Strachey   (Variant of Benson and Jacoby)

Benson and Jacoby have modified Strachey's method so that a large number of different magic squares of order n=2m=4k + 2 can be generated. The entire square is divided into four quadrants again.

A C
D B
0 2 m2
3 m2 m2

These quadrants are also filled with the basic numbers 0 , m2 , 2 m2und 3 m2 as before. However, the individual quadrants are no longer considered separately, but the entire upper half with quadrants A and B. To ensure that the basic numbers are equalized, there are two options for the number of occurrences of these numbers in rows, which are listed in the table.

0 m2 2 m2 3 m2
entweder k k + 2 k − 1 k + 1
oder k + 1 k − 1 k + 2 k

In both cases, row sums are the same. However, two other conditions have to be met in order to create a magic square from such an arrangement of base numbers.

If all the numbers in the upper half are chosen in accordance with these conditions, they are mirrored on the horizontal center row, where they are replaced by the numbers which are complementary with respect to 3 m2.

  • 00507550255075500
    50755050750250050
    075250752525752550
    50505007575002550
    075502502525757525
    0000000000
    0000000000
    0000000000
    0000000000
    0000000000
  • 00507550255075500
    50755050750250050
    075250752525752550
    50505007575002550
    075502502525757525
    75025507550500050
    252525750075755025
    75050750505005025
    250252507550757525
    757525025502502575

Finally, only the numbers of a existing magic square of odd order have to be added. In the top two quadrants you take any magic square, while before inserting it in the bottom two quadrants, it has to be mirrored vertically. For example, if you choose the Moschopoulos square of order m=5, these changes from Benson and Jacoby will create the magic square in the figure below.

  • 11247203
    41225816
    17513219
    101811422
    23619215
  • 1124579553367482703
    548775589143725866
    17803821844230884659
    6068511497851813972
    23816927154831947740
    986445290735619265
    35432689221093766447
    925639696755137134
    291250331679621008341
    8699322028614974578