source stringclasses 10 values | domain listlengths 1 3 | llama8b_solve_rate float64 0 0.09 ⌀ | data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|---|---|
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Along the road connecting Masha's and Sasha... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 2300,
"question": "Along the road connecting Masha's and Sasha's houses, there are 17 apple trees and 20 poplars. When Masha was walking to visit Sasha, she was photographing all the trees. Right after the tenth apple tree, Masha’s phone memory was full, and she couldn't take photos of the remaining 13 trees. The next day, when Sasha was walking to visit Masha, starting from the eighth apple tree, he picked one leaf from each tree. How many leaves did Sasha pick?",
"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 Two cyclists, $A$ and $B$, simultaneously s... | math | {
"ground_truth": "180",
"style": "rule"
} | {
"answer": "180",
"index": 2301,
"question": "Two cyclists, $A$ and $B$, simultaneously start from two different locations, $M$ and $N$, respectively, heading towards $P$. The distance $NP$ is $30$ km longer than the distance $MP$. Each cyclist completes their journey in 10 hours.\n\nWhat is the distance $MP$ if cyclist $B$ takes 20 minutes less than cyclist $A$ for every $42$ km?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Trigonometry -> Functions"
] | 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 points $A( \\frac {π}{6}, \\frac { \\... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 2302,
"question": "Given points $A( \\frac {π}{6}, \\frac { \\sqrt {3}}{2}) $, $B( \\frac {π}{4},1) $, $C( \\frac {π}{2},0) $, if and only if there are two of these three points on the graph of the function $f(x)=\\sin ωx $, then the minimum value of the positive number $ω $ is _____ .",
"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 A number is the product of four prime numbe... | math | {
"ground_truth": "1989",
"style": "rule"
} | {
"answer": "1989",
"index": 2303,
"question": "A number is the product of four prime numbers. What is this number if the sum of the squares of the four prime numbers is 476?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Calculus -> Other",
"Mathematics -> Discrete Mathematics -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The integer sequence \\( \\left\\{a_{n}\\ri... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 2304,
"question": "The integer sequence \\( \\left\\{a_{n}\\right\\} \\) is defined as follows:\n$$\na_{0}=3, a_{1}=4, a_{n+2}=a_{n+1} a_{n}+\\left\\lceil\\sqrt{\\left(a_{n+1}^{2}-1\\right)\\left(a_{n}^{2}-1\\right)} \\right\\rceil \\text{ for } n \\geq 0.\n$$\n\nFind the value of \\( \\sum_{n=0}^{+\\infty}\\left(\\frac{a_{n+3}}{a_{n+2}}-\\frac{a_{n+2}}{a_{n}}+\\frac{a_{n+1}}{a_{n+3}}-\\frac{a_{n}}{a_{n+1}}\\right) \\).",
"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 Peter knows that the distance an airplane t... | math | {
"ground_truth": "5404",
"style": "rule"
} | {
"answer": "5404",
"index": 2305,
"question": "Peter knows that the distance an airplane travels between two countries is 7019 km, while the distance between Spain and Germany is 1615 km. Peter took a flight from Spain, which made a stopover in Germany, while being there, he receives a call from his brother asking him how many kilometers he has to fly to get to the other country and then return to Spain. What is the distance between Spain and the other country?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Intermediate Algebra -> Rational Expressions"
] | 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 Simplify the expression: $\\frac{{x}^{2}+x}... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 2306,
"question": "Simplify the expression: $\\frac{{x}^{2}+x}{{x}^{2}-2x+1}\\div (\\frac{2}{x-1}-\\frac{1}{x})$, then choose a suitable integer value of $x$ from the range $-2 \\lt x\\leqslant 2$ to substitute and evaluate.",
"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 In right triangle $A B C$, a point $D$ is o... | math | {
"ground_truth": "8041",
"style": "rule"
} | {
"answer": "8041",
"index": 2307,
"question": "In right triangle $A B C$, a point $D$ is on hypotenuse $A C$ such that $B D \\perp A C$. Let $\\omega$ be a circle with center $O$, passing through $C$ and $D$ and tangent to line $A B$ at a point other than $B$. Point $X$ is chosen on $B C$ such that $A X \\perp B O$. If $A B=2$ and $B C=5$, then $B X$ can be expressed as $\\frac{a}{b}$ for relatively prime positive integers $a$ and $b$. Compute $100 a+b$.",
"split": "train"
} |
olympiads | [
"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 Let \\( A \\) and \\( B \\) be the endpoint... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 2308,
"question": "Let \\( A \\) and \\( B \\) be the endpoints of the major axis of an ellipse \\( \\Gamma \\), and let \\( E \\) and \\( F \\) be the foci of \\( \\Gamma \\). Given that \\( |AB|=4 \\) and \\( |AF|=2+\\sqrt{3} \\), and let \\( P \\) be a point on \\( \\Gamma \\) such that \\( |PE| \\cdot |PF|=2 \\). Determine the area of \\( \\triangle PEF \\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $x > 0$, $y > 0$, and $( \\sqrt ... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 2309,
"question": "Given that $x > 0$, $y > 0$, and $( \\sqrt {x^{2}+1}-x+1)( \\sqrt {y^{2}+1}-y+1)=2$, find the value of $xy-2$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 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 month can have at most 5 Sundays. In a ye... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 2310,
