If replacing each number by its square in a Magic Square produces another Magic Square, the square is said to be a bimagic square. The first bimagic square (shown above) has order 8 with magic constant 260 for addition and 11,180 after squaring. Bimagic squares are also called Doubly Magic Squares, and are 2-Multimagic Squares.

**References**

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.* New York: Dover, p. 212, 1987.

Hunter, J. A. H. and Madachy, J. S. ``Mystic Arrays.'' Ch. 3 in *Mathematical Diversions.* New York: Dover, p. 31, 1975.

Kraitchik, M. ``Multimagic Squares.'' §7.10 in
*Mathematical Recreations.* New York: W. W. Norton, pp. 176-178, 1942.

© 1996-9

1999-05-26