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 |
|---|---|---|---|---|---|---|---|
cn_k12 | [
"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 the sum of the coefficients of all ter... | math | {
"ground_truth": "671",
"style": "rule"
} | {
"answer": "671",
"index": 3000,
"question": "Find the sum of the coefficients of all terms, excluding the constant term, in the expansion of the binomial ${(\\frac{1}{x}-2{{x}^{2}})}^{9}$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 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 average of 20 numbers was calculated as... | math | {
"ground_truth": "92",
"style": "rule"
} | {
"answer": "92",
"index": 3001,
"question": "The average of 20 numbers was calculated as 75. It is discovered later on that while calculating the average, five numbers were incorrectly read. The original numbers 125, 186, 287, 144, and 230 were read as 65, 106, 197, 74, and 190, respectively. Let a, b, c, d, e represent the incorrectly read numbers and r, s, t, u, v be the actual numbers. Write a system of algebraic equations that relates the given information, including equations representing the changes in the averages and the relationships between the original and incorrectly read numbers. Calculate the correct average of the 20 numbers.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The quotient of dividing a certain three-di... | math | {
"ground_truth": "550",
"style": "rule"
} | {
"answer": "550",
"index": 3002,
"question": "The quotient of dividing a certain three-digit number by 11 is equal to the sum of the squares of the digits of the dividend. Find this number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Rachel has two indistinguishable tokens, an... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"answer": "42",
"index": 3003,
"question": "Rachel has two indistinguishable tokens, and places them on the first and second squares of a \\(1 \\times 6\\) grid of squares. She can move the pieces in two ways:\n- If a token has a free square in front of it, then she can move this token one square to the right.\n- If the square immediately to the right of a token is occupied by the other token, then she can \"leapfrog\" the first token; she moves the first token two squares to the right, over the other token, so that it is on the square immediately to the right of the other token.\n\nIf a token reaches the 6th square, then it cannot move forward anymore, and Rachel must move the other one until it reaches the 5th square. How many different sequences of moves for the tokens can Rachel make so that the two tokens end up on the 5th square and the 6th square?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Intermediate Algebra -> Logarithmic 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 $\\log_a + \\log_b = 1$, then $ab =$ ? Show... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 3004,
"question": "$\\log_a + \\log_b = 1$, then $ab =$ ?",
"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 If a three-digit number $n=\\overline{abc}$... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 3005,
"question": "If a three-digit number $n=\\overline{abc}$ is a perfect square, and the sum of its digits $a+b+c$ is also a perfect square, then $n$ is called a \"super square number.\" Find the number of such super square numbers.",
"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 rose is planted in the 7th row from the f... | math | {
"ground_truth": "462",
"style": "rule"
} | {
"answer": "462",
"index": 3006,
"question": "A rose is planted in the 7th row from the front, the 16th row from the back, the 13th row from the right, and the 9th row from the left. Assuming the same number of flowers are planted in each row, find the total number of flowers.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the ratio of the areas of an equila... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 3007,
"question": "What is the ratio of the areas of an equilateral triangle circumscribed around a circle to a regular hexagon inscribed in the same circle?",
"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 If the rate of interest is 15%, the princip... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"answer": "60",
"index": 3008,
"question": "If the rate of interest is 15%, the principal amount is 400, and the time is 2 years, what is the simple interest?",
"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 An airplane needs to fly 2900 km. After fly... | math | {
"ground_truth": "850",
"style": "rule"
} | {
"answer": "850",
"index": 3009,
"question": "An airplane needs to fly 2900 km. After flying 1700 km, it made an emergency landing for 1 hour and 30 minutes, after which it flew at a speed 50 km/h less than before. Find the airplane's initial speed, given that it arrived at its destination 5 hours after departure.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The sequence ${a_n}$ satisfies the equation... | math | {
"ground_truth": "3240",
"style": "rule"
} | {
"answer": "3240",
"index": 3010,
"question": "The sequence ${a_n}$ satisfies the equation $a_{n+1} + (-1)^n a_n = 2n - 1$. Determine the sum of the first 80 terms of the sequence.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the number $2 * 0 * 1 * 6 * 0 *$, each o... | math | {
"ground_truth": "3645",
"style": "rule"
} | {
"answer": "3645",
"index": 3011,
"question": "In the number $2 * 0 * 1 * 6 * 0 *$, each of the 5 asterisks must be replaced with any of the digits $0,1,2,3,4,5,6,7,8$ (digits can be repeated) so that the resulting 10-digit number is divisible by 18. How many ways can this be done?",
"split": "train"
} |
big_math | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find an angle in degrees that has the same ... | math | {
"ground_truth": "375",
"style": "rule"
} | {
"answer": "375",
