Magic hexagon
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A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M. A normal magic hexagon contains the consecutive integers from 1 to 3n2 − 3n + 1. It turns out that normal magic hexagons exist only for n = 1 (which is trivial, as it is composed of only 1 cell) and n = 3. Moreover, the solution of order 3 is essentially unique.[1] Meng also gave a less intricate constructive proof.[2]
Order n = 1 M = 1 |
Order n = 3 M = 38 |
The order-3 magic hexagon has been published many times as a 'new' discovery. An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887).