Prove that the central cell (the number in the middle cell) of any 3x3 magic square is always one-third the magic constant (the sum of any side, either 2 major diagonals, or either center row in the magic square).
Show that in any larger square (n x n), the central cell does not need to be 1/n the magic constant.

I am assuming that only odd order squares need to be considered since there is no center cell in an even order square.

For every odd n>=5, there is a magic square of order n which is pandiagonal.  Pandiagonal squares have the property that every diagonal (wrap around) sums up to the magic sum.  The rows and columns of a pandiagonal square can be cycled to bring any entry to the center.

Posted by Brian Smith on 2004-04-16 14:09:32