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 -> 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 Compute the number of permutations $\\pi$ o... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21200,
"question": "Compute the number of permutations $\\pi$ of the set $\\{1,2, \\ldots, 10\\}$ so that for all (not necessarily distinct) $m, n \\in \\{1,2, \\ldots, 10\\}$ where $m+n$ is prime, $\\pi(m)+\\pi(n)$ is prime.",
"split": "train"
} |
big_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 Two boys start moving from the same point A... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 21201,
"question": "Two boys start moving from the same point A on a circular track but in opposite directions. Their speeds are 5 ft. per second and 9 ft. per second. If they start at the same time and finish when they first meet at the point A again, calculate the number of times they meet, excluding the start and finish. Express your answer as a whole number.",
"split": "train"
} |
math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the positive solution to\n\\[\\frac 1{... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 21202,
"question": "Find the positive solution to\n\\[\\frac 1{x^2-10x-29}+\\frac1{x^2-10x-45}-\\frac 2{x^2-10x-69}=0.\\]",
"split": "train"
} |
olympiads | [
"Mathematics -> Precalculus -> Limits"
] | 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 \\(\\{x_{n}\\}_{n=1}^{\\infty}\\) be a ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 21203,
"question": "Let \\(\\{x_{n}\\}_{n=1}^{\\infty}\\) be a sequence of real numbers such that \\(x_{1}=3\\), \\(x_{2}=24\\), and \n\\[\nx_{n+2}=\\frac{1}{4} x_{n+1}+\\frac{3}{4} x_{n}\n\\]\nfor every positive integer \\(n\\). Determine the value of \\(\\lim_{n\\rightarrow \\infty} x_{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 natural number that is di... | math | {
"ground_truth": "1000001111131",
"style": "rule"
} | {
"answer": "1000001111131",
"index": 21204,
"question": "Find the smallest natural number that is divisible by 11 and whose representation contains 5 zeros and 7 ones. (You may use the divisibility rule for 11: a number is divisible by 11 if the difference between the sum of the digits in the even positions and the sum of the digits in the odd positions is divisible by 11.)",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a sphere $O$ with a diameter of $12$,... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21205,
"question": "Given a sphere $O$ with a diameter of $12$, when the volume of its inscribed regular tetrahedron is maximized, the height of the tetrahedron is __________.",
"split": "train"
} |
olympiads | [
"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 Consider equations of the form \\( ax^{2} +... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21206,
"question": "Consider equations of the form \\( ax^{2} + bx + c = 0 \\), where \\( a, b, c \\) are all single-digit prime numbers. How many of these equations have at least one solution for \\( x \\) that is an integer?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A positive integer $n$ is called *mythica... | math | {
"ground_truth": "135",
"style": "rule"
} | {
"answer": "135",
"index": 21207,
"question": "A positive integer $n$ is called *mythical* if every divisor of $n$ is two less than a prime. Find the unique mythical number with the largest number of divisors.",
"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 Xiaopang and Xiaoya both have their birthda... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"answer": "26",
"index": 21208,
"question": "Xiaopang and Xiaoya both have their birthdays in May, and both fall on a Wednesday. Xiaopang's birthday is later, and the sum of their birth dates is 38. What is Xiaopang's birthday in May?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The sequence ${a_{n}}$ has a sum of the fir... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"answer": "-4",
"index": 21209,
"question": "The sequence ${a_{n}}$ has a sum of the first $n$ terms given by $S_{n}=\\frac{n}{n+1}$, and the general term of the sequence ${b_{n}}$ is given by $b_{n}=n-8$. Find the minimum value of $b_{n}S_{n}$.",
"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 Using the digits 0 to 9, how many unique th... | math | {
"ground_truth": "296",
"style": "rule"
} | {
"answer": "296",
"index": 21210,
"question": "Using the digits 0 to 9, how many unique three-digit even numbers can be formed without repeating any digits?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Precalculus -> Functions"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given positive numbers $a$ and $b$ satisfy ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21211,
"question": "Given positive numbers $a$ and $b$ satisfy $\\log_{2}a=\\log_{5}b=\\lg(a+b)$, find the value of $\\dfrac{1}{a}+ \\dfrac{1}{b}$.",
"split": "train"
} |
omnimath | [
"Mathematics -> Algebra -> Other",
"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 Find the smallest number $n$ such that ther... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21212,
"question": "Find the smallest number $n$ such that there exist polynomials $f_1, f_2, \\ldots , f_n$ with rational coefficients satisfying \\[x^2+7 = f_1\\left(x\\right)^2 + f_2\\left(x\\right)^2 + \\ldots + f_n\\left(x\\right)^2.\\]",
"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 Chastity made 36 angel food cakes to give t... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"answer": "19",
"index": 21213,
