The knights problem asks for the maximum number of nonattacking knights that can be placed on an chessboard, where is a positive
integer. 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, up to rotations
and reflections of the board, given by 1, 1, 2, 3,
8, 23, 3, ... (OEIS A006076).
of nonattacking knights that can be placed on an 
chessboard, where 
is a positive
integer. For 
,
the solution is 32 (illustrated above). In general, the solutions are
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, up to rotations
and reflections of the board, given by 1, 1, 2, 3,
8, 23, 3, ... (OEIS A006076).
