# Make both colors connected

Is it possible to rearrange the 8 rectangles shown below (only translation, no rotation or reflection) so that the red squares form a connected region and the white squares form a connected region? Rectangles cannot overlap and corner-touching does not count as connected. (The black lines show each rectangle is made up of 3 squares; they have 0 width)

Source: some math contest problem (but I forgot which one)

• can red/white polygon squares be corner-touching or do they have to be side-touching? Commented Jul 26 at 0:02
• I said corner-touching does not count as connected. Commented Jul 26 at 0:03

I believe this arrangement qualifies:

• Nice symmetry, rfcrpvnyyl unys fvqr pbaarpgvba, but, white and red 'polygon' do not seem to be 'connected', or, am I misunderstanding? Commented Jul 26 at 2:34
• @FirstNameLastName The white squares form a single connected region. The red squares also form a single connected region. Commented Jul 26 at 2:39
• OK, fair enough, so 'connected' did not imply 'closed', which is what 'polygon' (as opposed to 'region') might suggest. Commented Jul 26 at 2:41
• @FirstNameLastName The border of each coloured region is a polygon. Commented Jul 26 at 7:54
• @FirstNameLastName You mean "convex" or at least "not to concave".
– z100
Commented Jul 26 at 8:04