Problem

Source: Moroccan TST 2019 P5

Tags: combinatorics, Grid problem



Let $n$ be a nonzero even integer. We fill up all the cells of an $n\times n$ grid with $+$ and $-$ signs ensuring that the number of $+$ signs equals the number of $-$ signs. Show that there exists two rows with the same number of $+$ signs or two collumns with the same number of $+$ signs.