Search is not available for this dataset
problem
string | solution
string | answer
string | problem_type
string | question_type
string | source
string | uuid
string | processed_answer
sequence | reward
sequence | min_length
int64 | max_length
int64 | pass@1
float64 | pass@16
bool | cons@16
float64 | roll_in_ids
sequence | roll_outs_ids
sequence |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"16. Given $\\sin \\left(\\frac{\\pi}{4}-x\\right)=\\frac{5}{13}$, and $x \\in\\left(0, \\frac{\\pi}(...TRUNCATED) | "16. Let $\\frac{\\pi}{4}-x=\\alpha$, then $\\alpha \\in\\left(0, \\frac{\\pi}{4}\\right), \\sin \\a(...TRUNCATED) | \frac{24}{13} | Algebra | math-word-problem | olympiads | 7cebe13e-a85f-541d-9e03-12e5cf98cd2b | ["\\frac{10}{13}","\\frac{24}{13}","\\frac{24}{13}","","","\\frac{119}{65}","\\frac{24}{13}","\\frac(...TRUNCATED) | [
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] | 2,785 | 16,384 | 0.75 | true | 1 | [151646,151644,16,21,13,16246,57960,15940,1124,2359,11520,37018,35702,2493,15170,19,19732,87,59,1291(...TRUNCATED) | [[151648,198,32313,11,773,358,614,419,52933,263,6988,3491,1588,13,1084,2727,429,7437,7,48245,14,19,4(...TRUNCATED) |
"Example 4 On a circular road, there are four middle schools arranged in sequence: $A_{1}, A_{2}, A_(...TRUNCATED) | "Solution: Let $A_{1}$ high school transfer $x_{1}$ color TVs to $A_{2}$ high school (if $x_{1}$ is (...TRUNCATED) | 10 | Logic and Puzzles | math-word-problem | cn_contest | 4b699cb1-aa26-5ecb-a6cd-e5a28667a01b | [
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] | 6,395 | 16,384 | 0.0625 | true | 0 | [151646,151644,13314,220,19,1913,264,26931,5636,11,1052,525,3040,6149,8682,27802,304,8500,25,400,32,(...TRUNCATED) | [[151648,198,32313,11,773,358,614,419,3491,911,3040,6149,8682,27802,304,264,12671,11,1817,448,264,36(...TRUNCATED) |
"6. If the polynomial in $x$\n$$\ny=x^{3}+3 x^{2}+6 x+c\n$$\n\nhas three roots that can form a geome(...TRUNCATED) | "6. 8 .\n\nLet the three roots form a geometric sequence $\\alpha, \\beta, \\gamma$, i.e., $\\alpha (...TRUNCATED) | 8 | Algebra | math-word-problem | olympiads | e6c0e952-9ec4-537e-bf59-9ffbadbaf8ae | [
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] | 4,903 | 16,384 | 0.3125 | true | 1 | [151646,151644,21,13,1416,279,47311,304,400,87,25046,14085,198,88,25387,47822,18,92,10,18,856,47822,(...TRUNCATED) | [[151648,198,32313,11,773,358,3003,2684,419,47311,25,379,284,856,43201,488,220,18,87,29456,488,220,2(...TRUNCATED) |
"1. Given that $D$ is any point on side $A B$ of $\\triangle A B C$ with area 1, $E$ is any point on(...TRUNCATED) | "1. Connect $B E$, then the area of $\\triangle B D F$\n$$S_{\\triangle B D F}=z S_{\\triangle B D E(...TRUNCATED) | \frac{1}{8} | Geometry | math-word-problem | inequalities | a28f8451-5a15-5c58-9f39-ea71d5addb3c | ["\\frac{1}{8}","\\frac{1}{8}","\\frac{1}{8}","\\frac{9}{16}","\\frac{1}{8}","\\frac{1}{16}","\\frac(...TRUNCATED) | [
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] | 4,094 | 16,384 | 0.8125 | true | 1 | [151646,151644,16,13,16246,429,400,35,3,374,894,1459,389,3108,400,32,425,3,315,57960,55114,362,425,3(...TRUNCATED) | [[151648,198,32313,11,773,358,614,419,17047,3491,1588,13,6771,752,1430,311,4715,432,3019,553,3019,13(...TRUNCATED) |
"11. In the Kingdom of Fantasy, the way of representing numbers is quite unique. If a number or a pa(...TRUNCATED) | Answer: 43149 | 43149 | Number Theory | math-word-problem | olympiads | cc817d80-785d-5d4f-aba9-94dc001a7af2 | [
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] | 3,480 | 16,384 | 0 | false | 0 | [151646,151644,16,16,13,758,279,15072,315,26484,11,279,1616,315,14064,5109,374,5008,4911,13,1416,264(...TRUNCATED) | [[151648,198,71486,11,773,358,3003,2525,3941,419,3491,504,279,15072,315,26484,11,323,432,594,264,269(...TRUNCATED) |
