Magic hexagon

Normal magic hexagons exist only for n = 1 (which is trivial, as it is composed of only 1 cell) and n = 3.

An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887).

Hence their sum is a triangular number, namely There are r = 2n − 1 rows running along any given direction (E-W, NE-SW, or NW-SE).

Although there are no normal magical hexagons with order greater than 3, certain abnormal ones do exist.

It was created by Louis Hoelbling, October 11, 2004: It starts with 21, ends with 111, and its sum is 546.

This magic hexagon of order 7 was discovered using simulated annealing by Arsen Zahray on 22 March 2006: It starts with 2, ends with 128 and its sum is 635.

An order 8 magic hexagon was generated by Louis K. Hoelbling on February 5, 2006: It starts with −84 and ends with 84, and its sum is 0.

An order 9 magic hexagon was found by Klaus Meffert on September 10, 2024 with help of an AI: It starts with -108 and ends with 108, and its sum is 0.

The solution was found by a python program that was created by the author, utilizing an AI for critical parts of the code.

The first was a magic T-hexagon of order 2, discovered by John Baker on 13 September 2003.

Since that time, John has been collaborating with David King, who discovered that there are 59,674,527 non-congruent magic T-hexagons of order 2.