Al-Asfizari:   9-Block-Method

This method is derived from the Method of diagonals, where numbers are left in their natural order on diagonals, but all other numbers are replaced by their complement.

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    12679
    810115
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Generally speaking, by marking the diagonals, the square is divided into nine different areas, which are filled identical. This principle is also used in higher orders n = 4k, where you have to enlarge the areas accordingly.

9-Block-Method (double-even)

With this basic principle, the areas from the figure on the left are obtained for a square of order n=8. First you have to create a square in the natural order. As mentioned, the numbers in blocks A, C, E, G and I are kept in their natural order, while the numbers in all other blocks will be replaced by their complements.

9-Block-Method (double-even n=8)