"question": "A month can have at most 5 Sundays. In a year of 12 months, the maximum number of months that can have 5 Sundays is __________.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $x^2-1$ is a factor of $x^4+mx^3... | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"answer": "-7",
"index": 2311,
"question": "Given that $x^2-1$ is a factor of $x^4+mx^3+nx^2-2x+8$, find the value of $m+n$.",
"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 Misha made a homemade darts game during the... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"answer": "48",
"index": 2312,
"question": "Misha made a homemade darts game during the summer at the dacha. A circular board is divided into several sectors by concentric circles, and darts can be thrown at it. Points are awarded based on the number written in the sector, as shown in the diagram.\n\nMisha threw 8 darts three times. In the second attempt, he scored twice as many points as he did in the first attempt, and in the third attempt, he scored 1.5 times more than in the second attempt. How many points did he score in the second attempt?",
"split": "train"
} |
aops_forum | [
"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 $A, B, C$ , and $D$ are all on a circle,... | math | {
"ground_truth": "504",
"style": "rule"
} | {
"answer": "504",
"index": 2313,
"question": " $A, B, C$ , and $D$ are all on a circle, and $ABCD$ is a convex quadrilateral. If $AB = 13$ , $BC = 13$ , $CD = 37$ , and $AD = 47$ , what is the area of $ABCD$ ?",
"split": "train"
} |
cn_k12 | [
"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 Xiaoming, a primary school student, asked h... | math | {
"ground_truth": "69",
"style": "rule"
} | {
"answer": "69",
"index": 2314,
"question": "Xiaoming, a primary school student, asked his grandfather how old he was this year. His grandfather replied, \"This year, my age is more than 7 times yours. In a few years, it will become 6 times yours, then 5 times after a few more years, and eventually 4 times after some years. Can you guess how old I am this year?\" After some calculations, Xiaoming finally figured out that his grandfather is years old this year.",
"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 Susan, Arthur, Tom, Bob, Emily, and David a... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"answer": "70",
"index": 2315,
"question": "Susan, Arthur, Tom, Bob, Emily, and David are siblings. Arthur is 2 years older than Susan, Tom is 3 years younger than Bob, Emily is half of Susan's age, and David is the average of Arthur, Tom, and Emily's ages. If Bob is 11 years old and Susan is 15 years old, how old are all six family members in total?",
"split": "train"
} |
olympiads | [
"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 As shown in the figure, an ant is crawling ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 2316,
"question": "As shown in the figure, an ant is crawling on a grid. Every step it takes is from one point to an adjacent point (two points connected by a dashed line are considered adjacent). The ant has to take a total of four steps. If it starts from point $A$, there are $m$ different crawling routes; if it starts from point $B$, there are $n$ different crawling routes. Find $n \\div m=$ $\\qquad$ .",
"split": "train"
} |
big_math | [
"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 Genevieve makes a small kite and a large ki... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 2317,
"question": "Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram. For her small kite, Genevieve draws the kite on a one-inch grid. Calculate the area of the small kite in square inches.\n\n[asy]\nfor (int a = 0; a < 7; ++a)\n{\nfor (int b = 0; b < 8; ++b)\n{\ndot((a,b));\n}\n}\ndraw((3,0)--(0,5)--(3,7)--(6,5)--cycle);[/asy]\n\nExpress your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Calculus -> Limits -> 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 limit of the function:\n\n$$\\l... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 2318,
"question": "Compute the limit of the function:\n\n$$\\lim _{x \\rightarrow 0}\\left(2-3^{\\sin ^{2} x}\\right)^{\\frac{1}{\\ln (\\cos x)}}$$",
"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 Mrs. Sheridan has 11 cats. She bought 43.5 ... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"answer": "54",
"index": 2319,
"question": "Mrs. Sheridan has 11 cats. She bought 43.5 more. How many cats does she have now?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the given figure, the diameter \\( AB \\... | math | {
"ground_truth": "65",
"style": "rule"
} | {
"answer": "65",
"index": 2320,
"question": "In the given figure, the diameter \\( AB \\) of the circle has a length that is a two-digit integer in decimal form. Reversing the digits of this integer gives the length of the chord \\( CD \\), which is perpendicular to the diameter \\( AB \\). The distance from the intersection point \\( H \\) to the center of the circle \\( O \\) is a positive rational number. Determine the length of \\( AB \\).",
"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 \nOn a chessboard of 8x8, 64 checkers are p... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 2321,
"question": "\nOn a chessboard of 8x8, 64 checkers are placed, numbered from 1 to 64. 64 students approach it one by one and flip only those checkers whose numbers are divisible by the order number of the current student. A \"Queen\" is a checker that has been flipped an odd number of times. How many \"Queens\" will be on the board after the last student steps away from it?",
"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 The ratio of incomes of two persons P1 and ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 2322,
