2018: August

The only non-trivial normal magic hexagon

3:42 pm PHT

If you arrange the natural numbers starting with 1 onto a hexagonal grid such that they fill in a hexagonal-shaped array of hexagons, there is only one non-trivial normal magic hexagon—that is, all of the numbers in every hexagonal row for all three directions sum up to the same number. This unique magic hexagon is shown above and the magic sum is 38. It has been proven in 1963 that this is the only normal magic hexagon (aside from the trivial solution of only 1 hexagon).

There are other “abnormal” magic hexagons of various sizes where the successive numbers don’t start with 1, but the one shown is the only normal one. Magic hexagons have only been studied relatively recently by mathematicians especially when compared with the vastly more popular magic squares which are known since ancient times.

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