14

Part of 1988 IMO Shortlist

Problems(1)

Sums obtained by summing the elements of the rows/columns

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

For what values of

n

does there exist an

n \times n

array of entries -1, 0 or 1 such that the

2 \cdot n

sums obtained by summing the elements of the rows and the columns are all different?

linear algebramatrixcombinatoricsExtremal combinatoricsIMO Shortlist