"question": "The ratio of incomes of two persons P1 and P2 is 5 : 4, and the ratio of their expenditures is unknown. At the end of the year, each saves Rs. 1200. If the income of P1 is Rs. 3000, what is the ratio of their expenditures?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Complex 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 Given that non-zero complex numbers \\( x \... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 2323,
"question": "Given that non-zero complex numbers \\( x \\) and \\( y \\) satisfy \\( x^{2} + xy + y^{2} = 0 \\), find the value of the algebraic expression \\(\\left(\\frac{x}{x + y}\\right)^{2005} + \\left(\\frac{y}{x + y}\\right)^{2005}\\). Express your answer as a single numerical value.",
"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 Every year, an amount increases by 5/12 of ... | math | {
"ground_truth": "4548",
"style": "rule"
} | {
"answer": "4548",
"index": 2324,
"question": "Every year, an amount increases by 5/12 of itself. How much will it be after three years if its present value is Rs. 1600 and the annual increment function follows a custom exponential formula: f(t) = (1 + (5/12))^t, where t is the number of years?",
"split": "train"
} |
math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Amy's grandmother gave her 3 identical choc... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"answer": "25",
"index": 2325,
"question": "Amy's grandmother gave her 3 identical chocolate chip cookies and 4 identical sugar cookies. In how many different orders can Amy eat the cookies such that either she eats a chocolate chip cookie first, she eats a chocolate chip cookie last, or both?",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a set of consecutive positive integer... | math | {
"ground_truth": "208",
"style": "rule"
} | {
"answer": "208",
"index": 2326,
"question": "Given a set of consecutive positive integers $I=\\{1, 2, 3, \\ldots, 238\\}$, if $T$ is a subset of $I$ and satisfies the condition: if $x \\in T$, then $7x \\notin T$, find the maximum number of elements in the set $T$. Express your answer as a whole number.",
"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 $x(x-1)(x+1)^{4}$, the ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 2327,
"question": "In the expansion of $x(x-1)(x+1)^{4}$, the coefficient of the term containing $x^{2}$ is _______. (Enter the answer as a number)",
"split": "train"
} |
big_math | [
"Mathematics -> 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 Given the function $f(x) = \\begin{cases} x... | math | {
"ground_truth": "1313",
"style": "rule"
} | {
"answer": "1313",
"index": 2328,
"question": "Given the function $f(x) = \\begin{cases} x^{2}-131, & x>10 \\\\ f(f(x+2)), & x\\leq 10 \\end{cases}$, calculate the exact value of $f(8)$. Provide your answer as a single integer.",
"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 A $10 \\times 10$ table consists of 100 uni... | math | {
"ground_truth": "39",
"style": "rule"
} | {
"answer": "39",
"index": 2329,
"question": "A $10 \\times 10$ table consists of 100 unit cells. A block is a $2 \\times 2$ square consisting of 4 unit cells of the table. A set $C$ of $n$ blocks covers the table (i.e. each cell of the table is covered by some block of $C$ ) but no $n-1$ blocks of $C$ cover the table. Find the largest possible value of n.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Riders on a Ferris wheel travel in a circle... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 2330,
"question": "Riders on a Ferris wheel travel in a circle in a vertical plane. A particular wheel has radius 20 feet and revolves at the constant rate of one revolution per minute. How many seconds does it take a rider to travel from the bottom of the wheel to a point 10 vertical feet above the bottom? Express your answer in seconds.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a right-angled trapezoid, with base $AB ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 2331,
"question": "In a right-angled trapezoid, with base $AB = 13$, $CD = 8$, $AD \\perp AB$, and $AD = 12$, calculate the distance from $A$ to $BC$. Express your answer as a single number.",
"split": "train"
} |
big_math | [
"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 Find the exact number of real roots for the... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 2332,
"question": "Find the exact number of real roots for the equation sin(x) = lg(x) within the domain 0 < x <= 10.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence $\\{x_{n}\\}$ satisfying... | math | {
"ground_truth": "1345",
"style": "rule"
} | {
"answer": "1345",
"index": 2333,
"question": "Given the sequence $\\{x_{n}\\}$ satisfying $x_{n+2}=|x_{n+1}-x_{n}|(n∈N^{})$ and $x_{1}=1$, $x_{2}=a(a≤slant 1,a≠ 0)$, if $x_{n+3}=x_{n}$ holds true for any positive integer $n$, find the sum of the first 2017 terms of the sequence $\\{x_{n}\\}$, denoted as $S_{2017}$. Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Precalculus -> Trigonometric 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 Given $3\\sin\\theta+\\cos\\theta=\\sqrt{10... | math | {
"ground_truth": "-14",
"style": "rule"
} | {
"answer": "-14",
"index": 2334,
"question": "Given $3\\sin\\theta+\\cos\\theta=\\sqrt{10}$, calculate the value of $\\tan(\\theta+\\frac{\\pi}{8})-\\frac{1}{\\tan(\\theta+\\frac{\\pi}{8})}$. Express your answer as a single integer.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If integers $a$ , $b$ , $c$ , and $d$ ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 2335,
