## Magic Hexagon

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.

A normal magic hexagon contains the consecutive integers from 1 to 3

*n*² − 3

*n*+ 1, whereas, an abnormal one begins with a number other than one. It turns out that magic hexagons exist only for

*n*= 1 (which is trivial) and

*n*= 3. Moreover, the solution of order 3 is essentially unique.

Although normal magical hexagons with order greater than three do not exist, certain abnormal ones do. As stated above, abnormal means beginning the sequence of numbers with something other than one.

Examples for n = 1, 3, 4, and 5 are presented below.