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arXiv · 1605.05601

Alternator Coins

Benjamin Chen·Ezra Erives·Leon Fan·Michael Gerovitch·Jonathan Hsu·Tanya Khovanova·Neil Malur·Ashwin Padaki·Nastia Polina·Will Sun·Jacob Tan·Andrew The
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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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Benjamin Chen, Ezra Erives, Leon Fan, Michael Gerovitch, Jonathan Hsu, Tanya Khovanova, Neil Malur, Ashwin Padaki, Nastia Polina, Will Sun, Jacob Tan, Andrew The. 2016-05-17. Alternator Coins. https://arxiv.org/abs/1605.05601

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