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.

 

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6x6, alt. method of Strachey.xlsx
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