  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.
