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A heterosquare is a square array of consecutive integers whose rowsums, columnsums, and two diagonal sums, are all different. It is named by analogy to magic square.
A heterosquare of size <math>n\times n<math> is said to be of order <math>n<math>.
A heterosquare of any even order may be formed by writing the integers 1 to <math>n^2<math> in order, then transposing the 1 and the 2:
2 1 3 4
5 6 7 8
9 10 11 12
13 14 15 16
(if the 1 and the 2 are not transposed, the two diagonals have the same sum).
It is strongly suspected that there are exactly 3120 essentially different three by three heterosquares.
See also antimagic square.
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