IMO 1992 LL JAP41

Origin: JAP

Problem

Let S be a set of positive integers n1, n2, . . . , n6 and let n(f) denote the number n1nf(1) + n2nf(2) + \cdot \cdot \cdot + n6nf(6), where f is a permu- tation of {1, 2, . . ., 6}. Let Ω= {n(f) | f is a permutation of {1, 2, . . ., 6}}. Give an example of positive integers n1, . . . , n6 such that Ωcontains as many elements as possible and determine the number of elements of Ω.