A square which is simultaneously a Magic Square and Multiplication Magic Square. The three squares shown above (the top square has order eight and the bottom two have order nine) have addition Magic Constants (840, 848, 1200) and multiplicative magic constants (2,058,068,231,856,000; 5,804,807,833,440,000; 1,619,541,385,529,760,000), respectively (Hunter and Madachy 1975, Madachy 1979).

References

Hunter, J. A. H. and Madachy, J. S. Mystic Arrays.'' Ch. 3 in Mathematical Diversions. New York: Dover, pp. 30-31, 1975.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 89-91, 1979.