source
stringclasses 10
values | domain
listlengths 1
3
| llama8b_solve_rate
float64 0
0.09
⌀ | data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|---|---|---|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.0625
|
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 \\( S \\) be a set of sequences of length 15 formed by using the letters \\( a \\) and \\( b \\) such that every pair of sequences in \\( S \\) differ in at least 3 places. What is the maximum number of sequences in \\( S \\)? 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": "2048",
"style": "rule"
}
|
{
"answer": "2048",
"index": 200,
"question": "Let \\( S \\) be a set of sequences of length 15 formed by using the letters \\( a \\) and \\( b \\) such that every pair of sequences in \\( S \\) differ in at least 3 places. What is the maximum number of sequences in \\( S \\)?",
"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 Stan is creating a playlist for his 90-minute run. He has 10 songs that are 3 minutes long, 12 songs that are 4 minutes long, and 15 songs that are 6 minutes long. Stan can only include up to 7 songs from each category in his playlist. Given these limitations, he wants to make sure his playlist also contains at least 3 songs from his favorite band. Each song from his favorite band is 4 minutes long. How many more minutes of songs will he need in his playlist if he wants it to cover the entire run and fulfill the desired conditions? 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": "91",
"style": "rule"
}
|
{
"answer": "91",
"index": 201,
"question": "Stan is creating a playlist for his 90-minute run. He has 10 songs that are 3 minutes long, 12 songs that are 4 minutes long, and 15 songs that are 6 minutes long. Stan can only include up to 7 songs from each category in his playlist. Given these limitations, he wants to make sure his playlist also contains at least 3 songs from his favorite band. Each song from his favorite band is 4 minutes long. How many more minutes of songs will he need in his playlist if he wants it to cover the entire run and fulfill the desired conditions?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers"
] | 0.0625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the imaginary number \\( z \\) satisfies \\( z^3 + 1 = 0 \\), \\( z \\neq -1 \\). Then \\( \\left( \\frac{z}{z-1} \\right)^{2018} + \\left( \\frac{1}{z-1} \\right)^{2018} = \\) . 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": 202,
"question": "Given the imaginary number \\( z \\) satisfies \\( z^3 + 1 = 0 \\), \\( z \\neq -1 \\). Then \\( \\left( \\frac{z}{z-1} \\right)^{2018} + \\left( \\frac{1}{z-1} \\right)^{2018} = \\) .",
"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 James' keyboard is designed for both English and Russian languages, and it also has customizable function keys. In addition to the 26 English alphabet keys, there are 33 Russian alphabet keys, 8 customizable function keys, 5 accent marks, and 3 special characters. If the keyboard is missing 3/8 of the English consonants, four English vowels, 1/4 of the Russian consonants, three Russian vowels, 1/3 of the customizable function keys, 2/5 of the accent marks, and half of the special characters, how many keys are missing in total? 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": 203,
"question": "James' keyboard is designed for both English and Russian languages, and it also has customizable function keys. In addition to the 26 English alphabet keys, there are 33 Russian alphabet keys, 8 customizable function keys, 5 accent marks, and 3 special characters. If the keyboard is missing 3/8 of the English consonants, four English vowels, 1/4 of the Russian consonants, three Russian vowels, 1/3 of the customizable function keys, 2/5 of the accent marks, and half of the special characters, how many keys are missing in total?",
"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 sum of 99 consecutive natural numbers equals $abcd$, where $a$, $b$, $c$, and $d$ are all prime numbers. What is the minimum value of $a+b+c+d$? 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": "70",
"style": "rule"
}
|
{
"answer": "70",
"index": 204,
"question": "The sum of 99 consecutive natural numbers equals $abcd$, where $a$, $b$, $c$, and $d$ are all prime numbers. What is the minimum value of $a+b+c+d$?",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A train leaves Mumbai at a certain time at a speed of 45 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 90 kmph. The two trains meet at a distance of 90 km from Mumbai. At what time did the first train leave Mumbai? 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": 205,
"question": "A train leaves Mumbai at a certain time at a speed of 45 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 90 kmph. The two trains meet at a distance of 90 km from Mumbai. At what time did the first train leave Mumbai?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 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 Group the set of positive odd numbers $\\{1,3,5, \\cdots\\}$ from smallest to largest, with the $n$-th group containing $(2n-1)$ odd numbers. For example, the first group is $\\{1\\}$, the second group is $\\{3,5,7\\}$, the third group is $\\{9,11,13,15,17\\}$, etc. Determine which group contains the number 1991. 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": 206,
"question": "Group the set of positive odd numbers $\\{1,3,5, \\cdots\\}$ from smallest to largest, with the $n$-th group containing $(2n-1)$ odd numbers. For example, the first group is $\\{1\\}$, the second group is $\\{3,5,7\\}$, the third group is $\\{9,11,13,15,17\\}$, etc. Determine which group contains the number 1991.",
"split": "train"
}
|
omnimath
|
[
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A set of 6 distinct lattice points is chosen uniformly at random from the set $\\{1,2,3,4,5,6\\}^{2}$. Let $A$ be the expected area of the convex hull of these 6 points. Estimate $N=\\left\\lfloor 10^{4} A\\right\\rfloor$. An estimate of $E$ will receive $\\max \\left(0,\\left\\lfloor 20-20\\left(\\frac{|E-N|}{10^{4}}\\right)^{1 / 3}\\right\\rfloor\\right)$ 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": "104552",
"style": "rule"
}
|
{
"answer": "104552",
"index": 207,
"question": "A set of 6 distinct lattice points is chosen uniformly at random from the set $\\{1,2,3,4,5,6\\}^{2}$. Let $A$ be the expected area of the convex hull of these 6 points. Estimate $N=\\left\\lfloor 10^{4} A\\right\\rfloor$. An estimate of $E$ will receive $\\max \\left(0,\\left\\lfloor 20-20\\left(\\frac{|E-N|}{10^{4}}\\right)^{1 / 3}\\right\\rfloor\\right)$ points.",
"split": "train"
}
|
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 In triangle $ABC$, $A'$, $B'$, and $C'$ are on the sides $BC$, $AC$, and $AB$, respectively. Given that $AA'$, $BB'$, and $CC'$ are concurrent at the point $O$, and that $\\frac{AO}{OA'}+\\frac{BO}{OB'}+\\frac{CO}{OC'}=92$, find $\\frac{AO}{OA'}\\cdot \\frac{BO}{OB'}\\cdot \\frac{CO}{OC'}$. 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": "94",
"style": "rule"
}
|
{
"answer": "94",
"index": 208,
"question": "In triangle $ABC$, $A'$, $B'$, and $C'$ are on the sides $BC$, $AC$, and $AB$, respectively. Given that $AA'$, $BB'$, and $CC'$ are concurrent at the point $O$, and that $\\frac{AO}{OA'}+\\frac{BO}{OB'}+\\frac{CO}{OC'}=92$, find $\\frac{AO}{OA'}\\cdot \\frac{BO}{OB'}\\cdot \\frac{CO}{OC'}$.",
"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 Jared counted 15% fewer cars than his sister Ann while they were watching the road from the school, and Ann counted 7 more cars than their friend Alfred. Alfred, however, counted 12% more cars than he initially thought upon recounting. Their friend Bella counted 20% more cars than Jared but 10% less than Alfred's recounted total. If Jared counted 300 cars, how many cars did all of them count after taking into account Alfred's recount? 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": "1365",
"style": "rule"
}
|
{
"answer": "1365",
"index": 209,
"question": "Jared counted 15% fewer cars than his sister Ann while they were watching the road from the school, and Ann counted 7 more cars than their friend Alfred. Alfred, however, counted 12% more cars than he initially thought upon recounting. Their friend Bella counted 20% more cars than Jared but 10% less than Alfred's recounted total. If Jared counted 300 cars, how many cars did all of them count after taking into account Alfred's recount?",
