Medjig method

 

The first grid is a 2x2 'blown up' pure 9x9 magic square. Construct the second grid using 81 Medjig tiles.

 
In a (2x2) medjig tile are all the digits from 0 up to 3, but each time in a different order. Take care that the sum of the digits in each row/column/diagonal is (18 x 1,5 =) 27.

Take 1x digit from first grid and add 81x digit from the same cell of the second grid.

 

 

1x digit from grid with 2x2 'blown up' 9x9 magic square 

77 77 58 58 39 39 20 20 1 1 72 72 53 53 34 34 15 15
77 77 58 58 39 39 20 20 1 1 72 72 53 53 34 34 15 15
6 6 68 68 49 49 30 30 11 11 73 73 63 63 44 44 25 25
6 6 68 68 49 49 30 30 11 11 73 73 63 63 44 44 25 25
16 16 78 78 59 59 40 40 21 21 2 2 64 64 54 54 35 35
16 16 78 78 59 59 40 40 21 21 2 2 64 64 54 54 35 35
26 26 7 7 69 69 50 50 31 31 12 12 74 74 55 55 45 45
26 26 7 7 69 69 50 50 31 31 12 12 74 74 55 55 45 45
36 36 17 17 79 79 60 60 41 41 22 22 3 3 65 65 46 46
36 36 17 17 79 79 60 60 41 41 22 22 3 3 65 65 46 46
37 37 27 27 8 8 70 70 51 51 32 32 13 13 75 75 56 56
37 37 27 27 8 8 70 70 51 51 32 32 13 13 75 75 56 56
47 47 28 28 18 18 80 80 61 61 42 42 23 23 4 4 66 66
47 47 28 28 18 18 80 80 61 61 42 42 23 23 4 4 66 66
57 57 38 38 19 19 9 9 71 71 52 52 33 33 14 14 76 76
57 57 38 38 19 19 9 9 71 71 52 52 33 33 14 14 76 76
67 67 48 48 29 29 10 10 81 81 62 62 43 43 24 24 5 5
67 67 48 48 29 29 10 10 81 81 62 62 43 43 24 24 5 5

 

 

+ 81x digit from grid with 81 Medjig tiles

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

 

 

= 18x18 magic square

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

 

 

Use this method to construct 'double odd' magic squares (= 6x6, 10x10, 14x14, 18x18, … magic square), although you can use this method to construct 'double even' magic squares (= 8x8, 12x12, 16x16, 20x20, ... magic square) as well.

 

 

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18x18, Medjig method.xls
Microsoft Excel werkblad 51.0 KB