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

Strachey'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 Loubère method) complete the individual magic squares of odd order 2*n+1 in subsquares A, B, C, D, first filling up the sub-square A with the numbers 1 to k^2/4, then the sub-square B with the numbers k^2/4 +1 to 2*k^2/4,then the sub-square C with the numbers 2*k^2/4 +1 to 3*k^2/4, then the sub-square 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 sub-square A with the corresponding columns of sub-square D.

92 99 1 8 15 67 74 51 58 65
98 80 7 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 sub-square C with the corresponding columns of sub-square 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 sub-square A with the corresponding cell of sub-square D. Exchange the central cell in sub-square A with the corresponding cell of sub-square 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.

Famous quotes containing the words method, magic and/or squares:

    “Women stand related to beautiful nature around us, and the enamoured youth mixes their form with moon and stars, with woods and waters, and the pomp of summer. They heal us of awkwardness by their words and looks. We observe their intellectual influence on the most serious student. They refine and clear his mind: teach him to put a pleasing method into what is dry and difficult.”
    —Ralph Waldo Emerson (1803–1882)

    “Thou treacherous, base deserter of my flame,
    False to my passion, fatal to my fame,
    Through what mistaken magic dost thou prove
    So true to lewdness, so untrue to love?”
    —John Wilmot, Earl Of Rochester (1647–1680)

    “An afternoon of nurses and rumours;
    The provinces of his body revolted,
    The squares of his mind were empty,
    Silence invaded the suburbs,”
    —W.H. (Wystan Hugh)