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Balanced Stellar (Posted on 2007-06-22) Difficulty: 3 of 5
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: ( You must be logged in to post comments.)
  Subject Author Date
Share timebrianjn2007-11-05 01:29:25
SolutionNot quite perfect.Leming2007-06-29 10:43:35
re: 2 1/2 out of 3.brianjn2007-06-22 20:06:37
re: Almost there, almost therebrianjn2007-06-22 20:02:44
1/2 separatelyCharlie2007-06-22 12:30:30
Some ThoughtsAlmost there, almost thereLeming2007-06-22 11:59:30
2 1/2 out of 3.Charlie2007-06-22 10:09:27
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