If you paint the six sides of a 3x3x3 cube and then slice it into 27 unit cubes, how many will have paint on 0, 1, 2, 3 of their square sides?
Generalize to any dimension:
If you paint the sides of a n dimensional cube with sides length 3 and slice it into 3^{n} unit cubes, how many will have paint on 0, 1, 2, ..., n of their (n1) dimensional sides?
The math certainly checks out.
Just to be clear (for my own sake), the term "paint", as it applies to a ndimensional cube, refers to a covering of n1 dimension, correct? So painting a 4cube implies covering it with some 3dimensional coating that makes it appear completely covered to a 4dimensional observer?

Posted by Bryan
on 20150313 11:30:34 