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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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was c(...TRUNCATED) | "3. (6 points) A construction company builds a tunnel. When $\\frac{1}{3}$ of the tunnel is complete(...TRUNCATED) | 180 | Algebra | math-word-problem | olympiads | 1d57f4b3-c516-5522-91cc-a60dd91f6f66 | ["","213\\frac{6}{13}","208.125","206.25","208.125","","","208.125","208.125","\\frac{1665}{8}","","(...TRUNCATED) | [
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] | 2,885 | 16,384 | 0 | false | 0 | [[151646,151644,18,13,320,21,3501,8,362,8086,2813,572,4752,264,25629,13,3197,57960,37018,90,16,15170(...TRUNCATED) | [[3039,279,4024,11,892,374,2686,13,2055,11,421,807,525,3730,2686,817,1899,11,807,1035,1896,803,2849,(...TRUNCATED) |
"Prove that number $1$ can be represented as a sum of a finite number $n$ of real numbers, less than(...TRUNCATED) | "1. **Restate the problem in a more manageable form:**\n We need to prove that the number \\(1\\) (...TRUNCATED) | 8 | Number Theory | math-word-problem | aops_forum | 1cd82e3d-2e7a-5eca-9571-62f5669824c4 | [
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] | 9,863 | 16,384 | 0 | false | 0 | [[151646,151644,1336,586,429,1372,400,16,3,646,387,15251,438,264,2629,315,264,34226,1372,400,77,3,31(...TRUNCATED) | [[22,284,220,16,15,271,22,353,264,62,16,284,220,18,271,23085,374,537,3204,1576,264,62,16,1969,387,45(...TRUNCATED) |
"1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$.(...TRUNCATED) | "1. $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$\n\n$\\frac{8 x+13}{3(...TRUNCATED) | \frac{1}{4} | Algebra | math-word-problem | olympiads | a583d65c-9b4c-56ce-8263-47edbc22baa3 | ["\\frac{1}{4}","\\frac{1}{4}","\\frac{1}{4}","\\frac{1}{4}","\\frac{1}{4}","\\frac{1}{4}","\\frac{1(...TRUNCATED) | [
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] | 2,226 | 16,384 | 0.9375 | true | 1 | [[151646,151644,16,13,63284,279,23606,25,57960,37018,90,23,856,10,16,18,15170,18,92,34433,37018,90,1(...TRUNCATED) | [[20,22,11,323,220,18,34299,16,17,87,8,374,481,18,21,87,13,2055,429,594,220,20,22,481,18,21,87,382,7(...TRUNCATED) |
"A right-angled triangle has side lengths that are integers. What could be the last digit of the are(...TRUNCATED) | "Let the lengths of the legs be $a$ and $b$, and the length of the hypotenuse be $c$. According to t(...TRUNCATED) | 0 | Geometry | math-word-problem | olympiads | 79e837be-2801-5a6a-bc7a-0acee3cdd5fd | [
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] | 10,370 | 16,384 | 0.125 | true | 1 | [[151646,151644,32,1290,12,38940,21495,702,3108,28316,429,525,25780,13,3555,1410,387,279,1537,15723,(...TRUNCATED) | [[3082,1410,387,11,2661,429,279,9751,65628,810,4436,944,74916,553,220,20,13,88190,11,1290,12,38940,4(...TRUNCATED) |
"Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Fi(...TRUNCATED) | "1. Define the integral \\( I_n(x) = \\int_x^{2x} e^{-t^n} \\, dt \\). We need to find the value of (...TRUNCATED) | -\ln2 | Calculus | math-word-problem | aops_forum | 167ecbbb-4270-534f-afa5-75d01d968ab5 | ["-\\ln2","-\\ln2","-\\ln2","-\\ln2","-\\ln2","-\\ln2","-\\ln2","-\\ln2","-\\ln2","0","-\\ln2","-\\l(...TRUNCATED) | [
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] | 2,300 | 15,772 | 0.9375 | true | 1 | [[151646,151644,10061,400,64,1089,59,320,77,59,709,80,220,16,15087,387,279,897,369,892,57960,396,321(...TRUNCATED) | [[382,4416,11,29390,7,17,86167,481,220,16,8,21103,230,308,29390,7,17,8,481,220,16,14,17,86167,271,54(...TRUNCATED) |
