There’s just one regular magic hexagon — just one hexagonal association of cells just like the one proven right here that may be full of the consecutive integers 1 to n such that each row, in all three instructions, sums to the identical whole. (This excludes the trivial instance of a single cell by itself, in addition to rotations and reflections of the hexagon proven right here.)
Amazingly, it seems that this lonely instance might not have been found till 1888! In a 1988 letter to the Mathematical Gazette, Martin Gardner reported that the magic hexagon was given as an issue within the German journal Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht (Quantity 19, web page 429) in 1888. The proposer was recognized solely as von Haselberg, of Stralsund; his resolution was printed within the subsequent quantity.
Gardner writes, “The construction might simply have been found by mathematicians in historic occasions, however as of now, that is the earliest identified publication.”
(Martin Gardner, “The Historical past of the Magic Hexagon,” Mathematical Gazette 72:460 [June 1988], 133.)