The 18th-order pan-Bimagic square

　

The 18th-order pan-Bimagic square

by Su Maoting for 2001-03

＋	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
1	1	225	711	1086	560	137	988	1378	1305	71	227	729	1114	500	87	946	1316	1237
2	712	327	893	1321	469	90	132	1375	1190	652	277	851	1259	401	20	130	1357	1162
3	564	147	968	1356	1285	6	201	699	1069	496	77	966	1338	1257	66	251	741	1131
4	449	25	106	1345	1145	648	267	871	1281	421	85	156	1387	1207	716	337	873	1299
5	1240	2	191	719	1091	516	142	992	1368	1302	70	261	721	1109	544	82	942	1326
6	1167	668	332	897	1311	466	89	166	1367	1185	696	272	847	1269	404	21	96	1365
7	1121	561	146	1002	1348	1280	50	196	695	1079	499	78	932	1346	1262	22	256	745
8	1291	444	69	101	1341	1155	651	268	837	1289	426	41	161	1391	1197	713	336	907
9	1322	1250	5	192	685	1099	521	98	997	1372	1292	67	260	755	1101	539	126	937
10	1331	1175	673	288	902	1315	456	86	165	1401	1177	691	316	842	1265	414	24	97
11	750	1125	551	143	1001	1382	1272	45	240	690	1075	509	81	933	1312	1270	27	212
12	906	1325	436	64	145	1336	1151	661	271	838	1255	434	46	117	1396	1201	703	333
13	981	1317	1246	15	195	686	1065	529	103	953	1377	1296	57	257	754	1135	531	121
14	100	1332	1141	681	293	858	1320	460	76	162	1400	1211	683	311	886	1260	410	34
15	217	706	1130	555	133	998	1381	1306	37	235	734	1070	505	91	936	1313	1236	35
16	323	903	1324	470	56	140	1380	1146	657	281	841	1256	400	54	122	1352	1206	707
17	113	976	1361	1241	11	205	689	1066	495	111	958	1333	1301	61	247	751	1134	565
18	30	110	1335	1142	647	301	863	1276	465	80	152	1397	1210	717	303	881	1304	405

18*18
Min=1; Max=1401；
that the sum of the entries of any row, any column, or any pan diagonal is the same. C₁= 12618 ；
that square sum of the entries of any row, any column, or any pan diagonal is the same. C₂= 12889482 ；
that the cube sum of the entries of any main and pan diagonal is the same. C₃= 14 705 585 010 ；