METHOD A-1:VARIANTS 2, 3 and 4

A Discussion of Variant 2, 3 and 4

For the 5x5 examples, variant 2 is set up using the same method as variant 1 except that the left diagonal with the group of numbers ½ (n²-n+2) to ½(n²+n) in reverse order (top left corner to the right lower corner) from the numbers listed in the 7x7 complementary table. These numbers in the left diagonal correspond to 12 → 11 → 13 → 15 → 14. Variant 3 is set up in forward zigzag fashion and variant 4 in reverse zigzag fashion, the last two corresponding to 11 → 14 → 13 → 12 → 15 and 12 → 15 → 13 → 11 → 14, respectively. Alternatively, these may be shown as templates in the partial complementary tables where ⤩ points independently into two directions:

It is seen that variants 1,2 or 3,4 are opposite to each other through template inversion. Method A-2 shows the step by step construction. The other diagonal, column and row of the wheel are then added using the templates obtained for the reverse (variant 2), forward zigzag (variant 3) or reverse zigzag (variant 4), followed by filling in of the "non-spoke" numbers. In two of these examples the parity of each row may be either all E or all O, respectively, so that the parity of each column is reversed to either all O or all E, respectively. Parity, however, is conserved since the number of E equals the number of O. Below are the the results of filling up 5x5 squares for variant 2, 3 and 4. Note that for variants 2 and 4 all rows are O, while all columns are E. For variant 3 rows/columns (1 and 5) are E, while rows/columns (2 and 4) are O:

The next page uses variants 2, 3 and 4 to construct 7x7 squares.
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