IMO 2014 problem 2

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Dodao/la: arhiva
21. rujna 2014.
Let n \geq 2 be an integer. Consider an n \times n chessboard consisting of n^2 unit squares. A configuration of n rooks on this board is peaceful if every row and every column contains exactly one rook. Find the greatest positive integer k such that, for each peaceful configuration of n rooks, there is a k \times k square which does not contain a rook on any of its k^2 unit squares.
Izvor: International Mathematical Olympiad 2014, day 1