"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 Simona suffered from numerous complexes. So, she went to a psychoanalyst, and after a course of treatment, she was freed from half of her complexes and half of one of the remaining complexes. Then she went to another psychoanalyst, and thanks to this, she was freed from half of her remaining complexes and half of one of the still remaining complexes. The result was the same after visiting a third psychoanalyst. After that, Simona was left with only one complex, which she will keep for the rest of her days.\n\nWhat was the total cost of Simona's treatment, assuming that each psychoanalyst charged 197 francs for each cured complex? 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": "1379",
"style": "rule"
}
|
{
"answer": "1379",
"index": 210,
"question": "Simona suffered from numerous complexes. So, she went to a psychoanalyst, and after a course of treatment, she was freed from half of her complexes and half of one of the remaining complexes. Then she went to another psychoanalyst, and thanks to this, she was freed from half of her remaining complexes and half of one of the still remaining complexes. The result was the same after visiting a third psychoanalyst. After that, Simona was left with only one complex, which she will keep for the rest of her days.\n\nWhat was the total cost of Simona's treatment, assuming that each psychoanalyst charged 197 francs for each cured complex?",
"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 Oleg has four cards, each with a natural number on each side (a total of 8 numbers). He considers all possible sets of four numbers where the first number is written on the first card, the second number on the second card, the third number on the third card, and the fourth number on the fourth card. For each set of four numbers, he writes the product of the numbers in his notebook. What is the sum of the eight numbers on the cards if the sum of the sixteen numbers in Oleg’s notebook is $330? 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": 211,
"question": "Oleg has four cards, each with a natural number on each side (a total of 8 numbers). He considers all possible sets of four numbers where the first number is written on the first card, the second number on the second card, the third number on the third card, and the fourth number on the fourth card. For each set of four numbers, he writes the product of the numbers in his notebook. What is the sum of the eight numbers on the cards if the sum of the sixteen numbers in Oleg’s notebook is $330?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.09375
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Circle \\(O\\) has chord \\(AB\\). A smaller circle is tangent to circle \\(O\\) at \\(T\\) and tangent to \\(AB\\) at \\(X\\) such that \\(AX = 2XB\\). What is \\(\\frac{AT}{BT}\\)? 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": 212,
"question": "Circle \\(O\\) has chord \\(AB\\). A smaller circle is tangent to circle \\(O\\) at \\(T\\) and tangent to \\(AB\\) at \\(X\\) such that \\(AX = 2XB\\). What is \\(\\frac{AT}{BT}\\)?",
"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 the line $x+ \\sqrt {3}y-2=0$ intersects with the circle $x^{2}+y^{2}=r^{2}$ ($r>0$) at points A and B, and O is the origin. If $\\angle AOB=120°$, then $r=$ ______. 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": 213,
"question": "Given the line $x+ \\sqrt {3}y-2=0$ intersects with the circle $x^{2}+y^{2}=r^{2}$ ($r>0$) at points A and B, and O is the origin. If $\\angle AOB=120°$, then $r=$ ______.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Number Theory -> Other"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Observe the following equations: $5^{5}=3125$, $5^{6}=15625$, $5^{7}=78125$, $...$, the last four digits of $5^{2018}$ are $\\_\\_\\_\\_\\_\\_\\_$. 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": "5625",
"style": "rule"
}
|
{
"answer": "5625",
"index": 214,
"question": "Observe the following equations: $5^{5}=3125$, $5^{6}=15625$, $5^{7}=78125$, $...$, the last four digits of $5^{2018}$ are $\\_\\_\\_\\_\\_\\_\\_$.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the numbers between a certain number and 50, exactly one number has two of the digits as 5. 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": "54",
"style": "rule"
}
|
{
"answer": "54",
"index": 215,
"question": "In the numbers between a certain number and 50, exactly one number has two of the digits as 5. What is the starting number?",
"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 Let $\\ell$ be a line and let points $A$ , $B$ , $C$ lie on $\\ell$ so that $AB = 7$ and $BC = 5$ . Let $m$ be the line through $A$ perpendicular to $\\ell$ . Let $P$ lie on $m$ . Compute the smallest possible value of $PB + PC$ . 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": "19",
"style": "rule"
}
|
{
"answer": "19",
"index": 216,
"question": "Let $\\ell$ be a line and let points $A$ , $B$ , $C$ lie on $\\ell$ so that $AB = 7$ and $BC = 5$ . Let $m$ be the line through $A$ perpendicular to $\\ell$ . Let $P$ lie on $m$ . Compute the smallest possible value of $PB + PC$ .",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Other"
] | 0.09375
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the coefficients of the 4th term and the 8th term in the expansion of $(1+x)^n$ are equal, find the sum of the binomial coefficients of the odd terms. 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": "512",
"style": "rule"
}
|
{
"answer": "512",
"index": 217,
"question": "Given that the coefficients of the 4th term and the 8th term in the expansion of $(1+x)^n$ are equal, find the sum of the binomial coefficients of the odd terms. Express your answer as a single integer.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A class of 30 students is completing an art project. They are assigned to separate groups and will need to take markers from some boxes of markers. The first group has 10 students who will have 2 markers each and the second group has 15 students who will have 4 markers each. The last group takes the remaining markers and divides them equally, with each student receiving 6 markers. How many boxes of markers are there? 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": "110",
"style": "rule"
}
|
{
"answer": "110",
"index": 218,
"question": "A class of 30 students is completing an art project. They are assigned to separate groups and will need to take markers from some boxes of markers. The first group has 10 students who will have 2 markers each and the second group has 15 students who will have 4 markers each. The last group takes the remaining markers and divides them equally, with each student receiving 6 markers. How many boxes of markers are there?",
"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 grocery shop has sales for 5 consecutive months. The sales for the other 4 months are Rs. 6735, Rs. 6927, Rs. 7230, and Rs. 6562. The shop owner wants an average sale of Rs. 6500 for 6 months and needs a sale of Rs. 4691 in the sixth month. What was the sale in the third month? 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": "6855",
"style": "rule"
}
|
{
"answer": "6855",
"index": 219,
"question": "A grocery shop has sales for 5 consecutive months. The sales for the other 4 months are Rs. 6735, Rs. 6927, Rs. 7230, and Rs. 6562. The shop owner wants an average sale of Rs. 6500 for 6 months and needs a sale of Rs. 4691 in the sixth month. What was the sale in the third month?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Intermediate Algebra -> Logarithmic Functions"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n $$\\frac{1-2 \\log _{6} 5 \\cdot \\log _{10} 3 \\cdot \\log _{15} 2}{\\log _{6} 5 \\cdot \\log _{10} 3+\\log _{10} 3 \\cdot \\log _{15} 2+\\log _{15} 2 \\cdot \\log _{6} 5} =$$ 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": 220,
"question": "$$\\frac{1-2 \\log _{6} 5 \\cdot \\log _{10} 3 \\cdot \\log _{15} 2}{\\log _{6} 5 \\cdot \\log _{10} 3+\\log _{10} 3 \\cdot \\log _{15} 2+\\log _{15} 2 \\cdot \\log _{6} 5} =$$",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the equation $sinαsin(\\frac{π}{3}-α)=3cosαsin(α+\\frac{π}{6})$, find the value of $sin(2α+\\frac{π}{6})$. Express your answer as a single 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": 221,
"question": "Given the equation $sinαsin(\\frac{π}{3}-α)=3cosαsin(α+\\frac{π}{6})$, find the value of $sin(2α+\\frac{π}{6})$. Express your answer as a single value.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Other"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the inequality \\(\\dfrac{m}{3a+b}-\\dfrac{3}{a}-\\dfrac{1}{b}\\leqslant 0\\), which always holds for positive real numbers \\(a\\) and \\(b\\), find the maximum value of \\(m\\). 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": "16",
"style": "rule"
}
|
{
"answer": "16",
"index": 222,
