdots, 16\\}\\), and any two elements of \\( A \\)",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Graph 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 We consider 2015 lines in a plane, no two o... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18967,
"question": "We consider 2015 lines in a plane, no two of which are parallel and no three of which meet at a single point. Let $E$ be the set of their intersection points.\n\nWe want to assign a color to each point in $E$ such that any two points on the same line, whose connecting segment contains no other points from $E$, are colored differently.\n\nWhat is the minimum number of colors needed to achieve such a coloring?",
"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 Triangle $ABC$ satisfies $\\tan A \\cdot... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 18968,
"question": "Triangle $ABC$ satisfies $\\tan A \\cdot \\tan B = 3$ and $AB = 5$ . Let $G$ and $O$ be the centroid and circumcenter of $ABC$ respectively. The maximum possible area of triangle $CGO$ can be written as $\\frac{a\\sqrt{b}}{c}$ for positive integers $a$ , $b$ , and $c$ with $a$ and $c$ relatively prime and $b$ not divisible by the square of any prime. Find $a + b + c$ .",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> 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 From 9 students, select 5 to form a class c... | math | {
"ground_truth": "41",
"style": "rule"
} | {
"answer": "41",
"index": 18969,
"question": "From 9 students, select 5 to form a class committee. The selection must meet the following conditions: both of students A and B must be either selected together or not selected together, and students C and D must not be selected together. How many possible selections are there? (Answer in numerical form).",
"split": "train"
} |
omnimath | [
"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 Let $r_{1}, \\ldots, r_{n}$ be the distinct... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 18970,
"question": "Let $r_{1}, \\ldots, r_{n}$ be the distinct real zeroes of the equation $x^{8}-14 x^{4}-8 x^{3}-x^{2}+1=0$. Evaluate $r_{1}^{2}+\\cdots+r_{n}^{2}$",
"split": "train"
} |
orca_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 If 6 parallel lines in a plane are intersec... | math | {
"ground_truth": "85",
"style": "rule"
} | {
"answer": "85",
"index": 18971,
"question": "If 6 parallel lines in a plane are intersected by a family of another set of parallel lines, there are 420 parallelograms in the network thus formed. How many parallel lines are in the second set?",
"split": "train"
} |
olympiads | [
"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 company conducted a survey among employ... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"answer": "240",
"index": 18972,
"question": "The company conducted a survey among employees to find out which social networks they use: VKontakte or Odnoklassniki. Some employees said they use VKontakte, some use Odnoklassniki, some said they use both social networks, and 40 employees said they do not use social networks. Among those who use social networks, 75% use VKontakte, and 65% use both networks. The proportion of employees who use Odnoklassniki from the total number of all employees is 5/6. How many employees are there in total at the company?",
"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 Use the Horner's method to calculate the va... | math | {
"ground_truth": "21324",
"style": "rule"
} | {
"answer": "21324",
"index": 18973,
"question": "Use the Horner's method to calculate the value of the polynomial \\\\(f(x)=7x^{7}+6x^{6}+5x^{5}+4x^{4}+3x^{3}+2x^{2}+x\\\\) when \\\\(x=3\\\\).",
"split": "train"
} |
orca_math | [
"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 The average height of 35 boys in a class wa... | math | {
"ground_truth": "226",
"style": "rule"
} | {
"answer": "226",
"index": 18974,
"question": "The average height of 35 boys in a class was calculated as 180 cm. It was later found that the height of one of the boys in the class was wrongly written as 156 cm whereas his actual height was a different value. The actual average height of the boys in the class is 178 cm. What is the actual height of the boy whose height was wrongly written?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> 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 How many unordered pairs of coprime numbers... | math | {
"ground_truth": "248",
"style": "rule"
} | {
"answer": "248",
"index": 18975,
"question": "How many unordered pairs of coprime numbers are there among the integers 2, 3, ..., 30? Recall that two integers are called coprime if they do not have any common natural divisors other than one.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> 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 In the following sum, \\( O \\) represents ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 18976,
"question": "In the following sum, \\( O \\) represents the digit 0. \\( A, B, X, \\) and \\( Y \\) each represent distinct digits. How many possible digits can \\( A \\) be?\n$$\n\\begin{array}{r}\nA O O B A O O B \\\\\n+\\quad B O O A B O O A \\\\\n\\hline X X O X Y X O X X\n\\end{array}\n$$\nExpress your answer as a single integer representing the count of possible digits for A.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 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=2002x+2003$, $b=2002x+2004$, $c=20... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18977,