"6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\triangle ABC$ with side lengt(...TRUNCATED) | "$$\n6.11 \\sqrt{3} \\text {. }\n$$\n\nFor the equilateral $\\triangle ABC$ with a height of $12 \\t(...TRUNCATED) | 11\sqrt{3} | Geometry | math-word-problem | cn_contest | 2a4c0374-d9ea-538e-8e0f-0811359d6cf6 | ["11\\sqrt{3}","\\frac{13\\sqrt{3}}{2}","\\frac{13\\sqrt{3}}{2}","","","11\\sqrt{3}","11\\sqrt{3}","(...TRUNCATED) | [
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] | 5,005 | 16,384 | 0.6875 | true | 1 | [[151646,151644,21,13,1634,6839,304,19037,220,17,11,1077,400,47,3,387,264,1459,4766,279,3232,42939,5(...TRUNCATED) | [[4647,856,5318,379,15159,72,10,16,92,481,856,15159,72,10,16,92,379,5318,1447,25477,425,323,422,1447(...TRUNCATED) |
"9.6. Find the minimum value of the expression $(\\sqrt{2(1+\\cos 2 x)}-\\sqrt{36-4 \\sqrt{5}} \\sin(...TRUNCATED) | Answer: -27 . Instructions. Exact answer: $4 \sqrt{5}-36$. | -27 | Algebra | math-word-problem | olympiads | 9224d27e-798f-569e-a808-122e2d76c789 | [
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] | 6,771 | 16,384 | 0.125 | true | 0.5 | [[151646,151644,24,13,21,13,7379,279,8028,897,315,279,7493,4930,59,26888,90,17,7,16,41715,9407,220,1(...TRUNCATED) | [[15,13,22,353,220,17,13,22,23,20,284,220,16,13,24,19,24,20,271,15,13,15,23,353,220,17,13,22,23,20,2(...TRUNCATED) |
"2. (9th Canadian Mathematical Competition) $N$ is an integer, its representation in base $b$ is 777(...TRUNCATED) | "2. This problem is equivalent to finding the smallest positive integer $b$, such that the equation (...TRUNCATED) | 18 | Number Theory | math-word-problem | olympiads | 39a6c760-dfa3-5201-aa87-105127951e16 | [
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] | 4,718 | 16,384 | 0.9375 | true | 1 | [[151646,151644,17,13,320,24,339,11888,91002,41221,8,400,45,3,374,458,7546,11,1181,13042,304,2331,40(...TRUNCATED) | [[23,382,14190,11,220,18,15,15,15,488,856,28,18,15,15,15,488,2494,13,13824,11,419,4977,537,10950,382(...TRUNCATED) |
"Problem 6. (8 points) In the plane, there is a non-closed, non-self-intersecting broken line consis(...TRUNCATED) | "Solution. Evaluation. Besides the ends, the broken line has 30 vertices, each of which is the inter(...TRUNCATED) | 9 | Geometry | math-word-problem | olympiads | bdcc2598-b04d-5cb8-8634-d35d03fc6bf2 | [
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] | 7,333 | 16,384 | 0.6875 | true | 1 | [[151646,151644,31198,220,21,13,320,23,3501,8,758,279,11031,11,1052,374,264,2477,1786,9259,11,2477,4(...TRUNCATED) | [[11,537,14312,13,1752,3110,11,1378,20632,389,279,1852,1555,1410,387,8433,553,264,2484,11,714,421,80(...TRUNCATED) |
"Four, (50 points) In an $n \\times n$ grid, fill each cell with one of the numbers 1 to $n^{2}$. If(...TRUNCATED) | "Four, take the row $l$ where the number 1 is located and the column $t$ where the number $n^{2}$ is(...TRUNCATED) | 2020 | Combinatorics | math-word-problem | olympiads | 0c6f58a5-af16-5fc6-b982-cdbffc29350d | [
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] | 4,415 | 16,384 | 0.0625 | true | 0 | [[151646,151644,26972,11,320,20,15,3501,8,758,458,400,77,1124,15136,308,3,5827,11,5155,1817,2779,448(...TRUNCATED) | [[16,15,16,16,382,4416,11,8365,11,358,646,1614,419,438,4460,311,30893,5109,304,279,5827,304,1741,264(...TRUNCATED) |
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