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 numbers 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 numbers, 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 numbers). The (yellow marked) ‘quarters’ top left and (red marked) 'quarters' 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 (green marked) blue numbers on the border between the two 'quarters’ from the second cell up to the crossing point must be swapped. Finally the (pink marked) numbers of the top half of the last column(s) must be swapped with the numbers of the bottom half of the last column(s). Because the numbers of the first three columns must be swapped, the numbers 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

ór

1x number from grid with 4x 7x7 magic square

32	40	48	7	8	16	24	32	40	48	7	8	16	24
38	46	5	13	21	22	30	38	46	5	13	21	22	30
44	3	11	19	27	35	36	44	3	11	19	27	35	36
1	9	17	25	33	41	49	1	9	17	25	33	41	49
14	15	23	31	39	47	6	14	15	23	31	39	47	6
20	28	29	37	45	4	12	20	28	29	37	45	4	12
26	34	42	43	2	10	18	26	34	42	43	2	10	18
32	40	48	7	8	16	24	32	40	48	7	8	16	24
38	46	5	13	21	22	30	38	46	5	13	21	22	30
44	3	11	19	27	35	36	44	3	11	19	27	35	36
1	9	17	25	33	41	49	1	9	17	25	33	41	49
14	15	23	31	39	47	6	14	15	23	31	39	47	6
20	28	29	37	45	4	12	20	28	29	37	45	4	12
26	34	42	43	2	10	18	26	34	42	43	2	10	18

+49x number from grid with numbers 0, 1, 2 and 3

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

= 14x14 magic square

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

Use the method of Strachey to construct magic squares of order is double odd. See 6x6, 10x10, 14x14, 18x18, 22x22, 26x26 en 30x30

14x14, Method of Strachey.xls

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14x14 magic square