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# GENERATOR (PROBLEM SOLVER) Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include: 1. A specific question or problem to solve 2. A cheatsheet containing relevant strate...
[ "<think>\nOkay, let's try to solve this problem step by step. The question is asking for the sum of all integer bases b > 9 for which the number 17_b (which is 17 in base b) divides 97_b (which is 97 in base b). \n\nFirst, I need to understand what the problem is really asking. In base b, the number 17_b represents...
70
[ true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true ]
1
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's tackle this problem step by step. First, I need to understand the given infor(...TRUNCATED)
588
[ true, true, false, true, true, true, true, true, false, false, true, true, true, true, true, true ]
0.8125
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to solve this problem step by step. \n\nFirst, let me understand the prob(...TRUNCATED)
16
[ true, true, true, true, true, true, true, true, true, true, true, true, true, true, true, true ]
1
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to solve this problem step by step. The question is asking for the number(...TRUNCATED)
117
[ true, true, true, false, true, true, true, true, false, true, false, true, true, true, true, true ]
0.8125
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to solve this problem step by step. The question is about finding the num(...TRUNCATED)
279
[ true, false, false, true, true, false, false, false, false, true, true, false, true, false, true, true ]
0.5
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to solve this problem step by step. So, we have an isosceles trapezoid wi(...TRUNCATED)
504
[ true, true, true, true, true, true, true, true, true, true, true, true, true, true, false, true ]
0.9375
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to solve this probability problem. So, we have twelve letters: A, B, C, D(...TRUNCATED)
821
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
0
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to solve this problem step by step. The problem involves finding the sum (...TRUNCATED)
77
[ false, false, false, false, false, false, false, true, false, false, false, false, true, false, true, true ]
0.25
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to solve this problem step by step. The question is about rotating a para(...TRUNCATED)
62
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
0
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
["<think>\nOkay, let's try to tackle this problem step by step. The question is about counting the n(...TRUNCATED)
81
[ false, false, false, false, false, true, false, false, false, false, false, false, false, false, false, false ]
0.0625
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