"question": "Given $a=2002x+2003$, $b=2002x+2004$, $c=2002x+2005$, calculate the value of the polynomial $a^{2}+b^{2}+c^{2}-ab-bc-ca$. Express your answer as a single integer.",
"split": "train"
} |
math | [
"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 What is $3^{-1} + 13^{-1} \\pmod{19}$? Expr... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 18978,
"question": "What is $3^{-1} + 13^{-1} \\pmod{19}$? Express your answer as an integer from $0$ to $18$, inclusive.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 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 Valley of the Five Lakes, there are ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18979,
"question": "In the Valley of the Five Lakes, there are five identical lakes, some of which are connected by streams. Small fish are born only in lake \\(S\\). While the fish grow up, each one moves exactly four times from one lake to another using some stream (the fish chooses the stream at random), and then it stays in the lake where it ends up living. Out of every thousand fish, on average 375 remain living in lake \\(S\\), and the rest remain in lake \\(B\\). No fish remain in the other lakes. Determine how many streams are in the Valley of the Five Lakes.",
"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 In the Karabas Barabas theater, a chess tou... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18980,
"question": "In the Karabas Barabas theater, a chess tournament took place among the actors. Each participant played exactly one match against each of the other participants. A win awarded one solido, a draw awarded half a solido, and a loss awarded nothing. It turned out that among every three participants, there was one chess player who earned exactly 1.5 solidos in the games against the other two. What is the maximum number of actors that could have participated in such a tournament?",
"split": "train"
} |
omnimath | [
"Mathematics -> Geometry -> Plane 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 A rectangle has positive integer side lengt... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18981,
"question": "A rectangle has positive integer side lengths and an area of 24. What perimeter of the rectangle cannot be?",
"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 The digits of \\( n \\) strictly increase f... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 18982,
"question": "The digits of \\( n \\) strictly increase from left to right. Find the sum of the digits of \\( 9n \\).",
"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 Let \\( a_{1}, a_{2}, \\ldots, a_{R} \\) be... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 18983,
"question": "Let \\( a_{1}, a_{2}, \\ldots, a_{R} \\) be positive integers such that \\( a_{1} < a_{2} < a_{3} < \\ldots < a_{R-1} < a_{R} \\). Given that the sum of these \\( R \\) integers is 90 and the maximum value of \\( a_{1} \\) is \\( S \\), find the value of \\( S \\).",
"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 For a positive integer \\( n \\), define \\... | math | {
"ground_truth": "792",
"style": "rule"
} | {
"answer": "792",
"index": 18984,
"question": "For a positive integer \\( n \\), define \\( s(n) \\) as the smallest positive integer \\( t \\) such that \\( n \\) is a factor of \\( t! \\). Compute the number of positive integers \\( n \\) for which \\( s(n) = 13 \\).",
"split": "train"
} |
big_math | [
"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 Find the number of positive integer solutio... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18985,
"question": "Find the number of positive integer solutions (a, b, c) that satisfy the conditions a >= b >= c and the equation abc = 2(a-1)(b-1)(c-1). Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $a$ makes the system of inequalities abo... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18986,
"question": "If $a$ makes the system of inequalities about $x$ $\\left\\{\\begin{array}{c}6x-5≥a\\\\ \\frac{x}{4}-\\frac{x-1}{6}＜\\frac{1}{2}\\end{array}\\right.$ have exactly $2$ integer solutions, and also makes the equation about $y$ $4y-3a=2\\left(y-3\\right)$ have a positive solution, then the number of all integers $a$ satisfying the conditions is ______.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Division -> Remainders"
] | 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 On dividing a number by 68, we get 269 as q... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 18987,
"question": "On dividing a number by 68, we get 269 as quotient and some remainder. On dividing the same number by 67, the remainder is 1. What is the remainder in the first division?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Graph Theory"
] | 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 Every city in a certain state is directly c... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 18988,
"question": "Every city in a certain state is directly connected by air with at most three other cities in the state, but one can get from any city to any other city with at most one change of plane. What is the maximum possible number of cities?",
"split": "train"
} |
big_math | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 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 What is the largest prime p that makes \\sq... | math | {