"Determine the number of integers $ n$ with $ 1 \\le n \\le N\\equal{}1990^{1990}$ such that $ n^2\\(...TRUNCATED) | "1. **Prime Factorization of \\( N \\):**\n \\[\n N = 1990^{1990} = (2 \\times 5 \\times 199)^{1(...TRUNCATED) | 591\times1990^{1989} | Number Theory | math-word-problem | aops_forum | b59b4305-7ad0-54ca-88c1-553895561a0f | ["","4\\times1990^{1989}","8","3\\times197\\times1990^{1989}","","2^{1989}\\times(5^{1990}-2)\\times(...TRUNCATED) | [
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] | 3,304 | 16,384 | 0.1875 | true | 1 | [151646,151644,35,24308,279,1372,315,25780,400,308,3,448,400,220,16,1124,273,308,1124,273,451,59,257(...TRUNCATED) | [[151648,198,32313,11,773,358,614,419,3491,25,358,1184,311,8253,279,1372,315,25780,17767,308,1124,8,(...TRUNCATED) |
"36. [25] The Marathon. Let $\\omega$ denote the incircle of triangle $A B C$. The segments $B C, C (...TRUNCATED) | "whence, $B Z / C Z=(A Y / A X)(B X / C Y)=(15 / 13)((77 \\cdot 13) /(21 \\cdot 15))=11 / 3$. We wri(...TRUNCATED) | 101 | Geometry | math-word-problem | olympiads | da7d0b96-7111-5059-b016-60f3263f32d6 | [
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] | 12,095 | 16,384 | 0 | false | 0 | [151646,151644,18,21,13,508,17,20,60,576,50173,13,6771,57960,32696,3,78064,279,3625,7074,315,21495,4(...TRUNCATED) | [[151648,198,32313,11,773,358,614,419,3491,911,264,21495,448,1045,3625,7074,323,5257,3501,323,5128,1(...TRUNCATED) |
"Find the number of integers $c$ such that the equation \\[\\left||20|x|-x^2|-c\\right|=21\\]has $12(...TRUNCATED) | "We take cases for the outermost absolute value, then rearrange: \\[\\left|20|x|-x^2\\right|=c\\pm21(...TRUNCATED) | 57 | Algebra | math-word-problem | amc_aime | 9a9985ee-65a7-5595-a019-de420ae41bd5 | [
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] | 13,104 | 16,384 | 0.0625 | true | 0.0625 | [151646,151644,9885,279,1372,315,25780,400,66,3,1741,429,279,23606,1124,26056,2359,8484,17,15,62827,(...TRUNCATED) | [[151648,198,71486,11,773,358,614,419,23606,311,11625,25,1369,17,15,62827,91,481,856,29456,91,481,27(...TRUNCATED) |
"Baba Yaga in her hut on chicken legs has kept fairy tale animals. All of them, except for two, are (...TRUNCATED) | "## Solution\n\nFrom the problem statement, it follows that there are two Wise Owls and Whiskered Co(...TRUNCATED) | 3 | Logic and Puzzles | math-word-problem | olympiads | e05537d0-a9aa-517d-9c31-d496047003ff | [
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] | 2,257 | 14,443 | 0.5 | true | 1 | [151646,151644,33,12004,809,12466,304,1059,75879,389,16158,14201,702,8604,44486,23281,9898,13,2009,3(...TRUNCATED) | [[151648,198,71486,11,773,358,614,419,3491,1588,911,96352,809,12466,594,75879,448,44486,23281,9898,1(...TRUNCATED) |
"8. (10 points) A frog starts climbing from the bottom of a 12-meter deep well at 8:00. It climbs up(...TRUNCATED) | "【Analysis】First, analyze the time of \"up and down\" as one cycle. When the fourth cycle reache(...TRUNCATED) | 22 | Logic and Puzzles | math-word-problem | olympiads | 9316d993-29ac-5772-845f-193ecf363f40 | ["\\frac{1490}{9}","","17","17","\\frac{221}{15}","\\frac{323}{16}","17","","18.7","22","","17","\\f(...TRUNCATED) | [
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] | 6,366 | 16,384 | 0.0625 | true | 0 | [151646,151644,23,13,320,16,15,3501,8,362,59881,8471,29508,504,279,5622,315,264,220,16,17,72501,5538(...TRUNCATED) | [[151648,198,71486,11,773,358,614,419,3491,911,264,59881,29508,264,1632,13,6771,752,1430,311,3535,43(...TRUNCATED) |
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