Perfect Magic Cube

by Michael A. Linton

Copyright © 2003 Steven Linton.


Click to run simulation

(Simulation only available on USB)

This 8 x 8 x 8 cube consists of an array of numbers from 1 to 512, with no number missing or repeated. These numbers are specially arranged so that the addition of the eight numbers in any line, column or file total 2052. Similarly, the addition of any diagonal across any plane, including the four corner to corner diagonals, also total 2052. This is the conventional definition of a magic cube.

Furthermore, this cube remains magic even when one of the faces is moved parallel to itself, top to bottom, side to side or back to front. A cube that does this is known as pan-diagonal.

Finally there are two additional features to make this cube unique and special. Firstly, the eight corners of any cube within the cube sum to 2052. There are more of these cubes than there are rows, columns, files and diagonals combined. Secondly, to prove that this was created by Michael he encoded his initials (MAL) into the top-back-left corner of the cube. This can be simply decoded by exchanging the first five numbers for their corresponding letters as follows...

where, A = 1, B = 2, C = 3, ...
M = 13, A = 1, L = 12
13112

The following is a listing of the 512 numbers on the cube.

131 121 327 444 134 128 322 445
286 488 218 37 283 481 223 36
123 321 447 132 126 328 442 133
486 224 34 285 483 217 39 284
323 441 135 124 326 448 130 125
222 40 282 485 219 33 287 484
443 129 127 324 446 136 122 325
38 288 482 221 35 281 487 220

 

370 397 179 73 375 396 182 80
239 20 302 472 234 21 299 465
394 181 75 369 399 180 78 376
23 300 470 240 18 301 467 233
178 77 371 393 183 76 374 400
303 468 238 24 298 469 235 17
74 373 395 177 79 372 398 184
471 236 22 304 466 237 19 297

 

158 104 346 421 155 97 351 420
315 449 255 4 318 456 250 5
102 352 418 157 99 345 423 156
451 249 7 316 454 256 2 317
350 424 154 101 347 417 159 100
251 1 319 452 254 8 314 453
422 160 98 349 419 153 103 348
3 313 455 252 6 320 450 253

 

367 404 174 88 362 405 171 81
202 53 267 497 207 52 270 504
407 172 86 368 402 173 83 361
50 269 499 201 55 268 502 208
175 84 366 408 170 85 363 401
266 501 203 49 271 500 206 56
87 364 406 176 82 365 403 169
498 205 51 265 503 204 54 272

 

187 65 383 388 190 72 378 389
294 480 226 29 291 473 231 28
67 377 391 188 70 384 386 189
478 232 26 293 475 225 31 292
379 385 191 68 382 392 186 69
230 32 290 477 227 25 295 476
387 185 71 380 390 192 66 381
30 296 474 229 27 289 479 228

 

330 437 139 113 335 436 142 120
215 44 278 496 210 45 275 489
434 141 115 329 439 140 118 336
47 276 494 216 42 277 491 209
138 117 331 433 143 116 334 440
279 492 214 48 274 493 211 41
114 333 435 137 119 332 438 144
495 212 46 280 490 213 43 273

 

166 96 354 413 163 89 359 412
259 505 199 60 262 512 194 61
94 360 410 165 91 353 415 164
507 193 63 260 510 200 58 261
358 416 162 93 355 409 167 92
195 57 263 508 198 64 258 509
414 168 90 357 411 161 95 356
59 257 511 196 62 264 506 197

 

343 428 150 112 338 429 147 105
242 13 307 457 247 12 310 464
431 148 110 344 426 149 107 337
10 309 459 241 15 308 462 248
151 108 342 432 146 109 339 425
306 461 243 9 311 460 246 16
111 340 430 152 106 341 427 145
458 245 11 305 463 244 14 312

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