Composite, AxB compact

It is possible to use a 3x3 magic square and a 4x4 magic square to construct a 12x12 magic square.

Use as first grid 4x4 the same 3x3 magic square and as second grid 3x3 the same 4x4 magic square. Take a number from a cell of the first grid and add (number -/- 1) x 9 from the same cell of the second grid.

1x number

2	9	4	2	9	4	2	9	4	2	9	4
7	5	3	7	5	3	7	5	3	7	5	3
6	1	8	6	1	8	6	1	8	6	1	8
2	9	4	2	9	4	2	9	4	2	9	4
7	5	3	7	5	3	7	5	3	7	5	3
6	1	8	6	1	8	6	1	8	6	1	8
2	9	4	2	9	4	2	9	4	2	9	4
7	5	3	7	5	3	7	5	3	7	5	3
6	1	8	6	1	8	6	1	8	6	1	8
2	9	4	2	9	4	2	9	4	2	9	4
7	5	3	7	5	3	7	5	3	7	5	3
6	1	8	6	1	8	6	1	8	6	1	8

+ (number -/- 1) x 9

1	8	13	12	1	8	13	12	1	8	13	12
15	10	3	6	15	10	3	6	15	10	3	6
4	5	16	9	4	5	16	9	4	5	16	9
14	11	2	7	14	11	2	7	14	11	2	7
1	8	13	12	1	8	13	12	1	8	13	12
15	10	3	6	15	10	3	6	15	10	3	6
4	5	16	9	4	5	16	9	4	5	16	9
14	11	2	7	14	11	2	7	14	11	2	7
1	8	13	12	1	8	13	12	1	8	13	12
15	10	3	6	15	10	3	6	15	10	3	6
4	5	16	9	4	5	16	9	4	5	16	9
14	11	2	7	14	11	2	7	14	11	2	7

= composite magic 12x12 square

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

This composite magic 12x12 square has as extra feature that each random chosen 3x4 or 4x3 rectangle inside the square gives the magic sum of 870.

I have used the method composite, AxB compact to construct

12x12, 15x15, 20x20, 21x21, 24x24, 28x28, 30x30a and 30x30b

12x12, Composite, AxB compact.xls

Microsoft Excel werkblad 53.0 KB

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12x12 magic square