Search for Three Forged Coins

Suppose we are given a set of t coins which look identical, but a known number s of them are counterfeit, with a known weight different from the others. Our problem is to locate the counterfeits by weighing subsets of the t coins, with as few weighings as possible. Despite a large literature on this problem, it remains wide open for s>2. In this paper, we give an efficient sequential weighing algorithm for the case s=3, with an average of 1.75 weighings per bit of t, as t approaches infinity. (It is known that any algorithm must have more than 1.5 weighings per bit.) We use our algorithm to give an efficient channel coding for the three-sender multiple-access adder channel with feedback.