Can you figure out why 3 knights on a chess board can't mutually attack one another?

Asked by LostInParadise (32216

) July 7th, 2010

I recently read a paper that gave a somewhat complicated proof of this. If you look at it the right way, it is really fairly easy to show. If you place 3 knights on a chess board, it is not possible for 1 and 2, 2 and 3 and 1 and 3 to all be positioned so as to be able to capture one another. Can you show why?

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3 Answers

Knights move to the opposite-colored square. Knight A on a white square can attack knight B on a black square, while knight B can attack knight C on a white square, but knights A and C are on the same-colored squares, so cannot attack each other.

frdelrosario (4278

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Exactly!

LostInParadise (32216

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Ditto! The argument is based on “parity”. By similar reasoning you cannot cover a chessboard using dominoes if opposite corner squares have been cut out.

gasman (11345

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