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Omni-MATH / Let n≥2 be an integer. Consider an n×n chessboard consisting of n² unit squares. A configuration of n rooks on this board is [i]peaceful[/i] if every row and every column contains …

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problem

Let n≥2n \ge 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 [i]peaceful[/i] 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.
Plain-text mathematical notation (without MathML)
Let n≥2 be an integer. Consider an n×n chessboard consisting of n² unit squares. A configuration of n rooks on this board is [i]peaceful[/i] 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×k square which does not contain a rook on any of its k² unit squares.
Original LaTeX notation
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 [i]peaceful[/i] 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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Source and history

task_id
f3a0ee02-bd6a-5c62-a574-29273f3316a7
task_key
test--f3a0ee02-bd6a-5c62-a574-29273f3316a7
task_revision_id
1
config / split
/ test

Official source

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