IMO 2011 Shortlist C7
On a square table of 2011 by 2011 cells we place a finite number of napkins that each cover a square of 52 by 52 cells. ...
Category: Combinatorics
Problem
On a square table of 2011 by 2011 cells we place a finite number of napkins that each cover a square of 52 by 52 cells. In each cell we write the number of napkins covering it, and we record the maximal number k of cells that all contain the same nonzero number. Considering all possible napkin configurations, what is the largest value of k?