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This problem offers students the opportunity to explore numerical relationships algebraically, and use their insights to make generalisations that can then be proved.
Is it always possible to find numbers to go at the vertices given any three numbers on the edges?
Begin by spending some time looking closely at the structure of addition Arithmagons.
For solving the simpler multiplication arithmagons, finding the factors of each number is a useful method. Why is there no analagous method for addition Arithmagons?