Perfect Magic Cube
by Michael A. Linton
Click to download
Extract the zip file to your hard drive and run the file cube.exe
(maximize the window with the little square box or use the windows logo key
and up arrow)
Press 'h' for a list of instructions when the program starts.
r will stop and start the cube rotating.
the arrow keys will move the cube left, right, up or down.
] will select a direction.
] ] will select the second direction.
] ] ] will select the third direction.
1 will select one level.
2 will select two levels.
etc, up to 7
+ will move the selected levels
page up and page down will zoom in and out (make sure the numbers lock is off)
escape will close the program
try the following ] 3 +
now try this r ] 2 + ] ] 4 + ] ] ] 3 + r
now click on the numbers to check the addition.
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. 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, Michael 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 |
Try searching for a new combination. Here are a few I have
found
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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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