"index": 3012,
"question": "Find an angle in degrees that has the same terminal side as the angle α = π/12 + 2kπ (k∈Z). Express your answer as a whole number in degrees.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Luana needs to place crosses in the shape s... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 3013,
"question": "Luana needs to place crosses in the shape shown below on an $8 \\times 8$ board, such that no two crosses occupy the same square. What is the maximum number of crosses Luana can place on the board?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The cost of filling a car fuel tank is $45,... | math | {
"ground_truth": "2900",
"style": "rule"
} | {
"answer": "2900",
"index": 3014,
"question": "The cost of filling a car fuel tank is $45, and this can take you 500 miles before refilling. Mallory was going to her grammy's house, a certain distance away. She used 3/5 times as much money on food as she spent on filling the car fuel tank for the whole journey. She spent a total of $288. How far away is her grammy's house?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If you add 2 to the last digit of the quoti... | math | {
"ground_truth": "9742",
"style": "rule"
} | {
"answer": "9742",
"index": 3015,
"question": "If you add 2 to the last digit of the quotient, you get the penultimate digit. If you add 2 to the third digit from the right of the quotient, you get the fourth digit from the right. For example, the quotient could end in 9742 or 3186.\n\nWe managed to find only one solution.",
"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 Let the sum of the coefficients of the expa... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 3016,
"question": "Let the sum of the coefficients of the expansion of $(5x- \\frac{1}{\\sqrt{x}})^{n}$ be $M$ and the sum of the binomial coefficients be $N$. If $M-N=56$, find the constant term in the expansion.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n From the set {1,2,3,…,10}, select three dif... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"answer": "64",
"index": 3017,
"question": "From the set {1,2,3,…,10}, select three different numbers such that at least two of them are adjacent. Find the number of different ways to do this. Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Complex Numbers"
] | 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 the complex numbers \\( z_{1}=1+a i \... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 3018,
"question": "Given the complex numbers \\( z_{1}=1+a i \\) and \\( z_{2}=2^{\\frac{3}{4}}\\left(\\cos \\frac{3 \\pi}{8}+i \\sin \\frac{3 \\pi}{8}\\right) \\), find all real values of \\( a \\) for which \\( z_{1}^{3}=z_{2}^{2} \\).",
"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 Indiana Jones reached an abandoned temple i... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 3019,
"question": "Indiana Jones reached an abandoned temple in the jungle and entered the treasury. There were 5 boxes, and it is known that only one of them contains the treasure, while the rest trigger a stone slab to fall on the person trying to open them. The boxes are numbered from left to right. The first, fourth, and fifth boxes are made of cedar, while the second and third boxes are made of sandalwood. The inscriptions on the boxes read as follows:\n\n- First box: \"The treasure is either in me or in the fourth box.\"\n- Second box: \"The treasure is in the box to my left.\"\n- Third box: \"The treasure is either in me or in the rightmost box.\"\n- Fourth box: \"There is no treasure in the boxes to the left of me.\"\n- Fifth box: \"The writings on all other boxes are lies.\"\n\nThe last guardian of the temple, before dying, revealed to Indiana a secret: The same number of false statements are written on the cedar boxes as on the sandalwood boxes. In which box is the treasure?",
"split": "train"
} |
cn_k12 | [
"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 If the sum of the coefficients of the expan... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 3020,
"question": "If the sum of the coefficients of the expansion of $(x+y)^{3}(2x-y+a)^{5}$ is $256$, find the coefficient of the term which contains the letter $x$ and in which $x$ is raised to the power of $1$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the value of 163861 x 454733 = m ? Sho... | math | {
"ground_truth": "74505853393",
"style": "rule"
} | {
"answer": "74505853393",
"index": 3021,
"question": "Find the value of 163861 x 454733 = m ?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A prison has $2004$ cells, numbered $1$ ... | math | {
"ground_truth": "44",
"style": "rule"
} | {
"answer": "44",
"index": 3022,
"question": "A prison has $2004$ cells, numbered $1$ through $2004$ . A jailer, carrying out the terms of a partial amnesty, unlocked every cell. Next he locked every second cell. Then he turned the key in every third cell, locking the opened cells, and unlocking the locked ones. He continued this way, on $n^{\\text{th}}$ trip, turning the key in every $n^{\\text{th}}$ cell, and he finished his mission after $2004$ trips. How many prisoners were released?",
"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 Given strictly increasing sequence $ a_1<a... | math | {
"ground_truth": "2010",
"style": "rule"
} | {
"answer": "2010",
"index": 3023,
"question": "Given strictly increasing sequence $ a_1<a_2<\\dots$ of positive integers such that each its term $ a_k$ is divisible either by 1005 or 1006, but neither term is divisible by $ 97$ . Find the least possible value of maximal difference of consecutive terms $ a_{i\\plus{}1}\\minus{}a_i$ .",
"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 While on vacation, Gwen took 802 pictures a... | math | {
"ground_truth": "1192",
"style": "rule"
} | {
"answer": "1192",
