| While the magic H-hexagon was first discovered in the 19th Century, it
wasn't until very recently that an arrangement of numbers 1 - 24 in the
form of a T-hexagon of side 2 was discovered in which the sum of the
numbers in all rows was the same.
This arrangement was discovered on 13th September, 2003 and as far as
we can ascertain is the first example of a magic T-hexagon. Since then,
working with David King, the existence of these arrangements has been
confirmed, and written up for the Mathematical Gazette. Part of that
article reads:
The number of non-congruent arrangements of the numbers 1 - 24
in a T-hexagon of order 2 is 24! ÷ 12 =
51,704,033,477,769,953,280,000 or some 52 septillion. To attempt to
test which of these forms a magic T-hexagon of order 2 would not be
feasible, thus the program we used to search for solutions was
shortened by use of row sum equations such as:
Much crunching of numbers later, the results found was that the
number of non-congruent magic T-hexagons of order 2 is 59,674,527,
which although a very small fraction of the total number of
arrangements of the numbers 1 - 24, is still a very substantial number
by comparison with say the 880 magic squares of order 4. 59,674,527 is
similar in magnitude to the 275,305,224 non-congruent magic squares of
order 5 which use the numbers 1 - 25.
Most of this site is devoted to giving further information about this
type of magic configuration and in showing that it has many remarkable
properties. Our main focus is on the T-hexagon configurations; for
completeness we have included a few comments on the H-hexagon.
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