Strachey method for magic squares
The Strachey method for magic squares is an algorithm for generating magic squares of singly even order 4n+2.
Example of magic square of order 6 constructed with the Strachey method:
example 35 1 6 26 19 24 3 32 7 21 23 25 31 9 2 22 27 20 8 28 33 17 10 15 30 5 34 12 14 16 4 36 29 13 18 11
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Strachy's method of construction of singly even magic square of order k=4*n+2 1.Divide the grid into 4 quarters each having k^2/4 cells and name them crosswise thus A C D B 2. Using the Siamese method( De la Loubiere method) complete the individual magic squares of odd order 2*n+1 in subsquares A,B,C,D, first filling up the subsquare A with the numbers 1 to k^2/4, then the subsquare B with the numbers k^2/4 +1 to 2*k^2/4,then the subsquare C with the numbers 2*k^2/4 +1 to 3*k^2/4, then the subsquare D with the numbers 3*k^2/4 +1 to k^2
17 24 1 8 15 67 74 51 58 65 23 5 7 14 16 73 55 57 64 66 4 6 13 20 22 54 56 63 70 72 10 12 19 21 3 60 62 69 71 53 11 18 25 2 9 61 68 75 52 59 92 99 76 83 90 42 49 26 33 40 98 80 82 89 91 48 30 32 39 41 79 81 88 95 97 29 31 38 45 47 85 87 94 96 78 35 37 44 46 28 86 93 100 77 84 36 43 50 27 34
3. Exchange the leftmost n columns in subsquare A with the corresponding columns of subsquare D
'92 '99 1 8 15 67 74 51 58 65
98 807 14 16 73 55 57 64 66
79 81 13 20 22 54 56 63 70 72
85 87 19 21 3 60 62 69 71 53
86 93 25 2 9 61 68 75 52 59
17 24 76 83 90 42 49 26 33 40
23 5 82 89 91 48 30 32 39 41
4 6 88 95 97 29 31 38 45 47
10 12 94 96 78 35 37 44 46 28
11 18 100 77 84 36 43 50 27 34
4. Exchange the rightmost n-1 columns in subsquare C with the corresponding columns of subsquare B
92 99 1 8 15 67 74 51 58 40
98 80 7 14 16 73 55 57 64 41
79 81 13 20 22 54 56 63 70 47
85 87 19 21 3 60 62 69 71 28
86 93 25 2 9 61 68 75 52 34
17 24 76 83 90 42 49 26 33 65
23 5 82 89 91 48 30 32 39 66
4 6 88 95 97 29 31 38 45 72
10 12 94 96 78 35 37 44 46 53
11 18 100 77 84 36 43 50 27 59
5 Exchange the middle cell of the leftmost column of subsquare A with the corresponding cell of subsquare D. Exchange the central cell in subsquare A with the corresponding cell of subsquare D
92 99 1 8 15 67 74 51 58 40
98 80 7 14 16 73 55 57 64 41
4 81 88 20 22 54 56 63 70 47
85 87 19 21 3 60 62 69 71 28
86 93 25 2 9 61 68 75 52 34
17 24 76 83 90 42 49 26 33 65
23 5 82 89 91 48 30 32 39 66
79 6 13 95 97 29 31 38 45 72
10 12 94 96 78 35 37 44 46 53
11 18 100 77 84 36 43 50 27 59
The result is a magic square of order k=4*n+2
From W W Rouse Ball Mathematical Recreations and Essays, (1911)