The Knights Dilemma

Discrete Mathematics Level 3

What is the maximum number of knights you can place on a \(8 \times 8\) chessboard such that no two of them attack each other?

Details and assumptions

  • The knights are placed on distinct cells.

  • Two knights attack each other if they are one cell vertically and two cells horizontally apart or two cells vertically and one cell horizontally apart.

  • A \(8 \times 8\) chessboard has \(8^2= 64\) cells.

  • Here's an example of \(2\) knights being placed on a \(3 \times 3\) chessboard which attack each other.

Image credit: Wikipedia

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