source
stringclasses 10
values | domain
listlengths 1
3
| llama8b_solve_rate
float64 0
0.09
⌀ | data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|---|---|---|
big_math
|
[
"Mathematics -> 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 school's participants in a math competition had an average score of 75. The number of male contestants was 80% more than the number of female contestants, and the average score of female contestants was 20% higher than that of male contestants. Calculate the average score of the female contestants. Express your answer as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "84",
"style": "rule"
}
|
{
"answer": "84",
"index": 0,
"question": "A school's participants in a math competition had an average score of 75. The number of male contestants was 80% more than the number of female contestants, and the average score of female contestants was 20% higher than that of male contestants. Calculate the average score of the female contestants. Express your answer as a whole number.",
"split": "train"
}
|
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 Suppose that $A$ and $B$ are digits in base $d > 6$ such that $\\overline{AB}_d + \\overline{AA}_d = 162_d$. Find $A_d - B_d$ in base $d$. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 1,
"question": "Suppose that $A$ and $B$ are digits in base $d > 6$ such that $\\overline{AB}_d + \\overline{AA}_d = 162_d$. Find $A_d - B_d$ in base $d$.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Quadratic Functions"
] | 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 a ( a - 4 ) = some number and b ( b - 4 ) = the same number , where a ≠ b , and a + b = 4. What is that number? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-3",
"style": "rule"
}
|
{
"answer": "-3",
"index": 2,
"question": "Given that a ( a - 4 ) = some number and b ( b - 4 ) = the same number , where a ≠ b , and a + b = 4. What is that number?",
"split": "train"
}
|
orca_math
|
[
"Applied Mathematics -> Math Word Problems -> 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 every 1 year a human ages, a dog ages 7 years. When Max is 3, his dog of a certain age will be 18 years older in dog years. How old is Max's dog? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "6",
"style": "rule"
}
|
{
"answer": "6",
"index": 3,
"question": "For every 1 year a human ages, a dog ages 7 years. When Max is 3, his dog of a certain age will be 18 years older in dog years. How old is Max's dog?",
"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 8 singers are participating in a festival and are scheduled to perform \\( m \\) times, with 4 singers performing in each show. Design a plan to minimize the number of performances \\( m \\) so that any two singers perform together the same number of times. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "14",
"style": "rule"
}
|
{
"answer": "14",
"index": 4,
"question": "8 singers are participating in a festival and are scheduled to perform \\( m \\) times, with 4 singers performing in each show. Design a plan to minimize the number of performances \\( m \\) so that any two singers perform together the same number of times.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 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 When 5 integers are arranged in ascending order, the median is 6. If the only mode of this data set is 8, then what is the possible maximum sum of these 5 integers? Express your answer as a single numerical value. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "31",
"style": "rule"
}
|
{
"answer": "31",
"index": 5,
"question": "When 5 integers are arranged in ascending order, the median is 6. If the only mode of this data set is 8, then what is the possible maximum sum of these 5 integers? Express your answer as a single numerical value.",
"split": "train"
}
|
cn_k12
|
[
"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 For the equation involving $x$, $\\frac{2x+1}{x-3}=\\frac{m}{3-x}+1$, if it has a root that increases, the value of $m$ is ______. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-7",
"style": "rule"
}
|
{
"answer": "-7",
"index": 6,
"question": "For the equation involving $x$, $\\frac{2x+1}{x-3}=\\frac{m}{3-x}+1$, if it has a root that increases, the value of $m$ is ______.",
"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 The sum of the non-prime numbers between a certain number and 60, non-inclusive, is 383. What is the starting number? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "50",
"style": "rule"
}
|
{
"answer": "50",
"index": 7,
"question": "The sum of the non-prime numbers between a certain number and 60, non-inclusive, is 383. What is the starting 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 Mary had 18 baseball cards, and 8 were torn. Fred gave Mary 26 new baseball cards. Mary bought 40 baseball cards. Then, she exchanged 10 of her cards with her friend Tom for unique editions and accidentally lost 5 cards. How many baseball cards does Mary have now? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "71",
"style": "rule"
}
|
{
"answer": "71",
"index": 8,
"question": "Mary had 18 baseball cards, and 8 were torn. Fred gave Mary 26 new baseball cards. Mary bought 40 baseball cards. Then, she exchanged 10 of her cards with her friend Tom for unique editions and accidentally lost 5 cards. How many baseball cards does Mary have now?",
"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 How many natural numbers $N \\leq 1000000$ exist such that $N$ is divisible by $\\lfloor \\sqrt{N} \\rfloor$? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "2998",
"style": "rule"
}
|
{
"answer": "2998",
"index": 9,
"question": "How many natural numbers $N \\leq 1000000$ exist such that $N$ is divisible by $\\lfloor \\sqrt{N} \\rfloor$?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods"
] | 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 2 different exams to be scheduled within 5 days, with at most one exam per day, and exams cannot be scheduled on two consecutive days. Calculate the total number of different scheduling plans. Express your answer as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "12",
"style": "rule"
}
|
{
"answer": "12",
"index": 10,
"question": "There are 2 different exams to be scheduled within 5 days, with at most one exam per day, and exams cannot be scheduled on two consecutive days. Calculate the total number of different scheduling plans. Express your answer as a whole 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 Vasya loves picking mushrooms. He calculated that during the autumn, he collected a three-digit number of mushrooms with the sum of its digits equal to 14. Then Vasya calculated that 8% of the mushrooms were white, and 14% were boletus. How many mushrooms did Vasya collect? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "950",
"style": "rule"
}
|
{
"answer": "950",
"index": 11,
"question": "Vasya loves picking mushrooms. He calculated that during the autumn, he collected a three-digit number of mushrooms with the sum of its digits equal to 14. Then Vasya calculated that 8% of the mushrooms were white, and 14% were boletus. How many mushrooms did Vasya collect?",
"split": "train"
}
|
math
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notices that no two adjacent houses ever get mail on the same day, but that there are never more than two houses in a row that get no mail on the same day. How many different patterns of mail delivery are possible? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "351",
"style": "rule"
}
|
{
"answer": "351",
"index": 12,
"question": "A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notices that no two adjacent houses ever get mail on the same day, but that there are never more than two houses in a row that get no mail on the same day. How many different patterns of mail delivery are possible?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the plane, there is a set of integer points \\( S = \\{ (a, b) \\mid 1 \\leqslant a, b \\leqslant 5, a, b \\in \\mathbf{Z} \\} \\). Now consider a subset \\( T \\) of integer points in the plane such that for any point \\( P \\) in \\( S \\), there exists a distinct point \\( Q \\) in \\( T \\) such that the line segment \\( PQ \\) contains no other integer points except \\( P \\) and \\( Q \\). What is the minimum number of elements required in the set \\( T \\)? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"answer": "2",
