problem string | prompt string | completions list | scores list | predictions list | hidden_states_files list | prompt_ids list | completions_ids list | thoughts_len list | thoughts_ids_len list | step_rewards_vgs list | step_rewards_qwen_math_prm_7b list | step_rewards_reasonflux_prm_7b list | answer string | id string | proof string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$ | "<｜begin▁of▁sentence｜><｜User｜>Find the sum of all integer bases $b>9$ for which $17_b$ i(...TRUNCATED) | ["Alright, so I have this problem: Find the sum of all integer bases \\( b > 9 \\) for which \\( 17_(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["70","70","70","70","70","70","70","70","70","70","70","70","70","70","70","70","70","70","70","70"(...TRUNCATED) | ["hidden_states_sample000000_completion00.npy","hidden_states_sample000000_completion01.npy","hidden(...TRUNCATED) | [151646,151644,9885,279,2629,315,678,7546,23092,400,65,29,24,3,369,892,400,16,22,880,3,374,264,49109(...TRUNCATED) | [[71486,11,773,358,614,419,3491,25,7379,279,2629,315,678,7546,23092,17767,293,861,220,24,1124,8,369,(...TRUNCATED) | [3926,3866,3937,3850,4191,4311,4614,4795,4445,4847,5210,5640,5703,6125,6734,6847,7393,8000,8129,9886(...TRUNCATED) | [1526,1483,1527,1451,1637,1648,1697,1797,1804,1836,2038,2028,2081,2343,2524,2628,2976,3034,3195,3624(...TRUNCATED) | [[0.9998592138290405],[0.9997298121452332],[0.9995508790016174],[0.999671459197998],[0.9987921118736(...TRUNCATED) | [[0.96484375,0.9921875,0.9609375,0.99609375,0.984375,0.99609375,0.98828125,0.99609375,0.99609375,0.9(...TRUNCATED) | [[0.99609375,1.0,0.99609375,1.0,0.99609375,1.0,1.0,1.0,1.0,0.9921875,0.99609375,0.99609375,0.9882812(...TRUNCATED) | 70 | 0 | "To find the sum of all integer bases \\( b > 9 \\) for which \\( 17_b \\) is a divisor of \\( 97_b (...TRUNCATED) |
"In $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{AB}$ so that $AD < AE < AB$, while points(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{(...TRUNCATED) | ["Okay, so I need to find the area of this heptagon AFNBCEM in triangle ABC. Hmm, that seems a bit c(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0,0.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["588","588","588","588","588","588","588","588","588","588","588","588","588","300","588","36","300(...TRUNCATED) | ["hidden_states_sample000001_completion00.npy","hidden_states_sample000001_completion01.npy","hidden(...TRUNCATED) | [151646,151644,641,57960,55114,19360,3,3501,400,35,3,323,400,36,3,10246,389,57960,1975,1056,90,1867,(...TRUNCATED) | [[32313,11,773,358,1184,311,1477,279,3082,315,419,566,417,6113,19885,33342,2104,44,304,21495,19360,1(...TRUNCATED) | [12034,13436,12252,17940,18166,19025,22872,24765,13539,16727,17389,22727,29075,36850,39605,37863,248(...TRUNCATED) | [4866,5406,5421,6163,6441,7470,8214,9183,5795,6779,6884,8139,11170,13556,14604,15005,9268,11531,5045(...TRUNCATED) | [[0.9990456700325012],[0.9781725406646729],[0.9683102369308472],[0.5877752304077148],[0.994825482368(...TRUNCATED) | [[0.98046875,0.9765625,0.96484375,0.984375,0.99609375,0.408203125,0.87890625,0.9609375,0.72265625,0.(...TRUNCATED) | [[0.99609375,0.99609375,0.99609375,0.99609375,1.0,0.85546875,0.98046875,0.99609375,0.953125,0.992187(...TRUNCATED) | 588 | 1 | "Given triangle \\( \\triangle ABC \\) with points \\( A, D, E, B \\) on \\( \\overline{AB} \\) such(...TRUNCATED) |
