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IMO 2014 Problem 2

Let {n \geq 2} be an integer. Consider a {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.

IMO 2014 Problem 2 (Day 1)

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