"index": 13,
"question": "In the plane, there is a set of integer points \\( S = \\{ (a, b) \\mid 1 \\leqslant a, b \\leqslant 5, a, b \\in \\mathbf{Z} \\} \\). Now consider a subset \\( T \\) of integer points in the plane such that for any point \\( P \\) in \\( S \\), there exists a distinct point \\( Q \\) in \\( T \\) such that the line segment \\( PQ \\) contains no other integer points except \\( P \\) and \\( Q \\). What is the minimum number of elements required in the set \\( T \\)?",
"split": "train"
}
|
omnimath
|
[
"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 Determine the largest of all integers $n$ with the property that $n$ is divisible by all positive integers that are less than $\\sqrt[3]{n}$. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "420",
"style": "rule"
}
|
{
"answer": "420",
"index": 14,
"question": "Determine the largest of all integers $n$ with the property that $n$ is divisible by all positive integers that are less than $\\sqrt[3]{n}$.",
"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 Among the four-digit numbers composed of the digits 0, 1, 2, and 5 without any repetition, find the total number of numbers that cannot be divided by 5. Express your answer as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "8",
"style": "rule"
}
|
{
"answer": "8",
"index": 15,
"question": "Among the four-digit numbers composed of the digits 0, 1, 2, and 5 without any repetition, find the total number of numbers that cannot be divided by 5. Express your answer as a whole number.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics -> Other"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the numbers from 100 to 999, how many numbers have digits in strictly increasing or strictly decreasing order? Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "204",
"style": "rule"
}
|
{
"answer": "204",
"index": 16,
"question": "In the numbers from 100 to 999, how many numbers have digits in strictly increasing or strictly decreasing order? Express your answer as a single integer.",
"split": "train"
}
|
omnimath
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n At the Lacsap Hospital, Emily is a doctor and Robert is a nurse. Not including Emily, there are five doctors and three nurses at the hospital. Not including Robert, there are $d$ doctors and $n$ nurses at the hospital. What is the product of $d$ and $n$? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "12",
"style": "rule"
}
|
{
"answer": "12",
"index": 17,
"question": "At the Lacsap Hospital, Emily is a doctor and Robert is a nurse. Not including Emily, there are five doctors and three nurses at the hospital. Not including Robert, there are $d$ doctors and $n$ nurses at the hospital. What is the product of $d$ and $n$?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 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 cylinder with a volume of 9 is inscribed in a cone. The plane of the upper base of this cylinder truncates the original cone, forming a frustum with a volume of 63. Find the volume of the original cone. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "64",
"style": "rule"
}
|
{
"answer": "64",
"index": 18,
"question": "A cylinder with a volume of 9 is inscribed in a cone. The plane of the upper base of this cylinder truncates the original cone, forming a frustum with a volume of 63. Find the volume of the original cone.",
"split": "train"
}
|
aops_forum
|
[
"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 $70$ foot pole stands vertically in a plane supported by three $490$ foot wires, all attached to the top of the pole, pulled taut, and anchored to three equally spaced points in the plane. How many feet apart are any two of those anchor points? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "840",
"style": "rule"
}
|
{
"answer": "840",
"index": 19,
"question": "A $70$ foot pole stands vertically in a plane supported by three $490$ foot wires, all attached to the top of the pole, pulled taut, and anchored to three equally spaced points in the plane. How many feet apart are any two of those anchor points?",
"split": "train"
}
|
cn_k12
|
[
"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 Given that the product of three prime numbers is exactly equal to 31 times their sum, find the sum of these three prime numbers. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "51",
"style": "rule"
}
|
{
"answer": "51",
"index": 20,
"question": "Given that the product of three prime numbers is exactly equal to 31 times their sum, find the sum of these three prime numbers.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Algebraic Expressions -> 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 Suppose \\( a_{i}, b_{i} (i=1,2,\\ldots,n) \\) are rational numbers, such that for any real number \\( x \\), the following holds:\n\\[ x^{2}+x+4=\\sum_{i=1}^{n}\\left(a_{i} x+b_{i}\\right)^{2}. \\]\n\nFind the minimum possible value of \\( n \\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 21,
"question": "Suppose \\( a_{i}, b_{i} (i=1,2,\\ldots,n) \\) are rational numbers, such that for any real number \\( x \\), the following holds:\n\\[ x^{2}+x+4=\\sum_{i=1}^{n}\\left(a_{i} x+b_{i}\\right)^{2}. \\]\n\nFind the minimum possible value of \\( n \\).",
"split": "train"
}
|
big_math
|
[
"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 smaller rectangle is formed by three squares, each with an area of 25 cm², placed inside a larger rectangle. Two of the vertices of the smaller rectangle lie on the midpoints of the shorter sides of the larger rectangle, and the other two vertices lie on the other two sides of the larger rectangle. Calculate the area of the larger rectangle in square centimeters (cm²). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "150",
"style": "rule"
}
|
{
"answer": "150",
"index": 22,
"question": "A smaller rectangle is formed by three squares, each with an area of 25 cm², placed inside a larger rectangle. Two of the vertices of the smaller rectangle lie on the midpoints of the shorter sides of the larger rectangle, and the other two vertices lie on the other two sides of the larger rectangle. Calculate the area of the larger rectangle in square centimeters (cm²).",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Calculus -> Differential Calculus -> Derivatives"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $f(x)$ be a differentiable function satisfying $\\lim_{x\\rightarrow 0} \\frac{f(1)-f(1+2x)}{2x} = 1$. Calculate the slope of the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$. Express your answer as a single numerical value. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-1",
"style": "rule"
}
|
{
"answer": "-1",
"index": 23,
"question": "Let $f(x)$ be a differentiable function satisfying $\\lim_{x\\rightarrow 0} \\frac{f(1)-f(1+2x)}{2x} = 1$. Calculate the slope of the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$. Express your answer as a single numerical value.",
"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 Given that the function y=f(x) is an odd function defined on R, and for any x in R, it satisfies f(x+2)=f(x)+f(2), and f(1)=2, calculate the exact value of f(2012). Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "4024",
"style": "rule"
}
|
{
"answer": "4024",
"index": 24,
"question": "Given that the function y=f(x) is an odd function defined on R, and for any x in R, it satisfies f(x+2)=f(x)+f(2), and f(1)=2, calculate the exact value of f(2012). Express your answer as a single integer.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the sum of all values of \\( x \\) that satisfy the equation \\( \\left(x^{2} - 5x + 5\\right)^{x^{2} + 4x - 60} = 1 \\). Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 25,
"question": "Find the sum of all values of \\( x \\) that satisfy the equation \\( \\left(x^{2} - 5x + 5\\right)^{x^{2} + 4x - 60} = 1 \\). Express your answer as a single integer.",
"split": "train"
}
|
olympiads
|
[
"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 How many two-digit numbers exist that, when their digits are reversed, increase by at least twice? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "14",
"style": "rule"
}
|
{
"answer": "14",
"index": 26,
"question": "How many two-digit numbers exist that, when their digits are reversed, increase by at least twice?",
"split": "train"
}
|
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 How many digits does the decimal equal to $\\frac{54317}{80000}$ have to the right of the decimal point? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"answer": "7",