"question": "Chastity made 36 angel food cakes to give to friends. She placed the cakes in boxes, and then walked them out to her car. But she had forgotten her keys. So, she placed the boxes of cakes in two separate stacks on the hood of her car, and then she ran back into the house to get her keys.\n\nWhile she was in the house, a black crow came and knocked over 60% of one of the stacks. A mischievous squirrel snuck up and stole 1/3 of the fallen cakes from the crow's attack. \n\nMeanwhile, a red squirrel approached the remaining stack and took away 25% of the cakes from that stack. This time, half of the stolen cakes were inadvertently dropped by the squirrel and were no longer edible. Chastity's dog, Belle, also ran out to the car and ate 4 of the fallen cakes from the crow's attack.\n\nWhen Chastity returned, she picked up all the untouched fallen cakes and found out that some fallen cakes were destroyed or eaten by animals. How many cakes were destroyed or stolen by the animals in total?",
"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 Juniper, the Irish Setter, initially has 4 ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21214,
"question": "Juniper, the Irish Setter, initially has 4 bones. Her master gives her bones equal to 50% more than what she currently has. Unfortunately, the neighbor's dog steals away 25% of Juniper's total bones. \n\nWhat is the final number of bones Juniper has after these transactions?",
"split": "train"
} |
big_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 Lucky Larry's teacher asked him to substitu... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 21215,
"question": "Lucky Larry's teacher asked him to substitute numbers for a, b, c, d, and e in the expression a - (b - (c - (d + e))) and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The number Larry substituted for a, b, c, and d were 1, 2, 3, and 4, respectively. Calculate the value of e that makes the expression evaluated without parentheses equal to the expression evaluated with correct use of parentheses.",
"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 \nMasha's tablet fully discharged and is ne... | math | {
"ground_truth": "288",
"style": "rule"
} | {
"answer": "288",
"index": 21216,
"question": "\nMasha's tablet fully discharged and is needed for a presentation at school. Using additional equipment, the tablet can be fully charged in 2 hours and 40 minutes, but without it, charging takes 8 hours. Masha initially put the discharged tablet on the regular charger and then switched it to the fast charger when she found the equipment, charging it fully. It is known that the tablet charges uniformly with both the regular and fast chargers. Find the total charging time of the tablet if it was on the fast charger for one-third of the total charging time. Provide the answer in minutes.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems",
"Mathematics -> Discrete Mathematics -> Combinatorics -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the theater troupe, there are 60 actors.... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21217,
"question": "In the theater troupe, there are 60 actors. Every pair of actors has performed in at least one play together. In each play, no more than 30 actors are involved.\n\nWhat is the minimum number of plays the theater could have produced?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> 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 a regular hexagon \\( A B C D E F \\)... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 21218,
"question": "Given a regular hexagon \\( A B C D E F \\) with a side length of 1, calculate \\((\\overrightarrow{A B}+\\overrightarrow{D C}) \\cdot(\\overrightarrow{A D}+\\overrightarrow{B E})\\).",
"split": "train"
} |
omnimath | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $A B C$ be a triangle with $A B=13, B C... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21219,
"question": "Let $A B C$ be a triangle with $A B=13, B C=14, C A=15$. The altitude from $A$ intersects $B C$ at $D$. Let $\\omega_{1}$ and $\\omega_{2}$ be the incircles of $A B D$ and $A C D$, and let the common external tangent of $\\omega_{1}$ and $\\omega_{2}$ (other than $B C$) intersect $A D$ at $E$. Compute the length of $A E$.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> 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 During the Tree Planting Festival, students... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21220,
"question": "During the Tree Planting Festival, students from a class are planting trees. There are three different types of saplings, labeled as A, B, and C, available in the nursery, with an ample supply of each type. They need to plant 5 saplings in a row in 5 pits, with the condition that the same type of sapling cannot be adjacent, and only type A saplings can be planted in the first and the fifth pits. Find the total number of planting methods available. Express your answer as a single integer.",
"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 Jack writes whole numbers starting from $ ... | math | {
"ground_truth": "156",
"style": "rule"
} | {
"answer": "156",
"index": 21221,
"question": "Jack writes whole numbers starting from $ 1$ and skips all numbers that contain either a $2$ or $9$ . What is the $100$ th number that Jack writes down?",
"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 Machine A takes some hours to complete a ce... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21222,
"question": "Machine A takes some hours to complete a certain job and starts that job at 7 am. After two hours of working alone, Machine A is joined by Machine B and together they complete the job at 12 pm. It would have taken Machine B 18.07228915662651 hours to complete the job if it had worked alone for the entire job. How long does it take for Machine A to complete the job alone?",
"split": "train"
} |
olympiads | [
"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 Determine the smallest integer $n$ such tha... | math | {
"ground_truth": "2022",
"style": "rule"
} | {
"answer": "2022",
"index": 21223,
"question": "Determine the smallest integer $n$ such that there exist $n$ real numbers $x_{1}, \\ldots, x_{n}$ all belonging to the interval $(-1, 1)$ and for which\n\n$$\nx_{1}+\\cdots+x_{n}=0 \\quad \\text{and} \\quad x_{1}^{2}+\\cdots+x_{n}^{2}=2020\n$$",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the sum of the first three terms... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 21224,
