The problem of determining how many nonattacking knights can be placed on an chessboard. For , the solution is 32 (illustrated above).
In general, the solutions are
(1)
giving the sequence 1, 4, 5, 8, 13, 18, 25, ... (OEIS A030978,
Dudeney 1970, p. 96; Madachy 1979).
The minimal number of knights needed to occupy or attack every square on an chessboard
(i.e., domination numbers for the knight graphs) are
given for ,
2, ... by 1, 4, 4, 4, 5, 8, 10, 12, 14, ... (OEIS A006075),
with corresponding numbers of such solutions given by 1, 1, 2, 3, 8, 22, 3, ... (OEIS
A006076).