"The $9$ members of a baseball team went to an ice-cream parlor after their game. Each player had a (...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>The $9$ members of a baseball team went to an ice-cream pa(...TRUNCATED) | ["Alright, so here's this problem I came across. Let me try to unpack it step by step.\n\nWe have 9 (...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["16","16","16","16","16","16","16","16","16","16","16","16","16","16","16","16","16","16","16","16"(...TRUNCATED) | ["hidden_states_sample000002_completion00.npy","hidden_states_sample000002_completion01.npy","hidden(...TRUNCATED) | [151646,151644,785,400,24,3,3613,315,264,19507,2083,3937,311,458,9853,12,46000,1346,9566,1283,862,18(...TRUNCATED) | [[71486,11,773,1588,594,419,3491,358,3697,3941,13,6771,752,1430,311,31065,432,3019,553,3019,382,1654(...TRUNCATED) | [9163,8028,9155,8103,9332,9634,10583,9412,11185,10071,10469,10245,12202,12753,11911,12474,11915,1188(...TRUNCATED) | [3100,2904,3307,3202,3391,3584,3648,3879,3923,3796,3946,3931,4368,4167,4057,4231,4199,4428,4311,4503(...TRUNCATED) | [[0.9980467557907104],[0.9987475872039795],[0.9988874793052673],[0.9901813864707947],[0.995667219161(...TRUNCATED) | [[0.9921875,0.984375,0.99609375,1.0,0.95703125,0.99609375,0.98828125,0.9921875,0.99609375,0.99609375(...TRUNCATED) | [[1.0,0.99609375,1.0,1.0,0.9921875,1.0,1.0,1.0,1.0,1.0,0.99609375,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 16 | 2 | "The 9 members of a baseball team each chose a single scoop of chocolate, vanilla, or strawberry ice(...TRUNCATED) |
"Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $1(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Find the number of ordered pairs $(x,y)$, where both $x$ a(...TRUNCATED) | ["Okay, so I need to find the number of ordered pairs (x, y) where both x and y are integers between(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["117","117","117","117","117","117","117","117","117","117","117","117","117","117","117","117","11(...TRUNCATED) | ["hidden_states_sample000003_completion00.npy","hidden_states_sample000003_completion01.npy","hidden(...TRUNCATED) | [151646,151644,9885,279,1372,315,11457,13530,4930,87,7358,15087,11,1380,2176,400,87,3,323,400,88,3,5(...TRUNCATED) | [[32313,11,773,358,1184,311,1477,279,1372,315,11457,13530,320,87,11,379,8,1380,2176,856,323,379,525,(...TRUNCATED) | [7254,9546,9898,10929,9964,10348,10410,11637,10103,11840,11585,12723,12567,12844,13741,12340,13395,1(...TRUNCATED) | [2978,3547,4156,3976,3865,4114,4016,4224,3971,4362,4638,4707,4686,4953,5016,4898,5467,5903,5721,5991(...TRUNCATED) | [[0.9674105048179626],[0.9314394593238831],[0.29393869638442993],[0.9512031078338623],[0.50395417213(...TRUNCATED) | [[0.96875,0.87890625,0.984375,0.984375,0.984375,0.94921875,1.0,0.9921875,0.94921875,0.99609375,0.992(...TRUNCATED) | [[0.99609375,0.984375,0.99609375,0.99609375,0.99609375,0.9921875,1.0,1.0,0.9921875,1.0,1.0,1.0,1.0,0(...TRUNCATED) | 117 | 3 | "To find the number of ordered pairs \\((x, y)\\) where both \\(x\\) and \\(y\\) are integers betwee(...TRUNCATED) |
"There are $8!= 40320$ eight-digit positive integers that use each of the digits $1, 2, 3, 4, 5, 6, (...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>There are $8!= 40320$ eight-digit positive integers that u(...TRUNCATED) | ["Okay, so I need to find the number of eight-digit integers, using each of the digits 1 through 8 e(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,1.0,0.0,0.0,1.0,1.0,0.0(...TRUNCATED) | ["279","279","279","279","279","279","279","297","279","279","279","279","8343","2583","279","9495",(...TRUNCATED) | ["hidden_states_sample000004_completion00.npy","hidden_states_sample000004_completion01.npy","hidden(...TRUNCATED) | [151646,151644,3862,525,400,23,5824,220,19,15,18,17,15,3,8063,48342,6785,25780,429,990,1817,315,279,(...TRUNCATED) | [[32313,11,773,358,1184,311,1477,279,1372,315,8063,48342,25780,11,1667,1817,315,279,18509,220,16,152(...TRUNCATED) | [16643,18352,19086,19865,24767,22997,26850,27436,23399,27054,27280,28047,26635,30932,38539,40121,408(...TRUNCATED) | [5977,6528,6605,6851,8104,8023,8219,8614,8717,8900,9040,9308,9477,10172,11868,12392,12506,14139,1444(...TRUNCATED) | [[0.8738378286361694],[0.14308933913707733],[0.02302486263215542],[0.09074807912111282],[0.438912868(...TRUNCATED) | [[0.97265625,0.97265625,0.984375,0.9453125,0.9921875,0.97265625,0.984375,0.98828125,0.98828125,0.992(...TRUNCATED) | [[0.99609375,0.99609375,0.99609375,0.9921875,1.0,0.99609375,0.99609375,1.0,0.99609375,1.0,0.98828125(...TRUNCATED) | 279 | 4 | "To find the number of eight-digit integers using each digit 1 through 8 exactly once that are divis(...TRUNCATED) |
