| Strachey Method For Magic Squares |
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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
1.Divide the grid into 4 quarters each having k^2/4 cells and name them crosswise thus A C D B
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 '''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 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
From W W Rouse Ball Mathematical Recreations and Essays, (1911) |
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