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[{"content":"A repunit is a positive integer, all of whose digits are 1s. Let $a_{1}<a_{2}<a_{3}<\\l(...TRUNCATED)
2/8
math
{ "ground_truth": "1223456", "style": "rule" }
{ "index": 212, "split": "train" }
[8160,369,264,7047,1817,310,11290,279,3377,25,271,16,13,220,2972,15771,2598,279,38622,64700,561,1605(...TRUNCATED)
[[-0.013270623981952667,-1.70208740234375,-0.0009567927336320281,-0.0037005534395575523,-0.001131371(...TRUNCATED)
[[-0.015193680301308632,-1.97847580909729,-0.01906440779566765,-0.004729631822556257,-0.004671374801(...TRUNCATED)
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212
[{"content":"Triangle \\( ABC \\) has incircle \\(\\omega\\) which touches \\(AB\\) at \\(C_1\\), \\(...TRUNCATED)
1/8
math
{ "ground_truth": "\\frac{14}{65}", "style": "rule" }
{ "index": 413, "split": "train" }
[8160,369,264,7047,1817,310,11290,279,3377,25,271,16,13,220,2972,15771,2598,279,37630,321,44959,6470(...TRUNCATED)
[[-0.22918614745140076,-0.9306749105453491,-0.32485076785087585,-0.04450656473636627,-0.153472244739(...TRUNCATED)
[[-0.0016988381976261735,-2.8121697902679443,-0.007829335518181324,-0.03925815969705582,-0.000111335(...TRUNCATED)
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413
[{"content":"Find the number of subsets $\\{a, b, c\\}$ of $\\{1,2,3,4, \\ldots, 20\\}$ such that $a(...TRUNCATED)
6/8
math
{ "ground_truth": "680", "style": "rule" }
{ "index": 543, "split": "train" }
[8160,579,264,7047,1817,421,11177,310,279,6093,25,271,16,13,220,2972,2014,53983,279,21397,64700,198,(...TRUNCATED)
[[-0.006475892383605242,-0.06997035443782806,-0.0004885195521637797,-0.000379132863599807,-0.0001325(...TRUNCATED)
[[-0.001999523490667343,-0.3811701238155365,-0.03749615699052811,-0.01083927508443594,-0.00605711992(...TRUNCATED)
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543
[{"content":"$ABCDEFGH$ is a rectangular prism with $AB=CD=EF=GH=1$, $AD=BC=EH=FG=2$, and $AE=BF=CG=(...TRUNCATED)
1/8
math
{ "ground_truth": "\\frac{3}{\\sqrt{14}}", "style": "rule" }
{ "index": 600, "split": "train" }
[8160,579,264,7047,1817,310,11290,279,3377,25,271,16,13,220,2972,15771,2598,279,38622,64700,561,1605(...TRUNCATED)
[[-6.886300563812256,-7.0353569984436035,-6.153162002563477,-7.047170639038086,-6.858303546905518,-5(...TRUNCATED)
[[-0.02055860124528408,-0.39413172006607056,-0.01437369268387556,-0.0010009760735556483,-0.036233119(...TRUNCATED)
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600
[{"content":"Find the integer $n,$ $-180 \\le n \\le 180,$ such that $\\cos n^\\circ = \\cos 430^\\c(...TRUNCATED)
2/8
math
{ "ground_truth": "-70", "style": "rule" }
{ "index": 642, "split": "train" }
[8160,579,264,7047,1817,421,11177,310,279,6093,25,271,16,13,220,2972,2014,53983,279,5952,64700,198,2(...TRUNCATED)
[[-5.461058139801025,-6.933951377868652,-7.173903465270996,-8.261478424072266,-7.452645301818848,-6.(...TRUNCATED)
[[-2.101271629333496,-3.0815253257751465,-2.3001866340637207,-9.231799125671387,-2.0346548557281494,(...TRUNCATED)
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642
[{"content":"Using systematic sampling, extract a sample of size 12 from a population of 123 individ(...TRUNCATED)
7/8
math
{ "ground_truth": "10", "style": "rule" }
{ "index": 718, "split": "train" }
[8160,579,821,3272,1817,364,24782,279,24102,9581,25,271,16,13,220,2972,2014,53983,279,5952,64700,198(...TRUNCATED)
[[-0.0004353767435532063,-0.003693308448418975,-0.8991453647613525,-0.002608470618724823,-0.00068450(...TRUNCATED)
[[-0.24144373834133148,-0.8419538140296936,-8.382749557495117,-0.6477605700492859,-0.026895707473158(...TRUNCATED)
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718
[{"content":"Let \\( ABC \\) be a triangle in which \\( \\angle ABC = 60^\\circ \\). Let \\( I \\) a(...TRUNCATED)
6/8
math
{ "ground_truth": "30", "style": "rule" }
{ "index": 724, "split": "train" }
[8160,369,264,7047,1817,310,11290,279,3377,25,271,16,13,220,2972,15771,2598,279,38622,64700,561,1605(...TRUNCATED)
[[-0.018927322700619698,-0.5232890248298645,-0.000034689302992774174,-0.004353213589638472,-0.006160(...TRUNCATED)
[[-0.008994420059025288,-2.241007089614868,-0.03194127604365349,-0.005702774040400982,-0.00316369230(...TRUNCATED)
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724
[{"content":"The Princeton University Band plays a setlist of 8 distinct songs, 3 of which are tirin(...TRUNCATED)
7/8
math
{ "ground_truth": "14400", "style": "rule" }
{ "index": 728, "split": "train" }
[8160,579,264,7047,1817,421,11177,310,279,6093,25,271,16,13,220,2972,2014,53983,279,21397,64700,198,(...TRUNCATED)
[[-0.0003311085747554898,-0.004637083038687706,-0.0001399419124936685,-0.00026925752172246575,-0.000(...TRUNCATED)
[[-0.005795935168862343,-0.033248718827962875,-0.009079950861632824,-0.0006086166249588132,-0.008037(...TRUNCATED)
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728
[{"content":"Given points O(0,0) and A(1,1), the slope angle of line OA is $\\boxed{\\text{answer}}$(...TRUNCATED)
2/8
math
{ "ground_truth": "\\frac{\\pi}{4}", "style": "rule" }
{ "index": 763, "split": "train" }
[8160,579,264,7047,1817,421,11177,310,279,6093,25,271,16,13,220,2972,2014,53983,279,5952,64700,198,2(...TRUNCATED)
[[-5.169899940490723,-6.3801469802856445,-4.805199146270752,-6.8858208656311035,-7.0679707527160645,(...TRUNCATED)
[[-0.028196314349770546,-0.0874020978808403,-0.023336872458457947,-0.001936228945851326,-0.101778984(...TRUNCATED)
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763
[{"content":"Given set \\( A = \\{0, 1, 2, 3, 4, 5, 9\\} \\), and \\( a, b \\in A \\) where \\( a \\(...TRUNCATED)
7/8
math
{ "ground_truth": "21", "style": "rule" }
{ "index": 780, "split": "train" }
[8160,579,264,7047,1817,310,11290,279,3377,25,271,16,13,220,2972,15771,2598,279,38622,64700,561,1605(...TRUNCATED)
[[-0.008263090625405312,-0.06198565289378166,-0.00038354191929101944,-0.0002461368858348578,-0.00031(...TRUNCATED)
[[-0.00321122445166111,-0.19046305119991302,-0.06524128466844559,-0.033290114253759384,-0.0165506266(...TRUNCATED)
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780
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