Magic Octahedron

Weekly Problem 20 - 2010
You have already used Magic Squares, now meet a Magic Octahedron...
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Problem



The diagram show the net of a regular octahedron.

Image
Magic Octahedron

In a magic octahedron, the four numbers on the faces that meet at a vertex add up to make the same total for every vertex. If the letters $F, G, H, J$ and $K$ are replaced with the numbers $2$, $4$, $6$, $8$, and some other number, in some order, to make a magic octahedron, what is the value of $G + J$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.