Composite, Proportional (1) a

Use 25 proportional (semi)magic 3x3 squares to produce a 15x15 magic square. Proportional means that all 25 (semi)magic 3x3 squares have the same magic sum of (1/5 x 1695 = ) 339. Use the row and column coordinates of the 3x3 magic square. Don't use the numbers 0 up to 2, but 1 up to (25x3 = ) 75 instead. You must divide the row coordinates proportional over the 25 magic 3x3 squares. Use the table and connect each of the 5 rows to the other 5 rows to get (5x5x3 =) 75 row coordinates:

1	3	5	9
2	5	2	9
3	2	4	9
4	4	1	9
5	1	3	9

Construct the 25 (semi)magic 3x3 squares.

Row coordinate +75x column coordinate = (semi)magic 3x3 square

38	1	75	0	2	1	38	151	150
75	38	1	2	1	0	225	113	1
1	75	38	1	0	2	76	75	188

40	2	72	0	2	1	40	152	147
72	40	2	2	1	0	222	115	2
2	72	40	1	0	2	77	72	190

37	3	74	0	2	1	37	153	149
74	37	3	2	1	0	224	112	3
3	74	37	1	0	2	78	74	187

39	4	71	0	2	1	39	154	146
71	39	4	2	1	0	221	114	4
4	71	39	1	0	2	79	71	189

36	5	73	0	2	1	36	155	148
73	36	5	2	1	0	223	111	5
5	73	36	1	0	2	80	73	186

48	6	60	0	2	1	48	156	135
60	48	6	2	1	0	210	123	6
6	60	48	1	0	2	81	60	198

50	7	57	0	2	1	50	157	132
57	50	7	2	1	0	207	125	7
7	57	50	1	0	2	82	57	200

47	8	59	0	2	1	47	158	134
59	47	8	2	1	0	209	122	8
8	59	47	1	0	2	83	59	197

49	9	56	0	2	1	49	159	131
56	49	9	2	1	0	206	124	9
9	56	49	1	0	2	84	56	199

46	10	58	0	2	1	46	160	133
58	46	10	2	1	0	208	121	10
10	58	46	1	0	2	85	58	196

33	11	70	0	2	1	33	161	145
70	33	11	2	1	0	220	108	11
11	70	33	1	0	2	86	70	183

35	12	67	0	2	1	35	162	142
67	35	12	2	1	0	217	110	12
12	67	35	1	0	2	87	67	185

32	13	69	0	2	1	32	163	144
69	32	13	2	1	0	219	107	13
13	69	32	1	0	2	88	69	182

34	14	66	0	2	1	34	164	141
66	34	14	2	1	0	216	109	14
14	66	34	1	0	2	89	66	184

31	15	68	0	2	1	31	165	143
68	31	15	2	1	0	218	106	15
15	68	31	1	0	2	90	68	181

43	16	55	0	2	1	43	166	130
55	43	16	2	1	0	205	118	16
16	55	43	1	0	2	91	55	193

45	17	52	0	2	1	45	167	127
52	45	17	2	1	0	202	120	17
17	52	45	1	0	2	92	52	195

42	18	54	0	2	1	42	168	129
54	42	18	2	1	0	204	117	18
18	54	42	1	0	2	93	54	192

44	19	51	0	2	1	44	169	126
51	44	19	2	1	0	201	119	19
19	51	44	1	0	2	94	51	194

41	20	53	0	2	1	41	170	128
53	41	20	2	1	0	203	116	20
20	53	41	1	0	2	95	53	191

28	21	65	0	2	1	28	171	140
65	28	21	2	1	0	215	103	21
21	65	28	1	0	2	96	65	178

30	22	62	0	2	1	30	172	137
62	30	22	2	1	0	212	105	22
22	62	30	1	0	2	97	62	180

27	23	64	0	2	1	27	173	139
64	27	23	2	1	0	214	102	23
23	64	27	1	0	2	98	64	177

29	24	61	0	2	1	29	174	136
61	29	24	2	1	0	211	104	24
24	61	29	1	0	2	99	61	179

26	25	63	0	2	1	26	175	138
63	26	25	2	1	0	213	101	25
25	63	26	1	0	2	100	63	176

Put the 25 (semi)magic 3x3 squares together (for example in sequence of the middle number of the 3x3 sub-square):

15x15 magic square

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

Each 1/5 row/column give 1/5 of the magic sum and the 15x15 magic square is 3x3 compact.

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) a.xls

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15x15 magic square