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Found problems: 1

2000 Saint Petersburg Mathematical Olympiad, 11.6
Tags: chess , coloring , rook , table , grid , tabels , combinatorics
What is the greatest amount of rooks that can be placed on an $n\times n$ board, such that each rooks beats an even number of rooks? A rook is considered to beat another rook, if they lie on one vertical or one horizontal line and no rooks are between them. [I]Proposed by D. Karpov[/i]