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
TL;DR
This paper introduces the alternator coin, a novel coin type that switches between real and fake states each weighing, and determines the minimum weighings needed to identify it among identical coins.
Contribution
It formally defines the alternator coin problem and provides solutions for the minimum number of weighings required to find the alternator.
Findings
Derived the minimum weighings needed for various N
Established bounds and optimal strategies for identification
Extended classical coin-weighing problems to the alternator case
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 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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Taxonomy
TopicsCellular Automata and Applications · Art History and Market Analysis · Economic theories and models