"index": 27,
"question": "How many digits does the decimal equal to $\\frac{54317}{80000}$ have to the right of the decimal point?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a triangle with sides of lengths 30, 70, and 80 units, an altitude is dropped upon the side of length 80. Find the length of the larger segment cut off on this side. Express your answer in units as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "65",
"style": "rule"
}
|
{
"answer": "65",
"index": 28,
"question": "In a triangle with sides of lengths 30, 70, and 80 units, an altitude is dropped upon the side of length 80. Find the length of the larger segment cut off on this side. Express your answer in units as a whole number.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A set containing three real numbers can be represented as $\\{a, \\frac{b}{a}, 1\\}$, and also as $\\{a^2, a+b, 0\\}$. Find the value of $a^{2003} + b^{2004}$. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-1",
"style": "rule"
}
|
{
"answer": "-1",
"index": 29,
"question": "A set containing three real numbers can be represented as $\\{a, \\frac{b}{a}, 1\\}$, and also as $\\{a^2, a+b, 0\\}$. Find the value of $a^{2003} + b^{2004}$.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a positive geometric sequence, the sum of the first 2 terms (S_2) is 7, and the sum of the first 6 terms (S_6) is 91. Find the sum of the first 4 terms (S_4). Express your answer as a single numerical value. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "28",
"style": "rule"
}
|
{
"answer": "28",
"index": 30,
"question": "In a positive geometric sequence, the sum of the first 2 terms (S_2) is 7, and the sum of the first 6 terms (S_6) is 91. Find the sum of the first 4 terms (S_4). Express your answer as a single numerical value.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Number Theory -> Congruences"
] | 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 is a least number which when divided by some numbers leaves a remainder 3, but when divided by 9 leaves no remainder. The number is 1680. What is one of the numbers that leaves a remainder of 3 when the least number is divided by it? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1677",
"style": "rule"
}
|
{
"answer": "1677",
"index": 31,
"question": "There is a least number which when divided by some numbers leaves a remainder 3, but when divided by 9 leaves no remainder. The number is 1680. What is one of the numbers that leaves a remainder of 3 when the least number is divided by it?",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Applied Mathematics -> Probability -> Combinations"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Form a six-digit number using the digits 1, 2, 3, 4, 5, 6 without repetition, requiring that any two adjacent digits have different parities, and 1 and 2 are adjacent. The number of such six-digit numbers is (answer in digits). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "40",
"style": "rule"
}
|
{
"answer": "40",
"index": 32,
"question": "Form a six-digit number using the digits 1, 2, 3, 4, 5, 6 without repetition, requiring that any two adjacent digits have different parities, and 1 and 2 are adjacent. The number of such six-digit numbers is (answer in digits).",
"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 The cost price of a radio is Rs. 3300 and it was sold for some amount. The loss percentage is 62.727272727272734%. What is the selling price of the radio? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1230",
"style": "rule"
}
|
{
"answer": "1230",
"index": 33,
"question": "The cost price of a radio is Rs. 3300 and it was sold for some amount. The loss percentage is 62.727272727272734%. What is the selling price of the radio?",
"split": "train"
}
|
olympiads
|
[
"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 As shown in the figure, the rectangle \\(ABCD\\) has a length \\(AB\\) of 20 cm and a width \\(BC\\) of 16 cm. Inside the rectangle, there are two overlapping squares \\(DEFG\\) and \\(BHIJ\\). It is known that the perimeters of the three shaded rectangles are equal. What is the area of the rectangle \\(INFM\\) in square centimeters? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "32",
"style": "rule"
}
|
{
"answer": "32",
"index": 34,
"question": "As shown in the figure, the rectangle \\(ABCD\\) has a length \\(AB\\) of 20 cm and a width \\(BC\\) of 16 cm. Inside the rectangle, there are two overlapping squares \\(DEFG\\) and \\(BHIJ\\). It is known that the perimeters of the three shaded rectangles are equal. What is the area of the rectangle \\(INFM\\) in square centimeters?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that \\(a, b, c\\) are nonzero real numbers and satisfy\n$$\n\\begin{array}{l}\n\\frac{a+b-c}{c}=\\frac{a-b+c}{b}=\\frac{-a+b+c}{a}, \\\\\nx=\\frac{(a+b)(b+c)(c+a)}{abc}, \\quad \\text { and } x<0,\n\\end{array}\n$$\ncalculate the value of \\(x\\). Express your answer as a single numerical value. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-1",
"style": "rule"
}
|
{
"answer": "-1",
"index": 35,
"question": "Given that \\(a, b, c\\) are nonzero real numbers and satisfy\n$$\n\\begin{array}{l}\n\\frac{a+b-c}{c}=\\frac{a-b+c}{b}=\\frac{-a+b+c}{a}, \\\\\nx=\\frac{(a+b)(b+c)(c+a)}{abc}, \\quad \\text { and } x<0,\n\\end{array}\n$$\ncalculate the value of \\(x\\). Express your answer as a single numerical value.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Number Theory -> Factorization"
] | 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 number 315 can be written as the product of two odd integers each greater than 1. How many distinct pairs of such factors exist? Express your answer as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 36,
"question": "The number 315 can be written as the product of two odd integers each greater than 1. How many distinct pairs of such factors exist? Express your answer as a whole number.",
"split": "train"
}
|
olympiads
|
[
"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 According to a survey conducted in the 7th \"E\" grade class, it was found that $20\\%$ of the students who are interested in mathematics are also interested in physics, and $25\\%$ of the students who are interested in physics are also interested in mathematics. Only Peter and Vasya are not interested in either of these subjects. How many students are there in the 7th \"E\" grade class, given that there are more than 20 but less than 30 of them? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "26",
"style": "rule"
}
|
{
"answer": "26",
"index": 37,
"question": "According to a survey conducted in the 7th \"E\" grade class, it was found that $20\\%$ of the students who are interested in mathematics are also interested in physics, and $25\\%$ of the students who are interested in physics are also interested in mathematics. Only Peter and Vasya are not interested in either of these subjects. How many students are there in the 7th \"E\" grade class, given that there are more than 20 but less than 30 of them?",
"split": "train"
}
|
olympiads
|
[
"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 For the numerical sequence \\(\\{x_n\\}\\), where all terms starting from \\(n \\geq 2\\) are distinct, the relation \\(x_n = \\frac{x_{n-1} + 298x_n + x_{n+1}}{300}\\) holds. Find \\(\\sqrt{\\frac{x_{2023} - x_2}{2021} \\cdot \\frac{2022}{x_{2023} - x_1}} - 2023\\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-2022",
"style": "rule"
}
|
{
"answer": "-2022",
"index": 38,
"question": "For the numerical sequence \\(\\{x_n\\}\\), where all terms starting from \\(n \\geq 2\\) are distinct, the relation \\(x_n = \\frac{x_{n-1} + 298x_n + x_{n+1}}{300}\\) holds. Find \\(\\sqrt{\\frac{x_{2023} - x_2}{2021} \\cdot \\frac{2022}{x_{2023} - x_1}} - 2023\\).",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Number Theory -> 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 Ben starts with an integer greater than $9$ and subtracts the sum of its digits from it to get a new integer. He repeats this process with each new integer he gets until he gets a positive $1$ -digit integer. Find all possible $1$ -digit integers Ben can end with from this process. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "9",
"style": "rule"
}
|
{
"answer": "9",
"index": 39,