"question": "Given that the sum of the first three terms of an arithmetic sequence $\\{a_n\\}$ is $4$, the sum of the last three terms is $7$, and the sum of all terms is $22$, determine the number of terms $n$ in the sequence. Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> 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 trapezoid \\(ABCD\\), points \\(K\\) and... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21225,
"question": "In trapezoid \\(ABCD\\), points \\(K\\) and \\(M\\) are the midpoints of the bases \\(AB = 5\\) and \\(CD = 3\\), respectively. Find the area of the trapezoid if triangle \\(AMB\\) is a right triangle and \\(DK\\) is the height of the trapezoid.",
"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 A walker walking at a constant rate of 4 mi... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21226,
"question": "A walker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour. The cyclist stops to wait for the hiker after passing her, while the walker continues to walk at her constant rate. The cyclist must wait 20 minutes until the walker catches up. How many minutes after passing the walker does the cyclist stop to wait?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 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 Using the Monte Carlo method to calculate t... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 21227,
"question": "Using the Monte Carlo method to calculate the area enclosed by $y=x^2+1$ and $y=5$, first generate two groups of uniform random numbers between 0 and 1, denoted $a_1=\\text{RAND}$ and $b_1=\\text{RAND}$, then perform translation and scaling transformations as $a=4a_1-2$ and $b=4b_1+1$. After 1000 experiments, the number of sample points that fall within the desired area for the first 998 trials is 624. If the uniform random numbers (between 0 and 1) generated by the last two experiments are (0.3, 0.1) and (0.9, 0.7), then estimate the area enclosed by $y=x^2+1$ and $y=5$. Provide your answer as a single numerical value.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 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 Rearrange the digits of the number 12345 in... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 21228,
"question": "Rearrange the digits of the number 12345 in any order to form a new five-digit number. How many of these new numbers are prime?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Calculus -> 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 If the function $f(x)=2\\sin(\\omega x+\\fr... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 21229,
"question": "If the function $f(x)=2\\sin(\\omega x+\\frac{\\pi}{3})(\\omega>0)$, and $A(\\alpha,2)$, $B(\\beta,0)$ are two points on the graph of the function $f(x)$, and the minimum value of $|AB|$ is $\\sqrt{4+\\frac{{\\pi}^{2}}{4}}$, then the value of $f(\\frac{5\\pi}{6})$ is ______.",
"split": "train"
} |
aops_forum | [
"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 Suppose that $x,$ $y,$ and $z$ are th... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21230,
"question": "Suppose that $x,$ $y,$ and $z$ are three positive numbers that satisfy the equations $xyz=1,$ $x+\\frac{1}{z}=5,$ and $y+\\frac{1}{x}=29.$ Then $z+\\frac{1}{y}=\\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$ ",
"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 On the board, the natural number \\( N \\) ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 21231,
"question": "On the board, the natural number \\( N \\) was written nine times (one below the other). Petya added a non-zero digit to the left or right of each of the 9 numbers; all added digits are distinct. What is the largest possible number of prime numbers that could result from these 9 new numbers?\n\n(I. Efremov)",
"split": "train"
} |
big_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 A person moved forward $100\\sqrt{5}$ meter... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 21232,
"question": "A person moved forward $100\\sqrt{5}$ meters along a slope with a ratio of $1:2$. Calculate the increase in the person's position. Express your answer in meters.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Divisibility"
] | 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 three-digit positive integer \\( n \\) ha... | math | {
"ground_truth": "870",
"style": "rule"
} | {
"answer": "870",
"index": 21233,
"question": "A three-digit positive integer \\( n \\) has digits \\( a, b, c \\). (That is, \\( a \\) is the hundreds digit of \\( n \\), \\( b \\) is the tens digit of \\( n \\), and \\( c \\) is the ones (units) digit of \\( n \\).) Determine the largest possible value of \\( n \\) for which:\n- \\( a \\) is divisible by 2,\n- the two-digit integer \\( ab \\) (where \\( a \\) is the tens digit and \\( b \\) is the ones digit) is divisible by 3 but is not divisible by 6, and\n- \\( n \\) is divisible by 5 but is not divisible by 7.",
"split": "train"
} |
amc_aime | [
"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 There exist unique positive integers $x$ an... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"answer": "80",
"index": 21234,
"question": "There exist unique positive integers $x$ and $y$ that satisfy the equation $x^2 + 84x + 2008 = y^2$. Find $x + y$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a string of 2021 characters consistin... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21235,
"question": "Given a string of 2021 characters consisting of the letters A and B, consider the longest palindromic substring. What is its minimally possible length? A palindrome is a string that reads the same forwards and backwards.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Analytic 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 Given an ellipse with its foci on the $y$-a... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21236,
