### 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 numbers 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 numbers, 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 numbers). The (yellow marked) ‘quarters’ top left and (red marked) 'quarters' 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 (green marked) blue numbers on the border between the two 'quarters’  from the second cell up to the crossing point must be swapped. Finally the (pink marked) numbers of the top half of the last column(s) must be swapped with the numbers of the bottom half of the last column(s). Because the numbers of the first three columns must be swapped, the numbers 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

ór

1x number from grid with 4x 7x7 magic square

 32 40 48 7 8 16 24 32 40 48 7 8 16 24 38 46 5 13 21 22 30 38 46 5 13 21 22 30 44 3 11 19 27 35 36 44 3 11 19 27 35 36 1 9 17 25 33 41 49 1 9 17 25 33 41 49 14 15 23 31 39 47 6 14 15 23 31 39 47 6 20 28 29 37 45 4 12 20 28 29 37 45 4 12 26 34 42 43 2 10 18 26 34 42 43 2 10 18 32 40 48 7 8 16 24 32 40 48 7 8 16 24 38 46 5 13 21 22 30 38 46 5 13 21 22 30 44 3 11 19 27 35 36 44 3 11 19 27 35 36 1 9 17 25 33 41 49 1 9 17 25 33 41 49 14 15 23 31 39 47 6 14 15 23 31 39 47 6 20 28 29 37 45 4 12 20 28 29 37 45 4 12 26 34 42 43 2 10 18 26 34 42 43 2 10 18

+49x number from grid with numbers 0, 1, 2 and 3

 0 0 0 0 3 3 3 2 2 2 2 2 1 1 0 3 3 3 0 0 0 2 2 2 2 2 1 1 0 3 3 3 0 0 0 2 2 2 2 2 1 1 0 3 3 3 0 0 0 2 2 2 2 2 1 1 0 3 3 3 0 0 0 2 2 2 2 2 1 1 0 3 3 3 0 0 0 2 2 2 2 2 1 1 0 0 0 0 3 3 3 2 2 2 2 2 1 1 3 3 3 3 0 0 0 1 1 1 1 1 2 2 3 0 0 0 3 3 3 1 1 1 1 1 2 2 3 0 0 0 3 3 3 1 1 1 1 1 2 2 3 0 0 0 3 3 3 1 1 1 1 1 2 2 3 0 0 0 3 3 3 1 1 1 1 1 2 2 3 0 0 0 3 3 3 1 1 1 1 1 2 2 3 3 3 3 0 0 0 1 1 1 1 1 2 2

= 14x14 magic square

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

Use the method of Strachey to construct magic squares of order is double odd. See 6x610x1014x1418x1822x2226x26 en 30x30

14x14, Method of Strachey.xls