"question": "Ben starts with an integer greater than $9$ and subtracts the sum of its digits from it to get a new integer. He repeats this process with each new integer he gets until he gets a positive $1$ -digit integer. Find all possible $1$ -digit integers Ben can end with from this process.",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $\\Omega$ and $\\omega$ be circles with radii $123$ and $61$ , respectively, such that the center of $\\Omega$ lies on $\\omega$ . A chord of $\\Omega$ is cut by $\\omega$ into three segments, whose lengths are in the ratio $1 : 2 : 3$ in that order. Given that this chord is not a diameter of $\\Omega$ , compute the length of this chord. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "42",
"style": "rule"
}
|
{
"answer": "42",
"index": 40,
"question": "Let $\\Omega$ and $\\omega$ be circles with radii $123$ and $61$ , respectively, such that the center of $\\Omega$ lies on $\\omega$ . A chord of $\\Omega$ is cut by $\\omega$ into three segments, whose lengths are in the ratio $1 : 2 : 3$ in that order. Given that this chord is not a diameter of $\\Omega$ , compute the length of this chord.",
"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 When walking at a combination of 7 / 6 and 5 / 6 of his usual rate, a boy reaches his school 2 min early. He walks 3 / 4 of the total distance at a rate of 7 / 6 his usual speed, and 1 / 4 of the total distance at a rate of 5 / 6 his usual speed. Find his usual time to reach the school. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "35",
"style": "rule"
}
|
{
"answer": "35",
"index": 41,
"question": "When walking at a combination of 7 / 6 and 5 / 6 of his usual rate, a boy reaches his school 2 min early. He walks 3 / 4 of the total distance at a rate of 7 / 6 his usual speed, and 1 / 4 of the total distance at a rate of 5 / 6 his usual speed. Find his usual time to reach the school.",
"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 The natural numbers from 1 to 100 are arranged on a circle with the characteristic that each number is either larger as their two neighbours or smaller than their two neighbours. A pair of neighbouring numbers is called \"good\", if you cancel such a pair, the above property remains still valid. What is the smallest possible number of good pairs? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "51",
"style": "rule"
}
|
{
"answer": "51",
"index": 42,
"question": "The natural numbers from 1 to 100 are arranged on a circle with the characteristic that each number is either larger as their two neighbours or smaller than their two neighbours. A pair of neighbouring numbers is called \"good\", if you cancel such a pair, the above property remains still valid. What is the smallest possible number of good pairs?",
"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 Jason initially has eight fish in his aquarium. He discovers that every day the number of fish triples. On the fourth day, he takes out two-fifths of the fish. On the sixth day, he removes three-sevenths of the fish. On the ninth day, he adds 20 more fish. How many fish in total does he have? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "18083",
"style": "rule"
}
|
{
"answer": "18083",
"index": 43,
"question": "Jason initially has eight fish in his aquarium. He discovers that every day the number of fish triples. On the fourth day, he takes out two-fifths of the fish. On the sixth day, he removes three-sevenths of the fish. On the ninth day, he adds 20 more fish. How many fish in total does he have?",
"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 Marvin had a birthday on Tuesday, May 27 in the leap year 2008. In what year will his birthday next fall on a Saturday? Express your answer as a single year in the format YYYY. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "2017",
"style": "rule"
}
|
{
"answer": "2017",
"index": 44,
"question": "Marvin had a birthday on Tuesday, May 27 in the leap year 2008. In what year will his birthday next fall on a Saturday? Express your answer as a single year in the format YYYY.",
"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 Let \\( a, b \\), and \\( c \\) be complex numbers such that \\( |a|=|b|=|c|=1 \\). If\n\\[ \\frac{a^{2}}{b c}+\\frac{b^{2}}{c a}+\\frac{c^{2}}{a b}=1 \\]\nas well, determine the product of all possible values of \\( |a+b+c| \\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"answer": "2",
"index": 45,
"question": "Let \\( a, b \\), and \\( c \\) be complex numbers such that \\( |a|=|b|=|c|=1 \\). If\n\\[ \\frac{a^{2}}{b c}+\\frac{b^{2}}{c a}+\\frac{c^{2}}{a b}=1 \\]\nas well, determine the product of all possible values of \\( |a+b+c| \\).",
"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 Assign five people, A, B, C, D, and E, to participate in three different activities. Activity 1 and Activity 2 each require two people, and Activity 3 requires one person. Given that A and B cannot participate in the same activity, there are a total of $\\_\\_\\_\\_\\_$ different distribution methods. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "24",
"style": "rule"
}
|
{
"answer": "24",
"index": 46,
"question": "Assign five people, A, B, C, D, and E, to participate in three different activities. Activity 1 and Activity 2 each require two people, and Activity 3 requires one person. Given that A and B cannot participate in the same activity, there are a total of $\\_\\_\\_\\_\\_$ different distribution methods.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the system of equations in terms of $x$ and $y$: $\\left\\{\\begin{array}{l}{2x+4y=20}\\\\{ax+by=1}\\end{array}\\right.$ and $\\left\\{\\begin{array}{l}{2x-y=5}\\\\{bx+ay=6}\\end{array}\\right.$ have the same solution, then $a+b=$____. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 47,
"question": "Given the system of equations in terms of $x$ and $y$: $\\left\\{\\begin{array}{l}{2x+4y=20}\\\\{ax+by=1}\\end{array}\\right.$ and $\\left\\{\\begin{array}{l}{2x-y=5}\\\\{bx+ay=6}\\end{array}\\right.$ have the same solution, then $a+b=$____.",
"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 Oleg writes a real number above each column of a blank $50 \\times 50$ grid (outside the grid) and a real number to the left of each row (outside the grid). It is known that all 100 real numbers he writes are distinct, and there are exactly 50 rational numbers and 50 irrational numbers among them. Then, Oleg writes the sum of the number to the left of the row and the number above the column in each cell of the grid (creating an addition table). What is the maximum number of rational numbers that can appear in this grid? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1250",
"style": "rule"
}
|
{
"answer": "1250",
"index": 48,
"question": "Oleg writes a real number above each column of a blank $50 \\times 50$ grid (outside the grid) and a real number to the left of each row (outside the grid). It is known that all 100 real numbers he writes are distinct, and there are exactly 50 rational numbers and 50 irrational numbers among them. Then, Oleg writes the sum of the number to the left of the row and the number above the column in each cell of the grid (creating an addition table). What is the maximum number of rational numbers that can appear in this grid?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the ellipse \\(\\frac{x^{2}}{4}+\\frac{y^{2}}{3}=1\\) with the left focus \\( F \\), and a line \\( l \\) passing through \\((1,1)\\) that intersects the ellipse at points \\( A \\) and \\( B \\). When the perimeter of triangle \\( \\triangle FAB \\) is at its maximum, what is the area of triangle \\( \\triangle FAB \\)? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 49,
"question": "Given the ellipse \\(\\frac{x^{2}}{4}+\\frac{y^{2}}{3}=1\\) with the left focus \\( F \\), and a line \\( l \\) passing through \\((1,1)\\) that intersects the ellipse at points \\( A \\) and \\( B \\). When the perimeter of triangle \\( \\triangle FAB \\) is at its maximum, what is the area of triangle \\( \\triangle FAB \\)?",
"split": "train"
}
|
olympiads
|
[
"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 What is the smallest possible area of a right-angled triangle whose hypotenuse contains the point \\( M(1, 3) \\) and whose legs lie on the lines \\( y = x \\) and \\( y = -x \\)? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "8",
"style": "rule"
}
|
{
"answer": "8",
"index": 50,
"question": "What is the smallest possible area of a right-angled triangle whose hypotenuse contains the point \\( M(1, 3) \\) and whose legs lie on the lines \\( y = x \\) and \\( y = -x \\)?",
