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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@8
bool | cons@8
float64 | roll_in_ids
sequence | roll_outs_ids
sequence |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"P.I. Find the largest natural number from which it is impossible to obtain a number divisible by 11(...TRUNCATED) | "If in the decimal representation of a number there is a digit 0 or two identical digits, then by er(...TRUNCATED) | 987654321 | Number Theory | math-word-problem | olympiads | 129904b9-074f-528a-983a-3a512a02276c | [
"",
"",
"",
"",
"",
"",
"",
""
] | [
true,
true,
true,
false,
false,
false,
false,
false
] | 16,429 | 16,429 | 0 | false | 0 | [[151646,151644,47,2447,13,7379,279,7772,5810,1372,504,892,432,374,11997,311,6851,264,1372,74916,553(...TRUNCATED) | [[488,220,21,8,481,320,22,488,220,19,8,284,220,16,20,481,220,16,16,284,220,19,11,537,74916,13,220,23(...TRUNCATED) |
"G1.3 A six-digit number 1234xy is divisible by both 8 and 9 . Given that $x+y=c$, find the value of(...TRUNCATED) | "The number formed by last 3 digits must be divisible by 8 and the sum of digits must be divisible b(...TRUNCATED) | 8 | Number Theory | math-word-problem | olympiads | e5d6ca48-175d-5435-af3b-2d6190441c41 | [
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8"
] | [
true,
true,
true,
true,
true,
true,
true,
false
] | 2,916 | 10,435 | 1 | true | 1 | [[151646,151644,38,16,13,18,362,4743,48342,1372,220,16,17,18,19,4130,374,74916,553,2176,220,23,323,2(...TRUNCATED) | [[13,88190,11,1077,752,1744,911,1246,311,5486,419,382,5338,11,358,6099,429,369,264,1372,311,387,7491(...TRUNCATED) |
"8. Find $\\sqrt{\\frac{x}{63}-32} \\times \\sqrt{\\frac{y}{63}-32}$, given that $\\frac{1}{x}+\\fra(...TRUNCATED) | "Solution: Let's make the substitution: $a=x / 63, b=y / 63$. Then we can rewrite the condition as: (...TRUNCATED) | 32 | Algebra | math-word-problem | olympiads | ca40d92d-2a65-5cff-991e-4deb4c5b192b | [
"32",
"32",
"32",
"32",
"32",
"32",
"32",
"32"
] | [
true,
true,
true,
true,
true,
true,
false,
false
] | 1,770 | 5,890 | 1 | true | 1 | [[151646,151644,23,13,7379,57960,26888,35702,37018,45340,15170,21,18,19732,18,17,92,1124,15136,1124,(...TRUNCATED) | [[151648,198,71486,11,773,358,3003,2684,419,3491,1588,25,358,1184,311,1477,279,897,315,279,1985,315,(...TRUNCATED) |
"10. It is required to fence a rectangular area adjacent to a wall. The fence should have a length o(...TRUNCATED) | "10. Solution. First method. Let the width of the site be \\(x \\mu\\), then its length will be ( \\(...TRUNCATED) | 450 | Algebra | math-word-problem | olympiads | b15f8d71-f552-50aa-abbf-d24f63b69dd1 | [
"15",
"15",
"15",
"15",
"30",
"30",
"30",
"30"
] | [
false,
false,
false,
false,
false,
false,
false,
false
] | 1,948 | 3,015 | 0 | false | 0 | [[151646,151644,16,15,13,1084,374,2567,311,24650,264,51424,3082,23942,311,264,7002,13,576,24650,1265(...TRUNCATED) | [[3983,2474,358,614,825,23606,448,1378,7332,11,358,1184,2441,1616,311,28143,17767,444,1124,8,323,177(...TRUNCATED) |
"4. Median. In a set of 100 numbers. If one number is removed, the median of the remaining numbers i(...TRUNCATED) | "Solution. Arrange the numbers in ascending order. If we remove a number from the first half of the (...TRUNCATED) | 72 | Logic and Puzzles | math-word-problem | olympiads | 2a1d6a5a-5d1b-5822-9f4a-80af2a1e57c4 | [
"78",
"",
"78",
"72",
"72",
"78",
"72",
""
] | [
true,
true,
true,
true,
false,
false,
false,
false
] | 2,948 | 16,457 | 0.375 | true | 0.5 | [[151646,151644,19,13,62590,13,758,264,738,315,220,16,15,15,5109,13,1416,825,1372,374,6963,11,279,22(...TRUNCATED) | [[151648,198,32313,11,773,358,614,419,3491,1588,911,1774,5380,304,264,738,315,5109,13,6771,752,1430,(...TRUNCATED) |