"question": "Given an ellipse with its foci on the $y$-axis, and the equation $mx^{2}+4y^{2}=1$, if the eccentricity of the ellipse is $\\dfrac{\\sqrt{2}}{2}$, then the real number $m$ equals \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
olympiads | [
"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 For which natural number $k$ does the expre... | math | {
"ground_truth": "2000",
"style": "rule"
} | {
"answer": "2000",
"index": 21237,
"question": "For which natural number $k$ does the expression $\\frac{k^{2}}{1.001^{k}}$ reach its maximum value?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n How many pairs (x, y) of non-negative integ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21238,
"question": "How many pairs (x, y) of non-negative integers with 0 <= x <= y satisfy the equation 5x^2 - 4xy + 2x + y^2 = 624? Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> 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 that $z \\in \\mathbb{C}$ and $|z-4+4... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21239,
"question": "Given that $z \\in \\mathbb{C}$ and $|z-4+4i| \\leqslant 2$, calculate the maximum value of $|z-1|$. Express your answer as a single number.",
"split": "train"
} |
aops_forum | [
"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 Karl likes the number $17$ his favorite p... | math | {
"ground_truth": "8960",
"style": "rule"
} | {
"answer": "8960",
"index": 21240,
"question": "Karl likes the number $17$ his favorite polynomials are monic quadratics with integer coefficients such that $17$ is a root of the quadratic and the roots differ by no more than $17$ . Compute the sum of the coefficients of all of Karl's favorite polynomials. (A monic quadratic is a quadratic polynomial whose $x^2$ term has a coefficient of $1$ .)",
"split": "train"
} |
olympiads | [
"Mathematics -> Calculus -> Applications of Derivatives"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the rectangular coordinate system, the g... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21241,
"question": "In the rectangular coordinate system, the graph of the function \\( y = \\frac{1}{|x|} \\) is denoted by \\( \\Gamma \\). Let points \\( P \\) and \\( Q \\) on \\( \\Gamma \\) satisfy the following conditions: \\( P \\) is in the first quadrant, \\( Q \\) is in the second quadrant, and the line segment \\( P Q \\) is tangent to the portion of \\( \\Gamma \\) in the second quadrant at point \\( Q \\). Find the minimum value of \\( |P Q| \\).",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 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 insect lives on the surface of a regular... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21242,
"question": "An insect lives on the surface of a regular tetrahedron with edges of length 1. It wishes to travel on the surface of the tetrahedron from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest such trip? Express your answer as a single number.",
"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 Into how many regions do the x-axis and the... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 21243,
"question": "Into how many regions do the x-axis and the graphs of \\( y = 2 - x^2 \\) and \\( y = x^2 - 1 \\) split the plane?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Solid Geometry -> 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 figure, \\( L_{1} \\) and \\( L_{2} ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 21244,
"question": "In the figure, \\( L_{1} \\) and \\( L_{2} \\) are tangents to the three circles. If the radius of the largest circle is 18 and the radius of the smallest circle is \\( 4b \\), find \\( c \\), where \\( c \\) is the radius of circle \\( W \\).",
"split": "train"
} |
orca_math | [
"Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The school cafeteria initially had 65 apple... | math | {
"ground_truth": "67",
"style": "rule"
} | {
"answer": "67",
"index": 21245,
"question": "The school cafeteria initially had 65 apples. They used 20% of these apples to make lunch for the students and afterwards, bought 15 and a half more apples. Calculate the total number of apples they had after these transactions.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the inequality ((x+y)^2+4)((x+y)^2-2)... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 21246,
"question": "Given the inequality ((x+y)^2+4)((x+y)^2-2) >= A*(x-y)^2, where x and y are real numbers such that xy = 1, calculate the largest value of A.",
"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 Sixty apples and sixty pears are to be pack... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 21247,
"question": "Sixty apples and sixty pears are to be packed into boxes so that each box contains the same number of apples, and no two boxes contain the same number of pears. What is the largest possible number of boxes that can be packed in this way? Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Suppose we keep rolling a fair 2014-sided d... | math | {
"ground_truth": "272",
"style": "rule"
} | {
"answer": "272",
"index": 21248,
"question": "Suppose we keep rolling a fair 2014-sided die (whose faces are labelled 1, 2, ..., 2014) until we obtain a value less than or equal to the previous roll. Let E be the expected number of times we roll the die. Find the nearest integer to 100E.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If the vertex of angle $\\alpha$ is at the ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 21249,
"question": "If the vertex of angle $\\alpha$ is at the origin, the initial side coincides with the non-negative half-axis of the $x$-axis, and the terminal side intersects the unit circle at point $P({-\\frac{3}{5},\\frac{4}{5}})$, then $tan({α+\\frac{{2023π}}{4}})=\\_\\_\\_\\_\\_\\_.$",
