Method of Strachey

Take a 7x7 magic square and construct the second, third and fourth 7x7 magic square by adding (7 x 7 =) 49, (2 x 49 = ) 98 respectively (3 x 49 = ) 147 to all digits of the first 7x7 magic square. Put the first square in the top left corner, put the second square in the bottom right corner, put the third square in the top right corner and put the fourth square in the bottom left corner.

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

The columns and the diagonals give already the magic sum. To get the right sum in the rows, you must swap digits, as follows. We split the 7x7 square in the top left corner and the 7x7 square in the bottom left corner in 'quarters' (marked by the blue digits). The ‘quarters’ top left and bottom left of the 7x7 square in the top left corner must be swapped with the ‘quarters’ top left and bottom left of the 7x7 square in the bottom left corner. Also the (blue) digits on the border between the two 'quarters’ from the second cell up to the crossing point must be swapped. Finally the digits of the top half of the last column(s) must be swapped with the digits of the bottom half of the last column(s). Because the digits of the first two columns must be swapped, the digits of the last (3 – 1 = ) 2 columns must be swapped. See below the result.

14x14 magic square

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

Use this method to construct double odd ( 6x6, 10x10, 14x14, 18x18, ...) magic squares.

14x14, Method of Strachey.xls

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14x14 magic square