"index": 3024,
"question": "While on vacation, Gwen took 802 pictures at the zoo, 526 at the museum, 391 at the beach, and 868 at the amusement park. After reviewing the photos, she realized that she had some duplicates and ended up deleting 1395 of them. How many pictures from her vacation did she still have?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems",
"Mathematics -> Discrete Mathematics -> Combinatorics -> 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 Ahmad walks up a flight of eight steps, goi... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 3025,
"question": "Ahmad walks up a flight of eight steps, going up either one or two steps at a time. There is a hole on the sixth step, so he cannot use this step. In how many different ways can Ahmad reach the top step?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In isosceles $\\triangle ABC$, where $BC=4$... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 3026,
"question": "In isosceles $\\triangle ABC$, where $BC=4$ and $AB=AC$, calculate the dot product of vectors $\\overrightarrow{BA}$ and $\\overrightarrow{BC}$. Express your answer as a single number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities",
"Mathematics -> Number Theory -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the inequality about $x$, $x^{2}+n^{2... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 3027,
"question": "Given the inequality about $x$, $x^{2}+n^{2}-x < 3nx-n^{2}-n (n \\in \\mathbb{N}^{*})$, let $a_{n}$ denote the number of integers in the solution set. Let $D_{n}$ denote the sum of the first $n$ terms of the sequence $\\{\\frac{2a_{n}+1}{2^{n}}\\}$. Find the smallest integer $t$ such that $D_{n} < t$ holds true for all $n \\in \\mathbb{N}^{*}$.",
"split": "train"
} |
math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the number of ordered triples $(x,y,z)... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 3028,
"question": "Find the number of ordered triples $(x,y,z)$ of real numbers such that\n\\[x^4 + y^4 + z^4 - 4xyz = -1.\\]",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Angles"
] | 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 Figure 1, \\( AB = AC \\) and \\( AB \\p... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"answer": "120",
"index": 3029,
"question": "In Figure 1, \\( AB = AC \\) and \\( AB \\parallel ED \\). If \\(\\angle ABC = P^{\\circ}\\) and \\(\\angle ADE = Q^{\\circ}\\), find the value of \\(Q\\).",
"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 Solve the following equation for real numbe... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 3030,
"question": "Solve the following equation for real numbers: $\\log _{a} x=x$, where $a=x^{\\log _{4} x}$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Other -> 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 Convert the binary number $1011001_{(2)}$ t... | math | {
"ground_truth": "131",
"style": "rule"
} | {
"answer": "131",
"index": 3031,
"question": "Convert the binary number $1011001_{(2)}$ to an octal number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In an infinite sequence of natural numbers,... | math | {
"ground_truth": "208",
"style": "rule"
} | {
"answer": "208",
"index": 3032,
"question": "In an infinite sequence of natural numbers, the product of any fifteen consecutive terms is equal to one million, and the sum of any ten consecutive terms is equal to \\(S\\). Find the maximum possible value of \\(S\\).",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Consider an angular sector on a plane with ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 3033,
"question": "Consider an angular sector on a plane with its vertex at the origin and an angle of 30 degrees. Place a ball (a material point of zero diameter) on one of the sides of the angle (ray) and launch it inside the sector with a constant speed at an angle of 110 degrees to the considered ray. The ball will fly within the sector, elastically bouncing off its sides, preserving the magnitude of its speed: the angle of incidence is equal to the angle of reflection. How many times will it hit the sides of the sector before flying off to infinity?",
"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 There is a set of numbers with an average o... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 3034,
"question": "There is a set of numbers with an average of 0. In this set, at least 1 number may be greater than or equal to zero. How many numbers are in the set?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Two vampires have come to a sleepy village ... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"answer": "72",
"index": 3035,
"question": "Two vampires have come to a sleepy village with a certain population. Every night, each vampire turns 5 more people into vampires. There are 72 vampires after two nights. What is the population of the village?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the numbers $49, 29, 9, 40, 22, 15, 5... | math | {
"ground_truth": "47",
"style": "rule"
} | {
"answer": "47",
"index": 3036,
"question": "Given the numbers $49, 29, 9, 40, 22, 15, 53, 33, 13, 47$, group them in pairs so that the sum of each pair is the same. What number is paired with 15? Express your answer as a single number from the original list.",
"split": "train"
} |
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 one hundredth positive integer tha... | math | {
"ground_truth": "981",
"style": "rule"
} | {
"answer": "981",
"index": 3037,
"question": "Find the one hundredth positive integer that can be written using no digits other than digits 0 and 1 in base 3. Express your answer as a base 10 integer.",
"split": "train"
} |
big_math | [
"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 Given the equation $\\log_{\\frac{1}{3}}(a-... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 3038,
