How to detect a counterfeit coin: Adaptive versus non-adaptive solutions


Born, Axel and Hurkens, Cor A.J. and Woeginger, Gerhard J. (2003) How to detect a counterfeit coin: Adaptive versus non-adaptive solutions. Information Processing Letters, 86 (3). pp. 137-141. ISSN 0020-0190

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Abstract:In an old weighing puzzle, there are n3 coins that are identical in appearance. All the coins except one have the same weight, and that counterfeit one is a little bit lighter or heavier than the others, though it is not known in which direction. What is the smallest number of weighings needed to identify the counterfeit coin and to determine its type, using balance scales without measuring weights? This question was fully answered in 1946 by Dyson [The Mathematical Gazette 30 (1946) 231–234]. For values of n that are divisible by three, Dyson's scheme is non-adaptive and hence its later weighings do not depend on the outcomes of its earlier weighings. For values of n that are not divisible by three, however, Dyson's scheme is adaptive. In this note, we show that for all values n3 there exists an optimal weighing scheme that is non-adaptive.
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Copyright:© 2003 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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