TOPICS
Search

Associative Magic Square


AssociativeMagicSquares4

An n×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. The numbers of associative magic squares of order 1, 2, ... are 1, 0, 1, 48, ... (OEIS A081262).

AssociativeMagicSquare

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). The numbers of associative panmagic squares of order 1, 2, ... are therefore 1, 0, 0, 0, 16, ... (OEIS A081263).


See also

Magic Square, Panmagic Square

Explore with Wolfram|Alpha

References

Gardner, M. "Magic Squares and Cubes." Ch. 17 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 213-225, 1988.Sloane, N. J. A. Sequences A081262 and A081263 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Associative Magic Square

Cite this as:

Weisstein, Eric W. "Associative Magic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AssociativeMagicSquare.html

Subject classifications