# IMO Problem 1

Discrete Mathematics Level 4

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.

This problem is from the IMO.This problem is part of this set.

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