Group testing to identify one defective and one mediocre item.

We study another instance of the difficult problem of finding an optimal search procedure for two items. In this case one is a defective and the other is a mediocre item. Here a test of a set of items will reveal whether neither of the two items is present, whether the mediocre item is present alone, or whether the defective is present, without revealing in this last case whether the mediocre item is also there. We give a procedure which requires 4/3 log(2)n tests, as opposed to 2 logs(2)n tests for a known procedure and (2 log(3)2) log (2)n =~ 1.26 log (2)n tests associated with an information- theoretic lower bound. It is known whether the proposed procedure is optimal.