"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 Find the number of subsets $S$ of $\\{1,2, \\ldots 6\\}$ satisfying the following conditions: - $S$ is non-empty. - No subset of $S$ has the property that the sum of its elements is 10. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "34",
"style": "rule"
}
|
{
"answer": "34",
"index": 51,
"question": "Find the number of subsets $S$ of $\\{1,2, \\ldots 6\\}$ satisfying the following conditions: - $S$ is non-empty. - No subset of $S$ has the property that the sum of its elements is 10.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a sequence 1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16,... where the first term is 2^0, the next two terms are 2^0, 2^1, the next three terms are 2^0, 2^1, 2^2, and so on, calculate the sum of the first 50 terms of this sequence. Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1044",
"style": "rule"
}
|
{
"answer": "1044",
"index": 52,
"question": "Given a sequence 1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16,... where the first term is 2^0, the next two terms are 2^0, 2^1, the next three terms are 2^0, 2^1, 2^2, and so on, calculate the sum of the first 50 terms of this sequence. Express your answer as a single integer.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a parabola with its vertex on the x-axis and its directrix being the y-axis, and point \\( A(4,0) \\) has the shortest distance of 2 from the parabola, find the total number of such parabolas. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 53,
"question": "Given a parabola with its vertex on the x-axis and its directrix being the y-axis, and point \\( A(4,0) \\) has the shortest distance of 2 from the parabola, find the total number of such parabolas.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Algebra -> Algebraic Expressions -> Exponents"
] | 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 number times (1/2)^2 will give the value of 2 raised to a certain power? The answer is 32. What is the power? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"answer": "7",
"index": 54,
"question": "What number times (1/2)^2 will give the value of 2 raised to a certain power? The answer is 32. What is the power?",
"split": "train"
}
|
aops_forum
|
[
"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 Let $A$ be a set of positive integers satisfying the following : $a.)$ If $n \\in A$ , then $n \\le 2018$ . $b.)$ If $S \\subset A$ such that $|S|=3$ , then there exists $m,n \\in S$ such that $|n-m| \\ge \\sqrt{n}+\\sqrt{m}$ What is the maximum cardinality of $A$ ? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "44",
"style": "rule"
}
|
{
"answer": "44",
"index": 55,
"question": "Let $A$ be a set of positive integers satisfying the following : $a.)$ If $n \\in A$ , then $n \\le 2018$ . $b.)$ If $S \\subset A$ such that $|S|=3$ , then there exists $m,n \\in S$ such that $|n-m| \\ge \\sqrt{n}+\\sqrt{m}$ What is the maximum cardinality of $A$ ?",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A chocolate box contains some bars. Thomas and his 4 friends take 1/4 of the bars and decide to divide them equally between them. One of Thomas's friends doesn't like chocolate bars very much and returns 5 of his bars to the box. Later, his sister Piper comes home and takes 5 fewer bars than those taken in total by Thomas and his friends so she can also share with her friends. There are 110 bars left in the box. How many bars were initially in the chocolate box? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "190",
"style": "rule"
}
|
{
"answer": "190",
"index": 56,
"question": "A chocolate box contains some bars. Thomas and his 4 friends take 1/4 of the bars and decide to divide them equally between them. One of Thomas's friends doesn't like chocolate bars very much and returns 5 of his bars to the box. Later, his sister Piper comes home and takes 5 fewer bars than those taken in total by Thomas and his friends so she can also share with her friends. There are 110 bars left in the box. How many bars were initially in the chocolate box?",
"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 Given \\(a\\in \\mathbb{R}\\), the line \\(l_1\\): \\(x+2y=a+2\\) and the line \\(l_2\\): \\(2x-y=2a-1\\) intersect the circle \\(E\\): \\((x-a)^2+(y-1)^2=4\\) at points \\(A\\), \\(C\\) and \\(B\\), \\(D\\) respectively. Calculate the area of the quadrilateral \\(ABCD\\). Express your answer as a single number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "8",
"style": "rule"
}
|
{
"answer": "8",
"index": 57,
"question": "Given \\(a\\in \\mathbb{R}\\), the line \\(l_1\\): \\(x+2y=a+2\\) and the line \\(l_2\\): \\(2x-y=2a-1\\) intersect the circle \\(E\\): \\((x-a)^2+(y-1)^2=4\\) at points \\(A\\), \\(C\\) and \\(B\\), \\(D\\) respectively. Calculate the area of the quadrilateral \\(ABCD\\). Express your answer as a single number.",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $x_1 \\dots, x_{42}$ , be real numbers such that $5x_{i+1}-x_i-3x_ix_{i+1}=1$ for each $1 \\le i \\le 42$ , with $x_1=x_{43}$ . Find all the product of all possible values for $x_1 + x_2 + \\dots + x_{42}$ . Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "588",
"style": "rule"
}
|
{
"answer": "588",
"index": 58,
"question": "Let $x_1 \\dots, x_{42}$ , be real numbers such that $5x_{i+1}-x_i-3x_ix_{i+1}=1$ for each $1 \\le i \\le 42$ , with $x_1=x_{43}$ . Find all the product of all possible values for $x_1 + x_2 + \\dots + x_{42}$ .",
"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 John and Roger can finish the work in 24 days if they work together. They worked together for 16 days and then Roger left. After Roger left, a third person, Anna, helped John for 8 days before leaving as well. John finished the remaining work in another 8 days. In how many days can John alone finish the work? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "48",
"style": "rule"
}
|
{
"answer": "48",
"index": 59,
"question": "John and Roger can finish the work in 24 days if they work together. They worked together for 16 days and then Roger left. After Roger left, a third person, Anna, helped John for 8 days before leaving as well. John finished the remaining work in another 8 days. In how many days can John alone finish the work?",
"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 A vertical line divides the triangle with vertices (0,0), (1,1), and (9,1) in the xy-plane into two regions of equal area. Find the equation of the line in the form x = k, where k is a single number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 60,
"question": "A vertical line divides the triangle with vertices (0,0), (1,1), and (9,1) in the xy-plane into two regions of equal area. Find the equation of the line in the form x = k, where k is a single number.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Precalculus -> Trigonometric 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 Simplify the following expression:\n\\\\(\\dfrac{{{\\\\sin }^{2}}(\\\\alpha +\\\\pi )\\\\cdot \\\\cos (\\\\pi +\\\\alpha )\\\\cdot \\\\cos (-\\\\alpha -2\\\\pi )}{\\\\tan (\\\\pi +\\\\alpha )\\\\cdot {{\\\\sin }^{3}}(\\\\dfrac{\\\\pi }{2}+\\\\alpha )\\\\cdot \\\\sin (-\\\\alpha -2\\\\pi )}=\\\\)\\_\\_\\_\\_\\_\\_\\_\\_． Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 61,
"question": "Simplify the following expression:\n\\\\(\\dfrac{{{\\\\sin }^{2}}(\\\\alpha +\\\\pi )\\\\cdot \\\\cos (\\\\pi +\\\\alpha )\\\\cdot \\\\cos (-\\\\alpha -2\\\\pi )}{\\\\tan (\\\\pi +\\\\alpha )\\\\cdot {{\\\\sin }^{3}}(\\\\dfrac{\\\\pi }{2}+\\\\alpha )\\\\cdot \\\\sin (-\\\\alpha -2\\\\pi )}=\\\\)\\_\\_\\_\\_\\_\\_\\_\\_．",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Number Theory -> Other"
] | 0.0625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the maximum number of digits that a natural number can have, where all the digits are different, and the number is divisible by each of its digits? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"answer": "7",
"index": 62,
"question": "What is the maximum number of digits that a natural number can have, where all the digits are different, and the number is divisible by each of its digits?",
"split": "train"
}
|
cn_k12
|
[
"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 sets $A={x|x^2-2x-3 > 0}$ and $B={x|x^2+ax+b≤0}$, if $A∪B=R$ and $A∩B={x|3 < x≤4}$, find the value of $a+b$. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-7",
