The Knights Dilemma

Probability Level 3

What is the maximum number of knights you can place on a 8×88 \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 8×88 \times 8 chessboard has 82=648^2= 64 cells.

  • Here's an example of 22 knights being placed on a 3×33 \times 3 chessboard which attack each other.

Image credit: Wikipedia
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