You are given 100 gold coins and told that one of them is counterfeit. In order to detect the counterfeit one, you decide to get support of an expert goldsmith. You will group the coins as you wish and ask whether the counterfeit coin is in that group or not. For every "yes" answer you will pay 3 $, and for every "no" answer you will pay 2 $.
What is the minimum amount you have to pay to guarantee that you find the counterfeit coin?
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