Detecting a fake coin of a known type
Springer Proceedings in Mathematics and Statistics
We are given c ≥ 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.
Sarkar, Jyotirmoy and Sinha, Bikas K., "Detecting a fake coin of a known type" (2018). Book Chapters. 20.