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Elbert

BMO 2016/17

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Bobby's booby trapped safe requires a 3-digit code to unlock it.Alex has a probe which can test combinations whithout typing them on the safe. The probe responds Fail if no individual digit is correct.Otherwise it responds to Close, Including when all digits are correct.Fore example, if the correct code is 014, then the responses to 099 and 014 are both Close,but the response to 140 is Fail. If Alex is following an optimal energy, what is the smallest number of attempts needed to guarantee that he knows the correct code, whatever it is?

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