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* 16 * 20 * 24 * 28 * 32 * 36 * 40 * 44 * 48 * 52 * 56 *
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A 44x44 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (42614)

A Magic Square is a square of numbers in which every row, every column, and both diagonals add up to the same number. This number is often called the magic sum. The 44 by 44 magic square shown below has a magic sum equal to 42614.
Though magic squares can be made with non-consecutive and non-regular sequences, they are usually seen made up of consecutive numbers, possibly because it is harder to be consecutive.

The method described below can be used to create all 4N+0 (multiple-of-four) magic squares. This is just one method for creating magic squares, there are many other methods, and many-many-many magic squares to be found.

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How to Create a 44x44 Magic Square
with a Magic Sum of 42614

The method described on this page can be used to create 4x4, 8x8, 12x12, 16x16 and larger 4N+0 magic squares

Steps:

Draw a 44x44 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 44x44 square.
Starting in the top left corner, moving left to right through the rows, count the squares, 1, 2, 3, 4, but only write down the numbers you say when you get to one of the colored in squares. If you do this properly, you will write 1 in the top left corner and write 1936 in the bottom right corner.
Next, do the same thing, starting in the bottom right corner, moving right-to-left upward through the rows, again count from 1 to 1936, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 44x44 blank grid and
shade in the two main diagonals

You don't necessarily have to shade in the squares. You could simply draw a light line that passes through these squares. You only need to be able to tell the difference between squares that are on these 4x4 diagonals and those that are not.

Step Two: Shade in all the 4x4 diagonals

If you are making a square larger than 4x4, the entire square can be visualized as a collection of 4x4 squares. Shade in the main diagonals of each 4x4 square within the big square.

If you do this correctly, by the time you are done, you will have shaded in exactly half the squares in your overall grid. If you had simply drawn diagonal lines through those squares, you would see a series of X's.

Step Three: Count the squares
(writing only on the shaded squares)

This is fairly straightforward. Starting in the top left corner, and moving left-to-right through each row, count the squares, but only write down the numbers in the shaded squares, but remember to count all the blank squares. In the first four spaces, you would write down 1, count 2 and 3, and write down 4. Continue until you have written down the last number (1936).

Step Four: Count the squares again, counting backward,
writing into the blank squares

This time, you can either

Start counting backward, starting with 1936 (which you would not write down) and count downward, writing down the number whenever you come to a blank square. The last two numbers you write down would be 3 and 2 just before you get to the 1936 which you wrote down in Step Three.
Or, if you prefer counting upward, start with 1 in the bottom right corner and move right-to-left through each row until you get to the top left corner. Working this way, you will skip 1 (because 1936 is already written in that square), write down 2 and 3, then skip 4, etc.

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A 44-by-44 Magic Square

(Magic Sum = 42614)