"question": "If integers $a$ , $b$ , $c$ , and $d$ satisfy $ bc + ad = ac + 2bd = 1 $ , find all possible values of $ \\frac {a^2 + c^2}{b^2 + d^2} $ .",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Binomial Theorem"
] | 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 coefficient of the $x^3$ term in t... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"answer": "64",
"index": 2336,
"question": "Find the coefficient of the $x^3$ term in the expansion of $(2\\sqrt{x} - \\frac{1}{\\sqrt{x}})^6$.",
"split": "train"
} |
orca_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 For the equations some x + y = 19 and x + 3... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 2337,
"question": "For the equations some x + y = 19 and x + 3y = 1, the value of 3x + 2y is 10. What is the coefficient of x in the first equation?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 100 chairs arranged in a circle. ... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"answer": "34",
"index": 2338,
"question": "There are 100 chairs arranged in a circle. If \\( n \\) people are sitting on these chairs, such that any new person sitting down will always sit on a chair adjacent to one of the \\( n \\) people, what is the minimum value of \\( n \\)?",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the greatest natural number whose rema... | math | {
"ground_truth": "900",
"style": "rule"
} | {
"answer": "900",
"index": 2339,
"question": "Find the greatest natural number whose remainder when divided by 91 is equal to the square of the quotient.",
"split": "train"
} |
big_math | [
"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 Given the equation y = x + 1/x, express the... | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"answer": "-6",
"index": 2340,
"question": "Given the equation y = x + 1/x, express the polynomial x^4 + x^3 - 4x^2 + x + 1 = 0 in terms of y. Use the format x^2(y^2 + y + n) = 0 and find the exact value of n.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Two circles \\( C_{1} \\) and \\( C_{2} \\)... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 2341,
"question": "Two circles \\( C_{1} \\) and \\( C_{2} \\) have their centers at the point \\( (3, 4) \\) and touch a third circle, \\( C_{3} \\). The center of \\( C_{3} \\) is at the point \\( (0, 0) \\) and its radius is 2. Find the sum of the radii of the two circles \\( C_{1} \\) and \\( C_{2} \\). 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 15 liters are taken out of a container full... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"answer": "49",
"index": 2342,
"question": "15 liters are taken out of a container full of liquid A and replaced with liquid B. This process is repeated 5 more times (for a total of 6 times). After this process, if the container contains liquid A and B in the ratio 9 : 16, what is the capacity of the container M?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 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 \\( x \\) and \\( y \\) are positive int... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 2343,
"question": "If \\( x \\) and \\( y \\) are positive integers such that \\( xyz = 240 \\), \\( xy + z = 46 \\), and \\( x + yz = 64 \\), calculate the value of \\( x + y + z \\). Express your answer as a single integer.",
"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 if 11 oranges bought 10 r and 10 oranges so... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 2344,
"question": "if 11 oranges bought 10 r and 10 oranges sold 11 r . what is the profit",
"split": "train"
} |
cn_k12 | [
"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 The arithmetic sequence 5, 8, 11, … and the... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 2345,
"question": "The arithmetic sequence 5, 8, 11, … and the arithmetic sequence 3, 8, 13, … both have 100 terms. How many terms do these two sequences have in common?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Prime Numbers",
"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 If x is equal to the sum of all squares of ... | math | {
"ground_truth": "60651",
"style": "rule"
} | {
"answer": "60651",
"index": 2346,
"question": "If x is equal to the sum of all squares of integers from 1 to 50, inclusive, y is the number of prime integers from 1 to 50, inclusive, and z is the sum of the first 20 numbers in the Fibonacci sequence, what is the value of x + y + z?",
"split": "train"
} |
olympiads | [
"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 An even power of a certain number is a four... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"answer": "55",
"index": 2347,
"question": "An even power of a certain number is a four-digit number with the first digit as 3 and the last digit as 5. Find this 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 bowl, there are 19 marbles of varying ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 2348,
"question": "In a bowl, there are 19 marbles of varying sizes and weights. Out of these marbles, 5 are yellow, and the remainder are blue and red marbles in the ratio 3:4 respectively. The yellow marbles have a combined weight of 8 grams. The red marbles weigh twice as much as the yellow marbles per gram. The blue marbles are not counted for this problem. Calculate the difference in total weight between the red marbles and the yellow marbles.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given sets $A=\\{x|x^2-2x-3>0\\}$, $B=\\{x|... | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"answer": "-7",
"index": 2349,
"question": "Given sets $A=\\{x|x^2-2x-3>0\\}$, $B=\\{x|x^2+ax+b\\leq0\\}$, if $A\\cup B=\\mathbb{R}$ and $A\\cap B=\\{x|3<x\\leq4\\}$, then the value of $a+b$ equals to.",
