An (m,n) comb is a polyomino composed of a straight 2m1 row of unit squares with m 'teeth' of length n. For example here's a (3,4) comb:
XXXXX
X
XXXXX
X
XXXXX
m must be at least 2 and n must be at least 1.
Can any set of various combs tile a rectangle? Provide an example or prove impossible.
How about a rectangle with one square removed?
A rectangle with 2 squares removed can be made from 2 comb polyominos: an (m,n) and an (m1,n). The rectangle will be 2m1 by n+2 but with 2 corner squares missing. (m>=3)
I suspect tiling a rectangle with comb polyominos cannot be done, but I do not have a proof.

Posted by Larry
on 20230207 09:20:41 