prompt_text stringlengths 20 1.73k | prompt_ids listlengths 8 791 | decode_ids listlengths 2.05k 2.05k | prompt_pattern listlengths 24 24 | decode_pattern listlengths 24 24 |
|---|---|---|---|---|
"Convert the point $(0,3)$ in rectangular coordinates to polar coordinates. Enter your answer in th(...TRUNCATED) | [12012,279,1459,4930,15,11,18,15087,304,51424,13934,311,24660,13934,13,220,11252,697,4226,304,279,13(...TRUNCATED) | [33975,33975,198,3,8,311,24660,13934,13,220,11252,697,4226,304,279,1352,4930,81,26266,15976,98406,13(...TRUNCATED) | [[[25,33,57,19],[19,30,29,57],[8,46,55,5],[36,19,25,17],[25,12,28,32],[14,45,11,51],[31,26,11,5],[14(...TRUNCATED) | [[[32,35,7,24],[32,35,7,24],[32,35,11,23],[6,18,31,54],[12,38,6,32],[38,43,12,29],[34,47,10,20],[35,(...TRUNCATED) |
"Define\n\\[p = \\sum_{k = 1}^\\infty \\frac{1}{k^2} \\quad \\text{and} \\quad q = \\sum_{k = 1}^\\i(...TRUNCATED) | [35338,198,78045,79,284,1124,1242,15159,74,284,220,16,92,24884,258,36958,1124,37018,90,16,15170,74,6(...TRUNCATED) | [33975,33975,33975,522,1296,397,262,366,1296,1472,1296,397,262,366,1296,1472,1296,397,262,366,1296,1(...TRUNCATED) | [[[33,25,12,21],[5,25,21,30],[6,5,23,9],[32,9,2,36],[44,48,8,3],[50,46,49,25],[56,35,22,49],[48,20,1(...TRUNCATED) | [[[32,35,47,24],[32,35,7,24],[32,35,7,24],[32,35,11,24],[47,30,10,32],[42,31,52,11],[55,5,21,51],[6,(...TRUNCATED) |
"If $f(x) = \\frac{3x-2}{x-2}$, what is the value of $f(-2) +f(-1)+f(0)$? Express your answer as a c(...TRUNCATED) | [2679,400,69,2075,8,284,1124,37018,90,18,87,12,17,15170,87,12,17,31716,11,1128,374,279,897,315,400,6(...TRUNCATED) | [33975,1,104438,104517,102096,100193,3837,100043,82166,9370,99813,111326,15,13,19,95053,100043,82166(...TRUNCATED) | [[[50,33,54,52],[50,54,4,7],[28,32,9,2],[52,3,12,54],[13,52,3,46],[38,31,56,11],[50,49,46,25],[56,34(...TRUNCATED) | [[[32,35,7,24],[32,35,49,11],[38,9,24,31],[16,15,10,8],[40,7,41,10],[17,11,2,39],[45,12,52,5],[31,5,(...TRUNCATED) |
How many positive whole-number divisors does 196 have? | [
4340,
1657,
6785,
4361,
25854,
3429,
41214,
1558,
220,
16,
24,
21,
614,
30
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"The results of a cross-country team's training run are graphed below. Which student has the greates(...TRUNCATED) | [785,3059,315,264,5312,55871,2083,594,4862,1598,525,4771,291,3685,13,15920,5458,702,279,12196,5461,4(...TRUNCATED) | [54275,12669,198,2,18614,279,24722,315,279,4143,438,17738,198,36,889,1872,284,220,16,13,17,20,220,67(...TRUNCATED) | [[[33,8,44,16],[8,18,44,33],[36,43,2,16],[51,34,24,35],[46,36,1,51],[20,19,35,7],[23,53,13,39],[53,4(...TRUNCATED) | [[[38,42,6,3],[38,24,13,40],[42,39,32,44],[6,34,15,54],[28,59,44,33],[37,48,25,21],[8,46,5,21],[43,0(...TRUNCATED) |
