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 3nē-3n+1.

Prove that the normal magic hexagon exists only for n=1(trivial) and n=3. http://mathworld.wolfram.com/MagicHexagon.html