Method of Strachey

 

Take a 9x9 magic square and construct the second, third and fourth 9x9 magic square by adding (9 x 9 =) 81, (2 x 81 = ) 162 respectively (3 x 81 = ) 243 to all digits of the first 9x9 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.

 

 

37 78 29 70 21 62 13 54 5 199 240 191 232 183 224 175 216 167
6 38 79 30 71 22 63 14 46 168 200 241 192 233 184 225 176 208
47 7 39 80 31 72 23 55 15 209 169 201 242 193 234 185 217 177
16 48 8 40 81 32 64 24 56 178 210 170 202 243 194 226 186 218
57 17 49 9 41 73 33 65 25 219 179 211 171 203 235 195 227 187
26 58 18 50 1 42 74 34 66 188 220 180 212 163 204 236 196 228
67 27 59 10 51 2 43 75 35 229 189 221 172 213 164 205 237 197
36 68 19 60 11 52 3 44 76 198 230 181 222 173 214 165 206 238
77 28 69 20 61 12 53 4 45 239 190 231 182 223 174 215 166 207
280 321 272 313 264 305 256 297 248 118 159 110 151 102 143 94 135 86
249 281 322 273 314 265 306 257 289 87 119 160 111 152 103 144 95 127
290 250 282 323 274 315 266 298 258 128 88 120 161 112 153 104 136 96
259 291 251 283 324 275 307 267 299 97 129 89 121 162 113 145 105 137
300 260 292 252 284 316 276 308 268 138 98 130 90 122 154 114 146 106
269 301 261 293 244 285 317 277 309 107 139 99 131 82 123 155 115 147
310 270 302 253 294 245 286 318 278 148 108 140 91 132 83 124 156 116
279 311 262 303 254 295 246 287 319 117 149 100 141 92 133 84 125 157
320 271 312 263 304 255 296 247 288 158 109 150 101 142 93 134 85 126

 

 

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 9x9 square in the top left corner and the 9x9 square in the bottom left corner in 'quarters' (marked by the blue digits). The ‘quarters’ top left and bottom left of the 9x9 square in the top left corner must be swapped with the ‘quarters’ top left and bottom left of the 9x9 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 (4 – 1 = ) 3 columns must be swapped. See below the result.

 

 

18x18 magic square

280 321 272 313 21 62 13 54 5 199 240 191 232 183 224 94 135 86
249 281 322 273 71 22 63 14 46 168 200 241 192 233 184 144 95 127
290 250 282 323 31 72 23 55 15 209 169 201 242 193 234 104 136 96
259 291 251 283 81 32 64 24 56 178 210 170 202 243 194 145 105 137
57 260 292 252 284 73 33 65 25 219 179 211 171 203 235 114 146 106
269 301 261 293 1 42 74 34 66 188 220 180 212 163 204 155 115 147
310 270 302 253 51 2 43 75 35 229 189 221 172 213 164 124 156 116
279 311 262 303 11 52 3 44 76 198 230 181 222 173 214 84 125 157
320 271 312 263 61 12 53 4 45 239 190 231 182 223 174 134 85 126
37 78 29 70 264 305 256 297 248 118 159 110 151 102 143 175 216 167
6 38 79 30 314 265 306 257 289 87 119 160 111 152 103 225 176 208
47 7 39 80 274 315 266 298 258 128 88 120 161 112 153 185 217 177
16 48 8 40 324 275 307 267 299 97 129 89 121 162 113 226 186 218
300 17 49 9 41 316 276 308 268 138 98 130 90 122 154 195 227 187
26 58 18 50 244 285 317 277 309 107 139 99 131 82 123 236 196 228
67 27 59 10 294 245 286 318 278 148 108 140 91 132 83 205 237 197
36 68 19 60 254 295 246 287 319 117 149 100 141 92 133 165 206 238
77 28 69 20 304 255 296 247 288 158 109 150 101 142 93 215 166 207

 

 

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

 

 

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18x18, Method of Strachey.xls
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