Coins and Cones

We discuss the problem of maximizing the number of coins, for which, using justnweighings, one can tell whether all of them are of the same 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 between this problem and a problem in lattice geometry. Using this approach, we are able to establish an upper bound on the number of coins and also to disprove the conjecture that the maximal number of coins is 2nby giving some quick algorithms for the original problem. We also conjecture that the upper bound is asymptotically tight.