Abstract
We are given \(c\ge 2\) coins which are otherwise identical, except that there may be exactly (or at most) one fake coin among them which is known to be slightly lighter than the other genuine coins. Using only a two-pan weighing balance, we weigh subsets of coins sequentially in order to identify the counterfeit coin (or declare that all coins are genuine) using the fewest weighings on average. We find a formula for the smallest expected number of weighings, and another formula which determines an optimal number of coins to place on each pan during the first (and hence during each successive) weighing.
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Acknowledgements
The first author thanks the Calcutta University Statistics Department for hosting his visit during which time the research was concluded. The second author thanks the audience who participated in a discussion during his talk on this topic at the Calcutta University Statistics Department’s Platinum Jubilee International Conference on Applications of Statistics.
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Appendix
Appendix
R codes to compute the minimum expected number of weighings, the number of coins to place on each pan during the first weighing, and the number of distinct optimal designs.
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Sarkar, J., Sinha, B.K. (2018). Detecting a Fake Coin of a Known Type. In: Chattopadhyay, A., Chattopadhyay, G. (eds) Statistics and its Applications. PJICAS 2016. Springer Proceedings in Mathematics & Statistics, vol 244. Springer, Singapore. https://doi.org/10.1007/978-981-13-1223-6_15
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DOI: https://doi.org/10.1007/978-981-13-1223-6_15
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