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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)