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?
A sign somewhere in the United States says that London, England, is 4386 miles away and that Tokyo, Japan, is 6182 miles away.
Where in the U.S. is the sign?
(Consider the earth to be a perfect sphere of radius 3959 miles, and that London is at 51°30’ North, 0°10’ West and Tokyo is at 35°40’ North, 139°45’ East.)