prompt_text stringclasses 30 values | prompt_ids listlengths 46 398 | decode_ids listlengths 64 64 | prompt_pattern listlengths 27 27 | decode_pattern listlengths 27 27 |
|---|---|---|---|---|
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, including $t$ minutes spent in the coffee shop. Suppose Aya walks at $s+\frac{1}{2}$ kilometers per hour. Find the number of minutes the walk takes her, including the $t$ minutes spent in the coffee shop. | [
100000,
10394,
4421,
338,
4206,
5014,
327,
245,
363,
24,
2943,
69892,
17377,
12,
5509,
3667,
285,
16981,
430,
245,
9356,
5554,
12769,
13,
2473,
838,
20391,
430,
245,
4081,
4583,
280,
363,
82,
3,
49785,
513,
5064,
11,
254,
3667,
4497,
... | [
185,
3673,
830,
317,
437,
317,
1296,
363,
50,
28,
17,
83,
3,
5064,
285,
363,
16,
17,
3,
8298,
13,
185,
2280,
363,
50,
28,
51,
10,
49,
3,
185,
3,
50,
28,
51,
10,
51,
10,
51,
3,
185,
3,
50,
28,
16,
51,
10,
16,
51,
10,
... | [
[
[
14,
34,
2,
42,
47,
1,
46,
40
],
[
14,
34,
42,
33,
21,
20,
57,
58
],
[
38,
34,
0,
14,
39,
33,
27,
37
],
[
37,
5,
24,
... | [
[
[
2,
47,
14,
44,
37,
3,
15,
18
],
[
6,
42,
48,
63,
22,
20,
25,
37
],
[
23,
62,
41,
36,
63,
37,
4,
29
],
[
4,
36,
30,
3... |
"Let $ABC$ be a triangle inscribed in circle $\\omega$. Let the tangents to $\\omega$ at $B$ and $C$(...TRUNCATED) | [100000,4160,363,37190,3,330,245,22320,71705,279,9982,628,3161,1332,3960,254,16881,713,276,628,3161,(...TRUNCATED) | [185,185,3673,1682,185,40,1006,344,254,3046,280,628,24550,37190,3,317,363,3339,9,7459,9,7459,3,285,2(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[18,34,42,56,20,45,14,54],[40,14,49,16,46,34,1,7],[43,5,34,52,20,0,4,37],[(...TRUNCATED) | [[[2,47,14,3,18,15,41,44],[47,2,34,3,10,15,54,58],[42,48,6,1,34,57,14,20],[45,34,41,23,38,30,29,1],[(...TRUNCATED) |
"Each vertex of a regular octagon is independently colored either red or blue with equal probability(...TRUNCATED) | [100000,10005,12049,280,245,4252,21105,5995,317,20919,24135,2818,3074,410,5501,366,5929,7599,13,429,(...TRUNCATED) | [185,185,13483,433,3514,2580,100001,100000,2,25451,21752,185,185,1679,2006,5612,1962,207,17,15,1555,(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[33,37,20,42,34,14,21,58],[34,60,61,35,33,63,4,23],[56,21,9,14,20,34,57,42(...TRUNCATED) | [[[2,47,14,44,18,15,40,34],[47,2,34,15,54,62,44,3],[1,42,34,14,7,45,32,16],[24,42,34,5,4,1,35,62],[3(...TRUNCATED) |
"Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$. Find the number of intersection(...TRUNCATED) | [100000,35115,363,69,7,87,4576,8705,1376,91,2120,19676,90,16,1061,17,63554,285,363,70,7,87,4576,8705(...TRUNCATED) | [185,185,40,6,313,803,3507,276,536,437,2512,327,245,1477,548,304,6,313,803,12273,13,185,185,549,1022(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[50,34,57,41,42,20,4,45],[49,16,40,14,46,7,1,53],[5,24,34,43,4,0,60,31],[4(...TRUNCATED) | [[[47,2,14,18,3,15,44,59],[47,2,34,15,37,41,54,55],[42,48,24,57,5,34,8,1],[53,1,34,6,14,46,42,18],[3(...TRUNCATED) |
