# Elegant solution to the Magic Hexagon problem

## The Magic Hexagon Problem

A magic hexagon of order $$n$$ is an arrangement of close-packed hexagons containing the numbers $$1, 2, ..., H_{n-1}$$, where $$H_n$$ is the $$n^{th}$$ hex number such that the numbers along each straight line add up to the same sum. (Here, the hex numbers are i.e., $$1, 7, 19, 37, 61, 91, 127$$, ...; Sloane's A003215. In the above magic hexagon of order $$n=3$$, each line (those of lengths $$3$$, $$4$$, and $$5$$) adds up to $$38$$.

Here is the programming puzzles entry to the Magic Hexagon problem. As you can see, the solutions there use appropriate systems of linear equations, and then try all the possibilities until it finds one. Boring, but effective; and can't be done by a human in a reasonable amount of time.

This is de la Loubere's method for magic squares. Much cleaner and more beautiful, and a human can do this process easily.

I want to know, is there such a solution / methodology to the Magic Hexagon problem that has the elegance of de la Loubere's method? How would you begin the process of coming up with one?