IMO Shortlist 2014 problem C3


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Dodao/la: arhiva
May 7, 2017
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Let n \geq 2 be an integer. Consider an n \times n chessboard divided into n^2 unit squares. We call a configutaion of n rooks on this board happy if every row and every column contains exactly one rook. Find the gretest positive integer k such that for every happy configuration of rooks, we can find a k \times k square without a rook on any of its k^2 unit squares.

(Croatia)

Source: https://www.imo-official.org/problems/IMO2014SL.pdf