"style": "rule"
}
|
{
"answer": "-7",
"index": 63,
"question": "Given the sets $A={x|x^2-2x-3 > 0}$ and $B={x|x^2+ax+b≤0}$, if $A∪B=R$ and $A∩B={x|3 < x≤4}$, find the value of $a+b$.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied 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 Allocate 7 \"Outstanding Student\" slots to 5 different schools, where schools A and B must each have at least two slots. Find the number of different allocation schemes. Express your answer as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "35",
"style": "rule"
}
|
{
"answer": "35",
"index": 64,
"question": "Allocate 7 \"Outstanding Student\" slots to 5 different schools, where schools A and B must each have at least two slots. Find the number of different allocation schemes. Express your answer as a whole number.",
"split": "train"
}
|
orca_math
|
[
"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 Serenity, Jordan, and Alex decided to buy color boxes to enhance their artistic skills. Serenity bought a Prismacolor box containing 24 unique colors, Jordan bought a Faber-Castell box with 36 colors, and Alex bought a Caran d'Ache color box containing 30 colors. However, there is some overlap between the brand selections in terms of colors. Serenity and Jordan share 8 colors, Serenity and Alex share 5 colors, and Jordan and Alex share 10 colors. Moreover, the three of them share 3 common colors across all their boxes. Determine the total number of unique colored pencils they have collectively. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "73",
"style": "rule"
}
|
{
"answer": "73",
"index": 65,
"question": "Serenity, Jordan, and Alex decided to buy color boxes to enhance their artistic skills. Serenity bought a Prismacolor box containing 24 unique colors, Jordan bought a Faber-Castell box with 36 colors, and Alex bought a Caran d'Ache color box containing 30 colors. However, there is some overlap between the brand selections in terms of colors. Serenity and Jordan share 8 colors, Serenity and Alex share 5 colors, and Jordan and Alex share 10 colors. Moreover, the three of them share 3 common colors across all their boxes. Determine the total number of unique colored pencils they have collectively.",
"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 When \\( x \\in [1, 2017] \\), find the minimum value of\n$$\nf(x) = \\sum_{i=1}^{2017} i |x - i|\n$$ Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "801730806",
"style": "rule"
}
|
{
"answer": "801730806",
"index": 66,
"question": "When \\( x \\in [1, 2017] \\), find the minimum value of\n$$\nf(x) = \\sum_{i=1}^{2017} i |x - i|\n$$",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the general term formula of the sequence $\\{{a_n}\\}$ as $a_n=n^2\\cos\\frac{n\\pi}{2}$, and the sum of the first $n$ terms as $S_n$, find the value of $\\frac{S_{2021}}{2020}=\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.$ Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1011",
"style": "rule"
}
|
{
"answer": "1011",
"index": 67,
"question": "Given the general term formula of the sequence $\\{{a_n}\\}$ as $a_n=n^2\\cos\\frac{n\\pi}{2}$, and the sum of the first $n$ terms as $S_n$, find the value of $\\frac{S_{2021}}{2020}=\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.$",
"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 thief is spotted by a policeman from a distance of 175 meters. When the policeman starts the chase, the thief also starts running. The speed of the thief is 8 km/hr, and the thief will have run 700 meters before he is overtaken. What is the speed of the policeman? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"answer": "10",
"index": 68,
"question": "A thief is spotted by a policeman from a distance of 175 meters. When the policeman starts the chase, the thief also starts running. The speed of the thief is 8 km/hr, and the thief will have run 700 meters before he is overtaken. What is the speed of the policeman?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \nIn the diagram below, the point \\( D \\) lies inside the triangle \\( ABC \\) such that \\(\\angle BAD = \\angle BCD\\) and \\(\\angle BDC = 90^\\circ\\). Given that \\( AB = 5 \\) and \\( BC = 6 \\), and the point \\( M \\) is the midpoint of \\( AC \\), find the value of \\( 8 \\times DM^2 \\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "22",
"style": "rule"
}
|
{
"answer": "22",
"index": 69,
"question": "\nIn the diagram below, the point \\( D \\) lies inside the triangle \\( ABC \\) such that \\(\\angle BAD = \\angle BCD\\) and \\(\\angle BDC = 90^\\circ\\). Given that \\( AB = 5 \\) and \\( BC = 6 \\), and the point \\( M \\) is the midpoint of \\( AC \\), find the value of \\( 8 \\times DM^2 \\).",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Algebra -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the following two sets of rational numbers, please select two integers and two fractions from each set. Then, use two types of operation symbols from $\\{+-×÷\\}$ to perform two operations on the selected four numbers, resulting in a positive integer.\nThe integers are $\\{0,-3,5,-100,2008,-1,…\\}$, and the fractions are $\\{ \\frac {1}{2},- \\frac {1}{3},0.2,-1 \\frac {1}{2},- \\frac {1}{100},…\\}$. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 70,
"question": "In the following two sets of rational numbers, please select two integers and two fractions from each set. Then, use two types of operation symbols from $\\{+-×÷\\}$ to perform two operations on the selected four numbers, resulting in a positive integer.\nThe integers are $\\{0,-3,5,-100,2008,-1,…\\}$, and the fractions are $\\{ \\frac {1}{2},- \\frac {1}{3},0.2,-1 \\frac {1}{2},- \\frac {1}{100},…\\}$.",
"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 How many different combinations of 4 marbles can be made from 5 indistinguishable red marbles, 4 indistinguishable blue marbles, and 2 indistinguishable black marbles? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "12",
"style": "rule"
}
|
{
"answer": "12",
"index": 71,
"question": "How many different combinations of 4 marbles can be made from 5 indistinguishable red marbles, 4 indistinguishable blue marbles, and 2 indistinguishable black marbles?",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $F_1$ and $F_2$ are the left and right foci of the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ (where $a > 0, b > 0$) respectively. A perpendicular line is drawn from $F_2$ to the asymptote of the hyperbola, with the foot of the perpendicular being $P$. If $|PF_1|^2 - |PF_2|^2 = c^2$, find the eccentricity of the hyperbola. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"answer": "2",
"index": 72,
"question": "Given $F_1$ and $F_2$ are the left and right foci of the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ (where $a > 0, b > 0$) respectively. A perpendicular line is drawn from $F_2$ to the asymptote of the hyperbola, with the foot of the perpendicular being $P$. If $|PF_1|^2 - |PF_2|^2 = c^2$, find the eccentricity of the hyperbola.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> 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 are 5 machines, and it is known that 2 of them are faulty. The cost of testing one machine is 2000 yuan. Calculate the average cost of testing required to identify the 2 faulty machines. Express your answer in yuan, rounded to the nearest whole number if necessary. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7000",
"style": "rule"
}
|
{
"answer": "7000",
"index": 73,
"question": "There are 5 machines, and it is known that 2 of them are faulty. The cost of testing one machine is 2000 yuan. Calculate the average cost of testing required to identify the 2 faulty machines. Express your answer in yuan, rounded to the nearest whole number if necessary.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If \\( a^{2} = 1000 \\times 1001 \\times 1002 \\times 1003 + 1 \\), find the value of \\( a \\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1002001",
"style": "rule"
}
|
{
"answer": "1002001",
"index": 74,
"question": "If \\( a^{2} = 1000 \\times 1001 \\times 1002 \\times 1003 + 1 \\), find the value of \\( a \\).",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 80 beads. Five years ago, two sisters divided the beads according to the ratio of their ages, and used all the beads. This year, they once again divided the beads according to the ratio of their ages, and again used all the beads. Given that the older sister is 2 years older than the younger sister, how many more beads did the older sister receive the second time compared to the first time? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"answer": "4",
