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Alternator Coins

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arxiv 1605.05601 v1 pith:GAHPA6IL submitted 2016-05-17 math.CO math.HO

Benjamin Chen , Ezra Erives , Leon Fan , Michael Gerovitch , Jonathan Hsu , Tanya Khovanova , Neil Malur , Ashwin Padaki
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Nastia Polina Will Sun Jacob Tan Andrew The
This is my paper · ORCID
classification math.COmath.HO
keywords alternatorrealcoincoinsbalanceeitherfakefind
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We introduce a new type of coin: \textit{the alternator}. The alternator can pretend to be either a real or a fake coin (which is lighter than a real one). Each time it is put on a balance scale it switches between pretending to be either a real coin or a fake one. In this paper, we solve the following problem: You are given $N$ coins that look identical, but one of them is the alternator. All real coins weigh the same. You have a balance scale which you can use to find the alternator. What is the smallest number of weighings that guarantees that you will find the alternator?

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