Valuations 4-5: you may modify the coloring if you prefer,
as long as you can still deduce the final result.
(I.e., you can change from a strict to
a nonstrict inequality or vice versa, if that's how things work out for
you. The coloring I gave will definitely work, though.)
Also, Ulrich noted that the odd number can only be equal to 1. True
enough. The reason I said "an odd number" is that
the statement is still true if the square is replaced by an
arbitrary convex polygon.