prompt stringlengths 97 927 | question stringlengths 24 854 | answer stringlengths 1.64k 33.1k | generations listlengths 10 10 | ave_token_logprob listlengths 10 10 | seq_len listlengths 10 10 | seq_logprob listlengths 10 10 | generations_gt listlengths 1 1 | ave_token_logprob_gt listlengths 1 1 | seq_len_gt listlengths 1 1 | seq_logprob_gt listlengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|
"In an incomplete space \\( l_1 \\) with an inner product from the space \\( l_2 \\), find the ortho(...TRUNCATED) | "In an incomplete space \\( l_1 \\) with an inner product from the space \\( l_2 \\), find the ortho(...TRUNCATED) | "<think>\nOkay, so I have this problem here: In an incomplete space l₁ with an inner product from (...TRUNCATED) | ["<think>\nOkay, let me try to figure out this problem. So, the question is about finding the orthog(...TRUNCATED) | [-0.1728515625,-0.2177734375,-0.1953125,-0.216796875,-0.2314453125,-0.1962890625,-0.18359375,-0.2187(...TRUNCATED) | [
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6760,
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8191
] | [
-1416,
-1784,
-1328,
-1488,
-1032,
-1496,
-1192,
-1472,
-1440,
-1856
] | ["<think>\nOkay, so I have this problem here: In an incomplete space l₁ with an inner product from(...TRUNCATED) | [
-0.51953125
] | [
5545
] | [
-2896
] |
"Find all positive integer solutions \\( x, n \\) of the equation \\( x^2 + 615 = 2^n \\).\nPlease t(...TRUNCATED) | Find all positive integer solutions \( x, n \) of the equation \( x^2 + 615 = 2^n \). | "<think>\nOkay, so I have this problem: Find all positive integer solutions x, n of the equation x²(...TRUNCATED) | ["<think>\nOkay, so I need to find all positive integer solutions x and n for the equation x² + 615(...TRUNCATED) | [-0.1435546875,-0.146484375,-0.1083984375,-0.10986328125,-0.1298828125,-0.1484375,-0.1640625,-0.1259(...TRUNCATED) | [
4223,
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] | [
-608,
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-644,
-456,
-900,
-976,
-952,
-452,
-1120
] | ["<think>\nOkay, so I have this problem: Find all positive integer solutions x, n of the equation x(...TRUNCATED) | [
-0.259765625
] | [
3271
] | [
-852
] |
"If \\( A = \\begin{pmatrix} 1 & -\\frac{x}{n} \\\\ \\frac{x}{n} & 1 \\end{pmatrix} \\), then find \(...TRUNCATED) | "If \\( A = \\begin{pmatrix} 1 & -\\frac{x}{n} \\\\ \\frac{x}{n} & 1 \\end{pmatrix} \\), then find \(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem. So we have the matrix A given as:\n\nA = [[1, -x/n](...TRUNCATED) | ["<think>\nOkay, let me try to figure out this problem. So, we have matrix A defined as a 2x2 matrix(...TRUNCATED) | [-0.1904296875,-0.26953125,-0.16796875,-0.2255859375,-0.23046875,-0.25,-0.22265625,-0.173828125,-0.2(...TRUNCATED) | [
8193,
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] | [
-1560,
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-1848,
-1888,
-1440,
-1480,
-1400,
-2008,
-1952
] | ["<think>\nOkay, let's try to solve this problem. So we have the matrix A given as:\n\nA = [[1, -x/n(...TRUNCATED) | [
-0.38671875
] | [
3627
] | [
-1400
] |
"Find all polynomials \\( P(x, y) \\) in two variables such that for any \\( x \\) and \\( y \\), \\(...TRUNCATED) | "Find all polynomials \\( P(x, y) \\) in two variables such that for any \\( x \\) and \\( y \\), \\(...TRUNCATED) | "<think>\nOkay, so I need to find all polynomials P(x, y) in two variables such that for any x and y(...TRUNCATED) | ["<think>\nOkay, so I need to find all polynomials P(x, y) in two variables such that for any x and (...TRUNCATED) | [-0.203125,-0.203125,-0.2099609375,-0.212890625,-0.25390625,-0.259765625,-0.216796875,-0.1943359375,(...TRUNCATED) | [
8149,
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] | [
-1656,
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-1776,
-1064,
-1848,
-1424
] | ["<think>\nOkay, so I need to find all polynomials P(x, y) in two variables such that for any x and (...TRUNCATED) | [
-0.388671875
] | [
6650
] | [
-2592
] |
"Let $\\mathcal{S}$ be the set of real numbers that can be represented as repeating decimals of th(...TRUNCATED) | "Let $\\mathcal{S}$ be the set of real numbers that can be represented as repeating decimals of th(...TRUNCATED) | "<think>\nOkay, so I need to solve this problem where I have to find the sum of all elements in the (...TRUNCATED) | ["<think>\nOkay, so I need to find the sum of all real numbers that can be represented as repeating (...TRUNCATED) | [-0.1591796875,-0.158203125,-0.1767578125,-0.193359375,-0.166015625,-0.2021484375,-0.205078125,-0.16(...TRUNCATED) | [
8193,
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8193,
8193
] | [
-1304,
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-1008,
-1072,
-1432,
-988,
-1392,
-1576,
-1832
