Magic squares (most perfect, [Franklin] panmagic & inlaid)

Inlaid square (2)

	Magic squares (most perfect, [Franklin] panmagic & inlaid)
	Detailed explanation about the structure and construction of magic squares

Inlaid square (2)

How to produce an even magic square with as well odd as (not diamond)
even inlays

See on the previous web page how I have produced a 14x14 (= even) square consisting of even inlays.
The challenge is to produce an even magic square with as well odd as (not diamond) even inlays. Look
at the following 22x22 magic square with a 20x20 inlay containing odd and even inlays.

The composition

The composition of the 20x20 inlay is as follows:

In the corners are four 7x7 panmagic squares. Around the 7x7 panmagic squares are ‘half’ borders.
The ‘cross’ in the middle contains five panmagic 4x4 squares (and eight ‘half’ panmagic 4x4 squares,
in which two times two digits have been swapped to get a correct magic square, which will be ex-
plained later on).

The 20x20 inlay consist of (to start with) the digits 1 up to 400 (and will be added by 42 later on to
complete the 22x22 square). The four panmagic 7x7 squares consist of the digits 103 up to 298.
The ‘half’ borders consist of the digits 73 up to 102 and 299 up to 328. The five complete and eight
‘half’ panmagic 4x4 squares consist of the digits 1 up to 72 and 329 up to 400.

The four panmagic 7x7 squares

To produce the four panmagic 7x7 squares we use the method of construction on page ‘panmagic
5x5 square’.

We produce the four panmagic 7x7 squares simultaneously. For the row coordinates we use four
times the digits 0 up to 6. For the column coordinates we use the digits 0 up to 27, which will be
spread as proportional as possible over the four panmagic 7x7 squares.

Column coordinates 1st square Row coordinates 1st square

0	4	11	13	18	23	25	0	1	2	3	4	5	6
11	13	18	23	25	0	4	3	4	5	6	0	1	2
18	23	25	0	4	11	13	6	0	1	2	3	4	5
25	0	4	11	13	18	23	2	3	4	5	6	0	1
4	11	13	18	23	25	0	5	6	0	1	2	3	4
13	18	23	25	0	4	11	1	2	3	4	5	6	0
23	25	0	4	11	13	18	4	5	6	0	1	2	3

7x column digit + 1x row digit +1 + 102 = first panmagic 7x7 square

1	30	80	95	131	167	182	103	132	182	197	233	269	284
81	96	132	168	176	2	31	183	198	234	270	278	104	133
133	162	177	3	32	82	97	235	264	279	105	134	184	199
178	4	33	83	98	127	163	280	106	135	185	200	229	265
34	84	92	128	164	179	5	136	186	194	230	266	281	107
93	129	165	180	6	35	78	195	231	267	282	108	137	180
166	181	7	29	79	94	130	268	283	109	131	181	196	232

Column coordinates 2nd square Row coordinates 2nd square

2	5	9	15	16	21	26	0	1	2	3	4	5	6
9	15	16	21	26	2	5	3	4	5	6	0	1	2
16	21	26	2	5	9	15	6	0	1	2	3	4	5
26	2	5	9	15	16	21	2	3	4	5	6	0	1
5	9	15	16	21	26	2	5	6	0	1	2	3	4
15	16	21	26	2	5	9	1	2	3	4	5	6	0
21	26	2	5	9	15	16	4	5	6	0	1	2	3

7x column digit + 1x row digit +1 + 102 = second panmagic 7x7 square

15	37	66	109	117	153	189	117	139	168	211	219	255	291
67	110	118	154	183	16	38	169	212	220	256	285	118	140
119	148	184	17	39	68	111	221	250	286	119	141	170	213
185	18	40	69	112	113	149	287	120	142	171	214	215	251
41	70	106	114	150	186	19	143	172	208	216	252	288	121
107	115	151	187	20	42	64	209	217	253	289	122	144	166
152	188	21	36	65	108	116	254	290	123	138	167	210	218

Column coordinates 3rd square Row coordinates 3rd square

3	7	10	14	17	20	24	0	1	2	3	4	5	6
10	14	17	20	24	3	7	3	4	5	6	0	1	2
17	20	24	3	7	10	14	6	0	1	2	3	4	5
24	3	7	10	14	17	20	2	3	4	5	6	0	1
7	10	14	17	20	24	3	5	6	0	1	2	3	4
14	17	20	24	3	7	10	1	2	3	4	5	6	0
20	24	3	7	10	14	17	4	5	6	0	1	2	3

7x column digit + 1x row digit +1 + 102 = third panmagic 7x7 square

22	51	73	102	124	146	175	124	153	175	204	226	248	277
74	103	125	147	169	23	52	176	205	227	249	271	125	154
126	141	170	24	53	75	104	228	243	272	126	155	177	206
171	25	54	76	105	120	142	273	127	156	178	207	222	244
55	77	99	121	143	172	26	157	179	201	223	245	274	128
100	122	144	173	27	56	71	202	224	246	275	129	158	173
145	174	28	50	72	101	123	247	276	130	152	174	203	225

Column coordinates 4th square Row coordinates 4th square

1	6	8	12	19	22	27	0	1	2	3	4	5	6
8	12	19	22	27	1	6	3	4	5	6	0	1	2
19	22	27	1	6	8	12	6	0	1	2	3	4	5
27	1	6	8	12	19	22	2	3	4	5	6	0	1
6	8	12	19	22	27	1	5	6	0	1	2	3	4
12	19	22	27	1	6	8	1	2	3	4	5	6	0
22	27	1	6	8	12	19	4	5	6	0	1	2	3

7x column digit + 1x row digit +1 + 102 = fourth panmagic 7x7 square

8	44	59	88	138	160	196	110	146	161	190	240	262	298
60	89	139	161	190	9	45	162	191	241	263	292	111	147
140	155	191	10	46	61	90	242	257	293	112	148	163	192
192	11	47	62	91	134	156	294	113	149	164	193	236	258
48	63	85	135	157	193	12	150	165	187	237	259	295	114
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