Composite, Proportional (1) b

Use 9 proportional panmagic 5x5 squares (shift) to construct a 15x15 magic square. Proportional means that all 9 panmagic 5x5 squares have the same magic sum of (1/3 x 1695 = ) 565. We use the shift method to construct the panmagic 5x5 squares. Only as column coordinates we do not use the numbers 0 up to 4 but 0 up to (9x5 -/- 1 = ) 44 and choose the column coordinates smart so we get 9 proportional panmagic 5x5 squares.

5x column coordinate + 1x row coordinate + 1 = panmagic 5x5 square

0	15	21	30	44	0	1	2	3	4	1	77	108	154	225
21	30	44	0	15	3	4	0	1	2	109	155	221	2	78
44	0	15	21	30	1	2	3	4	0	222	3	79	110	151
15	21	30	44	0	4	0	1	2	3	80	106	152	223	4
30	44	0	15	21	2	3	4	0	1	153	224	5	76	107

1	16	22	33	38	0	1	2	3	4	6	82	113	169	195
22	33	38	1	16	3	4	0	1	2	114	170	191	7	83
38	1	16	22	33	1	2	3	4	0	192	8	84	115	166
16	22	33	38	1	4	0	1	2	3	85	111	167	193	9
33	38	1	16	22	2	3	4	0	1	168	194	10	81	112

2	17	23	27	41	0	1	2	3	4	11	87	118	139	210
23	27	41	2	17	3	4	0	1	2	119	140	206	12	88
41	2	17	23	27	1	2	3	4	0	207	13	89	120	136
17	23	27	41	2	4	0	1	2	3	90	116	137	208	14
27	41	2	17	23	2	3	4	0	1	138	209	15	86	117

3	9	24	31	43	0	1	2	3	4	16	47	123	159	220
24	31	43	3	9	3	4	0	1	2	124	160	216	17	48
43	3	9	24	31	1	2	3	4	0	217	18	49	125	156
9	24	31	43	3	4	0	1	2	3	50	121	157	218	19
31	43	3	9	24	2	3	4	0	1	158	219	20	46	122

4	10	25	34	37	0	1	2	3	4	21	52	128	174	190
25	34	37	4	10	3	4	0	1	2	129	175	186	22	53
37	4	10	25	34	1	2	3	4	0	187	23	54	130	171
10	25	34	37	4	4	0	1	2	3	55	126	172	188	24
34	37	4	10	25	2	3	4	0	1	173	189	25	51	127

5	11	26	28	40	0	1	2	3	4	26	57	133	144	205
26	28	40	5	11	3	4	0	1	2	134	145	201	27	58
40	5	11	26	28	1	2	3	4	0	202	28	59	135	141
11	26	28	40	5	4	0	1	2	3	60	131	142	203	29
28	40	5	11	26	2	3	4	0	1	143	204	30	56	132

6	12	18	32	42	0	1	2	3	4	31	62	93	164	215
18	32	42	6	12	3	4	0	1	2	94	165	211	32	63
42	6	12	18	32	1	2	3	4	0	212	33	64	95	161
12	18	32	42	6	4	0	1	2	3	65	91	162	213	34
32	42	6	12	18	2	3	4	0	1	163	214	35	61	92

7	13	19	35	36	0	1	2	3	4	36	67	98	179	185
19	35	36	7	13	3	4	0	1	2	99	180	181	37	68
36	7	13	19	35	1	2	3	4	0	182	38	69	100	176
13	19	35	36	7	4	0	1	2	3	70	96	177	183	39
35	36	7	13	19	2	3	4	0	1	178	184	40	66	97

8	14	20	29	39	0	1	2	3	4	41	72	103	149	200
20	29	39	8	14	3	4	0	1	2	104	150	196	42	73
39	8	14	20	29	1	2	3	4	0	197	43	74	105	146
14	20	29	39	8	4	0	1	2	3	75	101	147	198	44
29	39	8	14	20	2	3	4	0	1	148	199	45	71	102

Combine the 9 panmagic 5x5 squares in sequence.

15x15 magic square consisting of 9 proportional panmagic 5x5 squares

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

This 15x15 magic square is panmagic, 5x5 compact and each 1/3 row/column/diagonal gives 1/3 of the magic sum.

I have used composite method, proportional (1) to construct

8x8, 9x9, 12x12a, 12x12b, 15x15a, 15x15b, 16x16a, 16x16b, 18x18, 20x20a, 20x20b, 21x21a, 21x21b, 24x24a, 24x24b, 24x24c, 27x27a, 27x27b, 28x28a, 28x28b, 30x30a, 30x30b,32x32a, 32x32b and 32x32c

15x15, Composite, Prop. (1) b.xls

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15x15 magic square