Talisman Magic Squares

A talisman square is a magic square that has the special additional requirement that the difference between horizontal, vertical and diagonal (no wrapping around) numbers is equal to or greater than a value k ((n,k)-talisman square). Talisman squares can exist for any order of n and the classic Lo Shu magic square is also a (3,1)-talisman square. A talisman hexagon also exists and functions in the same way as a talisman square; all neighbouring numbers must have a difference greater or equal to a value k, for example this (3,4)-talisman hexagon (picture right).