What is the maximum number of knights which can be placed on a chess board with none of the knights attacking each other.
32 knights:
All the knights are on black squares, and knights on black squares can only attack white squares.
Proof
Pair up squares as in the following diagram. Paired squares are identified by the same piece.
A knight can only be placed on one of each pair of squares. Since this arrangement can be tiled across the entire chessboard, the knights can take up at most half the chess board: 32 squares.