"question": "Given the inequality \\(\\dfrac{m}{3a+b}-\\dfrac{3}{a}-\\dfrac{1}{b}\\leqslant 0\\), which always holds for positive real numbers \\(a\\) and \\(b\\), find the maximum value of \\(m\\). Express your answer as a single 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 Jake initially amasses a fortune of 120 bitcoin. Seeing an opportunity, he invests 40 bitcoins into a venture when the price of bitcoin doubles the following day. He then donates 25 bitcoins to charity at a time when the value of bitcoin is half of what it was the previous day. After receiving his charity receipt, he gives half of all the bitcoins to his brother when bitcoin is at peak value. His brother being an honest man, returns 5 bitcoins back to Jake as payment for a debt, however, this was when bitcoin was at its lowest value in a month. Subsequently, Jake, being an excellent trader, quadruples the number of bitcoins he has with some skillful trades. In a twist of fate, he donates another 15 bitcoins on a day when the bitcoin value skyrockets to quadruple its initial value. How many bitcoins does Jake 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": "95",
"style": "rule"
}
|
{
"answer": "95",
"index": 223,
"question": "Jake initially amasses a fortune of 120 bitcoin. Seeing an opportunity, he invests 40 bitcoins into a venture when the price of bitcoin doubles the following day. He then donates 25 bitcoins to charity at a time when the value of bitcoin is half of what it was the previous day. After receiving his charity receipt, he gives half of all the bitcoins to his brother when bitcoin is at peak value. His brother being an honest man, returns 5 bitcoins back to Jake as payment for a debt, however, this was when bitcoin was at its lowest value in a month. Subsequently, Jake, being an excellent trader, quadruples the number of bitcoins he has with some skillful trades. In a twist of fate, he donates another 15 bitcoins on a day when the bitcoin value skyrockets to quadruple its initial value. How many bitcoins does Jake have now?",
"split": "train"
}
|
olympiads
|
[
"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 \\( x = \\cos \\frac{2}{5} \\pi + i \\sin \\frac{2}{5} \\pi \\), evaluate \\( 1 + x^4 + x^8 + x^{12} + x^{16} \\). 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": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 224,
"question": "Given \\( x = \\cos \\frac{2}{5} \\pi + i \\sin \\frac{2}{5} \\pi \\), evaluate \\( 1 + x^4 + x^8 + x^{12} + x^{16} \\).",
"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 It takes Avery 3 hours to build a brick wall, while Tom takes a certain amount of time to do it. If the two start working together and after an hour Avery leaves, it takes Tom 20.000000000000007 minutes to complete the wall on his own. How much time does it take Tom to build the wall? 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": 225,
"question": "It takes Avery 3 hours to build a brick wall, while Tom takes a certain amount of time to do it. If the two start working together and after an hour Avery leaves, it takes Tom 20.000000000000007 minutes to complete the wall on his own. How much time does it take Tom to build the wall?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Intermediate 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 In the geometric sequence {a_n}, the sum of the first 6 terms (S_6) is 120, and the sum of the 1st, 3rd, and 5th terms (a_1 + a_3 + a_5) is 30. Find the common ratio q of the geometric sequence. 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": 226,
"question": "In the geometric sequence {a_n}, the sum of the first 6 terms (S_6) is 120, and the sum of the 1st, 3rd, and 5th terms (a_1 + a_3 + a_5) is 30. Find the common ratio q of the geometric sequence.",
"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 a train 500 m long can cross an electric pole in 10 sec and then find the speed of 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": "50",
"style": "rule"
}
|
{
"answer": "50",
"index": 227,
"question": "a train 500 m long can cross an electric pole in 10 sec and then find the speed of the train ?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A regular triangular prism \\( A B C A_{1} B_{1} C_{1} \\) is inscribed in a sphere, with its base \\( A B C \\) and lateral edges \\( A A_{1}, B B_{1}, C C_{1} \\). Segment \\( C D \\) is the diameter of this sphere, and points \\( K \\) and \\( L \\) are the midpoints of edges \\( A A_{1} \\) and \\( A B \\) respectively. Find the volume of the prism if \\( D L = \\sqrt{2} \\) and \\( D K = \\sqrt{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": "4",
"style": "rule"
}
|
{
"answer": "4",
"index": 228,
"question": "A regular triangular prism \\( A B C A_{1} B_{1} C_{1} \\) is inscribed in a sphere, with its base \\( A B C \\) and lateral edges \\( A A_{1}, B B_{1}, C C_{1} \\). Segment \\( C D \\) is the diameter of this sphere, and points \\( K \\) and \\( L \\) are the midpoints of edges \\( A A_{1} \\) and \\( A B \\) respectively. Find the volume of the prism if \\( D L = \\sqrt{2} \\) and \\( D K = \\sqrt{3} \\).",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the circle $\\rho=8\\sin \\theta$ and the line $\\theta=\\frac{\\pi}{3}$, calculate the maximum distance from a point on the circle to the line. 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": "6",
"style": "rule"
}
|
{
"answer": "6",
"index": 229,
"question": "Given the circle $\\rho=8\\sin \\theta$ and the line $\\theta=\\frac{\\pi}{3}$, calculate the maximum distance from a point on the circle to the line. Express your answer as a single number.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Geometry -> Other"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $ab > 0$, and points $A(a, 0)$, $B(0, b)$, $C(-2, -2)$ are collinear, find the minimum value of $ab$. 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": 230,
"question": "If $ab > 0$, and points $A(a, 0)$, $B(0, b)$, $C(-2, -2)$ are collinear, find the minimum value of $ab$.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If \\(\\frac{30}{7} = x + \\frac{1}{y + \\frac{1}{z}}\\), where \\(x, y\\), and \\(z\\) are positive integers, then what is the value of \\(x + y + z\\)? 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": 231,
"question": "If \\(\\frac{30}{7} = x + \\frac{1}{y + \\frac{1}{z}}\\), where \\(x, y\\), and \\(z\\) are positive integers, then what is the value of \\(x + y + z\\)?",
"split": "train"
}
|
math
|
[
"Mathematics -> Algebra -> Algebraic Expressions"
] | 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 Evaluate the product \\[(\\sqrt 5+\\sqrt6+\\sqrt7)(-\\sqrt 5+\\sqrt6+\\sqrt7)(\\sqrt 5-\\sqrt6+\\sqrt7)(\\sqrt 5+\\sqrt6-\\sqrt7).\\] 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": "104",
"style": "rule"
}
|
{
"answer": "104",
"index": 232,
"question": "Evaluate the product \\[(\\sqrt 5+\\sqrt6+\\sqrt7)(-\\sqrt 5+\\sqrt6+\\sqrt7)(\\sqrt 5-\\sqrt6+\\sqrt7)(\\sqrt 5+\\sqrt6-\\sqrt7).\\]",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the idioms “虚有其表”, “表里如一”, “一见如故”, and “故弄玄虚”, each Chinese character represents one of 11 consecutive non-zero natural numbers. Identical characters represent the same number, different characters represent different numbers, and the following inequality holds: “表” > “一” > “故” > \"如” > “虚”. Moreover, the sum of the numbers represented by the four characters in each idiom is 21. What is the maximum value that the character “弄” can represent? 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": 233,
"question": "In the idioms “虚有其表”, “表里如一”, “一见如故”, and “故弄玄虚”, each Chinese character represents one of 11 consecutive non-zero natural numbers. Identical characters represent the same number, different characters represent different numbers, and the following inequality holds: “表” > “一” > “故” > \"如” > “虚”. Moreover, the sum of the numbers represented by the four characters in each idiom is 21. What is the maximum value that the character “弄” can represent?",
"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 At a bookstore, the number of people who purchased Book A is twice the number of people who purchased Book B. The number of people who purchased both Books A and B is 500, which is twice the number of people who purchased only Book B. In addition, there is a Book C, and 300 people purchased both Books B and C. The total revenue generated from the sale of all three books is $15,000. If the price of Book A is $25, the price of Book B is $20, and the price of Book C, is $15, find the number of people who purchased only Book 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": "1000",
"style": "rule"
}
|
{
"answer": "1000",
"index": 234,
