The graphic represents the partially exploded net of a stellated cube as viewed in its cubic layout; each face is a right pyramid viewed from above.

As with a problem of similar concept the letters are placeholders for numerals; in this case they are 1 through 24, [A=1].

The apices of the pyramids form 'external' vertices
while those which describe the foundation cube are the 'interior' vertices.

1. What is the global sum of the 6 'external' vertices and then their average?
2. What is the global sum of the 8 'interior' vertices and then their average?
3. How can the faces be labeled to optimise both #1 and #2 simultaneously?

The optimum outcome would be for all vertices to have the value of their type, 'external' and 'internal'.

(In reply to 2 1/2 out of 3. by Charlie)

Yes, those two parts are rather easily reasoned.

For Part 3 I was thinking about the layout of the numbers on a 6 sided die, eg 6 is opposite 1 totalling 7.  That was going to be the thrust of this part but it clearly didn't work.

Posted by brianjn on 2007-06-22 20:06:37