Strachey method for magic squares

The Strachey method for magic squares is an algorithm for generating magic squares of 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

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)