Composite, Proportional (2)

Take 1x number from a cell of the first grid with 4x the same 4x4 in 6x6 magic square and add number x 36 from the same cell of the second grid to produce a 12x12 composite magic square.

1x number

1	6	9	34	32	29	1	6	9	34	32	29
35	11	18	23	22	2	35	11	18	23	22	2
33	25	20	13	16	4	33	25	20	13	16	4
27	14	15	26	19	10	27	14	15	26	19	10
7	24	21	12	17	30	7	24	21	12	17	30
8	31	28	3	5	36	8	31	28	3	5	36
1	6	9	34	32	29	1	6	9	34	32	29
35	11	18	23	22	2	35	11	18	23	22	2
33	25	20	13	16	4	33	25	20	13	16	4
27	14	15	26	19	10	27	14	15	26	19	10
7	24	21	12	17	30	7	24	21	12	17	30
8	31	28	3	5	36	8	31	28	3	5	36

+ 36x number

0	3	0	3	0	3	1	2	1	2	1	2
3	0	3	0	3	0	2	1	2	1	2	1
0	3	0	3	0	3	1	2	1	2	1	2
3	3	0	3	0	0	2	2	1	2	1	1
3	0	3	0	3	0	2	1	2	1	2	1
0	0	3	0	3	3	1	1	2	1	2	2
2	1	2	1	2	1	3	0	3	0	3	0
1	2	1	2	1	2	0	3	0	3	0	3
2	1	2	1	2	1	3	0	3	0	3	0
1	1	2	1	2	2	0	0	3	0	3	3
1	2	1	2	1	2	0	3	0	3	0	3
2	2	1	2	1	1	3	3	0	3	0	0

= 12x12 composite magic square

1	114	9	142	32	137	37	78	45	106	68	101
143	11	126	23	130	2	107	47	90	59	94	38
33	133	20	121	16	112	69	97	56	85	52	76
135	122	15	134	19	10	99	86	51	98	55	46
115	24	129	12	125	30	79	60	93	48	89	66
8	31	136	3	113	144	44	67	100	39	77	108
73	42	81	70	104	65	109	6	117	34	140	29
71	83	54	95	58	74	35	119	18	131	22	110
105	61	92	49	88	40	141	25	128	13	124	4
63	50	87	62	91	82	27	14	123	26	127	118
43	96	57	84	53	102	7	132	21	120	17	138
80	103	64	75	41	72	116	139	28	111	5	36

Each 1/2 row/column/diagonal gives 1/2 of the magic sum and the 12x12 magic square is 6x6 compact. In the 12x12 magic square are 4 proportional 4x4 panmagic squares.

I have used method composite, proportional (2) to construct

12x12, 18x18, 24x24, 30x30a and 30x30b

12x12, Composite, Prop. (2).xls

Microsoft Excel werkblad 60.0 KB

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12x12 magic square