"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 Points $G$ and $N$ are chosen on the interi... | math | {
"ground_truth": "10324",
"style": "rule"
} | {
"answer": "10324",
"index": 2350,
"question": "Points $G$ and $N$ are chosen on the interiors of sides $E D$ and $D O$ of unit square $D O M E$, so that pentagon GNOME has only two distinct side lengths. The sum of all possible areas of quadrilateral $N O M E$ can be expressed as $\\frac{a-b \\sqrt{c}}{d}$, where $a, b, c, d$ are positive integers such that $\\operatorname{gcd}(a, b, d)=1$ and $c$ is square-free (i.e. no perfect square greater than 1 divides $c$ ). Compute $1000 a+100 b+10 c+d$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Non-Euclidean Geometry -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the asymptote equation of the hy... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 2351,
"question": "Given that the asymptote equation of the hyperbola $y^{2}+\\frac{x^2}{m}=1$ is $y=\\pm \\frac{\\sqrt{3}}{3}x$, find the value of $m$.",
"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 Select 3 teachers from 6 to teach in 3 diff... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"answer": "42",
"index": 2352,
"question": "Select 3 teachers from 6 to teach in 3 different poverty-stricken areas, one in each area. Teachers A and B cannot go to the same area, and teachers A and C must either both go or both not go. How many different selection plans are there?",
"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 Sari and Ken climb up a mountain. At night,... | math | {
"ground_truth": "500",
"style": "rule"
} | {
"answer": "500",
"index": 2353,
"question": "Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 05:00 and starts climbing at a constant pace. Ken starts climbing only at 07:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a certain pace, and reaches the summit before Sari. When Ken reaches the summit, Sari is 50 meters behind him. Ken reached the summit at 12. What is Ken's climbing pace in meters per hour?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A sphere with a radius of $\\sqrt{6}$ has a... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 2354,
"question": "A sphere with a radius of $\\sqrt{6}$ has an inscribed right square prism with a height of 4. Calculate the surface area of this right square prism. Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a city, there are 9 bus stops and severa... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 2355,
"question": "In a city, there are 9 bus stops and several buses. Any two buses share at most one common bus stop. Each bus has exactly three bus stops. What is the maximum number of buses that can be in the city?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The line $3x+4y-12=0$ intersects the $x$-ax... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 2356,
"question": "The line $3x+4y-12=0$ intersects the $x$-axis and $y$-axis at points $A$ and $B$ respectively. Point $P$ lies on the line $y=x+1$. Find the maximum value of $|PA|-|PB|$.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Discrete Mathematics -> Graph Theory"
] | 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 Consider the graph on $1000$ vertices $v... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 2357,
"question": "Consider the graph on $1000$ vertices $v_1, v_2, ...v_{1000}$ such that for all $1 \\le i < j \\le 1000$ , $v_i$ is connected to $v_j$ if and only if $i$ divides $j$ . Determine the minimum number of colors that must be used to color the vertices of this graph such that no two vertices sharing an edge are the same color.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 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 According to the rules of a chess match, th... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 2358,
"question": "According to the rules of a chess match, the winner is the one who gains two victories over the opponent. Draws do not count. The probabilities of winning for the opponents are equal. The number of decisive games in such a match is a random variable. Find its expected value.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A certain school arranges $5$ senior high s... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 2359,
"question": "A certain school arranges $5$ senior high school teachers to visit $3$ schools for exchange and learning. One school has $1$ teacher, one school has $2$ teachers, and one school has $2$ teachers. The total number of different arrangements is _______.",
"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 Find the smallest natural number n such tha... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 2360,
"question": "Find the smallest natural number n such that the equation \\(\\left\\lfloor \\frac{10^{n}}{x} \\right\\rfloor = 2006\\) has an integer solution for x. Express your answer as the smallest natural number n.",
"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 Find the smallest natural number \\( n \\) ... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 2361,
"question": "Find the smallest natural number \\( n \\) such that in any set of \\( n \\) different natural numbers that do not exceed 1000, it is always possible to choose two numbers where the larger number is not divisible by the smaller one.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A jogger running at 9 km/hr alongside a rai... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 2362,
