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:

    “Unlike Descartes, we own and use our beliefs of the moment, even in the midst of philosophizing, until by what is vaguely called scientific method we change them here and there for the better. Within our own total evolving doctrine, we can judge truth as earnestly and absolutely as can be, subject to correction, but that goes without saying.”
    —Willard Van Orman Quine (b. 1908)

    “The most refined skills of color printing, the intricate techniques of wide-angle photography, provide us pictures of trivia bigger and more real than life. We forget that we see trivia and notice only that the reproduction is so good. Man fulfils his dream and by photographic magic produces a precise image of the Grand Canyon. The result is not that he adores nature or beauty the more. Instead he adores his camera—and himself.”
    —Daniel J. Boorstin (b. 1914)

    “And New York is the most beautiful city in the world? It is not far from it. No urban night is like the night there.... Squares after squares of flame, set up and cut into the aether. Here is our poetry, for we have pulled down the stars to our will.”
    —Ezra Pound (1885–1972)