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 3ⁿ unit cubes, how many will have paint on 0, 1, 2, ..., n of their (n-1) dimensional sides?

(In reply to Thoughts by Bryan)

That's the interpretation I took.  It seems the best interpretation, as for example it wouldn't do in 3 dimensions to consider a 2-dimensional face to have paint on it merely because an adjacent face had paint and they share an edge.

Posted by Charlie on 2015-03-14 07:52:06