What is the smallest number of different colors of tiles needed to form 44 squares so that no tile touches another of the same color along the entire edge

Answer 1

Hi Mar N.,

It seems to me that you have some wiggle room in how you interpret those limits. If "touching along an edge" means tiles must share a non-infinitesimal length of their edges in common, then 44 tiles in a circle, with only their corners tangent, would allow using just 1 color. (assuming the tiles are infinitesimally thin, otherwise twisted so that corners meet only at single points). A "circle" would be nice, but you could go Moebius strip, too!

-- Cheers, -- Mr. d.

Answer 2

form a rectangle 2 x 22...

then you need TWO different colors along the edge of 2