IMO Problem 1

Probability Level 4

Let n2n \geq 2 be an integer. Consider an n×nn \times n chessboard consisting of n2n^2 unit squares. A configuration of nn rooks on this board is peaceful if every row and every column contains exactly one rook. Find the greatest positive integer kk such that, for each peaceful configuration of nn rooks, there is a k×kk \times k square which does not contain a rook on any of its k2k^2 unit squares.

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

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