] | ["<think>\nOkay, so I need to solve this problem where I have to find the sum of all elements in the(...TRUNCATED) | [
-0.388671875
] | [
4341
] | [
-1688
] |
"How many edges of a tetrahedron can a plane intersect if the plane does not pass through any of the(...TRUNCATED) | "How many edges of a tetrahedron can a plane intersect if the plane does not pass through any of the(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many edges a plane can intersect in a tetrahedron withou(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: \"How many edges of a tetrahedron can a plane intersec(...TRUNCATED) | [-0.302734375,-0.296875,-0.275390625,-0.26171875,-0.32421875,-0.30078125,-0.30859375,-0.28125,-0.304(...TRUNCATED) | [
6090,
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8193,
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8193,
8193,
8193
] | [
-1848,
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-494,
-2144,
-2656,
-2144,
-1536,
-2304,
-2496,
-2608
] | ["<think>\nOkay, so I need to figure out how many edges a plane can intersect in a tetrahedron witho(...TRUNCATED) | [
-0.5
] | [
5857
] | [
-2928
] |
"How many ordered pairs \\( (n, k) \\) are there such that \\( \\left| {n \\choose k} - 18 \\right| (...TRUNCATED) | "How many ordered pairs \\( (n, k) \\) are there such that \\( \\left| {n \\choose k} - 18 \\right| (...TRUNCATED) | "<think>\nOkay, so I need to find the number of ordered pairs (n, k) where the absolute difference b(...TRUNCATED) | ["<think>\nOkay, let's see. I need to find all ordered pairs (n, k) where n and k are positive integ(...TRUNCATED) | [-0.2158203125,-0.1640625,-0.1923828125,-0.2158203125,-0.1103515625,-0.15625,-0.17578125,-0.1796875,(...TRUNCATED) | [
5604,
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4223,
5338,
4791,
5761,
6401,
4418,
8193
] | [
-1208,
-1144,
-1576,
-912,
-588,
-752,
-1012,
-1152,
-672,
-1672
] | ["<think>\nOkay, so I need to find the number of ordered pairs (n, k) where the absolute difference (...TRUNCATED) | [
-0.375
] | [
7900
] | [
-2976
] |
"Convert the point $(\\rho,\\theta,\\phi) = \\left( 12, \\frac{7 \\pi}{6}, \\frac{\\pi}{3} \\right)$(...TRUNCATED) | "Convert the point $(\\rho,\\theta,\\phi) = \\left( 12, \\frac{7 \\pi}{6}, \\frac{\\pi}{3} \\right)$(...TRUNCATED) | "<think>\nOkay, let's see. I need to convert the spherical coordinates (ρ, θ, φ) = (12, 7π/6, π(...TRUNCATED) | ["<think>\nOkay, so I need to convert the spherical coordinates (ρ, θ, φ) = (12, 7π/6, π/3) to (...TRUNCATED) | [-0.23046875,-0.0966796875,-0.16796875,-0.08642578125,-0.1259765625,-0.1279296875,-0.07177734375,-0.(...TRUNCATED) | [
7693,
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1622,
1841,
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2156,
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1801
] | [
-1776,
-152,
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-140,
-231,
-270,
-129,
-280,
-314,
-184
] | ["<think>\nOkay, let's see. I need to convert the spherical coordinates (ρ, θ, φ) = (12, 7π/6, (...TRUNCATED) | [
-0.171875
] | [
1829
] | [
-316
] |
"Let \\( P(x) = 0 \\) be a polynomial equation of the least possible degree with rational coefficien(...TRUNCATED) | "Let \\( P(x) = 0 \\) be a polynomial equation of the least possible degree with rational coefficien(...TRUNCATED) | "<think>\nOkay, so I need to find the product of all the roots of the polynomial P(x) = 0 with the l(...TRUNCATED) | ["<think>\nOkay, let me try to figure out this problem. So, the question is about finding the produc(...TRUNCATED) | [-0.09765625,-0.1904296875,-0.1142578125,-0.123046875,-0.12890625,-0.125,-0.18359375,-0.138671875,-0(...TRUNCATED) | [
3229,
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] | [
-314,
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-304,
-1504,
-322,
-478,
-228
] | ["<think>\nOkay, so I need to find the product of all the roots of the polynomial P(x) = 0 with the (...TRUNCATED) | [
-0.36328125
] | [
2848
] | [
-1040
] |
"The number of seashells collected by 13 boys and \\( n \\) girls is \\( n^2 + 10n - 18 \\). If each(...TRUNCATED) | "The number of seashells collected by 13 boys and \\( n \\) girls is \\( n^2 + 10n - 18 \\). If each(...TRUNCATED) | "<think>\nOkay, let's see. So the problem says that 13 boys and n girls collected a total of n² + 1(...TRUNCATED) | ["<think>\nOkay, let's see. The problem says that 13 boys and n girls collected a total of n² + 10n(...TRUNCATED) | [-0.072265625,-0.1484375,-0.13671875,-0.10498046875,-0.1298828125,-0.13671875,-0.1044921875,-0.18945(...TRUNCATED) | [
1752,
6408,
2248,
1772,
3398,
2205,
1732,
6732,
8192,
2312
] | [
-126.5,
-948,
-308,
-186,
-440,
-300,
-181,
-1272,
-1808,
-348
] | ["<think>\nOkay, let's see. So the problem says that 13 boys and n girls collected a total of n² + (...TRUNCATED) | [
-0.29296875
] | [
2408
] | [
-708
] |
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