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 6x6, 10x10, 14x14, 18x18, 22x22, 26x26 en 30x30