Optimal non-adaptive solutions for the counterfeit coin problem

TL;DR

This paper presents optimal non-adaptive solutions for all variants of the counterfeit coin problem, addressing different knowledge scenarios about the counterfeit coin's weight and existence.

Contribution

It provides a comprehensive set of optimal non-adaptive strategies for various versions of the counterfeit coin problem, covering multiple knowledge assumptions.

Findings

Optimal solutions for all problem variants

Non-adaptive strategies achieve minimal weighings

Addresses multiple knowledge scenarios

Abstract

We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists, (iii) we have access to additional genuine coins, and (iv) we need to determine if the counterfeit coin is heavier or lighter than the genuine ones. Moreover, our solutions are non-adaptive.