"question": "At a bookstore, the number of people who purchased Book A is twice the number of people who purchased Book B. The number of people who purchased both Books A and B is 500, which is twice the number of people who purchased only Book B. In addition, there is a Book C, and 300 people purchased both Books B and C. The total revenue generated from the sale of all three books is $15,000. If the price of Book A is $25, the price of Book B is $20, and the price of Book C, is $15, find the number of people who purchased only Book A.",
"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 There are 4 members in a family. Their average income is some amount per month. 3 members get Rs. 8000, Rs. 15000, Rs. 6000 respectively. The income of the fourth member of the family is Rs. 11000. What is the average income of the family per month? 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": "10000",
"style": "rule"
}
|
{
"answer": "10000",
"index": 235,
"question": "There are 4 members in a family. Their average income is some amount per month. 3 members get Rs. 8000, Rs. 15000, Rs. 6000 respectively. The income of the fourth member of the family is Rs. 11000. What is the average income of the family per month?",
"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 Jake has 12 fewer peaches and some more apples than Steven. Steven has 19 peaches and 14 apples. How many more apples does Jake have compared to Steven? 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": 236,
"question": "Jake has 12 fewer peaches and some more apples than Steven. Steven has 19 peaches and 14 apples. How many more apples does Jake have compared to Steven?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Other"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Out of a class of 33 students, each day 22 go swimming and 22 play football. Everyone participates in at least one training session each day. Of those who are playing football today, 15 were swimming and 15 were playing football yesterday, and the same applies for those who are swimming today. How many students swam on both days? 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": 237,
"question": "Out of a class of 33 students, each day 22 go swimming and 22 play football. Everyone participates in at least one training session each day. Of those who are playing football today, 15 were swimming and 15 were playing football yesterday, and the same applies for those who are swimming today. How many students swam on both days?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n My friend and I are playing a game with the following rules: If one of us says an integer \\( n \\), the opponent then says an integer of their choice between \\( 2n \\) and \\( 3n \\), inclusive. Whoever first says 2007 or greater loses the game, and their opponent wins. I must begin the game by saying a positive integer less than 10. With how many of them can I guarantee a win? 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": 238,
"question": "My friend and I are playing a game with the following rules: If one of us says an integer \\( n \\), the opponent then says an integer of their choice between \\( 2n \\) and \\( 3n \\), inclusive. Whoever first says 2007 or greater loses the game, and their opponent wins. I must begin the game by saying a positive integer less than 10. With how many of them can I guarantee a win?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Number Theory -> Prime Numbers",
"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 From the integers 1 to 2020, there are a total of 1616 integers that are not multiples of 5. These 1616 numbers need to be divided into groups (each group may have a different number of elements), such that the difference (larger number minus smaller number) between any two numbers in the same group is a prime number. What is the minimum number of groups 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": "404",
"style": "rule"
}
|
{
"answer": "404",
"index": 239,
"question": "From the integers 1 to 2020, there are a total of 1616 integers that are not multiples of 5. These 1616 numbers need to be divided into groups (each group may have a different number of elements), such that the difference (larger number minus smaller number) between any two numbers in the same group is a prime number. What is the minimum number of groups required?",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Algebra -> Simple Equations -> 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 Calculate the product of 469157 and a number, which equals 4691100843. What is the 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": "10001",
"style": "rule"
}
|
{
"answer": "10001",
"index": 240,
"question": "Calculate the product of 469157 and a number, which equals 4691100843. What is the number?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Calculus -> Other"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $a,b \\in \\mathbb{R}$ and $a^{2} + 2b^{2} = 6$, find the minimum value of $a+b$. 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": "-3",
"style": "rule"
}
|
{
"answer": "-3",
"index": 241,
"question": "If $a,b \\in \\mathbb{R}$ and $a^{2} + 2b^{2} = 6$, find the minimum value of $a+b$. Express your answer as a single number.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If the function $f(x) = 2x^3 - 3x^2 - 12x + a$ has a maximum value of 5 on the interval $[0, 2]$, then the value of $a$ 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": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 242,
"question": "If the function $f(x) = 2x^3 - 3x^2 - 12x + a$ has a maximum value of 5 on the interval $[0, 2]$, then the value of $a$ is.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Probability -> 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 fair coin is tossed 5 times. The probability of getting exactly one heads is non-zero and is equal to the probability of getting exactly two heads. Let the simplified fraction \\(\\frac{i}{j}\\) represent the probability of getting exactly 3 heads out of 5 tosses. Find the value of \\(i + j\\). 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": "283",
"style": "rule"
}
|
{
"answer": "283",
"index": 243,
"question": "A fair coin is tossed 5 times. The probability of getting exactly one heads is non-zero and is equal to the probability of getting exactly two heads. Let the simplified fraction \\(\\frac{i}{j}\\) represent the probability of getting exactly 3 heads out of 5 tosses. Find the value of \\(i + j\\).",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Number Theory -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $f: N \\to N$ satisfy $n=\\sum_{d|n} f(d), \\forall n \\in N$ . Then sum of all possible values of $f(100)$ 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": "40",
"style": "rule"
}
|
{
"answer": "40",
"index": 244,
"question": "Let $f: N \\to N$ satisfy $n=\\sum_{d|n} f(d), \\forall n \\in N$ . Then sum of all possible values of $f(100)$ is? ",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Logic"
] | 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 group of adventurers displays their loot. It is known that exactly 9 adventurers have rubies; exactly 8 have emeralds; exactly 2 have sapphires; exactly 11 have diamonds. Additionally, it is known that:\n\n- If an adventurer has diamonds, they either have rubies or sapphires (but not both simultaneously);\n- If an adventurer has rubies, they either have emeralds or diamonds (but not both simultaneously).\n\nWhat is the minimum number of adventurers that could be in this group? 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": "17",
"style": "rule"
}
|
{
"answer": "17",
"index": 245,
"question": "A group of adventurers displays their loot. It is known that exactly 9 adventurers have rubies; exactly 8 have emeralds; exactly 2 have sapphires; exactly 11 have diamonds. Additionally, it is known that:\n\n- If an adventurer has diamonds, they either have rubies or sapphires (but not both simultaneously);\n- If an adventurer has rubies, they either have emeralds or diamonds (but not both simultaneously).\n\nWhat is the minimum number of adventurers that could be in this group?",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Tony can run a mile twice as fast as Tina, who with a certain time is one-third as fast a runner as Tom. Their mile times when added together are 11 minutes. What is Tina's mile 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": "6",
"style": "rule"
}
|
{
"answer": "6",
"index": 246,
"question": "Tony can run a mile twice as fast as Tina, who with a certain time is one-third as fast a runner as Tom. Their mile times when added together are 11 minutes. What is Tina's mile time?",
"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 As shown in Figure 7, a chessboard has 64 alternating black and white squares. Squares $P$ and $Q$ are located on the bottom row and the top row respectively. A chess piece starts moving from square $P$, and each move is to an adjacent white square in the row above. Then... 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": 247,
