IMO 2014 - Day 1 Problem 2

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IMO 2014 - Day 1 Problem 2

Unread post by *Mahi* » Wed Aug 20, 2014 8:12 pm

Let $n \ge 2$ 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.
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