Associative Magic Square

An $n\times n$ Magic Square for which every pair of numbers symmetrically opposite the center sum to $n^2+1$. The Lo Shu is associative but not Panmagic. Order four squares can be Panmagic or associative, but not both. Order five squares are the smallest which can be both associative and Panmagic, and 16 distinct associative Panmagic Squares exist, one of which is illustrated above (Gardner 1988).

See also Magic Square, Panmagic Square

References

Gardner, M. ``Magic Squares and Cubes.'' Ch. 17 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, 1988.