MULTIMAGIE.COM - 16th-order non-normal trimagic squares

16th-order non-normal trimagic squares

In taking some freedom with the strict definition of a magic square, we have to point out the results of an American, David M. Collison, which communicates in 1991 to John R. Hendricks a trimagic square of order-16.

*1991: 16th-order trimagic square using non consecutive numbers, of David M. Collison*
1160	1189	539	496	672	695	57	10	11	58	631	654	515	558	1123	1152
531	560	675	632	43	66	1179	1132	1133	1180	2	25	651	694	494	523
1155	1089	422	379	831	767	92	45	91	44	790	808	403	360	1118	1126
832	766	99	56	1154	1090	415	368	414	367	1113	1131	80	37	795	803
1106	1135	411	454	716	739	27	74	75	28	757	780	473	430	1143	1172
409	438	717	760	19	42	1115	1162	1163	1116	60	83	779	736	446	475
999	1007	192	235	977	995	164	211	163	210	1018	954	173	216	1036	970
982	990	175	218	994	1012	181	228	180	227	1035	971	156	199	1019	953
183	191	991	1034	195	213	963	1010	962	1009	236	172	972	1015	220	154
200	208	974	1017	178	196	980	1027	979	1026	219	155	955	998	237	171
715	744	20	63	1107	1130	418	465	466	419	1148	1171	82	39	752	781
18	47	1108	1151	410	433	724	771	772	725	451	474	1170	1127	55	84
101	35	1153	1110	423	359	823	776	822	775	382	400	1134	1091	64	72
424	358	830	787	100	36	1146	1099	1145	1098	59	77	811	768	387	395
667	696	46	3	1165	1188	550	503	504	551	1124	1147	22	65	630	659
38	67	1168	1125	536	559	686	639	640	687	495	518	1144	1187	1	30

S1 = 9,520. S2 = 8,228,000. S3 = 7,946,344,000.

His freedom was to have not taken consecutive numbers. The 16x16 = 256 used numbers are between 1 and 1,189, so there are numerous gaps. For example, no number between 237 and 358 was used. In spite of that freedom, hat's off to the artist!

Download the 16th-order non-normal trimagic square of David Collison, Excel file 69Kb.

Jacques Guéron (France), has communicated us in May 2002 a 16th-order non-normal trimagic square that he had constructed in 1987. Like the David Collison's square, he has taken some freedoms with the definition of the magic squares, but different freedoms: the numbers from 0 to 63 are here placed 4 times in his square. In fact, it is the same 8th-order square, more some rotations, placed in the 4 quarters of the 16th-order square.

1987 : 16th-order trimagic square of Jacques Guéron,
using 4 times the numbers from 0 to 63
4	11	29	18	56	55	33	46	17	30	8	7	45	34	52	59
40	39	49	62	20	27	13	2	61	50	36	43	1	14	24	23
15	0	22	25	51	60	42	37	26	21	3	12	38	41	63	48
35	44	58	53	31	16	6	9	54	57	47	32	10	5	19	28
54	57	47	32	10	5	19	28	35	44	58	53	31	16	6	9
26	21	3	12	38	41	63	48	15	0	22	25	51	60	42	37
61	50	36	43	1	14	24	23	40	39	49	62	20	27	13	2
17	30	8	7	45	34	52	59	4	11	29	18	56	55	33	46
46	33	55	56	18	29	11	4	59	52	34	45	7	8	30	17
2	13	27	20	62	49	39	40	23	24	14	1	43	36	50	61
37	42	60	51	25	22	0	15	48	63	41	38	12	3	21	26
9	6	16	31	53	58	44	35	28	19	5	10	32	47	57	54
28	19	5	10	32	47	57	54	9	6	16	31	53	58	44	35
48	63	41	38	12	3	21	26	37	42	60	51	25	22	0	15
23	24	14	1	43	36	50	61	2	13	27	20	62	49	39	40
59	52	34	45	7	8	30	17	46	33	55	56	18	29	11	4

S1 = 504, S2 = 21 336, S3 = 1 016 064.

