Proceedings ArticleDOI

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

01 Dec 2014-pp 337-340

TL;DR: This paper has developed a new algorithm for solving two counterfeit coins problem in linear time, where n is the total number of coins given and this is the first algorithm that identifies and solves the problem, given the false coins with type ω(ΔH) = ω (ΔL).

AbstractCounterfeit 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

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Book ChapterDOI

01 Jan 2016
TL;DR: Representing coins as any data items, an algorithm to determine three false coins out of n given coins is introduced and the objective is to solve the problem in minimum number of comparisons with the help of an equal arm balance.
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.

##### References
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Journal ArticleDOI
TL;DR: 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.
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.

35 citations

Proceedings ArticleDOI
Joydeb Ghosh
10 Jun 2011
TL;DR: Algorithms for solving the counterfeit coin problem for any given number n of coins are developed, 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.
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.

4 citations

### "The first algorithm for solving two..." refers background in this paper

• ...In papers [2] and [3], one classical solution for single counterfeiting is available in the fonn of a decision tree that represents a set of all possible conclusions by which we can acquire the desired solution(s) of the problem....

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