Method of Strachey

Take a 9x9 magic square and construct the second, third and fourth 9x9 magic square by adding (9 x 9 =) 81, (2 x 81 = ) 162 respectively (3 x 81 = ) 243 to all numbers of the first 9x9 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.

37	78	29	70	21	62	13	54	5	199	240	191	232	183	224	175	216	167
6	38	79	30	71	22	63	14	46	168	200	241	192	233	184	225	176	208
47	7	39	80	31	72	23	55	15	209	169	201	242	193	234	185	217	177
16	48	8	40	81	32	64	24	56	178	210	170	202	243	194	226	186	218
57	17	49	9	41	73	33	65	25	219	179	211	171	203	235	195	227	187
26	58	18	50	1	42	74	34	66	188	220	180	212	163	204	236	196	228
67	27	59	10	51	2	43	75	35	229	189	221	172	213	164	205	237	197
36	68	19	60	11	52	3	44	76	198	230	181	222	173	214	165	206	238
77	28	69	20	61	12	53	4	45	239	190	231	182	223	174	215	166	207
280	321	272	313	264	305	256	297	248	118	159	110	151	102	143	94	135	86
249	281	322	273	314	265	306	257	289	87	119	160	111	152	103	144	95	127
290	250	282	323	274	315	266	298	258	128	88	120	161	112	153	104	136	96
259	291	251	283	324	275	307	267	299	97	129	89	121	162	113	145	105	137
300	260	292	252	284	316	276	308	268	138	98	130	90	122	154	114	146	106
269	301	261	293	244	285	317	277	309	107	139	99	131	82	123	155	115	147
310	270	302	253	294	245	286	318	278	148	108	140	91	132	83	124	156	116
279	311	262	303	254	295	246	287	319	117	149	100	141	92	133	84	125	157
320	271	312	263	304	255	296	247	288	158	109	150	101	142	93	134	85	126

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 9x9 square in the top left corner and the 9x9 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 9x9 square in the top left corner must be swapped with the ‘quarters’ top left and bottom left of the 9x9 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 four columns must be swapped, the numbers of the last (4 – 1 = ) 3 columns must be swapped. See below the result.

18x18 magic square

280	321	272	313	21	62	13	54	5	199	240	191	232	183	224	94	135	86
249	281	322	273	71	22	63	14	46	168	200	241	192	233	184	144	95	127
290	250	282	323	31	72	23	55	15	209	169	201	242	193	234	104	136	96
259	291	251	283	81	32	64	24	56	178	210	170	202	243	194	145	105	137
57	260	292	252	284	73	33	65	25	219	179	211	171	203	235	114	146	106
269	301	261	293	1	42	74	34	66	188	220	180	212	163	204	155	115	147
310	270	302	253	51	2	43	75	35	229	189	221	172	213	164	124	156	116
279	311	262	303	11	52	3	44	76	198	230	181	222	173	214	84	125	157
320	271	312	263	61	12	53	4	45	239	190	231	182	223	174	134	85	126
37	78	29	70	264	305	256	297	248	118	159	110	151	102	143	175	216	167
6	38	79	30	314	265	306	257	289	87	119	160	111	152	103	225	176	208
47	7	39	80	274	315	266	298	258	128	88	120	161	112	153	185	217	177
16	48	8	40	324	275	307	267	299	97	129	89	121	162	113	226	186	218
300	17	49	9	41	316	276	308	268	138	98	130	90	122	154	195	227	187
26	58	18	50	244	285	317	277	309	107	139	99	131	82	123	236	196	228
67	27	59	10	294	245	286	318	278	148	108	140	91	132	83	205	237	197
36	68	19	60	254	295	246	287	319	117	149	100	141	92	133	165	206	238
77	28	69	20	304	255	296	247	288	158	109	150	101	142	93	215	166	207

ór

1x number from grid with 4x 9x9 magic square

1	68	54	6	70	47	8	66	49	1	68	54	6	70	47	8	66	49
44	21	58	37	23	63	42	25	56	44	21	58	37	23	63	42	25	56
78	34	11	80	30	13	73	32	18	78	34	11	80	30	13	73	32	18
46	5	72	51	7	65	53	3	67	46	5	72	51	7	65	53	3	67
62	39	22	55	41	27	60	43	20	62	39	22	55	41	27	60	43	20
15	79	29	17	75	31	10	77	36	15	79	29	17	75	31	10	77	36
64	50	9	69	52	2	71	48	4	64	50	9	69	52	2	71	48	4
26	57	40	19	59	45	24	61	38	26	57	40	19	59	45	24	61	38
33	16	74	35	12	76	28	14	81	33	16	74	35	12	76	28	14	81
1	68	54	6	70	47	8	66	49	1	68	54	6	70	47	8	66	49
44	21	58	37	23	63	42	25	56	44	21	58	37	23	63	42	25	56
78	34	11	80	30	13	73	32	18	78	34	11	80	30	13	73	32	18
46	5	72	51	7	65	53	3	67	46	5	72	51	7	65	53	3	67
62	39	22	55	41	27	60	43	20	62	39	22	55	41	27	60	43	20
15	79	29	17	75	31	10	77	36	15	79	29	17	75	31	10	77	36
64	50	9	69	52	2	71	48	4	64	50	9	69	52	2	71	48	4
26	57	40	19	59	45	24	61	38	26	57	40	19	59	45	24	61	38
33	16	74	35	12	76	28	14	81	33	16	74	35	12	76	28	14	81

+81x number from grid with numbers 0, 1, 2 and 3

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

= 18x18 magic square

1	68	54	6	70	290	251	309	292	163	230	216	168	232	209	89	147	130
44	264	301	280	266	63	42	25	56	206	183	220	199	185	225	123	106	137
78	277	254	323	273	13	73	32	18	240	196	173	242	192	175	154	113	99
46	248	315	294	250	65	53	3	67	208	167	234	213	169	227	134	84	148
62	282	265	298	284	27	60	43	20	224	201	184	217	203	189	141	124	101
15	322	272	260	318	31	10	77	36	177	241	191	179	237	193	91	158	117
64	293	252	312	295	2	71	48	4	226	212	171	231	214	164	152	129	85
26	300	283	262	302	45	24	61	38	188	219	202	181	221	207	105	142	119
33	16	74	35	12	319	271	257	324	195	178	236	197	174	238	109	95	162
244	311	297	249	313	47	8	66	49	82	149	135	87	151	128	170	228	211
287	21	58	37	23	306	285	268	299	125	102	139	118	104	144	204	187	218
321	34	11	80	30	256	316	275	261	159	115	92	161	111	94	235	194	180
289	5	72	51	7	308	296	246	310	127	86	153	132	88	146	215	165	229
305	39	22	55	41	270	303	286	263	143	120	103	136	122	108	222	205	182
258	79	29	17	75	274	253	320	279	96	160	110	98	156	112	172	239	198
307	50	9	69	52	245	314	291	247	145	131	90	150	133	83	233	210	166
269	57	40	19	59	288	267	304	281	107	138	121	100	140	126	186	223	200
276	259	317	278	255	76	28	14	81	114	97	155	116	93	157	190	176	243

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

18x18, Method of Strachey.xls

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18x18 magic square