### Alternative method of Strachey

With the alternative method of Strachey we make 4 as proportional as possible 3x3 magic squares to construct the 6x6 magic square, and than we swap numbers to get the magic square valid.

To construct the 4 magic 3x3 squares, take the numbers 0 up to 2 as row coordinates and take the numbers 0 up to (3 x 4 -/- 1 = ) 11 as column coordinates.

 1 7 11 19 2 8 10 20 3 5 12 20 4 6 9 19

Construct the 4 magic 3x3 squares.

3x column coordinate    +  1x row coordinate + 1     =     magic 3x3 square

 6 0 10 0 2 1 19 3 32 10 6 0 2 1 0 33 20 1 0 10 6 1 0 2 2 31 21 7 1 9 0 2 1 22 6 29 9 7 1 2 1 0 30 23 4 1 9 7 1 0 2 5 28 24 4 2 11 0 2 1 13 9 35 11 4 2 2 1 0 36 14 7 2 11 4 1 0 2 8 34 15 5 3 8 0 2 1 16 12 26 8 5 3 2 1 0 27 17 10 3 8 5 1 0 2 11 25 18

Put the four 3x3 sub-squares together.

 111 111 111 111 111 111 111 114 111 19 3 32 22 6 29 111 33 20 1 30 23 4 111 2 31 21 5 28 24 111 13 9 35 16 12 26 111 36 14 7 27 17 10 111 8 34 15 11 25 18

Swap 2x2 numbers to get the right magic sum in the main diagonal from top right to bottom left.

 111 111 111 111 111 111 111 111 111 19 3 32 22 6 29 111 30 20 1 33 23 4 111 5 31 21 2 28 24 111 13 9 35 16 12 26 111 36 14 7 27 17 10 111 8 34 15 11 25 18

What is the benefit of the alternative method of Strachey in comparison with the method of Strachey? We have swapped 2x2 instead of 3x2 numbers. For the 6x6 magic square the benefit is not big, but for the larger double odd magic squares the benefit is bigger.

Use the alternative method of Strachey to construct magic squares of order is double odd. See 6x610x1014x1418x1822x2226x26 en 30x30

6x6, alt. method of Strachey.xlsx