The most common adaptation of the magic square is the panmagic square.
This magic square is also referred to as a pandiagonal, diabolic and Nasik
magic square. The term Nasik magic square was coined by Andrew
Hollingworth Frost in 1866 . In this variation of the classic
magic square, not only the diagonals add up to the
magic constant,
but also the diagonals wrapping around the square. Take for example a 5x5
magic square (with numbers 1 through 25 placed from smallest to highest
from left to right(a(1) to a(25))), a panmagic square would have boxes
a(1), a(10), a(14), a(18) and a(22) add up to the squares magic constant.
Panmagic squares do not exist for orders of
4n+2 with n being an
integer. Magic squares of order
4n (4,8,12,16…) cannot
be both panmagic and
associative magic squares. A 5x5 magic square is the smallest square that can be both, having 16
variations for a panmagic square.
