Basic pattern method (3)

Use as first grid 16x the shifted versions of a 4x4 panmagic square and as second grid 16x the same or another (not shifted version of the) 4x4 panmagic square to construct a most perfect (Franklin pan)magic 16x16 square.

● In the first grid we need a panmagic 4x4 square (top left) and 15x a (different) shifted version of the panmagic 4x4 square. To get 15x shifted version of the panmagic 4x4 square we use starting positions (= coordinates) on a 2x2 carpet of the panmagic 4x4 square. We must arrange the shifted versions systematically in the 16x16 square to get a most perfect (franklin pan)magic 16x16 square.

	0	1	2	3
0	2	5	11	12	2	5	11	12	0,0	1,2	2,0	3,2
1	15	8	6	1	15	8	6	1	2,1	3,3	0,1	1,3
2	4	3	13	10	4	3	13	10	0,2	1,0	2,2	3,0
3	9	14	0	7	9	14	0	7	2,3	3,1	0,3	1,1
	2	5	11	12	2	5	11	12
	15	8	6	1	15	8	6	1
	4	3	13	10	4	3	13	10
	9	14	0	7	9	14	0	7

● The second grid is 16x a (not shifted version of a) panmagic 4x4 square..

1x number of grid with 16x shifted version of a panmagic 4x4 square

2	5	11	12	3	13	10	4	11	12	2	5	10	4	3	13
15	8	6	1	14	0	7	9	6	1	15	8	7	9	14	0
4	3	13	10	5	11	12	2	13	10	4	3	12	2	5	11
9	14	0	7	8	6	1	15	0	7	9	14	1	15	8	6
6	1	15	8	7	9	14	0	15	8	6	1	14	0	7	9
13	10	4	3	12	2	5	11	4	3	13	10	5	11	12	2
0	7	9	14	1	15	8	6	9	14	0	7	8	6	1	15
11	12	2	5	10	4	3	13	2	5	11	12	3	13	10	4
4	3	13	10	5	11	12	2	13	10	4	3	12	2	5	11
9	14	0	7	8	6	1	15	0	7	9	14	1	15	8	6
2	5	11	12	3	13	10	4	11	12	2	5	10	4	3	13
15	8	6	1	14	0	7	9	6	1	15	8	7	9	14	0
0	7	9	14	1	15	8	6	9	14	0	7	8	6	1	15
11	12	2	5	10	4	3	13	2	5	11	12	3	13	10	4
6	1	15	8	7	9	14	0	15	8	6	1	14	0	7	9
13	10	4	3	12	2	5	11	4	3	13	10	5	11	12	2

+16x number of a (not shifted version of a) panmagic 4x4 square

2	5	11	12	2	5	11	12	2	5	11	12	2	5	11	12
15	8	6	1	15	8	6	1	15	8	6	1	15	8	6	1
4	3	13	10	4	3	13	10	4	3	13	10	4	3	13	10
9	14	0	7	9	14	0	7	9	14	0	7	9	14	0	7
2	5	11	12	2	5	11	12	2	5	11	12	2	5	11	12
15	8	6	1	15	8	6	1	15	8	6	1	15	8	6	1
4	3	13	10	4	3	13	10	4	3	13	10	4	3	13	10
9	14	0	7	9	14	0	7	9	14	0	7	9	14	0	7
2	5	11	12	2	5	11	12	2	5	11	12	2	5	11	12
15	8	6	1	15	8	6	1	15	8	6	1	15	8	6	1
4	3	13	10	4	3	13	10	4	3	13	10	4	3	13	10
9	14	0	7	9	14	0	7	9	14	0	7	9	14	0	7
2	5	11	12	2	5	11	12	2	5	11	12	2	5	11	12
15	8	6	1	15	8	6	1	15	8	6	1	15	8	6	1
4	3	13	10	4	3	13	10	4	3	13	10	4	3	13	10
9	14	0	7	9	14	0	7	9	14	0	7	9	14	0	7

= most perfect (Franklin pan)magic 16x16 square

34	85	187	204	35	93	186	196	43	92	178	197	42	84	179	205
255	136	102	17	254	128	103	25	246	129	111	24	247	137	110	16
68	51	221	170	69	59	220	162	77	58	212	163	76	50	213	171
153	238	0	119	152	230	1	127	144	231	9	126	145	239	8	118
38	81	191	200	39	89	190	192	47	88	182	193	46	80	183	201
253	138	100	19	252	130	101	27	244	131	109	26	245	139	108	18
64	55	217	174	65	63	216	166	73	62	208	167	72	54	209	175
155	236	2	117	154	228	3	125	146	229	11	124	147	237	10	116
36	83	189	202	37	91	188	194	45	90	180	195	44	82	181	203
249	142	96	23	248	134	97	31	240	135	105	30	241	143	104	22
66	53	219	172	67	61	218	164	75	60	210	165	74	52	211	173
159	232	6	113	158	224	7	121	150	225	15	120	151	233	14	112
32	87	185	206	33	95	184	198	41	94	176	199	40	86	177	207
251	140	98	21	250	132	99	29	242	133	107	28	243	141	106	20
70	49	223	168	71	57	222	160	79	56	214	161	78	48	215	169
157	234	4	115	156	226	5	123	148	227	13	122	149	235	12	114

16x16, Basic pattern method (3).xls

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16x16 magic square