Searching for a counterfeit coin with b-balance

Authors:
Wen An Liu;Huan Huan Cui;Bing Qing Ma
Affiliations:
College of Mathematics and Information Science, Henan Normal University, Xinxiang, People's Republic of China;Department of Mathematics, Luoyang Normal University, Luoyang, People's Republic of China;College of Mathematics and Information Science, Henan Normal University, Xinxiang, People's Republic of China
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

We consider the classical problem of searching for a heavier coin in a set of n coins, n - 1 of which have the same weight. The weighing device is b-balance which is the generalization of two-arms balance. The minimum numbers of weighings are determined exactly for worst-case sequential algorithm, average-case sequential algorithm, worst-case predetermined algorithm, average-case predetermined algorithm.We also investigate the above search model with additional constraint: each weighing is only allowed to use the coins that are still in doubt. We present a worst-case optimal sequential algorithm and an average-case optimal sequential algorithm requiring the minimum numbers of weighings.