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:
“I have usually found that there was method in his madness.
Some folk might say there was madness in his method.”
—Sir Arthur Conan Doyle (18591930)
“Has the world ever been changed by anything save the thought and its magic vehicle the Word?”
—Thomas Mann (18751955)
“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 (18851972)