"question": "As shown in Figure 7, a chessboard has 64 alternating black and white squares. Squares $P$ and $Q$ are located on the bottom row and the top row respectively. A chess piece starts moving from square $P$, and each move is to an adjacent white square in the row above. Then...",
"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, how many numbers 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": 248,
"question": "Among the four-digit numbers composed of the digits 0, 1, 2, and 5 without any repetition, how many numbers cannot be divided by 5? Express your answer as a whole number.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Other"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a positive geometric sequence $\\{a_n\\}$, the sum of the first 2 terms is 7 and the sum of the first 6 terms is 91. Find the sum of the first 4 terms. 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": 249,
"question": "In a positive geometric sequence $\\{a_n\\}$, the sum of the first 2 terms is 7 and the sum of the first 6 terms is 91. Find the sum of the first 4 terms. Express your answer as a single numerical value.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A function f(n) has the property that f(f(n)) + f(n) = 2n + 3, and f(0) = 1. If f(2015) = 2016, what is the value of n for which we are finding f(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": "2016",
"style": "rule"
}
|
{
"answer": "2016",
"index": 250,
"question": "A function f(n) has the property that f(f(n)) + f(n) = 2n + 3, and f(0) = 1. If f(2015) = 2016, what is the value of n for which we are finding f(n)?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Using eight $2 \\times 1$ small rectangles as shown in the diagram, a $4 \\times 4$ square can be formed. If a formed square pattern is considered the same as another if it can be rotated to match, the question is: How many different square patterns can be formed such that it has only one diagonal as its axis of symmetry? 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": 251,
"question": "Using eight $2 \\times 1$ small rectangles as shown in the diagram, a $4 \\times 4$ square can be formed. If a formed square pattern is considered the same as another if it can be rotated to match, the question is: How many different square patterns can be formed such that it has only one diagonal as its axis of symmetry?",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In their first terms, Governor Sandoval gave twice as many commencement addresses as Governor Hawkins. Governor Sloan gave ten more commencement addresses than Governor Sandoval in the same amount of time. Plus, on rainy days, each governor gave one less commencement address than normal. Additionally, Governor Davenport gave three less than the average of Governor Sandoval and Governor Sloan's commencement addresses, excluding ones given on rainy days. Finally, Governor Adkins only gave commencement addresses on public holidays, but his total was still two more than the combined total of Governor Hawkins and Governor Davenport. If Governor Sandoval gave 12 commencement addresses, and considering that 5 of these speeches were given on rainy days and 2 on public holidays, how many commencement addresses did the five of them give altogether? 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": "70",
"style": "rule"
}
|
{
"answer": "70",
"index": 252,
"question": "In their first terms, Governor Sandoval gave twice as many commencement addresses as Governor Hawkins. Governor Sloan gave ten more commencement addresses than Governor Sandoval in the same amount of time. Plus, on rainy days, each governor gave one less commencement address than normal. Additionally, Governor Davenport gave three less than the average of Governor Sandoval and Governor Sloan's commencement addresses, excluding ones given on rainy days. Finally, Governor Adkins only gave commencement addresses on public holidays, but his total was still two more than the combined total of Governor Hawkins and Governor Davenport. If Governor Sandoval gave 12 commencement addresses, and considering that 5 of these speeches were given on rainy days and 2 on public holidays, how many commencement addresses did the five of them give altogether?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Graph Theory"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 30 people studying in the Slytherin House at Hogwarts. Some of them are friends (friendship is mutual, i.e., if A is friends with B, then B is also friends with A), but no three people are pairwise friends with each other. For New Year, everyone sent postcards to all their friends. What is the maximum number of postcards that could have been sent? 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": "450",
"style": "rule"
}
|
{
"answer": "450",
"index": 253,
"question": "There are 30 people studying in the Slytherin House at Hogwarts. Some of them are friends (friendship is mutual, i.e., if A is friends with B, then B is also friends with A), but no three people are pairwise friends with each other. For New Year, everyone sent postcards to all their friends. What is the maximum number of postcards that could have been sent?",
"split": "train"
}
|
omnimath
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The altitudes of a triangle are $12$, $15$, and $20$. What is the area of this triangle? 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": 254,
"question": "The altitudes of a triangle are $12$, $15$, and $20$. What is the area of this triangle?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.0625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the coefficient of $x^2$ in the expansion of $(x+2+\\frac{1}{x})^5$. 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": "120",
"style": "rule"
}
|
{
"answer": "120",
"index": 255,
"question": "Find the coefficient of $x^2$ in the expansion of $(x+2+\\frac{1}{x})^5$. Express your answer as a single integer.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Number Theory -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the set {1, 2, 3,..., 99, 100}, how many numbers n satisfy the condition that the tens digit of n^2 is odd? 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": "20",
"style": "rule"
}
|
{
"answer": "20",
"index": 256,
"question": "In the set {1, 2, 3,..., 99, 100}, how many numbers n satisfy the condition that the tens digit of n^2 is odd? Express your answer as a whole number.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Suppose \\( P(x) \\) is a monic polynomial of degree 2023 such that\n\\[ P(k) = k^{2023} P\\left( 1 - \\frac{1}{k} \\right) \\]\nfor every positive integer \\( 1 \\leq k \\leq 2023 \\). Then \\( P(-1) = \\frac{a}{b} \\), where \\( a \\) and \\( b \\) are relatively prime integers. Compute the unique integer \\( 0 \\leq n < 2027 \\) such that \\( bn - a \\) is divisible by the prime 2027. 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": "406",
"style": "rule"
}
|
{
"answer": "406",
"index": 257,
"question": "Suppose \\( P(x) \\) is a monic polynomial of degree 2023 such that\n\\[ P(k) = k^{2023} P\\left( 1 - \\frac{1}{k} \\right) \\]\nfor every positive integer \\( 1 \\leq k \\leq 2023 \\). Then \\( P(-1) = \\frac{a}{b} \\), where \\( a \\) and \\( b \\) are relatively prime integers. Compute the unique integer \\( 0 \\leq n < 2027 \\) such that \\( bn - a \\) is divisible by the prime 2027.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Number Theory -> Factorization"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If a = 105 and a ^ 3 = 21 * 25 * some number * 7, what is the value of 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": "105",
"style": "rule"
}
|
{
"answer": "105",
"index": 258,
"question": "If a = 105 and a ^ 3 = 21 * 25 * some number * 7, what is the value of that number?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics -> 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 Four objects of different masses are available. What is the minimum number of weighings on a balance scale without weights needed to determine the heaviest and the lightest of these objects? 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": 259,
"question": "Four objects of different masses are available. What is the minimum number of weighings on a balance scale without weights needed to determine the heaviest and the lightest of these objects?",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the ellipse $\\dfrac{x^2}{m^2} + y^2 = 1$ ($m > 1$) and the hyperbola $\\dfrac{x^2}{n^2} - y^2 = 1$ ($n > 0$), both sharing a common focus $F_1$. Let $F_2 P$ be the intersection point of the two curves. Calculate the area of the triangle $\\triangle F_1 P F_2$. 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": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 260,
