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:
“You that do search for every purling spring
Which from the ribs of old Parnassus flows,
And every flower, not sweet perhaps, which grows
Near thereabouts into your poesy wring;
You that do dictionarys method bring
Into your rhymes, running in rattling rows;”
—Sir Philip Sidney (15541586)
“You never see animals going through the absurd and often horrible fooleries of magic and religion.... Dogs do not ritually urinate in the hope of persuading heaven to do the same and send down rain. Asses do not bray a liturgy to cloudless skies. Nor do cats attempt, by abstinence from cats meat, to wheedle the feline spirits into benevolence. Only man behaves with such gratuitous folly. It is the price he has to pay for being intelligent but not, as yet, quite intelligent enough.”
—Aldous Huxley (18941963)
“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)