"question": "A jogger running at 9 km/hr alongside a railway track is 150 m ahead of the engine of a 100 m long train running at a certain speed in the same direction. The train takes 25 seconds to pass the jogger. What is the speed of the train in km/hr?",
"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 find the cost of fencing around a circular ... | math | {
"ground_truth": "396",
"style": "rule"
} | {
"answer": "396",
"index": 2363,
"question": "find the cost of fencing around a circular field of diameter 36 m at the rate of rs . 3.50 a meter ?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the sum of the first $n$ terms o... | math | {
"ground_truth": "1008",
"style": "rule"
} | {
"answer": "1008",
"index": 2364,
"question": "Given that the sum of the first $n$ terms of an arithmetic sequence ${a_n}$ is $S_n$, if $\\overrightarrow{OB}=a_3 \\overrightarrow{OA}+a_{2014} \\overrightarrow{OC}$, and points $A$, $B$, $C$ are collinear ($O$ is a point outside this line), then $S_{2016} =$ \\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the sum of the digits of the intege... | math | {
"ground_truth": "63",
"style": "rule"
} | {
"answer": "63",
"index": 2365,
"question": "What is the sum of the digits of the integer which is equal to \\(6666666^{2} - 3333333^{2}\\)? Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 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 Among the 27 points consisting of the 8 ver... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"answer": "49",
"index": 2366,
"question": "Among the 27 points consisting of the 8 vertices of a cube, the midpoints of its 12 edges, the centers of its 6 faces, and the center of the cube, how many groups of three collinear points are there? Express your answer as a whole number.",
"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 Four people each write a New Year's card. T... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 2367,
"question": "Four people each write a New Year's card. Then they put them together and each person picks a card written by someone else. How many different ways can the cards be picked?",
"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 If the distance between two parallel lines ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 2368,
"question": "If the distance between two parallel lines $l_{1}$: $x-2y+m=0\\left(m \\gt 0\\right)$ and $l_{2}$: $2x+ny-6=0$ is $2\\sqrt{5}$, then $m+n=\\_\\_\\_\\_\\_\\_$.",
"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 In triangle \\( ABC \\), it is known that \... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 2369,
"question": "In triangle \\( ABC \\), it is known that \\(\\angle BAC = 75^\\circ\\), \\( AB = 1 \\), and \\( AC = \\sqrt{6} \\). On the side \\( BC \\), a point \\( M \\) is chosen such that \\(\\angle BAM = 30^\\circ\\). The line \\( AM \\) intersects the circumcircle of triangle \\( ABC \\) at a point \\( N \\) different from \\( A \\). Find \\( AN \\).",
"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 Two trains of equal length are running on p... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"answer": "55",
"index": 2370,
"question": "Two trains of equal length are running on parallel inclined tracks in the same direction. The tracks have a uniform incline of 5 degrees. The trains initially have speeds of 47 km/hr and 36 km/hr while moving uphill. Considering the effects of gravity and friction on acceleration, the faster train passes the slower train in 36 seconds. Find the length of each train.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If \\[N=\\frac{\\sqrt{\\sqrt{5}+2}+\\sqrt{\... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 2371,
"question": "If \\[N=\\frac{\\sqrt{\\sqrt{5}+2}+\\sqrt{\\sqrt{5}-2}}{\\sqrt{\\sqrt{5}+1}}-\\sqrt{3-2\\sqrt{2}},\\] then calculate the value of N. Express your answer as a single number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A number contains only two kinds of digits:... | math | {
"ground_truth": "3444",
"style": "rule"
} | {
"answer": "3444",
"index": 2372,
"question": "A number contains only two kinds of digits: 3 or 4, and both 3 and 4 appear at least once. The number is a multiple of both 3 and 4. What is the smallest such number?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There were two decks of 36 cards each on th... | math | {
"ground_truth": "1260",
"style": "rule"
} | {
"answer": "1260",
"index": 2373,
"question": "There were two decks of 36 cards each on the table. The first deck was shuffled and placed on top of the second deck. Then, for each card in the first deck, the number of cards between it and the same card from the second deck was counted (i.e., the number of cards between the sevens of hearts, between the queens of spades, etc.). What is the sum of these 36 counted numbers?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Area"
] | 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 diagram, \\(PQRS\\) is a rectangle w... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 2374,
"question": "In the diagram, \\(PQRS\\) is a rectangle with \\(SR = 15\\). Point \\(T\\) is above \\(PS\\) and point \\(U\\) is on \\(PS\\) so that \\(TU\\) is perpendicular to \\(PS\\). If \\(PT = 10\\) and \\(US = 4\\) and the area of \\(PQRS\\) is 180, calculate the area of \\(\\triangle PTS\\). Express your answer as a whole number.",
"split": "train"
} |
math | [
"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 Triangle $ABC$ has side lengths $AB = 12$, ... | math | {
"ground_truth": "161",
"style": "rule"
} | {
"answer": "161",
"index": 2375,