Download the 16th-order non-normal trimagic square of Jacques Guéron, Excel file 44Kb.

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4	11	29	18	56	55	33	46	17	30	8	7	45	34	52	59
40	39	49	62	20	27	13	2	61	50	36	43	1	14	24	23
15	0	22	25	51	60	42	37	26	21	3	12	38	41	63	48
35	44	58	53	31	16	6	9	54	57	47	32	10	5	19	28
54	57	47	32	10	5	19	28	35	44	58	53	31	16	6	9
26	21	3	12	38	41	63	48	15	0	22	25	51	60	42	37
61	50	36	43	1	14	24	23	40	39	49	62	20	27	13	2
17	30	8	7	45	34	52	59	4	11	29	18	56	55	33	46
46	33	55	56	18	29	11	4	59	52	34	45	7	8	30	17
2	13	27	20	62	49	39	40	23	24	14	1	43	36	50	61
37	42	60	51	25	22	0	15	48	63	41	38	12	3	21	26
9	6	16	31	53	58	44	35	28	19	5	10	32	47	57	54
28	19	5	10	32	47	57	54	9	6	16	31	53	58	44	35
48	63	41	38	12	3	21	26	37	42	60	51	25	22	0	15
23	24	14	1	43	36	50	61	2	13	27	20	62	49	39	40
59	52	34	45	7	8	30	17	46	33	55	56	18	29	11	4

4	11	29	18	56	55	33	46	17	30	8	7	45	34	52	59
40	39	49	62	20	27	13	2	61	50	36	43	1	14	24	23
15	0	22	25	51	60	42	37	26	21	3	12	38	41	63	48
35	44	58	53	31	16	6	9	54	57	47	32	10	5	19	28
54	57	47	32	10	5	19	28	35	44	58	53	31	16	6	9
26	21	3	12	38	41	63	48	15	0	22	25	51	60	42	37
61	50	36	43	1	14	24	23	40	39	49	62	20	27	13	2
17	30	8	7	45	34	52	59	4	11	29	18	56	55	33	46
46	33	55	56	18	29	11	4	59	52	34	45	7	8	30	17
2	13	27	20	62	49	39	40	23	24	14	1	43	36	50	61
37	42	60	51	25	22	0	15	48	63	41	38	12	3	21	26
9	6	16	31	53	58	44	35	28	19	5	10	32	47	57	54
28	19	5	10	32	47	57	54	9	6	16	31	53	58	44	35
48	63	41	38	12	3	21	26	37	42	60	51	25	22	0	15
23	24	14	1	43	36	50	61	2	13	27	20	62	49	39	40
59	52	34	45	7	8	30	17	46	33	55	56	18	29	11	4

4	11	29	18	56	55	33	46	17	30	8	7	45	34	52	59
40	39	49	62	20	27	13	2	61	50	36	43	1	14	24	23
15	0	22	25	51	60	42	37	26	21	3	12	38	41	63	48
35	44	58	53	31	16	6	9	54	57	47	32	10	5	19	28
54	57	47	32	10	5	19	28	35	44	58	53	31	16	6	9
26	21	3	12	38	41	63	48	15	0	22	25	51	60	42	37
61	50	36	43	1	14	24	23	40	39	49	62	20	27	13	2
17	30	8	7	45	34	52	59	4	11	29	18	56	55	33	46
46	33	55	56	18	29	11	4	59	52	34	45	7	8	30	17
2	13	27	20	62	49	39	40	23	24	14	1	43	36	50	61
37	42	60	51	25	22	0	15	48	63	41	38	12	3	21	26
9	6	16	31	53	58	44	35	28	19	5	10	32	47	57	54
28	19	5	10	32	47	57	54	9	6	16	31	53	58	44	35
48	63	41	38	12	3	21	26	37	42	60	51	25	22	0	15
23	24	14	1	43	36	50	61	2	13	27	20	62	49	39	40
59	52	34	45	7	8	30	17	46	33	55	56	18	29	11	4