doubly magic square

If replacing each number by its square in a magic square produces another magic square, the square is said to be a bimagic square. Bimagic squares are also called doubly magic squares, and are 2-multimagic squares. Lucas and later Hendricks showed that a bimagic square of order 3 is impossible for any set of numbers except the trivial case of using the same number 9 times. The first known bimagic square, constructed by Pfeffermann (1891a; left figure), had order 8 with magic constant 260 for the base square and 11180 after squaring. Another order 8 bimagic square is shown at right.

bimagic cube | magic square | multimagic square | panmagic square | trimagic square