How to make perfect magic squares & cubes - Symmetric & panmagic 7x7x7 cube

Symmetric & panmagic 7x7x7 cube

	How to make perfect magic squares & cubes
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Symmetric & panmagic 7x7x7 cube

How to produce a symmetric & panmagic 7x7x7 cube

Read on http://en.wikipedia.org/wiki/Perfect_magic_cube everything about the features of the perfect magic
cube. Perfect magic cubes exist from the size (order) of 5x5x5 and bigger.

See on www.trump.de/magic-squares/magic-cubes/cubes-1.html the following perfect magic 5x5x5 cube.

The first known perfect magic cube of order 5

Walter Trump and Christian Boyer, 2003-11-13

The above mentioned 5x5x5 magic cube has the following magic features:

- the 5 rows, the 5 columns and the 2 diagonals in each level give the magic sum of 315:

- the 25 pillars give the magic sum of 315;

- the 20 diagonals (for example 115+64+38+87+11=315 or 106+44+58+87+20=315) through
the 5 levels give the magic sum of 315;

- The four space diagonals (for example 67+39+63+87+59=315) give the magic sum of 315.

Use the method to produce a panmagic 5x5 square also to produce a symmetric & panmagic 7x7x7cube.

If you want a symmetric (& panmagic) cube, put in the 1st row of the 1st level of the 1st grid the
middle digit of 0 up to 6, that is 3, on the 1st position (from the left), and put the other digits in a
'symmetric' order, for example: 3-4-5-6-0-1-2.
If you want only a panmagic cube, put in the 1st row of the 1st level of the 1st grid the 3 on the
1st position and put the other digits in random order (i.e. 3-2-1-6-4-0-5).
Make row 2 up to 7 of the 1st level of the 1st grid by moving the 1st row each time ([7+1]/2 = ) 4
places to the left. Make level 2 up to 7 of the 1st grid by moving the columns of the 1st level each
time 2 places to the left.

If you want a symmetric (& panmagic) cube, put in the 1st row of the 1st level of the 2nd grid the
middle digit of 0 up to 6, that is 3, on the 5th position (from the left) and put the other digits in a
'symmetric' order, for example: 6-0-1-2-3-4-5.
If you want only a panmagic cube, put in the 1st row of the 1st level of the 1st grid the 3 on the 5th
position and put the other digits in random order (i.e. 5-2-1-6-3-0-4).
Make row 2 up to 7 of the 1st level of the 2nd grid by moving the 1st row each time ([7+1]/2 = ) 4
places to the right. Make level 2 up to 7 of the 2nd grid by moving the columns of the 1st level each
time 2 places to the left.

The 3rd grid is the same as the 2nd grid, but the sequence of the levels is 7 up to 1 (in stead of 1 up
to 7).

Take 1x digit from the 1st grid + 7x digit from the 2nd grid + 49x digit from the 3rd grid and the
symmetric & panmagic 7x7x7 cube is ready.

*1x digit+1 [1st level] +7x digit[1st level] +49x digit [1st level]*
3	4	5	6	0	1	2	6	0	1	2	3	4	5	4	5	6	0	1	2	3
0	1	2	3	4	5	6	2	3	4	5	6	0	1	0	1	2	3	4	5	6
4	5	6	0	1	2	3	5	6	0	1	2	3	4	3	4	5	6	0	1	2
1	2	3	4	5	6	0	1	2	3	4	5	6	0	6	0	1	2	3	4	5
5	6	0	1	2	3	4	4	5	6	0	1	2	3	2	3	4	5	6	0	1
2	3	4	5	6	0	1	0	1	2	3	4	5	6	5	6	0	1	2	3	4
6	0	1	2	3	4	5	3	4	5	6	0	1	2	1	2	3	4	5	6	0

*1x digit +1 [2nd level] +7x digit [2nd level] +49x digit [2nd level]*
5	6	0	1	2	3	4	1	2	3	4	5	6	0	2	3	4	5	6	0	1
2	3	4	5	6	0	1	4	5	6	0	1	2	3	5	6	0	1	2	3	4
6	0	1	2	3	4	5	0	1	2	3	4	5	6	1	2	3	4	5	6	0
3	4	5	6	0	1	2	3	4	5	6	0	1	2	4	5	6	0	1	2	3
0	1	2	3	4	5	6	6	0	1	2	3	4	5	0	1	2	3	4	5	6
4	5	6	0	1	2	3	2	3	4	5	6	0	1	3	4	5	6	0	1	2
1	2	3	4	5	6	0	5	6	0	1	2	3	4	6	0	1	2	3	4	5

*1x digit+1 [3rd level] +7x digit [3rd level] +49x digit [3rd level]*
0	1	2	3	4	5	6	3	4	5	6	0	1	2	0	1	2	3	4	5	6
4	5	6	0	1	2	3	6	0	1	2	3	4	5	3	4	5	6	0	1	2
1	2	3	4	5	6	0	2	3	4	5	6	0	1	6	0	1	2	3	4	5
5	6	0	1	2	3	4	5	6	0	1	2	3	4	2	3	4	5	6	0	1
2	3	4	5	6	0	1	1	2	3	4	5	6	0	5	6	0	1	2	3	4
6	0	1	2	3	4	5	4	5	6	0	1	2	3	1	2	3	4	5	6	0
3	4	5	6	0	1	2	0	1	2	3	4	5	6	4	5	6	0	1	2	3

