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 Balanced Stellar (Posted on 2007-06-22)
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'.

 See The Solution Submitted by brianjn Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 1/2 separately | Comment 3 of 7 |

If we make pairs across edges of the original cube add up to 25, such as L and V, G and I, and H and U, then the interior vertices will all add up to 75.

But that of course prevents, say, L and J from adding to 25 also, but maybe there's a way to get the apices to add up right another way.

 Posted by Charlie on 2007-06-22 12:30:30

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