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 work through this problem step by step. The problem is about finding (...TRUNCATED) | [-0.16015625,-0.166015625,-0.1416015625,-0.1650390625,-0.1728515625,-0.1494140625,-0.173828125,-0.21(...TRUNCATED) | [
8193,
8193,
8193,
8193,
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5817,
7330,
6053,
6321,
6985
] | [
-1312,
-1360,
-1160,
-1352,
-876,
-872,
-1272,
-1312,
-1280,
-1544
] | ["<think>\nOkay, so I have this problem here: In an incomplete space l₁ with an inner product from(...TRUNCATED) | [
-0.4296875
] | [
5545
] | [
-2384
] |
"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, let's try to solve this equation: x² + 615 = 2ⁿ. We need to find all positive in(...TRUNCATED) | [-0.150390625,-0.14453125,-0.12890625,-0.1328125,-0.1220703125,-0.1337890625,-0.1220703125,-0.108398(...TRUNCATED) | [
7138,
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5242,
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4384,
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3421,
4205,
4925,
5617
] | [
-1072,
-1048,
-676,
-860,
-536,
-616,
-418,
-456,
-612,
-580
] | ["<think>\nOkay, so I have this problem: Find all positive integer solutions x, n of the equation x(...TRUNCATED) | [
-0.2412109375
] | [
3271
] | [
-788
] |
"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 solve this problem step by step. The problem is to find the limit as (...TRUNCATED) | [-0.14453125,-0.1953125,-0.1474609375,-0.19140625,-0.177734375,-0.1591796875,-0.1396484375,-0.140625(...TRUNCATED) | [
5231,
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5124,
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3148,
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5344
] | [
-756,
-1584,
-396,
-1504,
-912,
-664,
-440,
-564,
-1440,
-812
] | ["<think>\nOkay, let's try to solve this problem. So we have the matrix A given as:\n\nA = [[1, -x/n(...TRUNCATED) | [
-0.33984375
] | [
3627
] | [
-1232
] |
"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) | [-0.1591796875,-0.1533203125,-0.162109375,-0.193359375,-0.1982421875,-0.1728515625,-0.1962890625,-0.(...TRUNCATED) | [
6161,
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] | [
-976,
-1144,
-972,
-760,
-804,
-1368,
-1336,
-1408,
-1040,
-1272
] | ["<think>\nOkay, so I need to find all polynomials P(x, y) in two variables such that for any x and (...TRUNCATED) | [
-0.337890625
] | [
6650
] | [
-2256
] |
"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, let's see. I need to find the sum of all real numbers that can be represented as re(...TRUNCATED) | [-0.1796875,-0.1630859375,-0.169921875,-0.158203125,-0.1640625,-0.1376953125,-0.1904296875,-0.168945(...TRUNCATED) | [
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6077,
5006
] | [
-800,
-1240,
-1392,
-1024,
-740,
-840,
-1112,
-812,
-1032,
-932
] | ["<think>\nOkay, so I need to solve this problem where I have to find the sum of all elements in the(...TRUNCATED) | [
-0.35546875
] | [
4341
] | [
-1544
] |
"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, let's see. The problem is asking how many edges of a tetrahedron can a plane inters(...TRUNCATED) | [-0.2333984375,-0.22265625,-0.2734375,-0.259765625,-0.2734375,-0.19921875,-0.189453125,-0.1982421875(...TRUNCATED) | [
8193,
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3690,
6902,
8193,
6926,
3949,
5447
] | [
-1912,
-1824,
-1224,
-1696,
-1008,
-1376,
-1552,
-1376,
-944,
-1040
] | ["<think>\nOkay, so I need to figure out how many edges a plane can intersect in a tetrahedron witho(...TRUNCATED) | [
-0.416015625
] | [
5857
] | [
-2448
] |
"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 the absolute difference be(...TRUNCATED) | [-0.134765625,-0.12255859375,-0.0966796875,-0.1259765625,-0.1337890625,-0.1533203125,-0.1376953125,-(...TRUNCATED) | [
5993,
7229,
7198,
7071,
6561,
6807,
7075,
5977,
6201,
6966
] | [
-804,
-888,
-696,
-892,
-880,
-1048,
-976,
-864,
-848,
-1368
] | ["<think>\nOkay, so I need to find the number of ordered pairs (n, k) where the absolute difference (...TRUNCATED) | [
-0.328125
] | [
7900
] | [
-2592
] |
"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) | [-0.07373046875,-0.09619140625,-0.09375,-0.091796875,-0.08154296875,-0.07763671875,-0.09375,-0.08837(...TRUNCATED) | [
1659,
1951,
1632,
1791,
1730,
1610,
1532,
1644,
1626,
1574
] | [
-122.5,
-188,
-153,
-165,
-141,
-124.5,
-143,
-145,
-118,
-126
] | ["<think>\nOkay, let's see. I need to convert the spherical coordinates (ρ, θ, φ) = (12, 7π/6, (...TRUNCATED) | [
-0.1630859375
] | [
1829
] | [
-298
] |
"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, so I need to find the product of all the roots of the polynomial equation P(x) = 0,(...TRUNCATED) | [-0.15234375,-0.142578125,-0.1328125,-0.1220703125,-0.11279296875,-0.11767578125,-0.1240234375,-0.12(...TRUNCATED) | [
3434,
2991,
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2432,
2338,
3163,
2607,
3357,
2521,
2346
] | [
-524,
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-360,
-298,
-264,
-372,
-324,
-412,
-356,
-290
] | ["<think>\nOkay, so I need to find the product of all the roots of the polynomial P(x) = 0 with the (...TRUNCATED) | [
-0.330078125
] | [
2848
] | [
-940
] |
"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) | [-0.1142578125,-0.099609375,-0.13671875,-0.1474609375,-0.1650390625,-0.09814453125,-0.1201171875,-0.(...TRUNCATED) | [
2123,
2326,
2350,
2575,
2351,
2027,
2925,
2457,
1866,
2222
] | [
-243,
-232,
-320,
-380,
-388,
-199,
-352,
-316,
-232,
-244
] | ["<think>\nOkay, let's see. So the problem says that 13 boys and n girls collected a total of n² + (...TRUNCATED) | [
-0.279296875
] | [
2408
] | [
-672
] |
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