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Sums obtained by summing the elements of the rows/columns

Source: IMO ShortList 1988, Problem 14, Hungary 1, Problem 31 of ILL

October 22, 2005
linear algebramatrixcombinatoricsExtremal combinatoricsIMO Shortlist

Problem Statement

For what values of n n does there exist an n×n n \times n array of entries -1, 0 or 1 such that the 2⋅n 2 \cdot n sums obtained by summing the elements of the rows and the columns are all different?
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