Defective coin problem: an algorithmic analysis

Abstract

The defective coin problem involves identification of defective coin, if any, and ascertain the nature of t defect (heavier/lighter) from a set of coins containing at the most one defective coin, using an equal-ar -balance. The solution strategy to minimise number of weightings required to detect the defective coin is based on problem reduction approach involving successive decomposition of the problem into subproblems until it is trivially solved. One of the two types of subproblems is visualised as combination of pair of antithetic problems, leading to an optimal solution procedures which is simply a term by term merger of corresponding antithetic procedures. Also, the algorithm is capable of generating all possible optimal solutions.