"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 Forty children were holding hands in a circ... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 21250,
"question": "Forty children were holding hands in a circle. Among them, 22 were holding a boy's hand and 30 were holding a girl's hand. How many girls were in the circle?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given an arithmetic sequence $\\{a_n\\}$ wi... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21251,
"question": "Given an arithmetic sequence $\\{a_n\\}$ with a common difference $d>0$, let $S_n$ denote the sum of its first $n$ terms. If for any $T$ and $K$ that satisfy $T+K=19$, it is always true that $S_T=S_K$, then the number of solutions for $a_n-S_n\\geq0$ is $\\_\\_\\_\\_\\_\\_$.",
"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 Some men can complete a piece of work in 25... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 21252,
"question": "Some men can complete a piece of work in 25 days. If 20 men work on the same piece, they can complete it in 15 days. How many men were in the first group?",
"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 Determine all positive integers \\( x \\) s... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21253,
"question": "Determine all positive integers \\( x \\) such that \\( 2x + 1 \\) is a perfect square, but among the numbers \\( 2x + 2, 2x + 3, \\cdots, 3x + 2 \\), there are no perfect squares.",
"split": "train"
} |
aops_forum | [
"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 A book is published in three volumes, the p... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"answer": "17",
"index": 21254,
"question": "A book is published in three volumes, the pages being numbered from $1$ onwards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is $50$ more than that in the first volume, and the number pages in the third volume is one and a half times that in the second. The sum of the page numbers on the first pages of the three volumes is $1709$ . If $n$ is the last page number, what is the largest prime factor of $n$ ?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the sequence $\\{a\\_n\\}$, if $a\\_n = ... | math | {
"ground_truth": "-12",
"style": "rule"
} | {
"answer": "-12",
"index": 21255,
"question": "In the sequence $\\{a\\_n\\}$, if $a\\_n = -3a_{n+1}$ holds for all $n \\in \\mathbb{N}^*$, and $\\lim_{n \\to \\infty}(a\\_2 + a\\_4 + a\\_6 + \\dots + a_{2n}) = \\frac{9}{2}$, then the value of $a\\_1$ is $\\_\\_\\_\\_\\_\\_\\_\\_\\_.$",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Solid 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 Given that the base edge length of the regu... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21256,
"question": "Given that the base edge length of the regular triangular prism ABC-A<sub>1</sub>B<sub>1</sub>C<sub>1</sub> is 2 and the lateral edge length is $\\sqrt{3}$, with D being the midpoint of BC, find the volume of the tetrahedron A-B<sub>1</sub>DC<sub>1</sub>.",
"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 Norma takes her clothes to the laundry. She... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 21257,
"question": "Norma takes her clothes to the laundry. She leaves 9 T-shirts and twice as many sweaters as T-shirts in the washer. When she returns she finds 3 sweaters and triple the number of T-shirts. How many items are missing?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence $\\left\\{a_{n}\\right\\... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"answer": "26",
"index": 21258,
"question": "Given the sequence $\\left\\{a_{n}\\right\\}$, define $\\left\\{ {\\Delta _{1}}{a_{n}} \\right\\}$ as the first-order difference sequence of $\\left\\{a_{n}\\right\\}$, where ${\\Delta _{1}}{a_{n}}={{a}_{{n+1}}}-{{a}_{n}}(n\\in {\\mathbb{N}^{*}})$. For a positive integer $k$, define $\\left\\{ {\\Delta _{k}}{a_{n}} \\right\\}$ as the $k$-th order difference sequence of $\\left\\{a_{n}\\right\\}$, where ${\\Delta _{k}}{a_{n}}={\\Delta _{k-1}}{a_{n+1}}-{\\Delta _{k-1}}{a_{n}}$. If the sequence $\\left\\{a_{n}\\right\\}$ satisfies ${a_{1}}=1$, ${{a}_{2}}=2$, and ${\\Delta _{2}}{a_{n}}+{\\Delta _{1}}{a_{n}}-{2}={0}(n\\in {\\mathbb{N}^{*}})$, find the value of ${{a}_{14}}$.",
"split": "train"
} |
omnimath | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Teresa the bunny has a fair 8-sided die. Se... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"answer": "104",
"index": 21259,
"question": "Teresa the bunny has a fair 8-sided die. Seven of its sides have fixed labels $1,2, \\ldots, 7$, and the label on the eighth side can be changed and begins as 1. She rolls it several times, until each of $1,2, \\ldots, 7$ appears at least once. After each roll, if $k$ is the smallest positive integer that she has not rolled so far, she relabels the eighth side with $k$. The probability that 7 is the last number she rolls is $\\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100 a+b$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Least Common Multiples (LCM)"
] | 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 l . c . m . of two numbers is 42 . the ... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"answer": "70",
"index": 21260,
"question": "the l . c . m . of two numbers is 42 . the numbers are in the ratio 2 : 3 . then sum of the number is :",
"split": "train"
} |
aops_forum | [
"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 We define the ridiculous numbers recursivel... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 21261,
"question": "We define the ridiculous numbers recursively as follows:\n[list=a]\n[*]1 is a ridiculous number.\n[*]If $a$ is a ridiculous number, then $\\sqrt{a}$ and $1+\\sqrt{a}$ are also ridiculous numbers. \n[/list]\nA closed interval $I$ is ``boring'' if\n\n\n- $I$ contains no ridiculous numbers, and\n- There exists an interval $[b,c]$ containing $I$ for which $b$ and $c$ are both ridiculous numbers.\n\nThe smallest non-negative $l$ such that there does not exist a boring interval with length $l$ can be represented in the form $\\dfrac{a + b\\sqrt{c}}{d}$ where $a, b, c, d$ are integers, $\\gcd(a, b, d) = 1$ , and no integer square greater than 1 divides $c$ . What is $a + b + c + d$ ?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Least Common Multiples (LCM)"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the least whole number that should ... | math | {