"index": 75,
"question": "There are 80 beads. Five years ago, two sisters divided the beads according to the ratio of their ages, and used all the beads. This year, they once again divided the beads according to the ratio of their ages, and again used all the beads. Given that the older sister is 2 years older than the younger sister, how many more beads did the older sister receive the second time compared to the first time?",
"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 As shown in Figure 1, there is a $40 \\times 30$ piece of paper which contains a $10 \\times 5$ rectangle inside it. The rectangle needs to be cut out from the paper, ensuring the cuts are straight. Each cut must directly and completely segment the paper while keeping the rectangle intact. To minimize the total length of the cuts, how can this goal be achieved? What is the minimum total cut length? Draw the cutting method and provide the answer. Proof of the result is not required. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "65",
"style": "rule"
}
|
{
"answer": "65",
"index": 76,
"question": "As shown in Figure 1, there is a $40 \\times 30$ piece of paper which contains a $10 \\times 5$ rectangle inside it. The rectangle needs to be cut out from the paper, ensuring the cuts are straight. Each cut must directly and completely segment the paper while keeping the rectangle intact. To minimize the total length of the cuts, how can this goal be achieved? What is the minimum total cut length? Draw the cutting method and provide the answer. Proof of the result is not required.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 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 number of possible values for n, where n is an integer greater than 2, such that the measure of each interior angle of a regular n-gon is an integer. Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "22",
"style": "rule"
}
|
{
"answer": "22",
"index": 77,
"question": "Determine the number of possible values for n, where n is an integer greater than 2, such that the measure of each interior angle of a regular n-gon is an integer. Express your answer as a single integer.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 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 diagram, hexagon \\( P Q R S T U \\) has interior right angles at \\( P, Q, S, T \\), and \\( U \\) and an exterior right angle at \\( R \\). Also, \\( P U = U T \\), \\( P Q = S T = 10 \\), and \\( Q S = 8 \\). Calculate the perimeter of \\( P Q R S T U \\) and round your answer to the nearest whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "63",
"style": "rule"
}
|
{
"answer": "63",
"index": 78,
"question": "In the diagram, hexagon \\( P Q R S T U \\) has interior right angles at \\( P, Q, S, T \\), and \\( U \\) and an exterior right angle at \\( R \\). Also, \\( P U = U T \\), \\( P Q = S T = 10 \\), and \\( Q S = 8 \\). Calculate the perimeter of \\( P Q R S T U \\) and round your answer to the nearest whole number.",
"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 The seats in the Parliament of some country are arranged in a rectangle of $10$ rows of $10$ seats each. All the $100$ $MP$ s have different salaries. Each of them asks all his neighbours (sitting next to, in front of, or behind him, i.e. $4$ members at most) how much they earn. They feel a lot of envy towards each other: an $MP$ is content with his salary only if he has at most one neighbour who earns more than himself. What is the maximum possible number of $MP$ s who are satisfied with their salaries? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "72",
"style": "rule"
}
|
{
"answer": "72",
"index": 79,
"question": "The seats in the Parliament of some country are arranged in a rectangle of $10$ rows of $10$ seats each. All the $100$ $MP$ s have different salaries. Each of them asks all his neighbours (sitting next to, in front of, or behind him, i.e. $4$ members at most) how much they earn. They feel a lot of envy towards each other: an $MP$ is content with his salary only if he has at most one neighbour who earns more than himself. What is the maximum possible number of $MP$ s who are satisfied with their salaries?",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that point A is on the circle $x^2+y^2-2ax+4y-6=0$, and the symmetric point of A with respect to the line $x+2y+1=0$ is also on the circle, find the value of the real number $a$. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 80,
"question": "Given that point A is on the circle $x^2+y^2-2ax+4y-6=0$, and the symmetric point of A with respect to the line $x+2y+1=0$ is also on the circle, find the value of the real number $a$.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n How many nine-digit numbers composed of eight 3's and one 0 satisfy the condition that they leave a remainder of 1 when divided by 4? Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"answer": "7",
"index": 81,
"question": "How many nine-digit numbers composed of eight 3's and one 0 satisfy the condition that they leave a remainder of 1 when divided by 4? 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 a man walks at the rate of 4 kmph, he misses a train by only 6 minutes. However, if he walks at a certain rate, he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is 4 km. What is the rate at which he walks when he reaches the station 6 minutes before the train? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 82,
"question": "If a man walks at the rate of 4 kmph, he misses a train by only 6 minutes. However, if he walks at a certain rate, he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is 4 km. What is the rate at which he walks when he reaches the station 6 minutes before the train?",
"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 Which prime numbers can be expressed as the sum of two positive composite numbers? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "13",
"style": "rule"
}
|
{
"answer": "13",
"index": 83,
"question": "Which prime numbers can be expressed as the sum of two positive composite numbers?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> 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 Six athletes are preparing to compete on 6 tracks, where athlete A cannot stand on the first or second track, and athlete B must stand on either the fifth or sixth track. Find the total number of different arrangements. Express your answer as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "144",
"style": "rule"
}
|
{
"answer": "144",
"index": 84,
"question": "Six athletes are preparing to compete on 6 tracks, where athlete A cannot stand on the first or second track, and athlete B must stand on either the fifth or sixth track. Find the total number of different arrangements. Express your answer as a whole number.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The numbers from 1 to 8 are placed at the vertices of a cube such that the sum of the numbers at any three vertices on the same face is at least 10. What is the smallest possible sum of the numbers at the vertices on one face? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "16",
"style": "rule"
}
|
{
"answer": "16",
"index": 85,
"question": "The numbers from 1 to 8 are placed at the vertices of a cube such that the sum of the numbers at any three vertices on the same face is at least 10. What is the smallest possible sum of the numbers at the vertices on one face?",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 2008 congruent circles on a plane such that no two are tangent to each other and each circle intersects at least three other circles. Let $ N$ be the total number of intersection points of these circles. Determine the smallest possible values of $ N$ . Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "3012",
"style": "rule"
}
|
{
"answer": "3012",
"index": 86,
"question": "There are 2008 congruent circles on a plane such that no two are tangent to each other and each circle intersects at least three other circles. Let $ N$ be the total number of intersection points of these circles. Determine the smallest possible values of $ N$ .",