"question": "Given the ellipse $\\dfrac{x^2}{m^2} + y^2 = 1$ ($m > 1$) and the hyperbola $\\dfrac{x^2}{n^2} - y^2 = 1$ ($n > 0$), both sharing a common focus $F_1$. Let $F_2 P$ be the intersection point of the two curves. Calculate the area of the triangle $\\triangle F_1 P F_2$.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Number Theory -> Other"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n For a real number \\( x \\), let \\( [x] \\) denote the greatest integer that does not exceed \\( x \\). For a certain integer \\( k \\), there exist exactly 2008 positive integers \\( n_{1}, n_{2}, \\cdots, n_{2008} \\), such that \\( k=\\left[\\sqrt[3]{n_{1}}\\right]=\\left[\\sqrt[3]{n_{2}}\\right]=\\cdots=\\left[\\sqrt[3]{n_{2008}}\\right] \\), and \\( k \\) divides \\( n_{i} \\) (for \\( i = 1, 2, \\cdots, 2008 \\)). What is the value of \\( k \\)? 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": "668",
"style": "rule"
}
|
{
"answer": "668",
"index": 261,
"question": "For a real number \\( x \\), let \\( [x] \\) denote the greatest integer that does not exceed \\( x \\). For a certain integer \\( k \\), there exist exactly 2008 positive integers \\( n_{1}, n_{2}, \\cdots, n_{2008} \\), such that \\( k=\\left[\\sqrt[3]{n_{1}}\\right]=\\left[\\sqrt[3]{n_{2}}\\right]=\\cdots=\\left[\\sqrt[3]{n_{2008}}\\right] \\), and \\( k \\) divides \\( n_{i} \\) (for \\( i = 1, 2, \\cdots, 2008 \\)). What is the value of \\( k \\)?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Number Theory -> Other"
] | 0.09375
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( n \\) be the decimal integer 111...1 (with 1998 digits). What is the 1000th digit after the decimal point of \\( \\sqrt{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": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 262,
"question": "Let \\( n \\) be the decimal integer 111...1 (with 1998 digits). What is the 1000th digit after the decimal point of \\( \\sqrt{n} \\)?",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n george baked a total of 50 pizzas for 5 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ? 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": 263,
"question": "george baked a total of 50 pizzas for 5 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Algebra -> Prealgebra -> Simple Equations"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Two numbers have a certain relationship. Their sum is 124, and the smaller number is 31. What is the relationship between the two 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": "62",
"style": "rule"
}
|
{
"answer": "62",
"index": 264,
"question": "Two numbers have a certain relationship. Their sum is 124, and the smaller number is 31. What is the relationship between the two numbers?",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The school plans to use the first, second, and third classes on Friday afternoon to hold special lectures on four subjects: Chinese, Mathematics, English, and Science Comprehensive. Each subject has one class, and each class must have at least one subject. Mathematics and Science Comprehensive cannot be arranged in the same class. There are a total of \\_\\_\\_\\_\\_\\_ different arrangements. 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": "30",
"style": "rule"
}
|
{
"answer": "30",
"index": 265,
"question": "The school plans to use the first, second, and third classes on Friday afternoon to hold special lectures on four subjects: Chinese, Mathematics, English, and Science Comprehensive. Each subject has one class, and each class must have at least one subject. Mathematics and Science Comprehensive cannot be arranged in the same class. There are a total of \\_\\_\\_\\_\\_\\_ different arrangements.",
"split": "train"
}
|
olympiads
|
[
"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 From a sequence of natural numbers, all numbers that are squares or cubes of integers have been removed. Which number remains in the 100th position? 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": "112",
"style": "rule"
}
|
{
"answer": "112",
"index": 266,
"question": "From a sequence of natural numbers, all numbers that are squares or cubes of integers have been removed. Which number remains in the 100th position?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 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 triangle \\(ABC\\), \\(AC = 1\\), \\(AB = 2\\), and \\(O\\) is the point where the angle bisectors intersect. A segment passing through point \\(O\\) parallel to side \\(BC\\) intersects sides \\(AC\\) and \\(AB\\) at points \\(K\\) and \\(M\\) respectively. Find the perimeter of triangle \\(AKM\\). 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": 267,
"question": "In triangle \\(ABC\\), \\(AC = 1\\), \\(AB = 2\\), and \\(O\\) is the point where the angle bisectors intersect. A segment passing through point \\(O\\) parallel to side \\(BC\\) intersects sides \\(AC\\) and \\(AB\\) at points \\(K\\) and \\(M\\) respectively. Find the perimeter of triangle \\(AKM\\).",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A metal sphere with a radius of $\\sqrt[z]{16}$ is melted and recast into a cone whose lateral surface area is three times the area of its base. Find the height of the 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": "8",
"style": "rule"
}
|
{
"answer": "8",
"index": 268,
"question": "A metal sphere with a radius of $\\sqrt[z]{16}$ is melted and recast into a cone whose lateral surface area is three times the area of its base. Find the height of the cone.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In \"Dragon Poker,\" the deck has four suits. An ace is worth 1 point, a jack is worth 2 points, a 2 is worth \\( -2^{2} \\) points, a 3 is worth \\( -2^{3} \\) points, and so on, up to a 10, which is worth \\( -2^{10} = 1024 \\) points. Kings and queens are absent. You can choose any number of cards from the deck. How many ways are there to score 2018 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": "1373734330",
"style": "rule"
}
|
{
"answer": "1373734330",
"index": 269,
"question": "In \"Dragon Poker,\" the deck has four suits. An ace is worth 1 point, a jack is worth 2 points, a 2 is worth \\( -2^{2} \\) points, a 3 is worth \\( -2^{3} \\) points, and so on, up to a 10, which is worth \\( -2^{10} = 1024 \\) points. Kings and queens are absent. You can choose any number of cards from the deck. How many ways are there to score 2018 points?",
"split": "train"
}
|
math
|
[
"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 In this problem, $a$ and $b$ are positive integers.\n\nWhen $a$ is written in base $9$, its last digit is $5$.\n\nWhen $b$ is written in base $6$, its last two digits are $53$.\n\nWhen $a-b$ is written in base $3$, what are its last two digits? Assume $a-b$ is positive. 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": 270,
"question": "In this problem, $a$ and $b$ are positive integers.\n\nWhen $a$ is written in base $9$, its last digit is $5$.\n\nWhen $b$ is written in base $6$, its last two digits are $53$.\n\nWhen $a-b$ is written in base $3$, what are its last two digits? Assume $a-b$ is positive.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Calculus -> Differential Calculus -> Applications of 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 Given the quadratic function $f(x)=ax^{2}+bx+c$ with its derivative $f′(x)$, where $f′(0) > 0$, and $f(x)\\geqslant 0$ for any real number $x$, find the minimum value of $\\frac{f(1)}{f′(0)}$. 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": 271,
"question": "Given the quadratic function $f(x)=ax^{2}+bx+c$ with its derivative $f′(x)$, where $f′(0) > 0$, and $f(x)\\geqslant 0$ for any real number $x$, find the minimum value of $\\frac{f(1)}{f′(0)}$.",
"split": "train"
}
|
olympiads
|
[
"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 If \\( x_{1} > x_{2} > x_{3} > x_{4} > 0 \\) and the inequality\n\\[\n\\log_{\\frac{x_{1}}{x_{2}}} 2014 + \\log_{\\frac{x_{2}}{x_{3}}} 2014 + \\log_{\\frac{x_{3}}{x_{4}}} 2014 \\geqslant k \\log_{\\frac{x_{1}}{x_{4}}} 2014\n\\]\nalways holds, then the maximum value of the real number \\( k \\) 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": "9",
"style": "rule"
}
|
{
"answer": "9",
"index": 272,
"question": "If \\( x_{1} > x_{2} > x_{3} > x_{4} > 0 \\) and the inequality\n\\[\n\\log_{\\frac{x_{1}}{x_{2}}} 2014 + \\log_{\\frac{x_{2}}{x_{3}}} 2014 + \\log_{\\frac{x_{3}}{x_{4}}} 2014 \\geqslant k \\log_{\\frac{x_{1}}{x_{4}}} 2014\n\\]\nalways holds, then the maximum value of the real number \\( k \\) is ________.",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the minimum positive value of $ 1*2*3*4*...*2020*2021*2022$ where you can replace $*$ as $+$ or $-$ 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": 273,