"An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>An isosceles trapezoid has an inscribed circle tangent to (...TRUNCATED) | ["Okay, so I have this problem about an isosceles trapezoid with an inscribed circle. The radius of (...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["504","504","504","504","504","504","504","504","504","504","504","504","504","504","504","504","50(...TRUNCATED) | ["hidden_states_sample000005_completion00.npy","hidden_states_sample000005_completion01.npy","hidden(...TRUNCATED) | [151646,151644,2082,374,436,346,642,489,2027,89,588,702,458,1640,17433,12671,68660,311,1817,315,1181(...TRUNCATED) | [[32313,11,773,358,614,419,3491,911,458,374,436,346,642,489,2027,89,588,448,458,1640,17433,12671,13,(...TRUNCATED) | [4572,5357,5761,6053,6140,5919,6240,7318,7089,6867,6803,7521,8804,7778,6838,8326,7834,9105,10165,886(...TRUNCATED) | [1566,1840,2104,2236,2314,2220,2423,2596,2636,2553,2537,2619,3149,2822,2654,2933,3045,3260,3430,3382(...TRUNCATED) | [[0.9990768432617188],[0.9980588555335999],[0.999550998210907],[0.9984853863716125],[0.9933356046676(...TRUNCATED) | [[0.99609375,0.94921875,0.9765625,1.0,0.99609375,0.984375,0.99609375,1.0,1.0,0.91015625,0.99609375,1(...TRUNCATED) | [[1.0,0.9921875,0.99609375,1.0,1.0,0.99609375,1.0,1.0,1.0,0.98828125,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 504 | 5 | "Given an isosceles trapezoid with an inscribed circle (radius 3) and area 72, we need to find \\( r(...TRUNCATED) |
"The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are randomly grouped into s(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$(...TRUNCATED) | ["Okay, so here's this problem about probability with letters. We've got twelve letters: A, B, C, D,(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | ["12","12","12","271","701",null,"1",null,null,"0",null,null,null,null,null,"12","12","271",null,"12(...TRUNCATED) | ["hidden_states_sample000006_completion00.npy","hidden_states_sample000006_completion01.npy","hidden(...TRUNCATED) | [151646,151644,785,29235,11931,400,32,3,4779,33,3,4779,34,3,4779,35,3,4779,36,3,4779,37,3,4779,38,3,(...TRUNCATED) | [[32313,11,773,1588,594,419,3491,911,18927,448,11931,13,1205,3003,2684,29235,11931,25,362,11,425,11,(...TRUNCATED) | [23120,25750,36457,42435,42049,62169,49176,62209,63133,61834,64656,61907,66044,61760,62812,14000,286(...TRUNCATED) | [5758,6353,9167,11304,11646,16384,12493,16384,16384,15522,16384,16384,16382,16384,16384,3714,7397,13(...TRUNCATED) | [[0.058294281363487244],[0.005840964615345001],[0.003311713458970189],[0.9369297027587891],[0.003850(...TRUNCATED) | [[0.984375,0.9921875,0.97265625,0.98828125,1.0,0.94140625,0.94921875,0.9609375,0.9296875,0.99609375,(...TRUNCATED) | [[0.99609375,1.0,0.99609375,1.0,1.0,0.9921875,0.9921875,0.9921875,0.98828125,1.0,0.99609375,0.988281(...TRUNCATED) | 821 | 6 | "To solve the problem, we need to determine the probability that the last word in the alphabetically(...TRUNCATED) |
"Let $k$ be a real number such that the system \\begin{align*} &|25 + 20i - z| = 5 \\ &|z - 4 - k| =(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Let $k$ be a real number such that the system \\begin{alig(...TRUNCATED) | ["Okay, so I've got this system of equations involving complex numbers, and I'm supposed to find