
Pairs and pieces
Find all such pairs of positive integers (m,n), for which a rectangle with dimensions of m x n can be built from such pieces created from 6 squares marked as "O" (note that you can both rotate and flip the pieces):
(if it's not clear, it's a Ftype shape)
OK. So we now that we can create a 3x4 rectangle by simply putting together this shape and the one rotated by 180^:
As we can create 3x4, we can also create 4a x 3a for a positive integer a. But what else? I'm kind of clueless...

Re: Pairs and pieces
Hello, GGPaltrow!
Me too . . .
I've tried to find other possible rectangles, but have failed so far.

Re: Pairs and pieces
Hmm.. maybe sth like this:
Suppose we have:
in which the four squares form an edge. Then, let's try to put sth beside it (as putting above leads to a 3x4 rectangle):
This can't be transformed into a rectangle as our "F" can't be put inside it in any way. The same goes with this flipped:
Which is even more wrong as we leave our black F laying and blocked from the "open" side so we can only complete it to a 4x3.
Making any F lie on its "back" beside the black one doesn't make sense cause it leads to completing each of them to a 4x3 which means we eveantully end with 4ax3b.
What about this?

Re: Pairs and pieces
Is this the correct solution? Or it needs other formal handling? Or maybe it's wrong?