"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 There are 140 different cards on the table with the numbers $4, 8, 12, \\ldots, 556, 560$ (each card has exactly one number, and each number appears exactly once). In how many ways can 3 cards be selected so that the sum of the numbers on the selected cards is divisible by 3? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "149224",
"style": "rule"
}
|
{
"answer": "149224",
"index": 87,
"question": "There are 140 different cards on the table with the numbers $4, 8, 12, \\ldots, 556, 560$ (each card has exactly one number, and each number appears exactly once). In how many ways can 3 cards be selected so that the sum of the numbers on the selected cards is divisible by 3?",
"split": "train"
}
|
cn_k12
|
[
"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 The product of all integers whose absolute value is greater than 3 but not greater than 6 is ____. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-14400",
"style": "rule"
}
|
{
"answer": "-14400",
"index": 88,
"question": "The product of all integers whose absolute value is greater than 3 but not greater than 6 is ____.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Luther designs clothes for a high fashion company. His latest line of clothing uses both silk and cashmere fabrics. There are some pieces made with silk and half that number made with cashmere. His latest line has thirteen pieces, and 2 pieces use a blend of cashmere and silk. How many pieces are made with silk? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"answer": "7",
"index": 89,
"question": "Luther designs clothes for a high fashion company. His latest line of clothing uses both silk and cashmere fabrics. There are some pieces made with silk and half that number made with cashmere. His latest line has thirteen pieces, and 2 pieces use a blend of cashmere and silk. How many pieces are made with silk?",
"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 When writing the numbers 1 through 125 on the board, how many times is the number 2 used? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "29",
"style": "rule"
}
|
{
"answer": "29",
"index": 90,
"question": "When writing the numbers 1 through 125 on the board, how many times is the number 2 used?",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> 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 Club Truncator is in a soccer league with six other teams, each of which it plays once. In any of its 6 matches, the probabilities that Club Truncator will win, lose, or tie are each $\\frac{1}{3}$ . The probability that Club Truncator will finish the season with more wins than losses is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ . Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "341",
"style": "rule"
}
|
{
"answer": "341",
"index": 91,
"question": "Club Truncator is in a soccer league with six other teams, each of which it plays once. In any of its 6 matches, the probabilities that Club Truncator will win, lose, or tie are each $\\frac{1}{3}$ . The probability that Club Truncator will finish the season with more wins than losses is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"split": "train"
}
|
olympiads
|
[
"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 What is the smallest non-square positive integer that is the product of four prime numbers (not necessarily distinct)? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "24",
"style": "rule"
}
|
{
"answer": "24",
"index": 92,
"question": "What is the smallest non-square positive integer that is the product of four prime numbers (not necessarily distinct)?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combinations"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n From 5 students, 4 are to be selected to participate in competitions in four subjects: mathematics, physics, chemistry, and biology. Among them, student A cannot participate in the biology competition. Calculate the total number of different possible arrangements for the competition. Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "96",
"style": "rule"
}
|
{
"answer": "96",
"index": 93,
"question": "From 5 students, 4 are to be selected to participate in competitions in four subjects: mathematics, physics, chemistry, and biology. Among them, student A cannot participate in the biology competition. Calculate the total number of different possible arrangements for the competition. Express your answer as a single integer.",
"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 Points \\( A, B, C, \\) and \\( D \\) are marked on a line in that order. Point \\( M \\) is the midpoint of segment \\( AC \\), and point \\( N \\) is the midpoint of segment \\( BD \\). Find the length of segment \\( MN \\) if it is known that \\( AD = 68 \\) and \\( BC = 26 \\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "21",
"style": "rule"
}
|
{
"answer": "21",
"index": 94,
"question": "Points \\( A, B, C, \\) and \\( D \\) are marked on a line in that order. Point \\( M \\) is the midpoint of segment \\( AC \\), and point \\( N \\) is the midpoint of segment \\( BD \\). Find the length of segment \\( MN \\) if it is known that \\( AD = 68 \\) and \\( BC = 26 \\).",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Intermediate Algebra -> Exponential Functions",
"Mathematics -> Algebra -> Intermediate Algebra -> Logarithmic Functions"
] | 0.0625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $\\alpha$ and $\\beta$ be the roots of the equations $\\log _{2} x + x + 2 = 0$ and $2^{x} + x + 2 = 0$ respectively. What is the value of $\\alpha + \\beta$? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-2",
"style": "rule"
}
|
{
"answer": "-2",
"index": 95,
"question": "Let $\\alpha$ and $\\beta$ be the roots of the equations $\\log _{2} x + x + 2 = 0$ and $2^{x} + x + 2 = 0$ respectively. What is the value of $\\alpha + \\beta$?",
"split": "train"
}
|
olympiads
|
[
"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 the positive real numbers \\( x \\) and \\( y \\) satisfy \\( x - 2 \\sqrt{y} = \\sqrt{2x - y} \\), then the maximum value of \\( x \\) is ____ . Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"answer": "10",
"index": 96,
"question": "If the positive real numbers \\( x \\) and \\( y \\) satisfy \\( x - 2 \\sqrt{y} = \\sqrt{2x - y} \\), then the maximum value of \\( x \\) is ____ .",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the two sequences:\n\n\\[\n\\begin{array}{l}\n1,3,5,7, \\cdots, 1991 \\\\\n1,6,11,16, \\cdots, 1991\n\\end{array}\n\\]\n\nDetermine the number of numbers that appear in both sequences. Express your answer as a whole number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "200",
"style": "rule"
}
|
{
"answer": "200",
"index": 97,
"question": "Given the two sequences:\n\n\\[\n\\begin{array}{l}\n1,3,5,7, \\cdots, 1991 \\\\\n1,6,11,16, \\cdots, 1991\n\\end{array}\n\\]\n\nDetermine the number of numbers that appear in both sequences. Express your answer as a whole number.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> 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 Create a six-digit number using the digits 1, 2, 3, 4, 5, and 6 without repetition, such that the digit 1 is not at either end. Additionally, out of the three even digits 2, 4, and 6, there must be exactly one pair of adjacent even digits. How many such six-digit numbers can be formed? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "288",
"style": "rule"
}
|
{
"answer": "288",
"index": 98,
"question": "Create a six-digit number using the digits 1, 2, 3, 4, 5, and 6 without repetition, such that the digit 1 is not at either end. Additionally, out of the three even digits 2, 4, and 6, there must be exactly one pair of adjacent even digits. How many such six-digit numbers can be formed?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The integer sequence $\\left\\{a_{n}\\right\\}$ satisfies $a_{n}=a_{n-1}-a_{n-2}$ for $n \\geq 3$. If the sum of the first 1492 terms of this sequence is 1985, and the sum of the first 1985 terms is 1492, what is the sum of the first 2001 terms? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "986",
"style": "rule"
}
|
{
"answer": "986",
"index": 99,
"question": "The integer sequence $\\left\\{a_{n}\\right\\}$ satisfies $a_{n}=a_{n-1}-a_{n-2}$ for $n \\geq 3$. If the sum of the first 1492 terms of this sequence is 1985, and the sum of the first 1985 terms is 1492, what is the sum of the first 2001 terms?",
"split": "train"
}
|
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