Fourteen knights are required to attack every square.

Three knights are needed to attack h1, g2, and a8; two more for b1, a2, and b3, and another two for h7, g8, and f7.

Twelve knights are needed to control (attack or occupy) the board.

Each knight can control at most one of the twelve squares a1, b1, b2, h1, g1, g2, a8, b8, b7, h8, g8, g7. This position is unique up to reflection.

References

Martin Gardner,

Mathematical Magic Show.