problem stringlengths 91 1.51k | prompt stringlengths 250 1.67k | completions listlengths 128 128 | scores listlengths 128 128 | predictions listlengths 128 128 | hidden_states_files listlengths 128 128 | prompt_ids listlengths 51 650 | completions_ids listlengths 128 128 | thoughts_len listlengths 128 128 | thoughts_ids_len listlengths 128 128 | step_rewards_vgs listlengths 128 128 | step_rewards_qwen_math_prm_7b listlengths 128 128 | step_rewards_reasonflux_prm_7b listlengths 128 128 | answer stringlengths 2 46 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"A semicircle is inscribed in another semicircle if the smaller semicircle's diameter is a chord of (...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>A semicircle is inscribed in another semicircle if the sma(...TRUNCATED) | ["Okay, so I have this geometry problem here about semicircles inscribed inside each other. Let me t(...TRUNCATED) | [0.0,0.0,1.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0(...TRUNCATED) | ["4","\\frac{25}{8}","20",null,null,"20","20",null,null,null,null,null,null,null,null,null,null,"100(...TRUNCATED) | ["hidden_states_sample000000_completion00.npy","hidden_states_sample000000_completion01.npy","hidden(...TRUNCATED) | [151646,151644,32,5234,292,7074,374,1640,17433,304,2441,5234,292,7074,421,279,9155,5234,292,7074,594(...TRUNCATED) | [[32313,11,773,358,614,419,17047,3491,1588,911,5234,292,74263,1640,17433,4766,1817,1008,13,6771,752,(...TRUNCATED) | [27320,30446,38430,46726,49456,15717,24085,44537,45747,48700,48718,47718,49984,48951,43249,48784,480(...TRUNCATED) | [8716,10925,13709,16384,16384,6166,9460,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,(...TRUNCATED) | [[0.008546525612473488],[0.0042989845387637615],[0.03894659876823425],[0.000010209560969087761],[0.1(...TRUNCATED) | [[0.9765625,0.875,0.640625,0.453125,0.9609375,0.8046875,0.921875,0.9296875,0.9609375,0.80859375,0.97(...TRUNCATED) | [[0.99609375,0.98046875,0.94140625,0.8828125,0.99609375,0.97265625,0.98828125,0.98828125,0.9921875,0(...TRUNCATED) | 20 |
"Compute the number of ways to arrange $3$ copies of each of the $26$ lowercase letters of the Engli(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Compute the number of ways to arrange $3$ copies of each o(...TRUNCATED) | ["Okay, so I came across this interesting problem today. It goes like this:\n\n\"Compute the number (...TRUNCATED) | [0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | [null,null,null,null,"53","106",null,null,"55",null,null,null,null,null,null,null,null,null,"53",nul(...TRUNCATED) | ["hidden_states_sample000001_completion00.npy","hidden_states_sample000001_completion01.npy","hidden(...TRUNCATED) | [151646,151644,46254,279,1372,315,5510,311,30893,400,18,3,10993,315,1817,315,279,400,17,21,3,42047,1(...TRUNCATED) | [[32313,11,773,358,3697,3941,419,7040,3491,3351,13,1084,5780,1075,419,1447,1,46254,279,1372,315,5510(...TRUNCATED) | [56205,51469,64887,55775,28371,54378,56051,46956,60293,57965,55204,59358,51864,53909,59450,64206,613(...TRUNCATED) | [16384,16384,16384,16384,7665,16172,16384,16384,16268,16384,16384,16384,16384,16384,16384,16384,1638(...TRUNCATED) | [[0.000016165302440640517],[0.00006997202581260353],[0.00023073595366440713],[0.00002244392453576438(...TRUNCATED) | [[0.96484375,0.99609375,0.99609375,0.9921875,0.9921875,0.99609375,0.9921875,0.9921875,0.91015625,0.9(...TRUNCATED) | [[0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.984375,0.99609375,0.99609375,1.0,0.9765625,0.9921875,1.0,(...TRUNCATED) | 53 |
