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

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).

Abstract: 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

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### "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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