12 x 12 Magic Squares

The Composite Approach creates a magic square derived from combining an order-3 with an order-4 magic square. The order-3 square is used as a template for a 12x12 component with 4x4 blocks of numbers based on the original square. Each cell in this square is multiplied by 16.

The order-4 square is repeated three times in each axis to create the second 12x12 component.

7	2	3
0	4	8
5	6	1

Original 3x3

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

Original 4x4

7	7	7	7	2	2	2	2	3	3	3	3
7	7	7	7	2	2	2	2	3	3	3	3
7	7	7	7	2	2	2	2	3	3	3	3
7	7	7	7	2	2	2	2	3	3	3	3
0	0	0	0	4	4	4	4	8	8	8	8
0	0	0	0	4	4	4	4	8	8	8	8
0	0	0	0	4	4	4	4	8	8	8	8
0	0	0	0	4	4	4	4	8	8	8	8
5	5	5	5	6	6	6	6	1	1	1	1
5	5	5	5	6	6	6	6	1	1	1	1
5	5	5	5	6	6	6	6	1	1	1	1
5	5	5	5	6	6	6	6	1	1	1	1

16 x

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

+ 1 x

112	119	124	123	32	39	44	43	48	55	60	59
125	122	113	118	45	42	33	38	61	58	49	54
115	116	127	120	35	36	47	40	51	52	63	56
126	121	114	117	46	41	34	37	62	57	50	53
0	7	12	11	64	71	76	75	128	135	140	139
13	10	1	6	77	74	65	70	141	138	129	134
3	4	15	8	67	68	79	72	131	132	143	136
14	9	2	5	78	73	66	69	142	137	130	133
80	87	92	91	96	103	108	107	16	23	28	27
93	90	81	86	109	106	97	102	29	26	17	22
83	84	95	88	99	100	111	104	19	20	31	24
94	89	82	85	110	105	98	101	30	25	18	21

Total Order 12 magic Square

Resulting Magic Square

Using this technique, the final square cannot be Pan-Magic because the original 3x3 square is not Pan-Magic. This technique is included here to illusrate the use of the composite technique.

The 12x12 Magic Squares

Technique 2: The Composite Approach

Resulting Magic Square

112	119	124	123	32	39	44	43	48	55	60	59
125	122	113	118	45	42	33	38	61	58	49	54
115	116	127	120	35	36	47	40	51	52	63	56
126	121	114	117	46	41	34	37	62	57	50	53
0	7	12	11	64	71	76	75	128	135	140	139
13	10	1	6	77	74	65	70	141	138	129	134
3	4	15	8	67	68	79	72	131	132	143	136
14	9	2	5	78	73	66	69	142	137	130	133
80	87	92	91	96	103	108	107	16	23	28	27
93	90	81	86	109	106	97	102	29	26	17	22
83	84	95	88	99	100	111	104	19	20	31	24
94	89	82	85	110	105	98	101	30	25	18	21

112	119	124	123	32	39	44	43	48	55	60	59
125	122	113	118	45	42	33	38	61	58	49	54
115	116	127	120	35	36	47	40	51	52	63	56
126	121	114	117	46	41	34	37	62	57	50	53
0	7	12	11	64	71	76	75	128	135	140	139
13	10	1	6	77	74	65	70	141	138	129	134
3	4	15	8	67	68	79	72	131	132	143	136
14	9	2	5	78	73	66	69	142	137	130	133
80	87	92	91	96	103	108	107	16	23	28	27
93	90	81	86	109	106	97	102	29	26	17	22
83	84	95	88	99	100	111	104	19	20	31	24
94	89	82	85	110	105	98	101	30	25	18	21

112	119	124	123	32	39	44	43	48	55	60	59
125	122	113	118	45	42	33	38	61	58	49	54
115	116	127	120	35	36	47	40	51	52	63	56
126	121	114	117	46	41	34	37	62	57	50	53
0	7	12	11	64	71	76	75	128	135	140	139
13	10	1	6	77	74	65	70	141	138	129	134
3	4	15	8	67	68	79	72	131	132	143	136
14	9	2	5	78	73	66	69	142	137	130	133
80	87	92	91	96	103	108	107	16	23	28	27
93	90	81	86	109	106	97	102	29	26	17	22
83	84	95	88	99	100	111	104	19	20	31	24
94	89	82	85	110	105	98	101	30	25	18	21