problem stringclasses 10
values | answer stringclasses 10
values | init_response stringclasses 10
values | init_reward int64 0 0 | success_rate float64 0 0.95 | progress stringlengths 6 9 | action stringclasses 2
values | prefix stringlengths 0 45.2k | tokenized_conv stringlengths 194 45.5k | responses sequencelengths 16 16 | rewrads sequencelengths 16 16 | mean_reward float64 0 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 3 / 165 | Continue | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["But in the original problem, the sum goes up to a_{2011}, so maybe for each level, the number of t(...TRUNCATED) | [
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"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 3 / 165 | Terminate | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["\n\nTo evaluate the expression:\n\n$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}(...TRUNCATED) | [
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"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 21 / 165 | Continue | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["But this seems complicated. However, maybe there's a way to find that for each k, the sum S(k) is (...TRUNCATED) | [
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"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 21 / 165 | Terminate | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["\n\nTo evaluate the sum\n\n$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \(...TRUNCATED) | [
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] | 0.125 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 47 / 165 | Continue | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["But instead of computing all 3x2x3=18 terms, maybe find a pattern.\n\nAlternatively, use the previ(...TRUNCATED) | [
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] | 0.875 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 47 / 165 | Terminate | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["\n\nTo evaluate the given nested sum:\n\n$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_(...TRUNCATED) | [
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] | 0.0625 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 60 / 165 | Continue | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["Alternatively, maybe we can use the previous results.\n\nWait, for S(3) = 15, which is the sum ove(...TRUNCATED) | [
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1,
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1,
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0,
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] | 0.6875 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 60 / 165 | Terminate | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["\n\nTo evaluate the nested sum:\n\n$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}(...TRUNCATED) | [
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] | 0.1875 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 81 / 165 | Continue | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["Let me think again. If S(k) is the sum over sequences of length k of product, then for each sequen(...TRUNCATED) | [
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1,
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1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
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] | 0.75 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 0 | 0.95 | 81 / 165 | Terminate | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["\n\nTo evaluate the sum\n\n$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \(...TRUNCATED) | [
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] | 0.375 |
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