\AE quitas: Two-Player Counterfeit Coin Games

TL;DR

This paper analyzes two-player games involving identifying a counterfeit coin through strategic weighings, providing solutions for various game configurations and characterizing winning strategies.

Contribution

It introduces a comprehensive analysis of counterfeit coin games, including winning positions and Grundy numbers for different game variants.

Findings

Characterization of winning positions for various game setups

Calculation of Grundy numbers for different game variants

Strategies for optimal play in counterfeit coin games

Abstract

We discuss games involving a counterfeit coin. Given one counterfeit coin among a number of otherwise identical coins, two players with full knowledge of the fake coin take turns weighing coins on a two-pan scale, under the condition that on every turn they reveal some information to an Observer with limited prior knowledge about the coins. We study several games depending on the types of the counterfeit coin, the end-game condition, and the availability of extra genuine coins. We present the winning positions and the Grundy numbers for these games.