the(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["77","77","77","77","77","77","77","77","77","77","77","77","77","77","77","77","77","77","77","77"(...TRUNCATED) | ["hidden_states_sample000007_completion00.npy","hidden_states_sample000007_completion01.npy","hidden(...TRUNCATED) | [151646,151644,10061,400,74,3,387,264,1931,1372,1741,429,279,1849,1124,7265,90,6612,9,92,609,91,17,2(...TRUNCATED) | [[32313,11,773,358,3003,2684,419,1849,315,37906,15860,6351,5109,11,323,358,2776,9966,311,1477,279,26(...TRUNCATED) | [4534,5338,5922,5035,5738,5620,6231,5179,6087,6385,6245,6808,7116,6797,7000,7748,7521,7080,7954,7379(...TRUNCATED) | [1929,2259,2250,2016,2279,2204,2479,2224,2341,2484,2627,2774,2801,2847,2823,2866,2948,2988,3209,2942(...TRUNCATED) | [[0.9937973022460938],[0.9622748494148254],[0.998095691204071],[0.9978293776512146],[0.9987924098968(...TRUNCATED) | [[0.984375,1.0,0.98046875,0.953125,0.99609375,1.0,0.99609375,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,(...TRUNCATED) | [[0.99609375,1.0,0.99609375,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0(...TRUNCATED) | 77 | 7 | "The given system of equations involves finding a complex number \\( z \\) such that:\n\n\\[\n\\begi(...TRUNCATED) |
"The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin.(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>The parabola with equation $y = x^2 - 4$ is rotated $60^\\(...TRUNCATED) | ["Alright, so I've got this problem about rotating a parabola and finding an intersection point. The(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0(...TRUNCATED) | ["62","62","62","62","62","62",null,null,null,null,null,null,null,null,null,null,null,null,null,null(...TRUNCATED) | ["hidden_states_sample000008_completion00.npy","hidden_states_sample000008_completion01.npy","hidden(...TRUNCATED) | [151646,151644,785,1346,370,7924,448,23606,400,88,284,856,61,17,481,220,19,3,374,45620,400,21,15,248(...TRUNCATED) | [[71486,11,773,358,3003,2684,419,3491,911,41396,264,1346,370,7924,323,9271,458,19246,1459,13,576,402(...TRUNCATED) | [20907,24789,27607,28785,33417,33433,35154,35593,37422,39946,41394,36475,35883,41800,39353,37769,355(...TRUNCATED) | [9598,9999,11429,12305,14657,15106,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384(...TRUNCATED) | [[0.9955042004585266],[0.978142499923706],[0.891858696937561],[0.981105625629425],[0.57257080078125](...TRUNCATED) | [[0.9921875,0.9296875,0.984375,0.99609375,0.99609375,1.0,1.0,1.0,1.0,0.953125,0.99609375,0.99609375,(...TRUNCATED) | [[1.0,0.98828125,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,0.9921875,1.0,1.0,1.0,0.99609375,1.0,1.0,1.0,0.9(...TRUNCATED) | 62 | 8 | "To find the intersection point in the fourth quadrant between the original parabola \\( y = x^2 - 4(...TRUNCATED) |
"The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>The $27$ cells of a $3 \\times 9$ grid are filled in using(...TRUNCATED) | ["Okay, so I have this problem about counting the number of different ways to fill a 3x9 grid with n(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | [null,null,"21","9450","69",null,"17",null,"306180",null,"212",null,null,"114",null,null,null,"729",(...TRUNCATED) | ["hidden_states_sample000009_completion00.npy","hidden_states_sample000009_completion01.npy","hidden(...TRUNCATED) | [151646,151644,785,400,17,22,3,7761,315,264,400,18,1124,15136,220,24,3,5827,525,10199,304,1667,279,5(...TRUNCATED) | [[32313,11,773,358,614,419,3491,911,25009,279,1372,315,2155,5510,311,5155,264,220,18,87,24,5827,448,(...TRUNCATED) | [59319,60145,44896,54022,50152,62880,54523,60042,50837,63369,53265,64979,60565,48323,66433,65913,591(...TRUNCATED) | [16384,16384,12216,13968,13399,16384,14800,16384,14377,16384,14374,16384,16384,12356,16384,16384,163(...TRUNCATED) | [[0.000010322630259906873],[0.00001867914579634089],[0.19331461191177368],[0.05819041654467583],[0.0(...TRUNCATED) | [[0.96484375,0.74609375,0.921875,0.984375,0.9921875,0.99609375,0.91796875,0.96484375,0.98046875,0.96(...TRUNCATED) | [[0.99609375,0.96484375,0.98828125,1.0,1.0,1.0,0.98828125,0.99609375,0.99609375,0.99609375,0.9921875(...TRUNCATED) | 81 | 9 | "To solve the problem of counting the number of different ways to fill a 3×9 grid with numbers 1 th(...TRUNCATED) |
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