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.

Digital Microfluidic Biochips (DMFB) is revolutionizing many areas of Microelectronics, Biochemistry, and Biomedical sciences. It is also known as 'Lab-on-a-Chip' for its popularity as an alternative for laboratory experiments. Pin count reduction and cross contamination avoidance are some of the core design issues for practical applications. Nowadays, due to emergency and cost effectiveness, more than one assay operations are required to be performed simultaneously. So, parallelism is a necessity in DMFB. Having an area of a given chip as a constraint, how efficiently we can use a restricted sized biochip and how much parallelism can be incorporated are the objectives of this paper. The paper presents a design automation flow that augments parallelism in applications considering cross contamination problem as well.

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Digital micJ'ofluidic biochips are J'estJ'ucturing many aJ'eas of Biochemistry, Biomedical sciences, and Microelectronics, It is also known as 'Lab-on-a-Chip' for its recognition as a substitute for labomtOl"y experiments. Tn J'ecent times, due to emeJ'gency and cost efficacy, more than one assay operations are required to be performed at the same time. So, parallelism is a must in designing biochips. Having an area of a given chip as a constmint, how efficiently we can use a J'estl"icted sized chip and how much parallelism can be built-in are the objectives of this paper, A specific application of an assay may characterize a sample where, say only one type of reagent and multiple samples have been considered, or vice versa, and identify some parameter(s) of the sample(s) under requirement in parallel. In our experimentation, we essentially do this task in pamllel fOl' five such sets of subJ'egions of a given J'estl"icted sized chip in digital microfluidics using an army based partitioning pin assignment technique, where cross contamination problem has also been considered, and efficiency of proper taxonomy of a given sample has also been improved.

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