40th Putnam 1979 Problem A1 Find the set of positive integers with sum 1979 and maximum possible product.
Easy For n > 4, 2(n - 2) > n, so the maximum product cannot include any integer greater than 4. Also, 2 3  n x 1. So the maximum product must be made up mainly of 3s, with either no, one or two 2s (or equivalently one 4). Hence for 1979 = 2 + 659·3, the maximum product is 3 659 2. 40th Putnam 1979 © John Scholes jscholes@kalva.demon.co.uk 3 Nov 1999