Method of Strachey

 

Take a 7x7 magic square and construct the second, third and fourth 7x7 magic square by adding (7 x 7 =) 49, (2 x 49 = ) 98 respectively (3 x 49 = ) 147 to all digits of the first 7x7 magic square. Put the first square in the top left corner, put the second square in the bottom right corner, put the third square in the top right corner and put the fourth square in the bottom left corner.

 

 

46 31 16 1 42 27 12 144 129 114 99 140 125 110
5 39 24 9 43 35 20 103 137 122 107 141 133 118
13 47 32 17 2 36 28 111 145 130 115 100 134 126
21 6 40 25 10 44 29 119 104 138 123 108 142 127
22 14 48 33 18 3 37 120 112 146 131 116 101 135
30 15 7 41 26 11 45 128 113 105 139 124 109 143
38 23 8 49 34 19 4 136 121 106 147 132 117 102
193 178 163 148 189 174 159 95 80 65 50 91 76 61
152 186 171 156 190 182 167 54 88 73 58 92 84 69
160 194 179 164 149 183 175 62 96 81 66 51 85 77
168 153 187 172 157 191 176 70 55 89 74 59 93 78
169 161 195 180 165 150 184 71 63 97 82 67 52 86
177 162 154 188 173 158 192 79 64 56 90 75 60 94
185 170 155 196 181 166 151 87 72 57 98 83 68 53

 

 

The columns and the diagonals give already the magic sum. To get the right sum in the rows, you must swap digits, as follows. We split the 7x7 square in the top left corner and the 7x7 square in the bottom left corner in 'quarters' (marked by the blue digits). The ‘quarters’ top left and bottom left of the 7x7 square in the top left corner must be swapped with the ‘quarters’ top left and bottom left of the 7x7 square in the bottom left corner. Also the (blue) digits on the border between the two 'quarters’  from the second cell up to the crossing point must be swapped. Finally the digits of the top half of the last column(s) must be swapped with the digits of the bottom half of the last column(s). Because the digits of the first two columns must be swapped, the digits of the last (3 – 1 = ) 2 columns must be swapped. See below the result.

 

 

14x14 magic square

193 178 163 1 42 27 12 144 129 114 99 140 76 61
152 186 171 9 43 35 20 103 137 122 107 141 84 69
160 194 179 17 2 36 28 111 145 130 115 100 85 77
21 153 187 172 10 44 29 119 104 138 123 108 93 78
169 161 195 33 18 3 37 120 112 146 131 116 52 86
177 162 154 41 26 11 45 128 113 105 139 124 60 94
185 170 155 49 34 19 4 136 121 106 147 132 68 53
46 31 16 148 189 174 159 95 80 65 50 91 125 110
5 39 24 156 190 182 167 54 88 73 58 92 133 118
13 47 32 164 149 183 175 62 96 81 66 51 134 126
168 6 40 25 157 191 176 70 55 89 74 59 142 127
22 14 48 180 165 150 184 71 63 97 82 67 101 135
30 15 7 188 173 158 192 79 64 56 90 75 109 143
38 23 8 196 181 166 151 87 72 57 98 83 117 102

 

 

Use this method to construct double odd ( 6x6, 10x10, 14x14, 18x18, ...) magic squares.

 

 

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14x14, Method of Strachey.xls
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