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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...
70
[ "<think>\nOkay, let's tackle this problem step by step. The question is to find the sum of all integer bases b > 9 for which 17_b is a divisor of 97_b. \n\nFirst, I need to understand what 17_b and 97_b mean in decimal. In base b, the number 17_b is equal to 1*b + 7. Similarly, 97_b is 9*b + 7. So, we need to find ...
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
1
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
588
["<think>\nOkay, let's tackle this problem step by step. First, I need to understand the given infor(...TRUNCATED)
[ 1, 0, 1, 0, 1, 1, 1, 0, 1, 0 ]
0.6
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
16
["<think>\nOkay, let's try to solve this problem step by step. So, we have 9 players, each choosing (...TRUNCATED)
[ 1, 0, 1, 1, 1, 1, 0, 1, 1, 1 ]
0.8
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
117
["<think>\nOkay, let's tackle this problem step by step. The question is to find the number of order(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1 ]
0.9
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
279
["<think>\nOkay, let's tackle this problem step by step. The question is asking for the difference b(...TRUNCATED)
[ 1, 1, 0, 0, 1, 1, 0, 1, 1, 1 ]
0.7
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
504
["<think>\nOkay, let's try to solve this problem step by step. So, we have an isosceles trapezoid wi(...TRUNCATED)
[ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 ]
0.9
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
821
["<think>\nOkay, let's try to solve this problem step by step. \n\nFirst, let me understand the prob(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
0
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
77
["<think>\nOkay, let's try to solve this problem step by step. The question is about finding the sum(...TRUNCATED)
[ 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 ]
0.2
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
62
["<think>\nOkay, let's try to solve this problem step by step. The question is about rotating a para(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
0
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED)
81
["<think>\nOkay, let's try to tackle this problem step by step. So, we have a 3x9 grid filled with n(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
0
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