Detecting the two complementary defectives with a balance scale

Abstract

We consider the problem of finding a pair of irregular boxes from a set of n boxes using a balance scale. One irregular box is heavier and the other lighter than a regular box but the total weight of the two irregular boxes is the same as the total weight of two regular boxes. Let N(w) denote the maximum number of boxes w weighings can handle. We give a weighing scheme such that N(2t) ≥3t for t ≥2 and N(2t + 1) ≥ 5.3t-1 for t ≥ 1. The N(2t) result meets the information-theoretic bound and hence is the best possible.