We consider the problem of ascertaining the minimum number of weighings which suffice to determine all counterfeit (heavier) coins in a set of n coins of the same appearance, given a balance scale and the information that there are exactly three heavier coins present. A procedure which is either optimal or suboptimal is constructed for infinitely many $n$'s, i.e., for all $n=3^k$ $(k=1,2,3,\dots)$.