IMO 1992 LL ITA39

Origin: ITA

Problem

Let n \geq2 be an integer. Find the minimum k for which there exists a partition of {1, 2, . . ., k} into n subsets X1, X2, . . . , Xn such that the following condition holds: for any i, j, 1 \leqi < j \leqn, there exist x1 \inX1, x2 \inX2 such that |xi −xj| = 1.