The 18th-order pan-Bimagic square

　

The 18th-order pan-Bimagic square

by Su Maoting in China for 2000-09

＋	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
1	66	1921	98	1913	56	1834	1457	1226	1342	1330	1284	1431	1756	132	1839	36	1939	14
2	339	385	217	918	2109	888	2128	711	2118	2066	773	2110	812	2183	944	295	397	281
3	100	54	1473	78	1297	1899	1218	1850	1804	1786	1902	1292	1961	1375	2	1415	80	88
4	962	824	353	733	323	2129	262	2158	2175	2117	2080	250	2055	297	751	429	876	900
5	1345	1481	1281	133	1826	38	1838	34	1943	1917	46	1914	96	1764	55	1229	1407	1327
6	703	2063	813	2113	940	2133	417	294	341	279	218	365	2159	922	2125	887	2121	781
7	1808	1293	1882	1305	1959	1418	1	85	30	104	103	79	1470	1901	1367	1870	1217	1782
8	2081	2115	2105	230	748	301	879	428	892	970	354	821	319	736	282	2079	2177	2157
9	1893	1915	49	1766	93	1249	125	1323	1406	1482	1349	63	1261	41	1824	31	1837	1967
10	219	349	2155	362	2145	925	2123	837	704	780	863	2061	937	2093	420	2137	271	293
11	29	9	107	1904	1450	1867	1365	1832	1216	1294	1758	1307	1885	1438	1956	81	71	105
12	404	969	316	819	285	716	2107	2083	2082	2156	2101	2185	768	227	881	304	893	378
13	1405	65	1299	61	1264	27	1821	1968	1907	1845	1892	1769	53	1246	73	1373	123	1483
14	859	779	957	2131	422	2090	272	2140	269	243	2152	348	2148	360	2053	905	705	841
15	1286	1310	1757	1435	1889	131	1936	106	69	11	28	1924	57	1863	1453	1833	1362	1224
16	2098	2106	771	2184	811	225	894	284	400	382	336	968	287	889	2108	713	2132	2086
17	1905	1789	1891	1242	3	1374	76	1413	120	68	1475	58	1298	77	1268	1969	1801	1847
18	2172	247	2150	347	2054	430	755	902	856	844	960	729	352	2130	273	2088	265	2120

18*18
Min=1; Max=2185；
that the sum of the entries of any row, any column, or any pan diagonal is the same. C₁= 19 674 ；
that square sum of the entries of any row, any column, or any pan diagonal is the same.C₂= 31 866 762 ；
that the cube sum of the entries of any main and fan diagonal is the same.C₃= 57 484 063 746 ；

　