"ground_truth": "21073",
"style": "rule"
} | {
"answer": "21073",
"index": 21262,
"question": "What is the least whole number that should be added to 625573 if it is to be divisible by the least common multiple of 7, 11, 13, 17, and 19?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n From the 20 numbers 11, 12, 13, 14, ... 30,... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 21263,
"question": "From the 20 numbers 11, 12, 13, 14, ... 30, how many numbers must be chosen to ensure that there are at least two numbers whose sum is a multiple of 10?",
"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 two circles $O_{1}: x^{2}+y^{2}=5$ an... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21264,
"question": "Given two circles $O_{1}: x^{2}+y^{2}=5$ and $O_{2}: (x+m)^{2}+y^{2}=20$ ($m \\in \\mathbb{R}$) intersect at points $A$ and $B$, and the tangents to the circles at point $A$ are perpendicular to each other, then the length of segment $AB$ is ______.",
"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 certain cleaning solution, the ratio b... | math | {
"ground_truth": "160",
"style": "rule"
} | {
"answer": "160",
"index": 21265,
"question": "In a certain cleaning solution, the ratio by volume of bleach to detergent to water is 2 : 25 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled, and the ratio of detergent to water is halved. If the altered solution will contain 80 gallons of water, how many quarts of detergent will it contain? Note that 1 gallon equals 4 quarts.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The numbers \\( x \\) and \\( y \\) satisfy... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 21266,
"question": "The numbers \\( x \\) and \\( y \\) satisfy the equation \\(\\frac{x}{x+y}+\\frac{y}{2(x-y)}=1\\). Find all possible values of the expression \\(\\frac{5x+y}{x-2y}\\), and provide their sum as the answer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> 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 There is a sequence of numbers where the fi... | math | {
"ground_truth": "91",
"style": "rule"
} | {
"answer": "91",
"index": 21267,
"question": "There is a sequence of numbers where the first number is 105 and the second number is 85. Starting from the third number, each number is the average of the two preceding numbers. What is the integer part of the 2011th number?",
"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 pile of candies consists of three types o... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"answer": "53",
"index": 21268,
"question": "A pile of candies consists of three types of flavors: chocolate, fruit, and milk. If you take away 5 pieces of chocolate candy, the remaining candies can be divided into 2 identical portions; if you take away 2 pieces of fruit candy, the remaining candies can be divided into 3 identical portions; if you take away 3 pieces of milk candy, the remaining candies can be divided into 5 identical portions. What is the minimum number of candies in this pile?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities",
"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 the solution set of the inequality $\... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 21269,
"question": "Given the solution set of the inequality $\\frac{x+2}{x+1} < 0$ is $\\{x|a < x < b\\}$, and the point $A(a,b)$ lies on the line $mx+ny+1=0$, where $mn > 0$, then the minimum value of $\\frac{2}{m}+\\frac{1}{n}$ is ______.",
"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 an arithmetic sequence $\\{a\\_n\\}$ ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 21270,
"question": "Given an arithmetic sequence $\\{a\\_n\\}$ with a common difference $d∈(0,1)$, and $\\frac {\\sin ^{2}a_{3}-\\sin ^{2}a_{7}}{\\sin (a_{3}+a_{7})}=-1$, if $a_{1}∈(-\\frac {5π}{4},-\\frac {9π}{8})$ then the minimum value of $n$ for which the sum of the first $n$ terms of the sequence, $S_{n}$, is minimized is $\\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> Other",
"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 For two base-10 positive integers $a$ and... | math | {
"ground_truth": "3628800",
"style": "rule"
} | {
"answer": "3628800",
"index": 21271,
"question": "For two base-10 positive integers $a$ and $b$ , we say $a \\sim b$ if we can rearrange the digits of $a$ in some way to obtain $b$ , where the leading digit of both $a$ and $b$ is nonzero. For instance, $463 \\sim 463$ and $634 \\sim 463$ . Find the number of $11$ -digit positive integers $K$ such that $K$ is divisible by $2$ , $3$ , and $5$ , and there is some positive integer $K'$ such that $K' \\sim K$ and $K'$ is divisible by $7$ , $11$ , $13$ , $17$ , $101$ , and $9901$ .",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given any natural number \\( n \\) (where \... | math | {
"ground_truth": "243",
"style": "rule"
} | {
"answer": "243",
"index": 21272,
"question": "Given any natural number \\( n \\) (where \\( n > 3 \\)), if the set \\( S_{n} = \\{3, 4, \\cdots, n\\} \\) is divided into two groups arbitrarily, there will always be three numbers \\( a, b, c \\) (allowing \\( a = b \\)) in one of the groups such that \\( ab = c \\). Find the smallest value of \\( n \\) for which this property holds.\n\n(Source: 1988 National Training Team Test, China)",
"split": "train"
} |
olympiads | [
"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 From the cards with letters, you can form t... | math | {
"ground_truth": "30240",
"style": "rule"
} | {
"answer": "30240",
"index": 21273,
