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\begin{figure}\begin{center}\BoxedEPSF{Heterosquare.epsf scaled 800}\end{center}\end{figure}

A heterosquare is an $n\times n$ Array of the integers from 1 to $n^2$ such that the rows, columns, and diagonals have different sums. (By contrast, in a Magic Square, they have the same sum.) There are no heterosquares of order two, but heterosquares of every Odd order exist. They can be constructed by placing consecutive Integers in a Spiral pattern (Fults 1974, Madachy 1979).

An Antimagic Square is a special case of a heterosquare for which the sums of rows, columns, and main diagonals form a Sequence of consecutive integers.

See also Antimagic Square, Magic Square, Talisman Square


Duncan, D. ``Problem 86.'' Math. Mag. 24, 166, 1951.

Fults, J. L. Magic Squares. Chicago, IL: Open Court, 1974.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 101-103, 1979.

mathematica.gif Weisstein, E. W. ``Magic Squares.'' Mathematica notebook MagicSquares.m.

© 1996-9 Eric W. Weisstein