"ground_truth": "67",
"style": "rule"
} | {
"answer": "67",
"index": 18989,
"question": "What is the largest prime p that makes \\sqrt{17p + 625} an integer? Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let the sum of ages a, b, c, and d be P and... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 18990,
"question": "Let the sum of ages a, b, c, and d be P and their average be A. If the average age of a, c, and d is 30 years and the average age of a and c is 32 years, with an additional condition that the average age of b and d is 34 years, what is the age of a, b, c, and d in years?",
"split": "train"
} |
big_math | [
"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 The school plans to select 3 students from ... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"answer": "48",
"index": 18991,
"question": "The school plans to select 3 students from 5 applicants to serve as volunteers for the track and field, swimming, and ball games at the 2011 World University Games. It is known that student A cannot serve as a volunteer for the swimming competition. Find the total number of different arrangements. Express your answer as a numerical value.",
"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 Sean is a biologist, and is looking at a st... | math | {
"ground_truth": "2100",
"style": "rule"
} | {
"answer": "2100",
"index": 18992,
"question": "Sean is a biologist, and is looking at a string of length 66 composed of the letters $A, T, C, G$. A substring of a string is a contiguous sequence of letters in the string. For example, the string $AGTC$ has 10 substrings: $A, G, T, C, AG, GT, TC, AGT, GTC, AGTC$. What is the maximum number of distinct substrings of the string Sean is looking at?",
"split": "train"
} |
aops_forum | [
"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 Find the smallest positive integer $n$ fo... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 18993,
"question": "Find the smallest positive integer $n$ for which one can select $n$ distinct real numbers such that each of them is equal to the sum of some two other selected numbers.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other",
"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 that $a$ and $b$ are positive real nu... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"answer": "25",
"index": 18994,
"question": "Given that $a$ and $b$ are positive real numbers, and the line $(a+1)x+2y-1=0$ is perpendicular to the line $3x+(b-2)y+2=0$, calculate the minimum value of $\\dfrac{3}{a} + \\dfrac{2}{b}$. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 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 integers \\( a, b, c, d, e, f, \\) and ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 18995,
"question": "The integers \\( a, b, c, d, e, f, \\) and \\( g \\), none of which is negative, satisfy the following five simultaneous equations:\n$$\n\\begin{array}{l}\na + b + c = 2, \\\\\nb + c + d = 2, \\\\\nc + d + e = 2, \\\\\nd + e + f = 2, \\\\\ne + f + g = 2.\n\\end{array}\n$$\n\nWhat is the maximum possible value of \\( a + b + c + d + e + f + g \\)?",
"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 The integers \\(a_{1}, a_{2}, \\ldots, a_{1... | math | {
"ground_truth": "200200",
"style": "rule"
} | {
"answer": "200200",
"index": 18996,
"question": "The integers \\(a_{1}, a_{2}, \\ldots, a_{10}\\) are all greater than 1 and their sum is 2006. What is the smallest possible value of the sum\n\n\\[\n\\binom{a_{1}}{2} + \\ldots + \\binom{a_{10}}{2}?\n\\]",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the binomial coefficient of only... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"answer": "35",
"index": 18997,
"question": "Given that the binomial coefficient of only the fourth term in the expansion of (1+2x)^n is the largest, the constant term in the expansion of the polynomial (x^2+1)(x+1/x)^n is \\_\\_\\_\\_\\_\\_.",
"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 Haylee has 3 dozen guppies in her aquarium.... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"answer": "53",
"index": 18998,
"question": "Haylee has 3 dozen guppies in her aquarium. Jose has half as many guppies as the square root of Haylee's guppies in his tank. Charliz has one-third of what Jose has in his tank, but Charliz sells 1.5 guppies to a neighbor. Nicolai has 4 times as many guppies as Charliz in his pond, minus 2 guppies. Alice has 5 more guppies than Nicolai in her fishbowl, while Bob has half the guppies of ((Jose's guppies)^2)/3 + (Charliz's guppies after selling) in his aquarium. Sara has 3i guppies (where i is an imaginary unit) in her experimental tank. Cameron has 2^(Haylee's dozens of guppies) guppies in his fish tank. How many guppies do these eight friends have altogether, excluding imaginary guppies?",
"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 Gina chooses what she and her sister will w... | math | {
"ground_truth": "3600",
"style": "rule"
} | {
"answer": "3600",
"index": 18999,
"question": "Gina chooses what she and her sister will watch on Netflix three times as often as her sister does. If her sister watches a total of 24 shows on Netflix per week, and each show is 50 minutes long, how many minutes of Netflix does Gina get to choose?",
"split": "train"
} |
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