"question": "Find the minimum positive value of $ 1*2*3*4*...*2020*2021*2022$ where you can replace $*$ as $+$ or $-$ ",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.046875
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If x is an integer such that 0 < x < 7, 0 < x < 15, 5 > x > -1, 3 > x > 0, and x + some number < 4, then x is 1. What is the number added to x in the fifth inequality? 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": 274,
"question": "If x is an integer such that 0 < x < 7, 0 < x < 15, 5 > x > -1, 3 > x > 0, and x + some number < 4, then x is 1. What is the number added to x in the fifth inequality?",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a forest there are $5$ trees $A, B, C, D, E$ that are in that order on a straight line. At the midpoint of $AB$ there is a daisy, at the midpoint of $BC$ there is a rose bush, at the midpoint of $CD$ there is a jasmine, and at the midpoint of $DE$ there is a carnation. The distance between $A$ and $E$ is $28$ m; the distance between the daisy and the carnation is $20$ m. Calculate the distance between the rose bush and the jasmine. 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": 275,
"question": "In a forest there are $5$ trees $A, B, C, D, E$ that are in that order on a straight line. At the midpoint of $AB$ there is a daisy, at the midpoint of $BC$ there is a rose bush, at the midpoint of $CD$ there is a jasmine, and at the midpoint of $DE$ there is a carnation. The distance between $A$ and $E$ is $28$ m; the distance between the daisy and the carnation is $20$ m. Calculate the distance between the rose bush and the jasmine.",
"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 The numbers \\(a_{1}, a_{2}, \\ldots, a_{n}\\) are such that the sum of any seven consecutive numbers is negative, and the sum of any eleven consecutive numbers is positive. What is the largest possible \\(n\\) for which this is true? 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": 276,
"question": "The numbers \\(a_{1}, a_{2}, \\ldots, a_{n}\\) are such that the sum of any seven consecutive numbers is negative, and the sum of any eleven consecutive numbers is positive. What is the largest possible \\(n\\) for which this is true?",
"split": "train"
}
|
cn_k12
|
[
"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 Given the set $\\{1,a,\\frac{b}{a}\\}=\\{0,{a}^{2},a+b\\}$, then $\\left(a+b\\right)^{2023}=\\_\\_\\_\\_\\_\\_.$ 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": "-1",
"style": "rule"
}
|
{
"answer": "-1",
"index": 277,
"question": "Given the set $\\{1,a,\\frac{b}{a}\\}=\\{0,{a}^{2},a+b\\}$, then $\\left(a+b\\right)^{2023}=\\_\\_\\_\\_\\_\\_.$",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Number Theory -> Divisibility"
] | 0.03125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the largest natural number \\( n \\) for which the product of the numbers \\( n, n+1, n+2, \\ldots, n+20 \\) is divisible by the square of one of these 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": "20",
"style": "rule"
}
|
{
"answer": "20",
"index": 278,
"question": "Find the largest natural number \\( n \\) for which the product of the numbers \\( n, n+1, n+2, \\ldots, n+20 \\) is divisible by the square of one of these numbers.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Algebra -> Intermediate Algebra -> Logarithmic Functions"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the value of $lg^2 2 + lg2 \\cdot lg5 + lg50$. 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": 279,
"question": "Find the value of $lg^2 2 + lg2 \\cdot lg5 + lg50$.",
"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 A square was cut into four equal rectangles and used to form a large letter П, as shown in the figure, with a perimeter of 56. What is the perimeter of the original square? 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": 280,
"question": "A square was cut into four equal rectangles and used to form a large letter П, as shown in the figure, with a perimeter of 56. What is the perimeter of the original square?",
"split": "train"
}
|
math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the number of ordered pairs $(a,b)$ of real numbers such that\n\n$\\bullet$ $a$ is a root of $x^2 + ax + b = 0,$ and\n\n$\\bullet$ $b$ is a root of $x^2 + ax + b = 0.$ 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": 281,
"question": "Find the number of ordered pairs $(a,b)$ of real numbers such that\n\n$\\bullet$ $a$ is a root of $x^2 + ax + b = 0,$ and\n\n$\\bullet$ $b$ is a root of $x^2 + ax + b = 0.$",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 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 $\\vartriangle ABC$ be a triangle such that the area $ [ABC] = 10$ and $\\tan (\\angle ABC) = 5$ . If the smallest possible value of $(\\overline{AC})^2$ can be expressed as $-a + b\\sqrt{c}$ for positive integers $a, b, c$ , what is $a + b + c$ ?\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": "42",
"style": "rule"
}
|
{
"answer": "42",
"index": 282,
"question": "Let $\\vartriangle ABC$ be a triangle such that the area $ [ABC] = 10$ and $\\tan (\\angle ABC) = 5$ . If the smallest possible value of $(\\overline{AC})^2$ can be expressed as $-a + b\\sqrt{c}$ for positive integers $a, b, c$ , what is $a + b + c$ ?\n",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Geometry -> Other"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A circular coin \\(A\\) is rolled, without sliding, along the circumference of another stationary circular coin \\(B\\) with radius twice the radius of coin \\(A\\). Let \\(x\\) be the number of degrees that the coin \\(A\\) makes around its center until it first returns to its initial position. Find the value of \\(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": "1080",
"style": "rule"
}
|
{
"answer": "1080",
"index": 283,
"question": "A circular coin \\(A\\) is rolled, without sliding, along the circumference of another stationary circular coin \\(B\\) with radius twice the radius of coin \\(A\\). Let \\(x\\) be the number of degrees that the coin \\(A\\) makes around its center until it first returns to its initial position. Find the value of \\(x\\).",
"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 the equation \\(\\frac{\\left(\\frac{a}{c}+\\frac{a}{b}+1\\right)}{\\left(\\frac{b}{a}+\\frac{b}{c}+1\\right)}=11\\), where \\(a, b\\), and \\(c\\) are positive integers, find the number of different ordered triples \\((a, b, c)\\) such that \\(a+2b+c \\leq 40\\). 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": "42",
"style": "rule"
}
|
{
"answer": "42",
"index": 284,
"question": "Given the equation \\(\\frac{\\left(\\frac{a}{c}+\\frac{a}{b}+1\\right)}{\\left(\\frac{b}{a}+\\frac{b}{c}+1\\right)}=11\\), where \\(a, b\\), and \\(c\\) are positive integers, find the number of different ordered triples \\((a, b, c)\\) such that \\(a+2b+c \\leq 40\\). Express your answer as a single integer.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Algebra -> Algebraic Expressions -> 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 Find all positive integers \\( n \\) such that \\( n^{4} - n^{3} + 3n^{2} + 5 \\) is a perfect square. 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": 285,
"question": "Find all positive integers \\( n \\) such that \\( n^{4} - n^{3} + 3n^{2} + 5 \\) is a perfect square.",
"split": "train"
}
|
big_math
|
[
"Mathematics -> Geometry -> Solid 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 A cuboid with dimensions $77 \\times 81 \\times 100$ is cut into many small cubes with a side length of $1$. Each face of the small cubes is parallel to the corresponding face of the original cuboid. How many small cubes does a diagonal inside the cuboid pass through? 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": "256",
"style": "rule"
}
|
{
"answer": "256",
"index": 286,
"question": "A cuboid with dimensions $77 \\times 81 \\times 100$ is cut into many small cubes with a side length of $1$. Each face of the small cubes is parallel to the corresponding face of the original cuboid. How many small cubes does a diagonal inside the cuboid pass through? Express your answer as a whole number.",
"split": "train"
}
|
gsm8k
|
[
"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 Bob is building raised beds for his vegetable garden. Each bed is 2 feet high, 2 feet wide, and 8 feet long. The sides are going to be built of 1-foot wide planks. If Bob buys his lumber in 8-foot-long boards, planning to cut some of them for the shorter lengths he'll need, how many 8-foot long planks will he need to construct 10 raised beds? 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": "60",