"question": "Given the equation $\\log_{\\frac{1}{3}}(a-3^x) = x-2$, find the minimum value of the real number $a$ for the equation to have a solution. Express your answer as a single real number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the smallest positive integer \\( m \\... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"answer": "56",
"index": 3039,
"question": "Find the smallest positive integer \\( m \\) such that for any 14-partition \\( A = \\{1, 2, \\cdots, m\\} \\) into subsets \\( A_1, A_2, \\cdots, A_{14} \\), there always exists a subset \\( A_i \\) (with \\( 1 < i < 14 \\)) containing two elements \\( a \\) and \\( b \\) where \\( b < a \\leq \\frac{4}{3}b \\).",
"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 Justin needs to collect one flower for each... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 3040,
"question": "Justin needs to collect one flower for each classmate that is in his 2nd-grade class. It takes him some time to find a flower he likes. He has been gathering for 2 hours. Assuming he has lost 3 of the flowers he initially gathered, he needs 210 more minutes to look if he has 30 classmates. How many minutes does it take him on average to find a flower he likes?",
"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 Rebecca has 75 eggs, 99 bananas, 48 marbles... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"answer": "54",
"index": 3041,
"question": "Rebecca has 75 eggs, 99 bananas, 48 marbles, 6 dozen apples and half dozen oranges. She wants to split the collection into groups - eggs in group of 4, bananas in group of 5, marbles in group of 6, apples in dozen group and oranges in pair group. How many groups will be created?",
"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 Each cell of a $10 \\times 10$ table contai... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 3042,
"question": "Each cell of a $10 \\times 10$ table contains a natural number. Then, a cell is shaded if the number in that cell is less than one of its neighbors but greater than another neighbor. (Two cells are considered neighbors if they share a side.) As a result, only two cells remain unshaded. What is the minimal possible sum of the numbers in these two unshaded cells?",
"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 chocolate box contains 500 bars. Thomas a... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"answer": "96",
"index": 3043,
"question": "A chocolate box contains 500 bars. Thomas and his 6 friends take 1/3 of the bars and decide to divide them equally between them. However, they notice that one of Thomas's friends, Peter, has a birthday today, so they decide to give him 2 extra bars. Later, Thomas's sister Piper comes home and takes 1/4 of the initial number of chocolate bars to share with her own group of friends, but she decided to give 7 bars back because some of her friends are on a diet. Thomas's other sibling, Paul, who's part of the chess club at school, receives a message from his club members who are craving for some chocolate. He goes ahead and takes 5 more bars than what Piper took minus the bars she returned. How many chocolate bars are left in the box after everyone took their share?",
"split": "train"
} |
orca_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 I am trying to make a cube as small as poss... | math | {
"ground_truth": "600",
"style": "rule"
} | {
"answer": "600",
"index": 3044,
"question": "I am trying to make a cube as small as possible by stacking cuboid-shaped boxes that are 8 centimeters (cm) wide, 12 centimeters (cm) long, and 30 centimeters (cm) high in a certain direction. Find the number of boxes needed at this time.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $a>0$, $b>0$, and $a$, $b$, $-2$... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 3045,
"question": "Given that $a>0$, $b>0$, and $a$, $b$, $-2$ form an arithmetic sequence, and $a$, $b$, $-2$ can also form a geometric sequence after a proper rearrangement, find the value of $a+b$. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"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 The sum of all digits of a natural number $... | math | {
"ground_truth": "1990",
"style": "rule"
} | {
"answer": "1990",
"index": 3046,
"question": "The sum of all digits of a natural number $n$ is denoted as $S(n)$. If $n + S(n) = 2009$, then $n = \\ $",
"split": "train"
} |
gsm8k | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A bird is building a nest from twigs. The b... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"answer": "48",
"index": 3047,
"question": "A bird is building a nest from twigs. The bird has put twelve twigs together already to make a circle. For each twig it placed into the circle, it wants to weave in six more twigs to fill out the nest. It knows a tree that has dropped a third of the twigs it needs. How many twigs will the bird still need to find to finish its nest?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n 36 children are standing in a circle, each ... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 3048,
"question": "36 children are standing in a circle, each wearing either a red or blue sweater. It is known that next to each boy stands a girl, and next to each girl stands a person in a blue sweater. Find the maximum possible number of girls wearing red sweaters.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series",
"Mathematics -> Precalculus -> Functions"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a geometric sequence {a_n} where a_4 ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 3049,