"There exists a unique triple $(a, b, c)$ of positive real numbers that satisfies the equations\n$$\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>There exists a unique triple $(a, b, c)$ of positive real (...TRUNCATED) | ["Okay, so I've got this problem here where I need to find the unique triple (a, b, c) of positive r(...TRUNCATED) | [1.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | ["\\frac{9\\sqrt{23}}{23}","\\frac{9\\sqrt{23}}{23}","\\frac{15}{8}","\\frac{9\\sqrt{23}}{23}","2","(...TRUNCATED) | ["hidden_states_sample000002_completion00.npy","hidden_states_sample000002_completion01.npy","hidden(...TRUNCATED) | [151646,151644,3862,6724,264,4911,23725,4930,64,11,293,11,272,15087,315,6785,1931,5109,429,67901,279(...TRUNCATED) | [[32313,11,773,358,3003,2684,419,3491,1588,1380,358,1184,311,1477,279,4911,23725,320,64,11,293,11,27(...TRUNCATED) | [14904,14470,22570,24935,25709,27765,34253,32782,37288,32215,33078,34361,33399,35129,33153,15194,183(...TRUNCATED) | [6658,7397,11558,11569,12238,13397,16384,16384,16384,16384,16384,16384,16384,16384,16384,7162,9011,1(...TRUNCATED) | [[0.9989981055259705],[0.3547396659851074],[0.005686609074473381],[0.9890705347061157],[0.0228579752(...TRUNCATED) | [[0.97265625,0.99609375,1.0,0.98046875,1.0,0.99609375,0.99609375,0.98828125,0.9921875,1.0,0.9921875,(...TRUNCATED) | [[0.99609375,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1(...TRUNCATED) | \frac{9 \sqrt{23}}{23} |
"Let $a, b$, and $c$ be pairwise distinct complex numbers such that\n$$\na^{2}=b+6, \\quad b^{2}=c+6(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Let $a, b$, and $c$ be pairwise distinct complex numbers s(...TRUNCATED) | ["Alright, so I've got this problem here where a, b, and c are distinct complex numbers satisfying t(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | ["-\\sqrt{3}","\\frac{-1 - \\sqrt{17}}{2}","\\frac{5 - 3\\sqrt{17}}{2}",null,null,"\\frac{1 - \\sqrt(...TRUNCATED) | ["hidden_states_sample000003_completion00.npy","hidden_states_sample000003_completion01.npy","hidden(...TRUNCATED) | [151646,151644,10061,400,64,11,293,54876,323,400,66,3,387,92759,12460,6351,5109,1741,429,198,14085,1(...TRUNCATED) | [[71486,11,773,358,3003,2684,419,3491,1588,1380,264,11,293,11,323,272,525,12460,6351,5109,36054,279,(...TRUNCATED) | [21912,24093,26318,36681,31901,15417,22508,36850,34392,33804,35645,32933,40963,38164,33650,31983,326(...TRUNCATED) | [10259,10500,11316,16384,16384,6331,10867,16384,16384,16384,16384,16384,16384,15915,16384,16384,1638(...TRUNCATED) | [[0.42156678438186646],[0.31663963198661804],[0.10776714235544205],[0.000019163753677275963],[0.3439(...TRUNCATED) | [[0.96875,0.9921875,1.0,1.0,0.99609375,0.9140625,0.99609375,0.9921875,0.9921875,0.9921875,0.98828125(...TRUNCATED) | [[0.99609375,0.99609375,1.0,1.0,1.0,0.98828125,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.9960937(...TRUNCATED) | \frac{-1+\sqrt{17}}{2}, \frac{-1-\sqrt{17}}{2} |
"In an $11 \\times 11$ grid of cells, each pair of edge-adjacent cells is connected by a door. Karth(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In an $11 \\times 11$ grid of cells, each pair of edge-adj(...TRUNCATED) | ["Okay, so I have this problem where there's an 11x11 grid of cells, and each pair of edge-adjacent (...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) | ["120","120","222","120","120","120","202","202","224","202","120","120","120","202","120","120","12(...TRUNCATED) | ["hidden_states_sample000004_completion00.npy","hidden_states_sample000004_completion01.npy","hidden(...TRUNCATED) | [151646,151644,641,458,400,16,16,1124,15136,220,16,16,3,5827,315,7761,11,1817,6716,315,6821,12,24739(...TRUNCATED) | [[32313,11,773,358,614,419,3491,1380,1052,594,458,220,16,16,87,16,16,5827,315,7761,11,323,1817,6716,(...TRUNCATED) | [12277,14718,14304,15462,17175,18033,18016,17818,21075,19851,20647,20077,22953,23395,25318,6081,2041(...TRUNCATED) | [3245,3849,3647,4065,4364,4669,4641,4980,5173,5232,5419,5446,6075,6266,7068,1537,5585,6045,2698,3012(...TRUNCATED) | [[0.9593982696533203],[0.9955299496650696],[0.01420617289841175],[0.9959158301353455],[0.99220067262(...TRUNCATED) | [[0.9765625,0.87109375,0.88671875,0.6328125,0.671875,0.91015625,0.96484375,0.9375,0.98046875,0.98828(...TRUNCATED) | [[0.99609375,0.98046875,0.98046875,0.921875,0.93359375,0.98828125,0.99609375,0.98828125,0.99609375,0(...TRUNCATED) | 200 |