"question": "From the cards with letters, you can form the word \"ВОДОПРОВОД\". How many words (not necessarily meaningful) can be formed from these cards where the letters Р and П are adjacent?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A vase can hold 6 roses, 8 tulips, or 4 lil... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21274,
"question": "A vase can hold 6 roses, 8 tulips, or 4 lilies. If you have a total of 47 flowers consisting of 7 carnations, 20 roses, 15 tulips, and 5 lilies, how many vases would you need to hold the flowers if you removed all the carnations?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Discrete Mathematics -> Graph Theory"
] | 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 Sophia writes an algorithm to solve the gra... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 21275,
"question": "Sophia writes an algorithm to solve the graph isomorphism problem. Given a graph $G=(V,E)$ , her algorithm iterates through all permutations of the set $\\{v_1, \\dots, v_{|V|}\\}$ , each time examining all ordered pairs $(v_i,v_j)\\in V\\times V$ to see if an edge exists. When $|V|=8$ , her algorithm makes $N$ such examinations. What is the largest power of two that divides $N$ ?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Least Common Multiples (LCM)"
] | 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 If p # q denotes the least common multiple ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21276,
"question": "If p # q denotes the least common multiple of p and q, then p = ((some number # 16) # (18 # 24)) = 144. What is the first number in the first pair of parentheses?",
"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 the hyperbola $\\frac {x^{2}}{a^{2}} ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21277,
"question": "Given the hyperbola $\\frac {x^{2}}{a^{2}} - \\frac {y^{2}}{b^{2}} = 1$ ($a > 0$, $b > 0$) and the parabola $y^2 = 8x$ share a common focus $F$, and one of their intersection points is $P$. If $|PF| = 5$, find the eccentricity of the hyperbola.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( F(x) = |f(x) \\cdot g(x)| \\), wher... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21278,
"question": "Let \\( F(x) = |f(x) \\cdot g(x)| \\), where \\( f(x) = a x^{2} + b x + c \\) and \\( g(x) = c x^{2} + b x + a \\), with \\( x \\in [-1, 1] \\). For any \\( a, b, c \\) such that \\( |f(x)| \\leq 1 \\), find the maximum value of \\( F(x) \\) as \\( a, b, \\) and \\( c \\) vary.",
"split": "train"
} |
olympiads | [
"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 the positive number \\( x \\) satisfy... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 21279,
"question": "Given the positive number \\( x \\) satisfying the equation\n\\[ x^{10} + x^{5} + \\frac{1}{x^{5}} + \\frac{1}{x^{10}} = 15250, \\]\nfind the value of \\( x + \\frac{1}{x} \\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> 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 There are four excellent students A, B, C, ... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 21280,
"question": "There are four excellent students A, B, C, and D who have been recommended for admission to Peking University, Tsinghua University, and Fudan University, with each university receiving at least one student. Calculate the total number of different admission schemes.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given an arithmetic sequence $\\{a_n\\}$, t... | math | {
"ground_truth": "-110",
"style": "rule"
} | {
"answer": "-110",
"index": 21281,
"question": "Given an arithmetic sequence $\\{a_n\\}$, the sum of the first 10 terms is 100, and the sum of the first 100 terms is 10. Find the sum of the first 110 terms.",
"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 Mary is 20% older than Sally, and Sally is ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 21282,
"question": "Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. Calculate Mary's age on her next birthday.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Congruences"
] | 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 Some number leaves a remainder of 9 when di... | math | {
"ground_truth": "2143",
"style": "rule"
} | {
"answer": "2143",
"index": 21283,
"question": "Some number leaves a remainder of 9 when divided by 11, a remainder of 11 when divided by 13, and a remainder of 13 when divided by 15. What is the smallest such number?",
"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 A line passing through $(2,1)$ intersects t... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 21284,
"question": "A line passing through $(2,1)$ intersects the coordinate axes at points $A$ and $B$. The area of $\\triangle BO$ (where $O$ is the origin) is exactly $4$. Find the number of lines $l$ that satisfy the given conditions.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The sum of four different positive integers... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 21285,
"question": "The sum of four different positive integers is 100. The largest of these four integers is n. Find the smallest possible value of n. Express your answer as a single integer.",
"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 ball will drop from an original height ... | math | {
"ground_truth": "260",
"style": "rule"
} | {
"answer": "260",
"index": 21286,
"question": "One ball will drop from an original height of 104 cm. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 260 cm. On which rebound does the ball touch the floor to reach this total travel distance?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The average score of six students in a math... | math | {
"ground_truth": "95",
"style": "rule"
} | {
"answer": "95",
"index": 21287,
