Alternator Coins
  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? 
Benjamin Chen, Ezra Erives, Leon Fan, Michael Gerovitch, Jonathan Hsu,   Tanya Khovanova, Neil Malur, Ashwin Padaki, Nastia ...
math.CO math.HO