"style": "rule"
}
|
{
"answer": "60",
"index": 287,
"question": "Bob is building raised beds for his vegetable garden. Each bed is 2 feet high, 2 feet wide, and 8 feet long. The sides are going to be built of 1-foot wide planks. If Bob buys his lumber in 8-foot-long boards, planning to cut some of them for the shorter lengths he'll need, how many 8-foot long planks will he need to construct 10 raised beds?",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Logic"
] | 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 town, each knight gives one affirmative answer to every four questions, while each liar gives three affirmative answers. A total of \\( 109 + 98 + 104 + 119 = 430 \\) affirmative answers were received. If all the townspeople were knights, the total number of affirmative answers would have been 200. The extra 230 affirmative answers come from liars, indicating there are \\(\\frac{230}{2} = 115\\) liars.\n\nLet \\( k \\) be the number of knights living in quarter \\(\\Gamma\\). Therefore, \\( 119 - k \\) is the number of affirmative answers given by liars to the fourth question. This implies that the number of liars living in quarter \\(\\Gamma\\) is \\( 115 - (119 - k) = k - 4 \\). In the other quarters, the number of liars is greater than the number of knights. 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": 288,
"question": "In a town, each knight gives one affirmative answer to every four questions, while each liar gives three affirmative answers. A total of \\( 109 + 98 + 104 + 119 = 430 \\) affirmative answers were received. If all the townspeople were knights, the total number of affirmative answers would have been 200. The extra 230 affirmative answers come from liars, indicating there are \\(\\frac{230}{2} = 115\\) liars.\n\nLet \\( k \\) be the number of knights living in quarter \\(\\Gamma\\). Therefore, \\( 119 - k \\) is the number of affirmative answers given by liars to the fourth question. This implies that the number of liars living in quarter \\(\\Gamma\\) is \\( 115 - (119 - k) = k - 4 \\). In the other quarters, the number of liars is greater than the number of knights.",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Adam and Eve received a basket containing 31 apples. On the first day, Eve ate three-quarters of what Adam ate. On the second day, Eve ate two-thirds of what Adam ate that day. By the evening of the second day, the basket was empty. How many apples did Eve eat from the basket? (Adam and Eve eat whole apples and do not share 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": "13",
"style": "rule"
}
|
{
"answer": "13",
"index": 289,
"question": "Adam and Eve received a basket containing 31 apples. On the first day, Eve ate three-quarters of what Adam ate. On the second day, Eve ate two-thirds of what Adam ate that day. By the evening of the second day, the basket was empty. How many apples did Eve eat from the basket? (Adam and Eve eat whole apples and do not share them.)",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are the same number of cars in each row. Red cars are in the 14th row from the front, 19th row from the left, 11th row from the back, and 16th row from the right. How many cars are there in total? 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": "816",
"style": "rule"
}
|
{
"answer": "816",
"index": 290,
"question": "There are the same number of cars in each row. Red cars are in the 14th row from the front, 19th row from the left, 11th row from the back, and 16th row from the right. How many cars are there in total?",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.0625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $a+b+c$, $b+c-a$, $c+a-b$, and $a+b-c$ form a geometric sequence in order, with a common ratio of $q$, then find the value of $q^3+q^2+q$. 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": 291,
"question": "If $a+b+c$, $b+c-a$, $c+a-b$, and $a+b-c$ form a geometric sequence in order, with a common ratio of $q$, then find the value of $q^3+q^2+q$.",
"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 A certain year's number is a four-digit number, with 1 as its thousandth digit. If the 1 is moved to the unit place, the new four-digit number is 4 less than 5 times the original four-digit number. Find this year. 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": "1999",
"style": "rule"
}
|
{
"answer": "1999",
"index": 292,
"question": "A certain year's number is a four-digit number, with 1 as its thousandth digit. If the 1 is moved to the unit place, the new four-digit number is 4 less than 5 times the original four-digit number. Find this year.",
"split": "train"
}
|
big_math
|
[
"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 Find the smallest positive integer N whose digits have a product of 1728, and then calculate the sum of the digits of N. 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": "28",
"style": "rule"
}
|
{
"answer": "28",
"index": 293,
"question": "Find the smallest positive integer N whose digits have a product of 1728, and then calculate the sum of the digits of N. Express your answer as a single integer.",
"split": "train"
}
|
cn_k12
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other",
"Mathematics -> Algebra -> Other"
] | 0.09375
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the number of lines that pass through the point $(0,1)$ and intersect the parabola $y^2=4x$ at only one 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": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 294,
"question": "Find the number of lines that pass through the point $(0,1)$ and intersect the parabola $y^2=4x$ at only one point.",
"split": "train"
}
|
orca_math
|
[
"Mathematics -> Algebra -> Other"
] | 0.09375
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A number when multiplied by 3 is odd and divisible by 9. This number when multiplied by 4 equals a certain value. What is the original 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": "9",
"style": "rule"
}
|
{
"answer": "9",
"index": 295,
"question": "A number when multiplied by 3 is odd and divisible by 9. This number when multiplied by 4 equals a certain value. What is the original number?",
"split": "train"
}
|
aops_forum
|
[
"Mathematics -> Number Theory -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $$ N=2^5+2^{5^2}+2^{5^3}+\\cdots{}+2^{5^{2015}}. $$ Wrotten in the usual decimal form, find the last two digits of the number $N$ .\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": "80",
"style": "rule"
}
|
{
"answer": "80",
"index": 296,
"question": " Let $$ N=2^5+2^{5^2}+2^{5^3}+\\cdots{}+2^{5^{2015}}. $$ Wrotten in the usual decimal form, find the last two digits of the number $N$ .\n",
"split": "train"
}
|
big_math
|
[
"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 Let P be a point on the ellipse $\\frac {x^{2}}{9} + \\frac {y^{2}}{4} = 1$, and let $F_1$ and $F_2$ be the two foci of the ellipse. If the ratio $|PF_1| : |PF_2| = 2 : 1$, then find the area of $\\triangle PF_1F_2$. 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": "4",
"style": "rule"
}
|
{
"answer": "4",
"index": 297,
"question": "Let P be a point on the ellipse $\\frac {x^{2}}{9} + \\frac {y^{2}}{4} = 1$, and let $F_1$ and $F_2$ be the two foci of the ellipse. If the ratio $|PF_1| : |PF_2| = 2 : 1$, then find the area of $\\triangle PF_1F_2$. Express your answer as a single number.",
"split": "train"
}
|
math
|
[
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 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 solid $S$ consists of the set of all points $(x,y,z)$ such that $|x| + |y| \\le 1,$ $|x| + |z| \\le 1,$ and $|y| + |z| \\le 1.$ Find the volume of $S.$ 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": 298,
"question": "The solid $S$ consists of the set of all points $(x,y,z)$ such that $|x| + |y| \\le 1,$ $|x| + |z| \\le 1,$ and $|y| + |z| \\le 1.$ Find the volume of $S.$",
"split": "train"
}
|
olympiads
|
[
"Mathematics -> Number Theory -> Other"
] | 0.015625
|
xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A set of composite numbers from the set $\\{1,2,3,4, \\ldots, 2016\\}$ is called good if any two numbers in this set do not have common divisors (other than 1). What is the maximum number of numbers that a good set can 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": "14",
"style": "rule"
}
|
{
"answer": "14",
"index": 299,
"question": "A set of composite numbers from the set $\\{1,2,3,4, \\ldots, 2016\\}$ is called good if any two numbers in this set do not have common divisors (other than 1). What is the maximum number of numbers that a good set can have?",
"split": "train"
}
|
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