"Let $p$ be the least prime number for which there exists a positive integer $n$ such that $n^{4}+1$(...TRUNCATED) | [100000,4160,363,79,3,330,254,2754,9966,1604,327,588,745,6057,245,4864,10858,363,77,3,1108,344,363,7(...TRUNCATED) | [185,40,463,803,3507,276,1275,254,3510,327,437,2512,11,548,304,536,441,1006,946,276,1275,363,76,3,28(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[14,34,42,18,45,57,56,20],[40,14,16,49,46,11,7,1],[5,43,24,31,11,34,60,4],(...TRUNCATED) | [[[2,47,14,18,44,15,40,3],[5,22,24,48,42,25,31,61],[30,36,4,57,39,14,17,42],[30,4,36,34,14,57,44,39](...TRUNCATED) |
"Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$, $AC=BD= \\sqrt{80}$, and $BC=AD= \\sqrt{(...TRUNCATED) | [100000,4160,363,3339,6019,3,330,245,56211,63006,1108,344,363,3339,28,6019,28,357,4221,90,19,16,3001(...TRUNCATED) | [100001,100000,2,24324,25,8604,11372,185,185,6285,3638,207,16,22,11,207,17,15,16,17,25,17,185,185,12(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[34,14,18,42,45,57,56,20],[11,40,16,14,49,7,46,1],[5,11,10,43,24,34,4,52],(...TRUNCATED) | [[[43,50,6,29,27,2,52,41],[14,34,2,47,18,42,63,40],[34,14,1,49,7,42,45,46],[1,34,42,62,58,51,27,23],(...TRUNCATED) |
"Let $\\mathcal{B}$ be the set of rectangular boxes with surface area $54$ and volume $23$. Let $r$ (...TRUNCATED) | [100000,4160,628,1390,90,33,759,330,254,845,280,22069,14253,366,5438,3046,363,20,19,3,285,6530,363,1(...TRUNCATED) | [185,6572,25,5178,10723,207,17,15,18,6132,22398,12712,7603,22759,23243,185,46,2098,334,17,15,18,19,1(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[18,34,42,56,20,45,54,8],[16,14,49,53,1,40,11,8],[34,11,27,4,20,62,52,25],(...TRUNCATED) | [[[2,47,14,3,44,15,18,41],[42,23,27,1,20,4,34,55],[42,1,9,46,45,32,34,57],[42,15,43,20,57,52,14,24],(...TRUNCATED) |
"There exist real numbers $x$ and $y$, both greater than 1, such that $\\log_x\\left(y^x\\right)=\\l(...TRUNCATED) | [100000,2960,2639,1590,5750,363,87,3,285,363,88,1348,1572,6146,853,207,16,11,1108,344,628,2034,62,87(...TRUNCATED) | [3,185,40,1503,636,344,327,688,363,87,29,16,3,285,363,88,29,16,1348,363,87,781,88,12,16,23754,16,134(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[62,14,12,34,42,8,48,20],[38,62,4,30,36,29,20,58],[58,19,22,21,38,20,62,57(...TRUNCATED) | [[[16,7,49,55,53,62,48,1],[47,2,14,15,18,3,55,44],[42,48,24,34,5,57,1,8],[38,50,29,36,34,39,20,1],[4(...TRUNCATED) |
"Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take tur(...TRUNCATED) | [100000,50391,285,11073,1538,254,1893,2624,13,338,10200,280,363,77,3,23701,11012,1323,768,13,429,659(...TRUNCATED) | [185,3673,34601,185,1162,6,82,363,87,3,330,254,1604,280,23701,279,254,10200,13,2928,363,19,7,16,10,1(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[8,61,42,37,34,54,58,5],[45,28,32,20,34,57,8,46],[61,8,42,34,1,5,20,4],[41(...TRUNCATED) | [[[2,47,14,44,15,34,43,18],[6,42,48,20,63,22,25,37],[1,23,42,63,45,35,32,62],[47,2,14,3,44,23,22,63](...TRUNCATED) |
"Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers(...TRUNCATED) | [100000,71664,25882,245,48441,457,20288,363,19,3,8492,5750,473,363,50,26332,16,11,17,11,18,1412,8042(...TRUNCATED) | [100001,100000,2,1724,276,4359,13832,6337,276,1448,3863,30,185,185,16,13,2545,207,16,20,11,207,17,15(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[61,24,34,43,8,57,32,31],[4,50,2,20,57,41,29,10],[40,21,14,12,33,5,24,57],(...TRUNCATED) | [[[43,50,29,6,0,52,41,2],[14,34,2,42,18,52,47,63],[34,14,1,49,7,42,46,45],[1,42,34,53,8,14,56,57],[1(...TRUNCATED) |
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