IMO Shortlist 2011, Combinatorics 7
Source: IMO Shortlist 2011, Combinatorics 7
July 12, 2012
inequalitiescombinatoricsIMO ShortlistExtremal combinatorics
Problem Statement
On a square table of by cells we place a finite number of napkins that each cover a square of by cells. In each cell we write the number of napkins covering it, and we record the maximal number of cells that all contain the same nonzero number. Considering all possible napkin configurations, what is the largest value of ?Proposed by Ilya Bogdanov and Rustem Zhenodarov, Russia