Combinatorics · Extremal combinatorics · Chessboard placements · Double counting
Problem 4, 2023
← Prev · 37 / 37 · Next →Let \(n\) be a positive integer. What is the largest number of rooks that can be placed on an \(n \times n\) board so that every rook attacks at most \(3\) of the other rooks?
Attacks are the usual chess ones: a rook attacks another rook if the two stand in the same row or in the same column of the board and no further rook stands between them in that row or column.
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Serbian National Competition (Drzavno takmicenje) 2023, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source