"question": "Triangle $ABC$ has side lengths $AB = 12$, $BC = 25$, and $CA = 17$. Rectangle $PQRS$ has vertex $P$ on $\\overline{AB}$, vertex $Q$ on $\\overline{AC}$, and vertices $R$ and $S$ on $\\overline{BC}$. In terms of the side length $PQ = \\omega$, the area of $PQRS$ can be expressed as the quadratic polynomial\\[Area(PQRS) = \\alpha \\omega - \\beta \\omega^2.\\]\nThen the coefficient $\\beta = \\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.",
"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 The ratio of boys to girls in a math class ... | math | {
"ground_truth": "176",
"style": "rule"
} | {
"answer": "176",
"index": 2376,
"question": "The ratio of boys to girls in a math class is 5:8, the ratio of math to science students is 7:4, and the ratio of science to literature students is 3:5. If the total number of students across all three subjects (math, science, and literature) is 720, how many girls are in the math class?",
"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 Given positive real numbers \\(a,b\\), find... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 2377,
"question": "Given positive real numbers \\(a,b\\), find the maximum value of \\(m\\) such that the inequality \\(\\dfrac{m}{3a+b}-\\dfrac{3}{a}-\\dfrac{1}{b}\\leqslant 0\\) always holds.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Select 3 out of 5 members from the class co... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 2378,
"question": "Select 3 out of 5 members from the class committee to serve as the class's Academic Affairs, Entertainment, and Sports commissioners. Given that members A and B cannot serve as the Entertainment commissioner, determine the number of different methods for this selection.",
"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 rectangular tiled patio is composed of 60... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 2379,
"question": "A rectangular tiled patio is composed of 60 rectangular tiles, where each tile has a length of 2 units and a width of 1 unit. The initial rectangular patio has its length and width in a 3:2 ratio. The patio will be rearranged so that there will be 3 fewer columns of tiles and 5 more rows of tiles. After the change in layout, the patio will still have 60 rectangular tiles, and it will still be rectangular. How many rows are in the initial tile patio before the change in layout?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 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 math teacher is 176 cm tall. The heights ... | math | {
"ground_truth": "185",
"style": "rule"
} | {
"answer": "185",
"index": 2380,
"question": "A math teacher is 176 cm tall. The heights of his grandfather, father, and son are 173 cm, 170 cm, and 182 cm, respectively. Since the son's height is related to the father's height, the teacher uses the method of linear regression analysis to predict his grandson's height as ______ cm.",
"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 \nInvestigator Podberezovikov is pursuing M... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 2381,
"question": "\nInvestigator Podberezovikov is pursuing Maxim Detochkin (each driving their own car). Initially, both were driving on the highway at a speed of 60 km/h, with Podberezovikov trailing Detochkin by 2 km. Upon entering the city, each reduced their speed to 40 km/h, and upon exiting the city onto a good road, each increased their speed to 70 km/h. When the road ended and transitioned to a dirt road, each had to reduce their speed again to 30 km/h. What was the distance between them on the dirt road?",
"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 Let \\( n \\) be the answer to this problem... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 2382,
"question": "Let \\( n \\) be the answer to this problem. We define the digit sum of a date as the sum of its 4 digits when expressed in mmdd format (e.g. the digit sum of 13 May is \\( 0+5+1+3=9 \\)). Find the number of dates in the year 2021 with digit sum equal to the positive integer \\( n \\).",
"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 Among the six number cards 8, 3, 6, 5, 0, a... | math | {
"ground_truth": "342",
"style": "rule"
} | {
"answer": "342",
"index": 2383,
"question": "Among the six number cards 8, 3, 6, 5, 0, and 7, A is the largest two-digit number, and B is the smallest two-digit number. Find the value of (A-B)×6.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Non-Euclidean Geometry -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $F_1$ and $F_2$ are the two foci... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 2384,
"question": "Given that $F_1$ and $F_2$ are the two foci of the hyperbola $\\frac{x^2}{4} - y^2 = 1$, and point $P$ is on the hyperbola such that $\\overrightarrow{PF_1} \\cdot \\overrightarrow{PF_2} = 0$, find the area of $\triangle F_1PF_2$. Express your answer as a single 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 How many 9-digit numbers divisible by 2 can... | math | {
"ground_truth": "3360",
"style": "rule"
} | {
"answer": "3360",
"index": 2385,
"question": "How many 9-digit numbers divisible by 2 can be formed by rearranging the digits of the number 131152152?",
"split": "train"
} |
olympiads | [
"Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals"
] | 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 Calculate the area of the figure bounded by... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 2386,
"question": "Calculate the area of the figure bounded by the graphs of the functions:\n\n$$\ny=(x-2)^{3}, \\quad y=4x-8\n$$",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the largest 4-digit number exactly ... | math | {