"question": "Given a geometric sequence {a_n} where a_4 = 2 and a_5 = 5, find the sum of the first 8 terms of the sequence {lg a_n}. Express your answer as a single number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Meiyangyang is using two types of decoratio... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 3050,
"question": "Meiyangyang is using two types of decorations to decorate a \"Christmas tree\". The decorations are hung on each vertex of small triangles. Meiyangyang can decorate in any order. If two vertices of a small triangle already have the same decoration, then the third vertex will have the other decoration; otherwise, the third vertex will have the same decoration. How many different designs of the \"Christmas tree\" are there? (No rotation or flipping is allowed)",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the vertices of a regular 100-sided p... | math | {
"ground_truth": "117600",
"style": "rule"
} | {
"answer": "117600",
"index": 3051,
"question": "Given the vertices of a regular 100-sided polygon \\( A_{1}, A_{2}, A_{3}, \\ldots, A_{100} \\). In how many ways can three vertices be chosen that form an obtuse triangle?",
"split": "train"
} |
orca_math | [
"Mathematics -> Geometry -> Plane Geometry -> Area"
] | 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 area of the quadrilateral ABCD whe... | math | {
"ground_truth": "400",
"style": "rule"
} | {
"answer": "400",
"index": 3052,
"question": "Find the area of the quadrilateral ABCD where one of its diagonals, BD, is 40 cm long and its off sets, AE and CF, perpendicular to diagonal BD are 11 cm and 9 cm long respectively. In addition, the angle between the diagonal BD and the off set AE is 45 degrees, and quadrilateral ABCD contains an isosceles triangle with base BC and equal sides BA and CA.",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n if m equals the sum of the squares of the o... | math | {
"ground_truth": "1507880",
"style": "rule"
} | {
"answer": "1507880",
"index": 3053,
"question": "if m equals the sum of the squares of the odd integers from 1 to 215, inclusive, and t equals the sum of the squares of the even integers from 2 to 100, inclusive, what is the value of m - t?",
"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 Determine all three-digit numbers $N$ hav... | math | {
"ground_truth": "550",
"style": "rule"
} | {
"answer": "550",
"index": 3054,
"question": "Determine all three-digit numbers $N$ having the property that $N$ is divisible by $11,$ and $\\frac{N}{11}$ is equal to the sum of the squares of the digits of $N.$ ",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Five lanterns of the same size but differen... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 3055,
"question": "Five lanterns of the same size but different colors (red, orange, yellow, green, purple) are connected from top to bottom and hung together end to end. It is required that red and purple are adjacent, orange and green are not adjacent, and orange cannot be at the top. The number of different ways to hang the lanterns is ______.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> 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 \\\\(a > 0\\\\), \\\\(b > 0\\\\), and... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 3056,
"question": "Given \\\\(a > 0\\\\), \\\\(b > 0\\\\), and \\\\(\\frac{2}{a} + \\frac{1}{b} = \\frac{1}{4}\\\\), if the inequality \\\\(2a + b \\geqslant 9m\\\\) always holds, then the maximum value of \\\\(m\\\\) is \\_\\_\\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n With eight small cubes each with an edge le... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 3057,
"question": "With eight small cubes each with an edge length of $1 \\text{ cm}$ stacked into a three-dimensional shape, and given its top view as shown in the diagram, how many distinct stacking methods are there (considering rotations that result in the same shape as one method)?",
"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 Two circles with radii 13 and 5 intersect, ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 3058,
"question": "Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Find the length of their common chord. Express your answer as a single number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let the sides opposite to the angles \\\\(A... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 3059,
"question": "Let the sides opposite to the angles \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) in \\\\(\\triangle ABC\\\\) be \\\\(a\\\\), \\\\(b\\\\), and \\\\(c\\\\) respectively, and it is given that \\\\(a\\cos B - b\\cos A = \\frac{3}{5}c\\\\). Find the value of \\\\(\\frac{\\tan A}{\\tan B}\\\\).",
"split": "train"
} |
omnimath | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n (Caos) A cao [sic] has 6 legs, 3 on each si... | math | {
"ground_truth": "1416528",
"style": "rule"
} | {
"answer": "1416528",
"index": 3060,
"question": "(Caos) A cao [sic] has 6 legs, 3 on each side. A walking pattern for the cao is defined as an ordered sequence of raising and lowering each of the legs exactly once (altogether 12 actions), starting and ending with all legs on the ground. The pattern is safe if at any point, he has at least 3 legs on the ground and not all three legs are on the same side. Estimate $N$, the number of safe patterns.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a geometric sequence $\\{a_n\\}$, the... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 3061,
"question": "Given a geometric sequence $\\{a_n\\}$, the sum of the first $n$ terms is $S_n$. If $S_2 = 2a_2 + 3$ and $S_3 = 2a_3 + 3$, then the value of the common ratio $q$ is ______.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Distribute 10 identical one-yuan coins into... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 3062,