*1x digit +1 [4th level] +7x digit [4th level] +49x digit [4th level]*
2	3	4	5	6	0	1	5	6	0	1	2	3	4	5	6	0	1	2	3	4
6	0	1	2	3	4	5	1	2	3	4	5	6	0	1	2	3	4	5	6	0
3	4	5	6	0	1	2	4	5	6	0	1	2	3	4	5	6	0	1	2	3
0	1	2	3	4	5	6	0	1	2	3	4	5	6	0	1	2	3	4	5	6
4	5	6	0	1	2	3	3	4	5	6	0	1	2	3	4	5	6	0	1	2
1	2	3	4	5	6	0	6	0	1	2	3	4	5	6	0	1	2	3	4	5
5	6	0	1	2	3	4	2	3	4	5	6	0	1	2	3	4	5	6	0	1

*1x digit +1 [5th level] +7x getal [5th level] +49x digit [5th level]*
4	5	6	0	1	2	3	0	1	2	3	4	5	6	3	4	5	6	0	1	2
1	2	3	4	5	6	0	3	4	5	6	0	1	2	6	0	1	2	3	4	5
5	6	0	1	2	3	4	6	0	1	2	3	4	5	2	3	4	5	6	0	1
2	3	4	5	6	0	1	2	3	4	5	6	0	1	5	6	0	1	2	3	4
6	0	1	2	3	4	5	5	6	0	1	2	3	4	1	2	3	4	5	6	0
3	4	5	6	0	1	2	1	2	3	4	5	6	0	4	5	6	0	1	2	3
0	1	2	3	4	5	6	4	5	6	0	1	2	3	0	1	2	3	4	5	6

*1x digit +1 [6th level] +7x digit [6th level] +49x digit [6th level]*
6	0	1	2	3	4	5	2	3	4	5	6	0	1	1	2	3	4	5	6	0
3	4	5	6	0	1	2	5	6	0	1	2	3	4	4	5	6	0	1	2	3
0	1	2	3	4	5	6	1	2	3	4	5	6	0	0	1	2	3	4	5	6
4	5	6	0	1	2	3	4	5	6	0	1	2	3	3	4	5	6	0	1	2
1	2	3	4	5	6	0	0	1	2	3	4	5	6	6	0	1	2	3	4	5
5	6	0	1	2	3	4	3	4	5	6	0	1	2	2	3	4	5	6	0	1
2	3	4	5	6	0	1	6	0	1	2	3	4	5	5	6	0	1	2	3	4

*1x digit +1 [7th level] +7x digit [7th level] +49x digit [7th level]*
1	2	3	4	5	6	0	4	5	6	0	1	2	3	6	0	1	2	3	4	5
5	6	0	1	2	3	4	0	1	2	3	4	5	6	2	3	4	5	6	0	1
2	3	4	5	6	0	1	3	4	5	6	0	1	2	5	6	0	1	2	3	4
6	0	1	2	3	4	5	6	0	1	2	3	4	5	1	2	3	4	5	6	0
3	4	5	6	0	1	2	2	3	4	5	6	0	1	4	5	6	0	1	2	3
0	1	2	3	4	5	6	5	6	0	1	2	3	4	0	1	2	3	4	5	6
4	5	6	0	1	2	3	1	2	3	4	5	6	0	3	4	5	6	0	1	2

*Sym. & panm. 7x7x7 [1st level]*
242	250	307	21	71	128	185
15	72	129	186	243	251	308
187	244	252	302	16	73	130
303	17	74	131	188	245	246
132	189	239	247	304	18	75
248	305	19	76	133	183	240
77	127	184	241	249	306	20


*Sym. & panm. 7x7x7 [2nd level]*
111	168	218	275	332	46	54
276	333	47	55	112	162	219
56	106	163	220	277	334	48
221	278	335	49	50	107	164
43	51	108	165	222	279	336
166	223	280	330	44	52	109
331	45	53	110	167	224	274


*Sym. & panm. 7x7x7 [3rd level]*
22	79	136	193	201	258	315
194	202	259	309	23	80	137
310	24	81	138	195	203	253
139	196	197	254	311	25	82
255	312	26	83	140	190	198
84	134	191	199	256	313	27
200	257	314	28	78	135	192


*Sym. & panm. 7x7x7 [4th level]*
283	340	5	62	119	169	226
63	113	170	227	284	341	6
228	285	342	7	57	114	171
1	58	115	172	229	286	343
173	230	287	337	2	59	116
338	3	60	117	174	231	281
118	175	225	282	339	4	61


*Sym. & panm. 7x7x7 [5th level]*
152	209	266	316	30	87	144
317	31	88	145	153	210	260
146	154	204	261	318	32	89
262	319	33	90	147	148	205
91	141	149	206	263	320	34
207	264	321	35	85	142	150
29	86	143	151	208	265	322


*Sym. & panm. 7x7x7 [6th level]*
70	120	177	234	291	299	13
235	292	300	14	64	121	178
8	65	122	179	236	293	301
180	237	294	295	9	66	123
296	10	67	124	181	238	288
125	182	232	289	297	11	68
290	298	12	69	126	176	233


*Sym. & panm. 7x7x7 [7th level]*
324	38	95	103	160	217	267
104	161	211	268	325	39	96
269	326	40	97	105	155	212
98	99	156	213	270	327	41
214	271	328	42	92	100	157
36	93	101	158	215	272	329
159	216	273	323	37	94	102

EXTRA MAGIC FEATURES:

The 7x7x7 cube is symmetric;
The 7x7x7 cube is panmagic in all levels;
The 7x7x7 cube is pandiagonal magic through all levels (i.e. 15+56+139+173+207+290+324=1204 or 302+277+203+171+146+65+40=1204);

N.B.: Use the same method to produce a perfect (Nasik) magic 11x11x11 cube

Download for construction in EXCEL: 7x7x7 panmagic cube

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