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Comb polyominos (Posted on 2023-02-06) Difficulty: 3 of 5
An (m,n) comb is a polyomino composed of a straight 2m-1 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?

No Solution Yet Submitted by Jer    
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observation Comment 1 of 1
A rectangle with 2 squares removed can be made from 2 comb polyominos: an (m,n) and an (m-1,n).  The rectangle will be 2m-1 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 2023-02-07 09:20:41
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