IMO Shortlist 2011 problem C7

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Dodao/la: arhiva
23. lipnja 2013.
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?

Proposed by Ilya Bogdanov and Rustem Zhenodarov, Russia
Izvor: Međunarodna matematička olimpijada, shortlist 2011