problem string | answer string | init_response string | init_reward int64 | success_rate float64 | progress string | action string | prefix string | tokenized_conv string | responses sequence | rewrads sequence | mean_reward float64 |
|---|---|---|---|---|---|---|---|---|---|---|---|
"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) | 1 | 0.95 | 3 / 66 | 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 since the upper limit for each a_i is the previous one, the sequence is non-increasing. So for(...TRUNCATED) | [
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1,
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1,
1,
1,
0,
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1,
1
] | 0.8125 |
"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) | 1 | 0.95 | 3 / 66 | 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$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} (...TRUNCATED) | [
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0
] | 0.0625 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 1 | 0.95 | 8 / 66 | Continue | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["But how can I compute this?\n\nAlternatively, maybe there's a generating function approach here. L(...TRUNCATED) | [
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1,
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1,
1,
1,
1,
1
] | 0.75 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 1 | 0.95 | 8 / 66 | Terminate | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["\n\nTo evaluate the given nested sum:\n\n$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_(...TRUNCATED) | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1
] | 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) | 1 | 0.95 | 15 / 66 | 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 I need to think about how to model the sum.\n\nAlternatively, maybe I can find a recurrence re(...TRUNCATED) | [
1,
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0,
1,
1,
1,
1,
1,
1,
0,
1,
1,
1,
1,
1
] | 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) | 1 | 0.95 | 15 / 66 | 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,
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0,
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0
] | 0 |
"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) | 1 | 0.95 | 28 / 66 | 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 the pattern is S(k) = 2^{k+1} - 1. Let me check for k=1, 2, 3.\n\nFor k=1: 2^(...TRUNCATED) | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1
] | 0.9375 |
"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) | 1 | 0.95 | 28 / 66 | 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$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_(...TRUNCATED) | [
0,
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0,
0,
1,
1,
0,
0,
1,
1,
0,
1,
1,
0,
0,
0
] | 0.375 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 1 | 0.95 | 35 / 66 | Continue | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["But if we consider that for each sequence of length k, the product is a_1 * a_2 * ... * a_k. If we(...TRUNCATED) | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | 1 |
"Let\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} =(...TRUNCATED) | 95 | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | 1 | 0.95 | 35 / 66 | Terminate | "<think>\nOkay, so I need to find the value of this big nested sum N, which is a sum over a bunch of(...TRUNCATED) | "<|im_start|>user\nLet\n\\[ N = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots(...TRUNCATED) | ["\n\nTo evaluate the sum:\n\n$$\nN = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} (...TRUNCATED) | [
1,
0,
0,
1,
1,
0,
0,
0,
0,
1,
1,
0,
0,
0,
1,
0
] | 0.375 |
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