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[{"content":"Define the function \\( f \\) on positive integers such that \n\n\\[ f(1) = 1, \\quad f(...TRUNCATED)
1/8
math
{ "ground_truth": "92", "style": "rule" }
{ "index": 10, "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)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
10
[{"content":"Let $p(x)$ be a polynomial of degree strictly less than $100$ and such that it does(...TRUNCATED)
1/8
math
{ "ground_truth": "200", "style": "rule" }
{ "index": 28, "split": "train" }
[8160,579,264,7047,1817,310,16821,506,279,6093,25,271,16,13,220,2972,2014,53983,279,21397,21085,6470(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
28
[{"content":"If $a+b=1$, find the supremum of $$- \\frac {1}{2a}- \\frac {2}{b}.$$ Let's think step (...TRUNCATED)
3/8
math
{ "ground_truth": "- \\frac {9}{2}", "style": "rule" }
{ "index": 85, "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)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
85
[{"content":"Let $n$ be a positive integer, $n\\geq 2$ . For each $t\\in \\mathbb{R}$ , $t\\neq(...TRUNCATED)
1/8
math
{ "ground_truth": "\\tan(\\frac{nt}{2})=n\\tan(\\frac{}{2})", "style": "rule" }
{ "index": 108, "split": "train" }
[8160,579,264,7047,1817,310,16821,506,279,10741,25,271,16,13,220,2972,2014,53983,279,21397,21085,647(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
108
[{"content":"Given a positive integer \\( n \\) and a sequence of real numbers \\( a_{1}, a_{2}, \\c(...TRUNCATED)
5/8
math
{ "ground_truth": "2n-1", "style": "rule" }
{ "index": 116, "split": "train" }
[8160,579,264,7047,1817,310,16821,506,279,6093,25,271,16,13,220,2972,15771,2598,279,38622,64700,561,(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
116
[{"content":"In Mr. Jacob's class, $12$ of the $20$ students received a 'B' on the latest exam. If t(...TRUNCATED)
5/8
math
{ "ground_truth": "14", "style": "rule" }
{ "index": 151, "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)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
151
[{"content":"Prove that the reciprocal of the real root of the equation \\( x^3 - x + 1 = 0 \\) sati(...TRUNCATED)
4/8
math
{ "ground_truth": "-0.8", "style": "rule" }
{ "index": 178, "split": "train" }
[8160,579,264,7047,1817,310,16821,506,279,6093,25,271,16,13,220,2972,2014,53983,279,5952,64700,198,2(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
178
[{"content":"How many three-digit whole numbers have at least one 7 or at least one 9 as digits? Let(...TRUNCATED)
6/8
math
{ "ground_truth": "452", "style": "rule" }
{ "index": 281, "split": "train" }
[8160,579,264,7047,1817,421,11177,310,279,6093,25,271,16,13,220,2972,15771,2598,279,38622,64700,561,(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
281
[{"content":"The number of scalene triangles having all sides of integral lengths, and perimeter les(...TRUNCATED)
1/8
math
{ "ground_truth": "\\textbf{(C)}\\3", "style": "rule" }
{ "index": 574, "split": "train" }
[760,3377,16561,364,279,1324,314,23255,1885,41036,440,7308,3008,27396,321,264,44798,24660,2599,1056,(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
574
[{"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)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
600
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