"question": "The average score of six students in a math exam is 92.5 points, and their scores are distinct integers with the highest being 99 points and the lowest being 76 points. What is the minimum score of the student who ranks third from the top? Express your answer as an integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 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 regular triangular prism ABC-A1B1C1,... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 21288,
"question": "In the regular triangular prism ABC-A1B1C1, there are six diagonals on the sides: AB1, A1B, BC1, B1C, C1A, CA1. Given that AB1 ⊥ BC1, how many other pairs of these diagonals are also perpendicular to each other? Express your answer as a whole number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a group of 42 kids, 650 lollipops must b... | math | {
"ground_truth": "1975",
"style": "rule"
} | {
"answer": "1975",
"index": 21289,
"question": "In a group of 42 kids, 650 lollipops must be distributed so that the number of lollipops each kid receives varies within a specified range. Each kid must receive at least one lollipop, and no kid should receive the same number of lollipops. The minimum and maximum number of lollipops a kid can receive are consecutive integers (n and n + 1), and their sum is divisible by 42. How many additional lollipops are needed to meet these conditions?",
"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 How many diagonals in a regular 32-sided po... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"answer": "240",
"index": 21290,
"question": "How many diagonals in a regular 32-sided polygon are not parallel to any of its sides?",
"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 Given a non-zero common difference arithmet... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 21291,
"question": "Given a non-zero common difference arithmetic sequence $\\{a_n\\}$ that satisfies $a_1$, $a_3$, and $a_4$ forming a geometric sequence, where $S_n$ is the sum of the first $n$ terms of the sequence $\\{a_n\\}$, calculate the value of $$\\frac{S_{3}-S_{2}}{S_{5}-S_{3}}.$$ Express your answer as a single number.",
"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 Two runners are competing in a 10-mile race... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"answer": "56",
"index": 21292,
"question": "Two runners are competing in a 10-mile race. The first runs at an average pace of 8 minutes per mile, while the second runs at an average pace of 7 minutes per mile. At some point, the second runner stops for a drink of water. The second runner could remain stopped for 8 minutes before the first runner catches up with him. How many minutes into the race did the second runner stop for a drink of water?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given two numbers $a$ and $b$, a new number... | math | {
"ground_truth": "499",
"style": "rule"
} | {
"answer": "499",
"index": 21293,
"question": "Given two numbers $a$ and $b$, a new number $c$ is generated according to the rule $c = a + b + ab$, and such a new number $c$ is called a \"lucky number\". Then, from the three numbers $a$, $b$, and $c$, any two numbers can be chosen, and according to the rule, another \"lucky number\" can be generated. Each generation of a \"lucky number\" is considered one operation. Now, with the numbers 1 and 4, and operating according to the above rule three times, the largest \"lucky number\" obtained is.",
"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 You are standing at a pole and a snail is m... | math | {
"ground_truth": "5050",
"style": "rule"
} | {
"answer": "5050",
"index": 21294,
"question": "You are standing at a pole and a snail is moving directly away from the pole at 1 cm/s. When the snail is 1 meter away, you start \"Round 1\". In Round \\( n (n \\geq 1) \\), you move directly toward the snail at \\( n+1 \\) cm/s. When you reach the snail, you immediately turn around and move back to the starting pole at \\( n+1 \\) cm/s. When you reach the pole, you immediately turn around and Round \\( n+1 \\) begins. At the start of Round 100, how many meters away is the snail?",
"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 On a circle, 103 natural numbers are writte... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"answer": "42",
"index": 21295,
"question": "On a circle, 103 natural numbers are written. It is known that among any 5 consecutive numbers, there will be at least two even numbers. What is the minimum number of even numbers that can be in the entire circle?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the function $f(x)=(x^{2}-6x+c_{1})(x... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21296,
"question": "Given the function $f(x)=(x^{2}-6x+c_{1})(x^{2}-6x+c_{2})(x^{2}-6x+c_{3})$, where the set of solutions to $f(x)=0$ is $M={x|f(x)=0}={x_{1},x_{2},x_{3},x_{4},x_{5}}⊆N^{*}$ and $c_{1}≥c_{2}≥c_{3}$, calculate the value of $c_{1}-c_{3}$. Express your answer as a single integer.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Compute the number of ordered quadruples of... | math | {
"ground_truth": "52",
"style": "rule"
} | {
"answer": "52",
"index": 21297,
"question": "Compute the number of ordered quadruples of positive integers $(a,b,c,d)$ such that \n\\[ a!\\cdot b!\\cdot c!\\cdot d!=24!. \\]",
"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 Find the area of the figure defined on the ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 21298,
"question": "Find the area of the figure defined on the coordinate plane by the system\n\n$$\n\\left\\{\\begin{array}{l}\n\\sqrt{1-x}+2 x \\geqslant 0 \\\\\n-1-x^{2} \\leqslant y \\leq 2+\\sqrt{x}\n\\end{array}\\right.\n$$",
"split": "train"
} |
cn_k12 | [
"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 There are five people, named A, B, C, D, an... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 21299,
"question": "There are five people, named A, B, C, D, and E, standing in a row. It is required that both A and B are not adjacent to C. How many different arrangements are possible?",
"split": "train"
} |
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