COINS AND CONES

We discuss the problem of maximizing the number of coins, for which, u sing just n weighings, one can tell whether all of them are of the sam e weight or not, under the condition that the weights of the coins are generic. The first purpose of the paper is to show the connection bet ween this problem and a problem in lattice geometry. Using this approa ch. rye are able to establish an upper bound on the number of coins an d also to disprove the conjecture that the maximal number of reins is 2 '' by giving some quick algorithms for the original problem. We also conjecture that the upper bound is asymptotically tight. (C) 1997 Aca demic Press.