"Trapezoid $A B C D$, with $A B \\| C D$, has side lengths $A B=11, B C=8, C D=19$, and $D A=4$. Com(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Trapezoid $A B C D$, with $A B \\| C D$, has side lengths (...TRUNCATED) | ["Alright, so I have this trapezoid ABCD where AB is parallel to CD. The sides are given as AB=11, B(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,0.0,0.0,1.0(...TRUNCATED) | ["9\\sqrt{15}","9\\sqrt{15}","9\\sqrt{15}","9\\sqrt{15}","9\\sqrt{15}","9\\sqrt{15}","9\\sqrt{15}","(...TRUNCATED) | ["hidden_states_sample000005_completion00.npy","hidden_states_sample000005_completion01.npy","hidden(...TRUNCATED) | [151646,151644,51,19842,89,588,400,32,425,356,422,54876,448,400,32,425,97155,356,422,54876,702,3108,(...TRUNCATED) | [[71486,11,773,358,614,419,489,2027,89,588,19360,35,1380,14137,374,15279,311,11078,13,576,11067,525,(...TRUNCATED) | [14714,15695,15323,16791,16501,17788,16582,18458,17537,18187,16948,20584,19495,19508,19976,19623,212(...TRUNCATED) | [6229,6546,6787,6976,7128,7155,7551,7624,7436,7807,7646,8129,7912,8232,8220,8725,8858,9201,9431,9743(...TRUNCATED) | [[0.9953886270523071],[0.9994499087333679],[0.9976176619529724],[0.9995772242546082],[0.999275982379(...TRUNCATED) | [[0.97265625,0.6953125,0.99609375,0.99609375,0.97265625,0.90234375,0.95703125,0.98828125,0.99609375,(...TRUNCATED) | [[0.99609375,0.9609375,1.0,1.0,0.99609375,0.984375,0.99609375,1.0,1.0,1.0,0.99609375,0.98828125,0.99(...TRUNCATED) | 9\sqrt{15} |
"Albert writes $2025$ numbers $a_{1}, \\ldots, a_{2025}$ in a circle on a blackboard. Initially, eac(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Albert writes $2025$ numbers $a_{1}, \\ldots, a_{2025}$ in(...TRUNCATED) | ["Alright, so I have this problem where Albert writes 2025 numbers in a circle. Each number is initi(...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,"1","1280",null,"675","1825","\\frac{675}{67}","1825","1","1","2025","10","1825","1","1825","1(...TRUNCATED) | ["hidden_states_sample000006_completion00.npy","hidden_states_sample000006_completion01.npy","hidden(...TRUNCATED) | [151646,151644,66622,13914,400,17,15,17,20,3,5109,400,64,15159,16,2137,1124,507,2412,11,264,15159,17(...TRUNCATED) | [[71486,11,773,358,614,419,3491,1380,17513,13914,220,17,15,17,20,5109,304,264,12671,13,8886,1372,374(...TRUNCATED) | [58987,61202,58585,56789,23980,30607,30964,23145,34814,41576,50169,53448,50078,33426,37852,58864,550(...TRUNCATED) | [16384,16048,15533,16384,5427,7538,8002,6153,9429,11475,12145,12972,12611,10579,11221,14834,14672,15(...TRUNCATED) | [[0.000037726225855294615],[0.059924229979515076],[0.003976915497332811],[4.5581587073684204e-6],[0.(...TRUNCATED) | [[0.984375,0.99609375,0.8828125,0.953125,0.98046875,0.96875,0.9921875,0.80859375,0.99609375,0.964843(...TRUNCATED) | [[0.99609375,1.0,0.98046875,0.9921875,0.99609375,0.99609375,1.0,0.96484375,1.0,0.99609375,0.98828125(...TRUNCATED) | \frac{2025}{101} |