"question": "Distribute 10 identical one-yuan coins into 3 identical lucky bags, with at least 1 coin in each bag. Ignoring the order of the bags, calculate the number of different ways to distribute the coins. Express your answer as a single integer.",
"split": "train"
} |
omnimath | [
"Mathematics -> Algebra -> Exponential 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 smallest positive integer $n$ such... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 3063,
"question": "Find the smallest positive integer $n$ such that $\\frac{5^{n+1}+2^{n+1}}{5^{n}+2^{n}}>4.99$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the power function $f(x)=k\\cdot x^{\... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 3064,
"question": "Given the power function $f(x)=k\\cdot x^{\\alpha}$ whose graph passes through the point $\\left( \\frac{1}{2},2 \\right)$, find the value of $k+\\alpha$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The difference between the place value and ... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"answer": "70",
"index": 3065,
"question": "The difference between the place value and the face value of 7 in a numeral is 63. What is the numeral?",
"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 What is the difference between the largest ... | math | {
"ground_truth": "198",
"style": "rule"
} | {
"answer": "198",
"index": 3066,
"question": "What is the difference between the largest and smallest four-digit integers that can be made using three 2's and one 0 as digits?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the smallest positive integer that ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 3067,
"question": "What is the smallest positive integer that can be multiplied by 45,216 to make it a perfect cube?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Simplify the expression: \n\n\\[\n\\frac{\\... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 3068,
"question": "Simplify the expression: \n\n\\[\n\\frac{\\left(p q^{-1}+1\\right)^{2}}{p q^{-1}-p^{-1} q} \\cdot \\frac{p^{3} q^{-3}-1}{p^{2} q^{-2}+p q^{-1}+1} \\div \\frac{p^{3} q^{-3}+1}{p q^{-1}+p^{-1} q-1}\n\\]",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the expansion of $ (x+\\frac{3}{\\sqrt{x... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 3069,
"question": "In the expansion of $ (x+\\frac{3}{\\sqrt{x}})^n $, the ratio of the sum of coefficients of all terms to the sum of binomial coefficients is $32$. Find the coefficient of $x^2$.",
"split": "train"
} |
cn_k12 | [
"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 Spring is a season when infectious diseases... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 3070,
"question": "Spring is a season when infectious diseases are prevalent. In March 2023, a certain place in China had a very fast spread of influenza A virus. At the beginning, 4 people were infected, and after two rounds of transmission, 256 people had contracted influenza A. If the speed of transmission is the same in each round, find the number of people infected by each person in each round.",
"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 Nikolai invented a game for himself: he rea... | math | {
"ground_truth": "1050",
"style": "rule"
} | {
"answer": "1050",
"index": 3071,
"question": "Nikolai invented a game for himself: he rearranges the digits in the number 2015 and then places a multiplication sign between any two digits. Neither of the resulting numbers should start with a zero. He then calculates the value of this expression. For example: \\( 150 \\times 2 = 300 \\) or \\( 10 \\times 25 = 250 \\). What is the maximum number he can get as a result of such a calculation?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The new individual income tax law has been ... | math | {
"ground_truth": "9720",
"style": "rule"
} | {
"answer": "9720",
"index": 3072,
"question": "The new individual income tax law has been implemented since January 1, 2019. According to the \"Individual Income Tax Law of the People's Republic of China,\" it is known that the part of the actual wages and salaries (after deducting special, additional special, and other legally determined items) obtained by taxpayers does not exceed $5000$ yuan (commonly known as the \"threshold\") is not taxable, and the part exceeding $5000$ yuan is the taxable income for the whole month. The new tax rate table is as follows:\n\n2019年1月1日后个人所得税税率表\n\n| 全月应纳税所得额 | 税率$(\\%)$ |\n|------------------|------------|\n| 不超过$3000$元的部分 | $3$ |\n| 超过$3000$元至$12000$元的部分 | $10$ |\n| 超过$12000$元至$25000$元的部分 | $20$ |\n| 超过$25000$元至$35000$元的部分 | $25$ |\n\nIndividual income tax special additional deductions refer to the six special additional deductions specified in the individual income tax law, including child education, continuing education, serious illness medical treatment, housing loan interest, housing rent, and supporting the elderly. Among them, supporting the elderly refers to the support expenses for parents and other legally supported persons aged $60$ and above paid by taxpayers. It can be deducted at the following standards: for taxpayers who are only children, a standard deduction of $2000$ yuan per month is allowed; for taxpayers with siblings, the deduction amount of $2000$ yuan per month is shared among them, and the amount shared by each person cannot exceed $1000$ yuan per month.\n\nA taxpayer has only one older sister, and both of them meet the conditions for supporting the elderly as specified. If the taxpayer's personal income tax payable in May 2020 is $180$ yuan, then the taxpayer's monthly salary after tax in that month is ____ yuan.",
"split": "train"
} |
big_math | [
"Mathematics -> Number Theory -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Patrícia wrote, in ascending order, the pos... | math | {
"ground_truth": "1113",
"style": "rule"
} | {
"answer": "1113",
"index": 3073,
