2nd Irish Mathematical Olympiad Problems 1989

A1.  S is a square side 1. The points A, B, C, D lie on the sides of S in that order, and each side of S contains at least one of A, B, C, D. Show that 2 ≤ AB2 + BC2 + CD2 + DA2 ≤ 4. A2.  A sumsquare is a 3 x 3 array of positive integers such that each row, each column and each of the two main diagonals has sum m. Show that m must be a multiple of 3 and

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