The number

to which the numbers in any horizontal, vertical, or

(Hunter and Madachy 1975, Madachy 1979). In a Panmagic Square, in addition to the main diagonals, the broken diagonals also sum to .

For a Magic Cube, the magic constant is

The first few values are 1, 9, 42, 130, 315, 651, 1204, ... (Sloane's A027441).

There is a corresponding multiplicative magic constant for Multiplication Magic Squares.

**References**

Hunter, J. A. H. and Madachy, J. S. ``Mystic Arrays.'' Ch. 3 in *Mathematical Diversions.* New York: Dover,
pp. 23-34, 1975.

Madachy, J. S. *Madachy's Mathematical Recreations.* New York: Dover, p. 86, 1979.

Sloane, N. J. A. Sequences
A027441 and
A006003/M3849
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26