- Heterosquare
A heterosquare of order "n" is an arrangement of the
integer s 1 to "n"² in a square, such that the rows, columns, and diagonals all sum to different values. There are no heterosquares of order 2, but heterosquares exist for any order "n" ≥ 3.Order 3 Order 4 Order 5 Heterosquares are easily constructed, as shown in the above examples. If "n" is odd, filling the square in a
spiral pattern will produce a heterosquare. And if "n" is even, a heterosquare results from writing the numbers 1 to "n"² in order, then exchanging 1 and 2.It is strongly suspected that there are exactly 3120 essentially different heterosquares of order 3.
An
antimagic square is a special kind of heterosquare where the 2"n" + 2 row, sum and diagonal sums are "consecutive" integers.
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