Question 16
Given an integer $n \ge 2$, colour red exactly $n$ cells of an infinite sheet of grid paper. A rectangular grid array is called *special* if it contains at least two red opposite corner cells; single red cells and 1-row or 1-column grid arrays whose end-cells are both red are special. Given a configuration of exactly $n$ red cells, let $N$ be the largest number of red cells a special rectangular grid array may contain. Determine the least value $N$ may take on over all possible configurations of exactly $n$ red cells.
Based on Mathematical Olympiad Rioplatense, 2010, Level 2
Based on Mathematical Olympiad Rioplatense, 2010, Level 2