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Radcliffe

Historical Background to Magic Hexagons

Until the discovery of magic T-hexagons, there was  only one well-known magic hexagon. A number of websites refer to this configuration - the following is a brief extract from the David King website. This configuration also features in Mathworld.
Apparently a gentleman named Clifford W. Adams started work on this problem in 1910, and only solved it in 1957. He found that there was only one magic hexagon:

If only he'd waited a few more years he could have used a computer....

The same configuration appears on the John Rausch website .. but this time with the following comment

In 1895, William Radcliffe discovered, after much trial and error, that nineteen hexagonal pieces numbered from one to nineteen can be assembled so that each row of three, four or five hexagons adds up to thirty-eight. In 1963, Charles Trigg proved that it is the only magic hexagon of any size!

Somehow one has to feel a bit sorry for Mr Adams! Not that he is the only person to have claimed authorship. The following from Jens Lorenz suggests another source.

I have this from my Highschool teacher, who says it is due to a railroad engineer of the Old Wild West.
For the details of why this hexagon of side 3 is the only one of its shape that can be made magic, see the proof given by David King.
There is another, close cousin of the H-hexagon, which follows a similar honeycomb arrangement hexagons. This example is given on the Magic Configurations site of Harvey Heinz:

In these configurations, the numbers 1 to 30 are arranged so that the corners of each of the nine hexagons (7 black and 2 green) sums to 93. These examples are two of many solutions. Interestingly, only the number 93 is offered as the magic total. But given that numbers in the extreme corners are used only once, while numbers in the centre are used 3 times, it does seem likely that other magic totals are possible.