Knights on a chessboard

In chess a knight may move 2 up/down and one sideways, or 2 sideways followed by one up/down. See the following illustration:
chessboard knightmoves

How many knights can you put on a normal 8×8 chessboard so that no knight may take another knight? And can you show that that is the maximum?

This problem was posted at the Dutch mathematics olympiad 1996.

You can check your solution here


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