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In chess, a knight placed on a chess board can move by jumping to an adjacent square in one direction (up, down, left, or right) then jumping to the next two squares in a perpendicular direction. We then say that a square in a chess board can be attacked by a knight if the knight can end up on that square after a move. Thus, depending on where a knight is placed, it can attack as many as eight squares, or maybe even less.
In a

10 \times 10

chess board, what is the maximum number of knights that can be placed such that each square on the board can be attacked by at most one knight?

Problem 5

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