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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

108 competition/games/chess/knight.most.p


What is the maximum number of knights that can be put on n x n chessboard
without threatening each other?

competition/games/chess/knight.most.s

n^2/2 for n even >= 4.

Divide the board in parts of 2x4 squares. The squares within
each part are paired as follows:

-----
|A|B|
-----
|C|D|
-----
|B|A|
-----
|D|C|
-----

Clearly, not more than one square per pair can be occupied by a knight.

 

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