Compute the sum of the positive divisors (including $1$) of $9!$ that have units digit $1$. | "<｜begin▁of▁sentence｜><｜User｜>Compute the sum of the positive divisors (including $1$) o(...TRUNCATED) | ["Alright, so I have this problem: I need to compute the sum of the positive divisors of 9! that hav(...TRUNCATED) | [1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["103","103","103","22","103","103","103","103","103","103","103","103","103","103","103","103","103(...TRUNCATED) | ["hidden_states_sample000007_completion00.npy","hidden_states_sample000007_completion01.npy","hidden(...TRUNCATED) | [151646,151644,46254,279,2629,315,279,6785,3429,41214,320,16169,400,16,3,8,315,400,24,0,3,429,614,81(...TRUNCATED) | [[71486,11,773,358,614,419,3491,25,358,1184,311,12564,279,2629,315,279,6785,3429,41214,315,220,24,0,(...TRUNCATED) | [7695,7782,7860,8963,8474,8554,9134,8994,9422,9590,10278,9253,11056,11878,11456,11121,12056,13678,13(...TRUNCATED) | [3177,3239,3172,3228,3434,3541,3814,3897,4179,3979,4063,4417,4656,4813,4923,4957,5144,5409,5551,5256(...TRUNCATED) | [[0.018942907452583313],[0.8280827403068542],[0.9397383332252502],[0.04448768123984337],[0.158080160(...TRUNCATED) | [[0.98828125,0.984375,0.99609375,0.97265625,0.9921875,0.9921875,1.0,1.0,0.99609375,0.97265625,0.9257(...TRUNCATED) | [[1.0,0.99609375,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,0.99609375,0.9921875,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 103 |
"Let $A B C D$ be a rectangle with $B C=24$. Point $X$ lies inside the rectangle such that $\\angle (...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Let $A B C D$ be a rectangle with $B C=24$. Point $X$ lies(...TRUNCATED) | ["Okay, so I have this geometry problem here. It involves a rectangle ABCD with BC = 24. There's a p(...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) | ["\\frac{162}{5}","\\frac{154}{5}",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) | [151646,151644,10061,400,32,425,356,422,3,387,264,22756,448,400,33,356,28,17,19,12947,5126,400,55,3,(...TRUNCATED) | [[32313,11,773,358,614,419,17047,3491,1588,13,1084,17601,264,22756,19360,35,448,18040,284,220,17,19,(...TRUNCATED) | [21121,24313,38799,35156,36680,35341,39494,37215,34430,32980,32661,33668,36768,34943,36791,35947,365(...TRUNCATED) | [10134,12193,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,163(...TRUNCATED) | [[0.19427970051765442],[0.014820871874690056],[0.000012009193596895784],[0.000020970670448150486],[0(...TRUNCATED) | [[0.9921875,0.9921875,0.96484375,0.984375,0.99609375,1.0,0.9921875,0.99609375,1.0,1.0,1.0,0.99609375(...TRUNCATED) | [[1.0,1.0,0.99609375,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1(...TRUNCATED) | 14+4\sqrt{37} |
"In a two-dimensional cave with a parallel floor and ceiling, two stalactites of lengths $16$ and $3(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In a two-dimensional cave with a parallel floor and ceilin(...TRUNCATED) | ["Alright, so I came across this geometry problem, and it seemed pretty interesting. Let me try to p(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,1.0(...TRUNCATED) | ["63","63","63","63","63","63","63",null,null,null,null,null,null,null,null,null,null,null,null,null(...TRUNCATED) | ["hidden_states_sample000009_completion00.npy","hidden_states_sample000009_completion01.npy","hidden(...TRUNCATED) | [151646,151644,641,264,1378,32420,25385,448,264,15279,6422,323,22170,11,1378,79476,531,3611,315,2831(...TRUNCATED) | [[71486,11,773,358,3697,3941,419,17047,3491,11,323,432,9324,5020,7040,13,6771,752,1430,311,4715,1526(...TRUNCATED) | [19968,22201,21217,30679,31773,41771,41565,50071,47634,52259,49909,44368,46357,46766,48652,45641,402(...TRUNCATED) | [5796,7040,7808,9665,11683,13811,13715,16384,16384,16384,16384,16384,16384,16384,16384,16384,16384,1(...TRUNCATED) | [[0.9917163252830505],[0.973999559879303],[0.9931065440177917],[0.9225872755050659],[0.5863619446754(...TRUNCATED) | [[0.9765625,0.96875,0.98046875,0.953125,0.765625,0.99609375,0.9765625,0.9609375,0.96484375,0.9921875(...TRUNCATED) | [[0.99609375,0.99609375,0.99609375,0.9921875,0.96484375,1.0,0.99609375,0.9921875,0.9921875,1.0,1.0,1(...TRUNCATED) | 63 |
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