Side-tracked from a slightly related problem, I derived this general set of attributes:

{8, 12n, 6n^2, n^2, n}.

The first 5 situations of this generalisation are:

[8, 0, 0, 0, 0],
[8, 12, 6, 1, 1],
[8, 24, 24, 4, 2],
[8, 36, 54, 9, 3],
[8, 48, 96, 16, 4].

What does this set of attributes describe?

(Attributes #1 & #4 may provide clues. Also, take note of the Title.)

8 is the number of vertices, but also refers to something else. Consider the cube as being painted and the name I have given the puzzle.

I believe that I saw the "order 1" example in a book by Martin Gardiner many years ago.

Posted by Brian Nowell on 2003-05-10 17:33:47