PROBLEM

Cover a chess board by knights (``at'' in Turkish chess terminology). In a covered chess board each square is occupied by a knight or under attack by some knight (or both). Below you see for an arbitrary placed knight the squares under attack (Marked with a black spot).

It is not important whether some knights attack each other. Clearly it is desirable to achieve a covering by using a minimum number of knights. It is known that a standard $8\times 8$ chess board can be covered by 12 knights.