"A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the tri(...TRUNCATED) | [32,5792,12371,6113,646,387,17779,1119,4743,3232,42939,42446,13,1416,279,46342,315,825,315,279,42446(...TRUNCATED) | [37175,264,3175,3232,42939,21495,448,264,46342,315,220,17,16,14924,13,576,3108,3084,315,279,21495,64(...TRUNCATED) | [[[1,33,36,35],[1,36,35,39],[56,53,57,58],[54,47,27,52],[39,19,43,10],[32,20,47,31],[20,40,54,47],[4(...TRUNCATED) | [[[25,10,53,32],[25,32,10,29],[36,46,1,27],[14,7,48,11],[35,1,24,16],[34,41,58,40],[43,34,19,21],[34(...TRUNCATED) |
"What is the smallest positive perfect cube that can be written as the sum of three consecutive inte(...TRUNCATED) | [
3838,
374,
279,
24632,
6785,
4727,
23739,
429,
646,
387,
5326,
438,
279,
2629,
315,
2326,
23921,
25780,
30
] | [46254,279,4734,897,315,279,7493,57960,2359,91,18,59,2493,481,760,1124,2493,481,220,23,760,1124,1291(...TRUNCATED) | [[[33,4,32,24],[4,32,24,11],[40,37,11,24],[8,46,5,40],[52,0,58,39],[7,56,32,57],[58,7,32,35],[28,43,(...TRUNCATED) | [[[25,55,41,26],[25,19,44,48],[8,46,44,5],[11,7,58,54],[43,41,27,31],[51,37,24,44],[42,8,46,51],[36,(...TRUNCATED) |
"The set of points $(x,y,z)$ that satisfy\n\\[2x = 3y = -z\\]is a line.\n\nThe set of points $(x,y,z(...TRUNCATED) | [785,738,315,3501,4930,87,7358,22669,15087,429,26553,198,78045,17,87,284,220,18,88,284,481,89,59,60,(...TRUNCATED) | [33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,339(...TRUNCATED) | [[[33,8,44,16],[8,18,44,21],[29,53,30,55],[51,34,3,15],[36,2,19,51],[25,32,12,9],[52,13,22,1],[1,52,(...TRUNCATED) | [[[32,35,7,24],[32,35,7,24],[32,35,7,24],[32,35,7,24],[32,35,7,24],[32,35,7,24],[32,35,7,24],[32,35,(...TRUNCATED) |
"What is the distance, in units, between the points $(2, -6)$ and $(-4, 3)$? Express your answer in (...TRUNCATED) | [3838,374,279,6010,11,304,8153,11,1948,279,3501,4930,17,11,481,21,15087,323,400,4080,19,11,220,18,15(...TRUNCATED) | [33975,33975,698,1249,1477,279,6010,1948,1378,3501,11,4930,87,62,16,11,379,62,16,15087,323,4930,87,6(...TRUNCATED) | [[[33,4,32,24],[4,32,24,11],[40,37,11,24],[8,46,5,44],[45,56,52,27],[31,17,49,59],[10,15,37,31],[56,(...TRUNCATED) | [[[32,35,7,24],[32,35,7,24],[32,35,11,24],[6,38,32,51],[10,1,15,47],[49,25,37,57],[8,46,55,5],[41,43(...TRUNCATED) |
"The expression $2\\cdot 3 \\cdot 4\\cdot 5+1$ is equal to 121, since multiplication is carried out (...TRUNCATED) | [785,7493,400,17,59,50853,220,18,1124,50853,220,19,59,50853,220,20,10,16,3,374,6144,311,220,16,17,16(...TRUNCATED) | [3379,678,429,3796,25974,3,16,15,3,871,3,16,17,3,871,3,16,18,3,871,3,16,19,3,871,3,16,20,3,871,3,16,(...TRUNCATED) | [[[33,8,44,16],[8,18,44,21],[36,2,19,23],[28,12,19,58],[14,3,34,1],[56,38,9,13],[5,40,57,52],[26,58,(...TRUNCATED) | [[[29,0,30,25],[29,0,30,19],[28,4,51,24],[26,4,51,5],[42,25,58,55],[6,4,48,53],[38,28,12,32],[7,38,5(...TRUNCATED) |
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