The torus cutting problem asks for the maximum number of pieces obtained by planar cuts of a solid ring
torus, without moving or rearranging the pieces. For a positive
integer,
the maximum is
The first few terms for ,
2, ... are 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, ... (OEIS A003600).
With no cuts, there is one piece.