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« given coins, two or more false coins (the coins are classified as false because their weights are different when compared to a standard coin) are present which have the same appearance as the other coins. This problem belongs to the class of combinatorial group testing problem which finds several applications in hidden graph construction problem etc. In this paper, we have constructed an optimal algorithm to determine two false coins out of a given number of coins. In addition, our objective is to solve the problem in minimum number of comparisons with the help of an equal arm balance. Our proposed algorithm is able to find out the fake coins using O(log n) comparisons.

An algorithm for identifying two unequal heavier / lighter coins out of n given coins

The counterfeit coin problem is well-known and truly interesting in Computer Science, Game theory, and also in Mathematics In this problem the objective is to detect the fake coin(s) of identical appearance but different weight in minimum number of comparisons The word counterfeit most frequently describes forgeries of currency or documents, but can also describe software, pharmaceuticals, clothing, and more recently, motorcycles and cars, especially when these result in patent or trademark infringement Finding one fake coin among n coins is tricky enough and complex The problem becomes rigorous when there are two fake coins, as the false coin pair may form several different combinations that make the problem particularly tricky and complex to solve In this paper we have developed a new algorithm for solving two versions of the two counterfeit coins problem in O(log n) time, where n is the number of coins given

An endeavour to find two unequal false coins

Counterfeit coin problem is of utmost importance and it is truly interesting in Computer Science and Game theory as well as in Mathematics In this problem the objective is to detect the fake coin(s) of identical appearance but of different weight in minimum number of comparisons The word counterfeit is most frequently applicable to forgeries of currency or documents, but can also describe software, pharmaceuticals, clothing, and more recently, motorcycles and other vehicles, especially when these result in patent or trademark infringement In this paper we have developed a new algorithm for solving two counterfeit coins problem in linear time, where n is the total number of coins given However, this is the first algorithm that identifies and solves the problem, given the false coins with type ω(ΔH) = ω(ΔL), ie, one false coin is heavier and another is lighter than a true coin, and their difference in weight from the true coin is equal However, this is the degenerate case in the field of two counterfeit coins problem

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

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.

Anomaly Detection and Three Anomalous Coins Problem

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.

Srijoni Maitra

Papers

A generalized algorithm for solving n coins problem