For explanation of the Medjig method, see 6x6 magic square.
Use as first grid 10x10 medjig tiles and us second grid the '2x2 blown up' version of a 10x10 magic square to construct a (simple) 20x20 magic square.
Take a number from a cell of the first grid +1 and add (number -/- 1) x 4 from the same cell of the second grid.
1x number +1
0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 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 | 1 | 2 |
3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 |
2 | 1 | 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 | 0 | 3 |
1 | 2 | 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 | 3 | 0 |
2 | 1 | 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 | 0 | 3 |
1 | 2 | 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 | 3 | 0 |
2 | 1 | 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 | 0 | 3 |
1 | 2 | 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 | 3 | 0 |
2 | 1 | 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 | 0 | 3 |
1 | 2 | 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 | 3 | 0 |
2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 |
+ (number -/- 1) x 4
92 | 92 | 99 | 99 | 1 | 1 | 8 | 8 | 15 | 15 | 67 | 67 | 74 | 74 | 51 | 51 | 58 | 58 | 40 | 40 |
92 | 92 | 99 | 99 | 1 | 1 | 8 | 8 | 15 | 15 | 67 | 67 | 74 | 74 | 51 | 51 | 58 | 58 | 40 | 40 |
98 | 98 | 80 | 80 | 7 | 7 | 14 | 14 | 16 | 16 | 73 | 73 | 55 | 55 | 57 | 57 | 64 | 64 | 41 | 41 |
98 | 98 | 80 | 80 | 7 | 7 | 14 | 14 | 16 | 16 | 73 | 73 | 55 | 55 | 57 | 57 | 64 | 64 | 41 | 41 |
4 | 4 | 81 | 81 | 88 | 88 | 20 | 20 | 22 | 22 | 54 | 54 | 56 | 56 | 63 | 63 | 70 | 70 | 47 | 47 |
4 | 4 | 81 | 81 | 88 | 88 | 20 | 20 | 22 | 22 | 54 | 54 | 56 | 56 | 63 | 63 | 70 | 70 | 47 | 47 |
85 | 85 | 87 | 87 | 19 | 19 | 21 | 21 | 3 | 3 | 60 | 60 | 62 | 62 | 69 | 69 | 71 | 71 | 28 | 28 |
85 | 85 | 87 | 87 | 19 | 19 | 21 | 21 | 3 | 3 | 60 | 60 | 62 | 62 | 69 | 69 | 71 | 71 | 28 | 28 |
86 | 86 | 93 | 93 | 25 | 25 | 2 | 2 | 9 | 9 | 61 | 61 | 68 | 68 | 75 | 75 | 52 | 52 | 34 | 34 |
86 | 86 | 93 | 93 | 25 | 25 | 2 | 2 | 9 | 9 | 61 | 61 | 68 | 68 | 75 | 75 | 52 | 52 | 34 | 34 |
17 | 17 | 24 | 24 | 76 | 76 | 83 | 83 | 90 | 90 | 42 | 42 | 49 | 49 | 26 | 26 | 33 | 33 | 65 | 65 |
17 | 17 | 24 | 24 | 76 | 76 | 83 | 83 | 90 | 90 | 42 | 42 | 49 | 49 | 26 | 26 | 33 | 33 | 65 | 65 |
23 | 23 | 5 | 5 | 82 | 82 | 89 | 89 | 91 | 91 | 48 | 48 | 30 | 30 | 32 | 32 | 39 | 39 | 66 | 66 |
23 | 23 | 5 | 5 | 82 | 82 | 89 | 89 | 91 | 91 | 48 | 48 | 30 | 30 | 32 | 32 | 39 | 39 | 66 | 66 |
79 | 79 | 6 | 6 | 13 | 13 | 95 | 95 | 97 | 97 | 29 | 29 | 31 | 31 | 38 | 38 | 45 | 45 | 72 | 72 |
79 | 79 | 6 | 6 | 13 | 13 | 95 | 95 | 97 | 97 | 29 | 29 | 31 | 31 | 38 | 38 | 45 | 45 | 72 | 72 |
10 | 10 | 12 | 12 | 94 | 94 | 96 | 96 | 78 | 78 | 35 | 35 | 37 | 37 | 44 | 44 | 46 | 46 | 53 | 53 |
