12 x 12 Magic Squares

The magic Square below has been created using the technique descibed by Bree and Ollerenshaw.

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

Bree/Ollerensshaw 12x12

Construction

The following two squares illustrate their technique. In the first square, an simple number array has been modified so that the right columns and lower rows have been arranged in reverse order. The cells have also been colored to facilitate following the changes in the second square.

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

Bree/Ollerenshaw Prepared

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

Bree/Ollerenshaw Transformed

Features

The square demonstrates the features they describe. For order n where S = n² - 1:

Download the Spreadsheet

A spreadsheet is available for Download. This spreadsheet will create Bree/Ollerenshaw Magic squares for order 4 to order 40 in steps of 4.

The 12x12 Magic Squares

Technique 3: The Bree/Ollerenshaw Approach

Construction

Features

Download the Spreadsheet