"31. Given that $\\alpha$ is an acute angle satisfying\n$$\n\\sqrt{369-360 \\cos \\alpha}+\\sqrt{544(...TRUNCATED) | "31. Answer: 30\nLet $X=\\sqrt{369-360 \\cos \\alpha}$ and $Y=\\sqrt{544-480 \\sin \\alpha}$. Observ(...TRUNCATED) | 30 | Algebra | math-word-problem | olympiads | ed1c35a8-bbd2-5232-a240-79be83fa76c1 | [
"",
"\\frac{40\\sqrt{3}}{3}",
"",
"30",
"",
"",
"",
"30"
] | [
true,
true,
true,
true,
false,
false,
false,
false
] | 7,892 | 16,466 | 0.25 | true | 1 | [[151646,151644,18,16,13,16246,429,57960,7141,3,374,458,29783,9210,36054,198,14085,198,59,26888,90,1(...TRUNCATED) | [[151648,198,71486,11,773,358,614,419,23606,311,11625,1447,144336,7,18,21,24,481,220,18,21,15,7960,1(...TRUNCATED) |
"## Task 7 - V00607 = V00503\n\nTo an imagined number, 16 is added, then multiplied by 7, followed b(...TRUNCATED) | "Let $x$ be the thought number. Then the operations yield the term\n\n$$\n((x+16) \\cdot 7-8): 9\n$$(...TRUNCATED) | 14 | Algebra | math-word-problem | olympiads | 6dd42fb8-b448-54e4-9002-6c2899aeb4c1 | [
"\\frac{1714}{7}",
"14",
"\\frac{94}{7}",
"14",
"14",
"14",
"244\\frac{6}{7}",
"14"
] | [
true,
true,
true,
true,
true,
false,
false,
false
] | 1,795 | 11,479 | 0.625 | true | 1 | [[151646,151644,565,5430,220,22,481,647,15,15,21,15,22,284,647,15,15,20,15,18,271,1249,458,34606,137(...TRUNCATED) | [[22,25,856,488,220,16,21,284,220,18,15,382,3136,2144,287,220,16,21,25,856,284,220,16,19,382,80022,1(...TRUNCATED) |
"IMO 1974 Problem A1 Three players play the following game. There are three cards each with a differ(...TRUNCATED) | "The player with 9 counters. The total of the scores, 39, must equal the number of rounds times the (...TRUNCATED) | 9 | Logic and Puzzles | math-word-problem | olympiads | 7c90c2f5-6a89-5413-83b7-98a0a091a322 | [
"",
"10",
"13",
"",
"",
"10",
"10",
"1"
] | [
false,
false,
false,
false,
false,
false,
false,
false
] | 14,153 | 16,502 | 0 | false | 0 | [[151646,151644,83404,220,16,24,22,19,22079,362,16,14513,4217,1486,279,2701,1809,13,2619,525,2326,74(...TRUNCATED) | [[279,2629,315,279,5109,807,3949,1817,4778,382,4416,11,369,1817,2781,11,862,2790,374,279,2629,315,27(...TRUNCATED) |
9.1. Solve the equation:
$$
\left(x^{2}-20\right)^{2}+\left(x^{2}-19\right)^{2}=2019
$$ | "Solution. Let $x^{2}-20=y$; then $y^{2}+y-1009=0(D=4037)$ and $y=\\frac{-1 \\pm \\sqrt{4037}}{2}$. (...TRUNCATED) | \\sqrt{\frac{39+\sqrt{4037}}{2}} | Algebra | math-word-problem | olympiads | f6a179f2-45c3-5550-9081-17c2483b9331 | ["-\\sqrt{\\frac{39+\\sqrt{4037}}{2}}","\\pm\\sqrt{\\frac{39+\\sqrt{4037}}{2}}","-\\sqrt{\\frac{39+\(...TRUNCATED) | [
false,
false,
false,
false,
false,
false,
false,
false
] | 4,472 | 11,068 | 0 | false | 0 | [[151646,151644,24,13,16,13,63284,279,23606,1447,14085,198,59,2359,2075,47822,17,19732,17,15,59,1291(...TRUNCATED) | [[151648,198,32313,11,773,358,3003,2684,419,23606,311,11625,25,1124,1188,87,47822,17,92,481,220,17,1(...TRUNCATED) |
"7. Encode the letters $a \\sim z$ as $(\\mathbf{a}=1, \\mathbf{b}=2, \\ldots, \\mathbf{z}=26)$, so (...TRUNCATED) | "【Analysis】(Method one) To be a \"middle ring number\", the prime factors decomposed must includ(...TRUNCATED) | 106 | Number Theory | math-word-problem | olympiads | 50bfa035-acc4-500d-aea0-37fdac65f86f | [
"",
"106",
"107",
"106",
"",
"106",
"106",
""
] | [
true,
true,
true,
true,
false,
false,
false,
false
] | 4,170 | 16,596 | 0.5 | true | 1 | [[151646,151644,22,13,56562,279,11931,400,64,1124,14781,1147,3,438,4930,59,10374,13233,90,64,51185,1(...TRUNCATED) | [[374,16910,11,714,220,16,20,13,16,19,4436,944,458,7546,13,220,16,15,21,17779,553,220,16,16,374,2163(...TRUNCATED) |
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