10 | 10 | 12 | 12 | 94 | 94 | 96 | 96 | 78 | 78 | 35 | 35 | 37 | 37 | 44 | 44 | 46 | 46 | 53 | 53 |
11 | 11 | 18 | 18 | 100 | 100 | 77 | 77 | 84 | 84 | 36 | 36 | 43 | 43 | 50 | 50 | 27 | 27 | 59 | 59 |
11 | 11 | 18 | 18 | 100 | 100 | 77 | 77 | 84 | 84 | 36 | 36 | 43 | 43 | 50 | 50 | 27 | 27 | 59 | 59 |
= (simple) 20x20 magic square
365 | 368 | 393 | 396 | 1 | 4 | 29 | 32 | 57 | 60 | 265 | 268 | 293 | 296 | 201 | 204 | 229 | 232 | 157 | 160 |
366 | 367 | 394 | 395 | 2 | 3 | 30 | 31 | 58 | 59 | 266 | 267 | 294 | 295 | 202 | 203 | 230 | 231 | 158 | 159 |
392 | 389 | 320 | 317 | 28 | 25 | 56 | 53 | 64 | 61 | 292 | 289 | 220 | 217 | 228 | 225 | 256 | 253 | 164 | 161 |
391 | 390 | 319 | 318 | 27 | 26 | 55 | 54 | 63 | 62 | 291 | 290 | 219 | 218 | 227 | 226 | 255 | 254 | 163 | 162 |
13 | 16 | 321 | 324 | 349 | 352 | 77 | 80 | 85 | 88 | 213 | 216 | 221 | 224 | 249 | 252 | 277 | 280 | 185 | 188 |
14 | 15 | 322 | 323 | 350 | 351 | 78 | 79 | 86 | 87 | 214 | 215 | 222 | 223 | 250 | 251 | 278 | 279 | 186 | 187 |
340 | 337 | 348 | 345 | 76 | 73 | 84 | 81 | 12 | 9 | 240 | 237 | 248 | 245 | 276 | 273 | 284 | 281 | 112 | 109 |
339 | 338 | 347 | 346 | 75 | 74 | 83 | 82 | 11 | 10 | 239 | 238 | 247 | 246 | 275 | 274 | 283 | 282 | 111 | 110 |
341 | 344 | 369 | 372 | 97 | 100 | 5 | 8 | 33 | 36 | 241 | 244 | 269 | 272 | 297 | 300 | 205 | 208 | 133 | 136 |
342 | 343 | 370 | 371 | 98 | 99 | 6 | 7 | 34 | 35 | 242 | 243 | 270 | 271 | 298 | 299 | 206 | 207 | 134 | 135 |
68 | 65 | 96 | 93 | 304 | 301 | 332 | 329 | 360 | 357 | 168 | 165 | 196 | 193 | 104 | 101 | 132 | 129 | 260 | 257 |
67 | 66 | 95 | 94 | 303 | 302 | 331 | 330 | 359 | 358 | 167 | 166 | 195 | 194 | 103 | 102 | 131 | 130 | 259 | 258 |
89 | 92 | 17 | 20 | 325 | 328 | 353 | 356 | 361 | 364 | 189 | 192 | 117 | 120 | 125 | 128 | 153 | 156 | 261 | 264 |
90 | 91 | 18 | 19 | 326 | 327 | 354 | 355 | 362 | 363 | 190 | 191 | 118 | 119 | 126 | 127 | 154 | 155 | 262 | 263 |
316 | 313 | 24 | 21 | 52 | 49 | 380 | 377 | 388 | 385 | 116 | 113 | 124 | 121 | 152 | 149 | 180 | 177 | 288 | 285 |
315 | 314 | 23 | 22 | 51 | 50 | 379 | 378 | 387 | 386 | 115 | 114 | 123 | 122 | 151 | 150 | 179 | 178 | 287 | 286 |
37 | 40 | 45 | 48 | 373 | 376 | 381 | 384 | 309 | 312 | 137 | 140 | 145 | 148 | 173 | 176 | 181 | 184 | 209 | 212 |
38 | 39 | 46 | 47 | 374 | 375 | 382 | 383 | 310 | 311 | 138 | 139 | 146 | 147 | 174 | 175 | 182 | 183 | 210 | 211 |
44 | 41 | 72 | 69 | 400 | 397 | 308 | 305 | 336 | 333 | 144 | 141 | 172 | 169 | 200 | 197 | 108 | 105 | 236 | 233 |
43 | 42 | 71 | 70 | 399 | 398 | 307 | 306 | 335 | 334 | 143 | 142 | 171 | 170 | 199 | 198 | 107 | 106 | 235 | 234 |
Use this method to construct even magic squares.
See 6x6, 8x8, 10x10, 12x12, 14x14, 16x16, 18x18, 20x20, 22x22, 24x24, 26x26, 28x28, 30x30 en 32x32