Detecting two complementary defectives with a balance scale.

We consider the problem of finding a pair of counterfeit coins from a set of n coins using a balance scale. One counterfeit coin is heavier and the other lighter than a regular coin but the total weight of the two counterfeit coins is the same as the total weight of two regular coins. Let N(w) denote the maximum number of coins w weighings can handle. We give a weighing scheme such that N(2t) >= 3 sup t for t >= 2 and N (2t + 1) >= 5 . 3 sup (t-1) for t >= 1. The N(2t) result meets the information-theoretic bound and hence is the best possible.