1	1935	1934	4	5	1931	1930	8	9	1927	1926	12	13	1923	1922	16	17	1919	1918	20	21	1915	1914	24	25	1911	1910	28	29	1907	1906	32	33	1903	1902	36	37	1899	1898	40	41	1895	1894	44
1892	46	47	1889	1888	50	51	1885	1884	54	55	1881	1880	58	59	1877	1876	62	63	1873	1872	66	67	1869	1868	70	71	1865	1864	74	75	1861	1860	78	79	1857	1856	82	83	1853	1852	86	87	1849
1848	90	91	1845	1844	94	95	1841	1840	98	99	1837	1836	102	103	1833	1832	106	107	1829	1828	110	111	1825	1824	114	115	1821	1820	118	119	1817	1816	122	123	1813	1812	126	127	1809	1808	130	131	1805
133	1803	1802	136	137	1799	1798	140	141	1795	1794	144	145	1791	1790	148	149	1787	1786	152	153	1783	1782	156	157	1779	1778	160	161	1775	1774	164	165	1771	1770	168	169	1767	1766	172	173	1763	1762	176
177	1759	1758	180	181	1755	1754	184	185	1751	1750	188	189	1747	1746	192	193	1743	1742	196	197	1739	1738	200	201	1735	1734	204	205	1731	1730	208	209	1727	1726	212	213	1723	1722	216	217	1719	1718	220
1716	222	223	1713	1712	226	227	1709	1708	230	231	1705	1704	234	235	1701	1700	238	239	1697	1696	242	243	1693	1692	246	247	1689	1688	250	251	1685	1684	254	255	1681	1680	258	259	1677	1676	262	263	1673
1672	266	267	1669	1668	270	271	1665	1664	274	275	1661	1660	278	279	1657	1656	282	283	1653	1652	286	287	1649	1648	290	291	1645	1644	294	295	1641	1640	298	299	1637	1636	302	303	1633	1632	306	307	1629
309	1627	1626	312	313	1623	1622	316	317	1619	1618	320	321	1615	1614	324	325	1611	1610	328	329	1607	1606	332	333	1603	1602	336	337	1599	1598	340	341	1595	1594	344	345	1591	1590	348	349	1587	1586	352
353	1583	1582	356	357	1579	1578	360	361	1575	1574	364	365	1571	1570	368	369	1567	1566	372	373	1563	1562	376	377	1559	1558	380	381	1555	1554	384	385	1551	1550	388	389	1547	1546	392	393	1543	1542	396
1540	398	399	1537	1536	402	403	1533	1532	406	407	1529	1528	410	411	1525	1524	414	415	1521	1520	418	419	1517	1516	422	423	1513	1512	426	427	1509	1508	430	431	1505	1504	434	435	1501	1500	438	439	1497
1496	442	443	1493	1492	446	447	1489	1488	450	451	1485	1484	454	455	1481	1480	458	459	1477	1476	462	463	1473	1472	466	467	1469	1468	470	471	1465	1464	474	475	1461	1460	478	479	1457	1456	482	483	1453
485	1451	1450	488	489	1447	1446	492	493	1443	1442	496	497	1439	1438	500	501	1435	1434	504	505	1431	1430	508	509	1427	1426	512	513	1423	1422	516	517	1419	1418	520	521	1415	1414	524	525	1411	1410	528
529	1407	1406	532	533	1403	1402	536	537	1399	1398	540	541	1395	1394	544	545	1391	1390	548	549	1387	1386	552	553	1383	1382	556	557	1379	1378	560	561	1375	1374	564	565	1371	1370	568	569	1367	1366	572
1364	574	575	1361	1360	578	579	1357	1356	582	583	1353	1352	586	587	1349	1348	590	591	1345	1344	594	595	1341	1340	598	599	1337	1336	602	603	1333	1332	606	607	1329	1328	610	611	1325	1324	614	615	1321
1320	618	619	1317	1316	622	623	1313	1312	626	627	1309	1308	630	631	1305	1304	634	635	1301	1300	638	639	1297	1296	642	643	1293	1292	646	647	1289	1288	650	651	1285	1284	654	655	1281	1280	658	659	1277
661	1275	1274	664	665	1271	1270	668	669	1267	1266	672	673	1263	1262	676	677	1259	1258	680	681	1255	1254	684	685	1251	1250	688	689	1247	1246	692	693	1243	1242	696	697	1239	1238	700	701	1235	1234	704
