The Defective Coin Problem: An Algorithmic Analysis

The defective coin problem involves the identification of a defective coin, if any, and ascertaining the nature of the defect (heavier/lighter) from a set of coins containing at the most one defective coin, using an equal‐arm‐pan‐balance. An algorithmic analysis of the problem is considered. The solution strategy to minimise the number of weighings required to detect the defective coin is based on a problem reduction approach involving successive decomposition of the problem into subproblems until it is trivially solved. The algorithm is capable of generating all possible optimal solutions.