An Advanced Approach to Solve two Counterfeit Coins Problem

Though the counterfeit coin problem is well known as a fascinating puzzle it claims great importance in Computer science, Game theory, and Mathematics. In terms of the puzzle the objective is to detect the counterfeit coins which are identical in appearance but different in weight. The word counterfeit not only describes forgeries of currency or documents, but can also be applied to software, pharmaceuticals, clothing, and more recently, motorcycles and cars, especially when these result in patent or trademark infringement. Furthermore, the goal in this problem is to minimize the number of weighing, i.e., the number of comparisons required to find the false coin/s and their type (whether heavier or lighter than the original coin). Finding one counterfeit coin among n coins is complex and tricky enough. The problem gets more complicated when the set of n coins contains two false coins as the false coins pair may appear in several different combinations. In this paper, we have developed a new algorithm for solving two counterfeit coin problem in O(logn) time, where n is the total number of coins.