705	1231	1230	708	709	1227	1226	712	713	1223	1222	716	717	1219	1218	720	721	1215	1214	724	725	1211	1210	728	729	1207	1206	732	733	1203	1202	736	737	1199	1198	740	741	1195	1194	744	745	1191	1190	748
1188	750	751	1185	1184	754	755	1181	1180	758	759	1177	1176	762	763	1173	1172	766	767	1169	1168	770	771	1165	1164	774	775	1161	1160	778	779	1157	1156	782	783	1153	1152	786	787	1149	1148	790	791	1145
1144	794	795	1141	1140	798	799	1137	1136	802	803	1133	1132	806	807	1129	1128	810	811	1125	1124	814	815	1121	1120	818	819	1117	1116	822	823	1113	1112	826	827	1109	1108	830	831	1105	1104	834	835	1101
837	1099	1098	840	841	1095	1094	844	845	1091	1090	848	849	1087	1086	852	853	1083	1082	856	857	1079	1078	860	861	1075	1074	864	865	1071	1070	868	869	1067	1066	872	873	1063	1062	876	877	1059	1058	880
881	1055	1054	884	885	1051	1050	888	889	1047	1046	892	893	1043	1042	896	897	1039	1038	900	901	1035	1034	904	905	1031	1030	908	909	1027	1026	912	913	1023	1022	916	917	1019	1018	920	921	1015	1014	924
1012	926	927	1009	1008	930	931	1005	1004	934	935	1001	1000	938	939	997	996	942	943	993	992	946	947	989	988	950	951	985	984	954	955	981	980	958	959	977	976	962	963	973	972	966	967	969
968	970	971	965	964	974	975	961	960	978	979	957	956	982	983	953	952	986	987	949	948	990	991	945	944	994	995	941	940	998	999	937	936	1002	1003	933	932	1006	1007	929	928	1010	1011	925
1013	923	922	1016	1017	919	918	1020	1021	915	914	1024	1025	911	910	1028	1029	907	906	1032	1033	903	902	1036	1037	899	898	1040	1041	895	894	1044	1045	891	890	1048	1049	887	886	1052	1053	883	882	1056
1057	879	878	1060	1061	875	874	1064	1065	871	870	1068	1069	867	866	1072	1073	863	862	1076	1077	859	858	1080	1081	855	854	1084	1085	851	850	1088	1089	847	846	1092	1093	843	842	1096	1097	839	838	1100
836	1102	1103	833	832	1106	1107	829	828	1110	1111	825	824	1114	1115	821	820	1118	1119	817	816	1122	1123	813	812	1126	1127	809	808	1130	1131	805	804	1134	1135	801	800	1138	1139	797	796	1142	1143	793
792	1146	1147	789	788	1150	1151	785	784	1154	1155	781	780	1158	1159	777	776	1162	1163	773	772	1166	1167	769	768	1170	1171	765	764	1174	1175	761	760	1178	1179	757	756	1182	1183	753	752	1186	1187	749
1189	747	746	1192	1193	743	742	1196	1197	739	738	1200	1201	735	734	1204	1205	731	730	1208	1209	727	726	1212	1213	723	722	1216	1217	719	718	1220	1221	715	714	1224	1225	711	710	1228	1229	707	706	1232
1233	703	702	1236	1237	699	698	1240	1241	695	694	1244	1245	691	690	1248	1249	687	686	1252	1253	683	682	1256	1257	679	678	1260	1261	675	674	1264	1265	671	670	1268	1269	667	666	1272	1273	663	662	1276
660	1278	1279	657	656	1282	1283	653	652	1286	1287	649	648	1290	1291	645	644	1294	1295	641	640	1298	1299	637	636	1302	1303	633	632	1306	1307	629	628	1310	1311	625	624	1314	1315	621	620	1318	1319	617
616	1322	1323	613	612	1326	1327	609	608	1330	1331	605	604	1334	1335	601	600	1338	1339	597	596	1342	1343	593	592	1346	1347	589	588	1350	1351	585	584	1354	1355	581	580	1358	1359	577	576	1362	1363	573
1365	571	570	1368	1369	567	566	1372	1373	563	562	1376	1377	559	558	1380	1381	555	554	1384	1385	551	550	1388	1389	547	546	1392	1393	543	542	1396	1397	539	538	1400	1401	535	534	1404	1405	531	530	1408
