The first algorithm for solving two coins counterfeiting with ω(ΔH) = ω(ΔL)

Anomaly Detection and Three Anomalous Coins Problem

Abstract: Counterfeit coin problem has been considered for a very long time and is a topic of great significance in Mathematics as well as in Computer Science. In this problem, out of n given coins, one or more false coins (the coins are classified as false because of their different weight from a standard coin) are present which have the same appearance as the other coins. The word counterfeit or anomalous means something deviated from the standard one. In this respect, finding out these anomalous objects from a given set of data items is of utmost importance in data learning problem. Thus, representing coins as any data items, we have introduced an algorithm to determine three false coins out of n given coins. In addition, our objective is to solve the problem in minimum number of comparisons with the help of an equal arm balance.

On Various Versions of the Defective Coin Problem.

Abstract: The problem of ascertaining the minimum number of weighings which suffice to determine the defective coin in a set of N coins of the same appearance, given an equal arm balance and the information that there is precisely one defective coin present, is well known. A large number of ingenious solutions exist, some based upon sequential procedures and some not. The problem in the case where there are known to be two or more defective coins is far more complex because we cannot draw any simple definite conclusions at the end of a single test. We shall analyze this in detail in the following paper. The purpose of this paper is to indicate a systematic way in which the theory of dynamic programming can be used to provide a computational solution to the determination of optimal and suboptimal testing policies. We shall illustrate this by means of some numerical results obtained using a digital computer.

A generalized algorithm for solving n coins problem

Abstract: Eight coins problem is a well-known problem in mathematics as well as in computer science. In this problem eight coins are given, say A, B, C, D, E, F, G, and H, and we are told that only one is counterfeit (or false), as it has a different weight than each of the others. We want to determine which coin it is, making use of an equal arm balance. At the same time we want to identify the counterfeit coin using a minimum number of comparisons and determine whether the false coin is heavier or lighter than each of the remaining. In this paper, we develop algorithms for solving the counterfeit coin problem for any given number n of coins. The first algorithm is in essence based on the existing classical solution for the eight coins problem (with slight modification) for larger values of n, where n is a power of two beyond eight, as two and four being base cases. Then we develop an algorithm for solving n coins problem, where n is even but not power of two, i.e., the numbers are six, ten, 12, 14, 18, 20, etc. At the end, we have extended the same to solve the counterfeit coin problem for odd number of coins as well.