"question": "Patrícia wrote, in ascending order, the positive integers formed only by odd digits: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 31, 33,... What is the 157th number she wrote? Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Least Common Multiples (LCM)"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the lcm of 23, 46, and 827. Show your ... | math | {
"ground_truth": "38042",
"style": "rule"
} | {
"answer": "38042",
"index": 3074,
"question": "Find the lcm of 23, 46, and 827.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given an arithmetic sequence $\\left\\{a_n\... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 3075,
"question": "Given an arithmetic sequence $\\left\\{a_n\\right\\}$ where all terms are distinct, satisfying $a_{2n}=2a_n-3$, and $a_6^2=a_1\\cdot a_{21}$, the sum of the first $n$ terms of $\\left\\{a_n\\right\\}$ is $S_n$. Then, the maximum value among the terms of the sequence $\\left\\{\\frac{S_n}{2^{n-1}}\\right\\}$ is.",
"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 For a given positive integer \\( k \\), den... | math | {
"ground_truth": "256",
"style": "rule"
} | {
"answer": "256",
"index": 3076,
"question": "For a given positive integer \\( k \\), denote the square of the sum of its digits by \\( f_1(k) \\) and let \\( f_{n+1}(k) = f_1(f_n(k)) \\). Determine the value of \\( f_{1001}(2^{1990}) \\).",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given an geometric sequence $\\{a_{n}\\}$ t... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 3077,
"question": "Given an geometric sequence $\\{a_{n}\\}$ that satisfies $a_{1}+a_{3}=5$, $a_{2}+a_{4}=\\frac{5}{2}$, find the maximum value of the product $a_{1}a_{2}...a_{n}$.",
"split": "train"
} |
math | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 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 integer $n,$ $-90 < n < 90,$ such ... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"answer": "72",
"index": 3078,
"question": "Find the integer $n,$ $-90 < n < 90,$ such that $\\tan n^\\circ = \\tan 252^\\circ.$",
"split": "train"
} |
openmath | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 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 When the digits in the number $2005$ are re... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 3079,
"question": "When the digits in the number $2005$ are reversed we obtain the number $5002,$ and $5002 = a \\cdot b \\cdot c$, such that $a$, $b$ and $c$ are three distinct primes. How many other positive integers are the products of exactly three distinct primes $p_1$, $p_2$ and $p_3$ such that $p_1 + p_2 + p_3 = a+b+c$?",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 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 sequence $1001, 1004, 1009$ has a gener... | math | {
"ground_truth": "4001",
"style": "rule"
} | {
"answer": "4001",
"index": 3080,
"question": "The sequence $1001, 1004, 1009$ has a general term $a_{n} = n^{2} + 1000$, where $n \\in \\mathbf{N}_{+}$. For each $n$, let $d_{n}$ denote the greatest common divisor (GCD) of $a_{n}$ and $a_{n+1}$. Determine the maximum value of $d_{n}$ as $n$ ranges over all positive integers.",
"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 A peasant woman sold eggs to two buyers: to... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 3081,
"question": "A peasant woman sold eggs to two buyers: to the first one, she sold $\\frac{1}{3}$ of the eggs she had along with 15 more eggs, and to the second one, she sold $\\frac{7}{9}$ of the remaining eggs along with the last 10 eggs. How many eggs did the peasant woman sell in total?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If the sum of the coefficients in the expan... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 3082,
"question": "If the sum of the coefficients in the expansion of $(3x- \\frac{1}{\\sqrt[3]{x^{2}}})^{n}$ is $128$, then the coefficient of $\\frac{1}{x^{3}}$ in the expansion is __________.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a group of 6 students, from which we ... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"answer": "96",
"index": 3083,
"question": "Given a group of 6 students, from which we must select 3 to serve as representatives for mathematics, physics, and chemistry, respectively, if at least one of students A or B must be selected, calculate the total number of different methods of selection. Express your answer as a single numerical value.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Using the recursive definition of the binar... | math | {
"ground_truth": "2013",
"style": "rule"
} | {
"answer": "2013",
"index": 3084,
"question": "Using the recursive definition of the binary operation $\\otimes$, where $1 \\otimes 1 = 2$, $(m+1) \\otimes n = m \\otimes n - 1$, and $m \\otimes (n+1) = m \\otimes n + 2$, calculate the result of $2004 \\otimes 2008$. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the largest \\( n \\) for which a c... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 3085,
"question": "What is the largest \\( n \\) for which a convex \\( n \\)-gon exists such that the lengths of its diagonals take no more than two different values? (I. Rubanov)",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Consider an iterative process where you sta... | math | {
"ground_truth": "123",
"style": "rule"
} | {
"answer": "123",
"index": 3086,
"question": "Consider an iterative process where you start with any natural number and apply the following rules to generate a new three-digit number: the hundreds digit is the count of even digits in the original number, the tens digit is the count of odd digits, and the units digit is the total number of digits. Repeat this process with the new number until it no longer changes. What is the eventual unchanging three-digit number that results from this process?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the least number that must be subtract... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 3087,