"ground_truth": "9984",
"style": "rule"
} | {
"answer": "9984",
"index": 2387,
"question": "What is the largest 4-digit number exactly divisible by a certain number? The answer is 9984. What is the divisor?",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If ( 2 to the x ) - ( 2 to the ( x - 2 ) ) ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 2388,
"question": "If ( 2 to the x ) - ( 2 to the ( x - 2 ) ) equals 3 ( 2 to the 12 ), what is the value of x?",
"split": "train"
} |
omnimath | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Jim wrote a sequence of symbols a total of ... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"answer": "150",
"index": 2389,
"question": "Jim wrote a sequence of symbols a total of 50 times. How many more of one symbol than another did he write?",
"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 We say an integer $n$ is naoish if $n \\... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 2390,
"question": "We say an integer $n$ is naoish if $n \\geq 90$ and the second-to-last digit of $n$ (in decimal notation) is equal to $9$ . For example, $10798$ , $1999$ and $90$ are naoish, whereas $9900$ , $2009$ and $9$ are not. Nino expresses 2020 as a sum:\n \\[\n 2020=n_{1}+n_{2}+\\ldots+n_{k}\n \\]\n where each of the $n_{j}$ is naoish.\n\n What is the smallest positive number $k$ for which Nino can do this?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Distribute $5$ volunteers into $3$ groups, ... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 2391,
"question": "Distribute $5$ volunteers into $3$ groups, with two groups of $2$ people each and one group of $1$ person, to three different service venues at the \"March 3\" event in Eastern City. How many different distribution methods are there? (Answer with a number.)",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the quadratic equation \\(x^{2} + bx ... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"answer": "19",
"index": 2392,
"question": "Given the quadratic equation \\(x^{2} + bx + c = 0\\) where the coefficients \\(b\\) and \\(c\\) are elements of the set \\(\\{1, 2, 3, 4, 5, 6\\}\\), count the number of equations that have real roots. Express your answer as a single integer.",
"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 the sequence $\\left\\{x_{n}\\right\\... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 2393,
"question": "Given the sequence $\\left\\{x_{n}\\right\\}$, with $x_{1}=1$ and $x_{n+1}=\\frac{\\sqrt{3} x_{n}+1}{\\sqrt{3}-x_{n}}$, determine the value of $\\sum_{n=1}^{2008} x_{n}$. Express your answer as a single integer or a mathematical expression.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> 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 Given a finite set\n$$\nA = \\left\\{a_{i} ... | math | {
"ground_truth": "3600",
"style": "rule"
} | {
"answer": "3600",
"index": 2394,
"question": "Given a finite set\n$$\nA = \\left\\{a_{i} \\mid 1 \\leq i \\leq n, i \\in \\mathbf{Z}_{+}\\right\\} \\left( n \\in \\mathbf{Z}_{+} \\right), \n$$\nlet $S = \\sum_{i=1}^{n} a_{i}$, so $S$ is called the \"sum\" of set $A$ and is denoted as $|A|$. The set $P = \\{2n-1 \\mid n=1,2,\\cdots,10\\}$ is given, and the set of all three-element subsets of $P$ is denoted as $P_{1}, P_{2}, \\cdots, P_{k}$. Find $\\sum_{i=1}^{k} \\left|P_{i}\\right|$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n From the set ${1, 3, 5}$, select two number... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 2395,
"question": "From the set ${1, 3, 5}$, select two numbers, and from the set ${2, 4}$, select one number to form a three-digit number without repeated digits. Determine the number of odd three-digit numbers that can be formed under these conditions.",
"split": "train"
} |
big_math | [
"Mathematics -> 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 hyperbola $C:\\frac{x^2}{a^2}-\\fra... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 2396,
"question": "Given a hyperbola $C:\\frac{x^2}{a^2}-\\frac{y^2}{b^2}=1 (a > 0, b > 0)$, one of its asymptotes is intercepted by a circle $(x-2)^2 + y^2 = 4$ to form a chord of length $2$. Calculate the eccentricity of hyperbola $C$. Express your answer as a single number.",
"split": "train"
} |
omnimath | [
"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 It can be shown that there exists a unique ... | math | {
"ground_truth": "-2445",
"style": "rule"
} | {
"answer": "-2445",
"index": 2397,
"question": "It can be shown that there exists a unique polynomial $P$ in two variables such that for all positive integers $m$ and $n$, $$P(m, n)=\\sum_{i=1}^{m} \\sum_{j=1}^{n}(i+j)^{7}$$ Compute $P(3,-3)$.",
"split": "train"
} |
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 man nearing retirement wants to invest so... | math | {
"ground_truth": "74726",
"style": "rule"
} | {
"answer": "74726",
"index": 2398,
"question": "A man nearing retirement wants to invest some money in a fund that compounds annually at a rate of 6 percent, so that in five years, he will have at least $\\$100,000$. How much money must he invest now to make that happen? (Give your answer to the nearest dollar.)",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n As shown in the figure, the diagonals $AC$ ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 2399,
"question": "As shown in the figure, the diagonals $AC$ and $BD$ of quadrilateral $ABCD$ intersect at point $O$. If the area of $\\triangle ABD$ is 10, the area of $\\triangle ABC$ is 12, and the area of $\\triangle BDC$ is 20, what is the area of $\\triangle BOC$?",
"split": "train"
} |
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