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Magic Octahedron

Stage: 3 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
See all short problems arranged by curriculum topic in the short problems collection

The diagram show the net of a regular 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 $2$, $4$, $6$, $7$ and $8$, 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.

 

 

This problem is taken from the UKMT Mathematical Challenges.