1409	527	526	1412	1413	523	522	1416	1417	519	518	1420	1421	515	514	1424	1425	511	510	1428	1429	507	506	1432	1433	503	502	1436	1437	499	498	1440	1441	495	494	1444	1445	491	490	1448	1449	487	486	1452
484	1454	1455	481	480	1458	1459	477	476	1462	1463	473	472	1466	1467	469	468	1470	1471	465	464	1474	1475	461	460	1478	1479	457	456	1482	1483	453	452	1486	1487	449	448	1490	1491	445	444	1494	1495	441
440	1498	1499	437	436	1502	1503	433	432	1506	1507	429	428	1510	1511	425	424	1514	1515	421	420	1518	1519	417	416	1522	1523	413	412	1526	1527	409	408	1530	1531	405	404	1534	1535	401	400	1538	1539	397
1541	395	394	1544	1545	391	390	1548	1549	387	386	1552	1553	383	382	1556	1557	379	378	1560	1561	375	374	1564	1565	371	370	1568	1569	367	366	1572	1573	363	362	1576	1577	359	358	1580	1581	355	354	1584
1585	351	350	1588	1589	347	346	1592	1593	343	342	1596	1597	339	338	1600	1601	335	334	1604	1605	331	330	1608	1609	327	326	1612	1613	323	322	1616	1617	319	318	1620	1621	315	314	1624	1625	311	310	1628
308	1630	1631	305	304	1634	1635	301	300	1638	1639	297	296	1642	1643	293	292	1646	1647	289	288	1650	1651	285	284	1654	1655	281	280	1658	1659	277	276	1662	1663	273	272	1666	1667	269	268	1670	1671	265
264	1674	1675	261	260	1678	1679	257	256	1682	1683	253	252	1686	1687	249	248	1690	1691	245	244	1694	1695	241	240	1698	1699	237	236	1702	1703	233	232	1706	1707	229	228	1710	1711	225	224	1714	1715	221
1717	219	218	1720	1721	215	214	1724	1725	211	210	1728	1729	207	206	1732	1733	203	202	1736	1737	199	198	1740	1741	195	194	1744	1745	191	190	1748	1749	187	186	1752	1753	183	182	1756	1757	179	178	1760
1761	175	174	1764	1765	171	170	1768	1769	167	166	1772	1773	163	162	1776	1777	159	158	1780	1781	155	154	1784	1785	151	150	1788	1789	147	146	1792	1793	143	142	1796	1797	139	138	1800	1801	135	134	1804
132	1806	1807	129	128	1810	1811	125	124	1814	1815	121	120	1818	1819	117	116	1822	1823	113	112	1826	1827	109	108	1830	1831	105	104	1834	1835	101	100	1838	1839	97	96	1842	1843	93	92	1846	1847	89
88	1850	1851	85	84	1854	1855	81	80	1858	1859	77	76	1862	1863	73	72	1866	1867	69	68	1870	1871	65	64	1874	1875	61	60	1878	1879	57	56	1882	1883	53	52	1886	1887	49	48	1890	1891	45
1893	43	42	1896	1897	39	38	1900	1901	35	34	1904	1905	31	30	1908	1909	27	26	1912	1913	23	22	1916	1917	19	18	1920	1921	15	14	1924	1925	11	10	1928	1929	7	6	1932	1933	3	2	1936

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A 44x44 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (42614)

Read more about Magic Squares

How to Create a 44x44 Magic Square with a Magic Sum of 42614

Step One: Draw a 44x44 blank grid and shade in the two main diagonals

Step Two: Shade in all the 4x4 diagonals

Step Three: Count the squares (writing only on the shaded squares)

Step Four: Count the squares again, counting backward, writing into the blank squares

A 44-by-44 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (42614)

How to Create a 44x44 Magic Square
with a Magic Sum of 42614

Step One: Draw a 44x44 blank grid and
shade in the two main diagonals

Step Three: Count the squares
(writing only on the shaded squares)

Step Four: Count the squares again, counting backward,
writing into the blank squares