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

✍ Scribed by Axel Born; Cor A.J. Hurkens; Gerhard J. Woeginger

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 80 KB
• Volume: 86
• Category: Article
• ISSN: 0020-0190
• DOI: 10.1016/s0020-0190(02)00483-0

✦ Synopsis

In an old weighing puzzle, there are n 3 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 n 3 there exists an optimal weighing scheme that is non-adaptive.