"question": "Find the least number that must be subtracted from 964807 so that the remaining number is divisible by 13.",
"split": "train"
} |
orca_math | [
"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 On Sunday morning, Pugsley and Wednesday ar... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 3088,
"question": "On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday some of his spiders, Wednesday would then have 9 times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley 6 of her spiders, Pugsley would now have 6 fewer spiders than Wednesday had before they traded. Pugsley has 4 pet spiders before the trading game commences. How many spiders did Pugsley give to Wednesday in the first scenario?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are two types of containers: 27 kg an... | math | {
"ground_truth": "66",
"style": "rule"
} | {
"answer": "66",
"index": 3089,
"question": "There are two types of containers: 27 kg and 65 kg. How many containers of the first and second types were there in total, if the load in the containers of the first type exceeds the load of the container of the second type by 34 kg, and the number of 65 kg containers does not exceed 44 units?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $\\alpha$ , $\\beta$ , and $\\gamma$ ... | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"answer": "-7",
"index": 3090,
"question": "If $\\alpha$ , $\\beta$ , and $\\gamma$ are the roots of $x^3 - x - 1 = 0$ , compute $\\frac{1+\\alpha}{1-\\alpha} + \\frac{1+\\beta}{1-\\beta} + \\frac{1+\\gamma}{1-\\gamma}$ .",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The set \\( A \\) consists of integers, wit... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 3091,
"question": "The set \\( A \\) consists of integers, with the smallest element being 1 and the largest being 100. Except for 1, every element is equal to the sum of two (not necessarily distinct) elements from the set \\( A \\). Find the minimum number of elements in set \\( A \\).",
"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 If $10^{51} - 9$ is written as an integer i... | math | {
"ground_truth": "451",
"style": "rule"
} | {
"answer": "451",
"index": 3092,
"question": "If $10^{51} - 9$ is written as an integer in standard form, what is the sum of the integer's digits?",
"split": "train"
} |
big_math | [
"Mathematics -> Number Theory -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n An increasing sequence \\(1, 3, 4, 9, 10, 1... | math | {
"ground_truth": "981",
"style": "rule"
} | {
"answer": "981",
"index": 3093,
"question": "An increasing sequence \\(1, 3, 4, 9, 10, 12, 13, \\cdots\\) is formed by positive integers, which are either a multiple of 3 or a sum of several different multiples of 3. Determine the 100th term of this sequence. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the figure, the center of square \\(ABCD... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"answer": "42",
"index": 3094,
"question": "In the figure, the center of square \\(ABCD\\) is \\(O\\), and its area is \\(1989 \\text{ cm}^2\\). Point \\(P\\) is a point inside the square such that \\(\\angle OPB = 45^\\circ\\) and \\(PA : PB = 5 : 14\\). Find \\(PB\\) in centimeters.",
"split": "train"
} |
cn_k12 | [
"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 A positive integer $a_1a_2…a_n…a_{2n-2}a_{2... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"answer": "240",
"index": 3095,
"question": "A positive integer $a_1a_2…a_n…a_{2n-2}a_{2n-1}$ is called a concave number if $a_1 > a_2 > … > a_n$ and $a_{2n-1} > a_{2n-2} > … > a_n$, where $a_i$ ($i=1,2,3,…$) $\\in \\{0,1,2,…,9\\}$. Please answer how many three-digit concave numbers $a_1a_2a_3$ ($a_1 \\neq a_3$) there are in total (answer in digits).",
"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 Sabrina initially had 84 cookies. She gave ... | math | {
"ground_truth": "46",
"style": "rule"
} | {
"answer": "46",
"index": 3096,
"question": "Sabrina initially had 84 cookies. She gave 20 cookies to her brother. Her mother then gave Sabrina twice the number of cookies she gave her brother. After that, Sabrina gave one-fifth of her remaining cookies to her sister. Next, her father gave her a quarter of the cookies he had, which was 36. Subsequently, her grandmother gave her one-third of the cookies she had, adding another 15 cookies to Sabrina's collection. Finally, Sabrina gave three-sevenths of her remaining cookies to her cousin and then shared one-fourth of her remaining cookies with her best friend. How many cookies does Sabrina have left?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a group of \\( n \\) freshmen, any 3 peo... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 3097,
"question": "In a group of \\( n \\) freshmen, any 3 people include at least 2 who know each other, and any 4 people include at least 2 who do not know each other. Find the maximum value of \\( n \\).",
"split": "train"
} |
omnimath | [
"Mathematics -> Geometry -> Plane Geometry -> Angles"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the value of $x$ if $P Q S$ is a st... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 3098,
"question": "What is the value of $x$ if $P Q S$ is a straight line and $\\angle P Q R=110^{\\circ}$?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the expansion of $(x^2-x+2y)^5$, find th... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"answer": "120",
"index": 3099,
"question": "In the expansion of $(x^2-x+2y)^5$, find the coefficient of $x^4y^2$. Express your answer as a single integer.",
"split": "train"
} |
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