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A 48x48 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (55320)

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 48 by 48 magic square shown below has a magic sum equal to 55320.
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 48x48 Magic Square
with a Magic Sum of 55320

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

Steps:

Draw a 48x48 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 48x48 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 2304 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 2304, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 48x48 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 (2304).

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

This time, you can either

Start counting backward, starting with 2304 (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 2304 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 2304 is already written in that square), write down 2 and 3, then skip 4, etc.

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A 48-by-48 Magic Square

(Magic Sum = 55320)

1	2303	2302	4	5	2299	2298	8	9	2295	2294	12	13	2291	2290	16	17	2287	2286	20	21	2283	2282	24	25	2279	2278	28	29	2275	2274	32	33	2271	2270	36	37	2267	2266	40	41	2263	2262	44	45	2259	2258	48
2256	50	51	2253	2252	54	55	2249	2248	58	59	2245	2244	62	63	2241	2240	66	67	2237	2236	70	71	2233	2232	74	75	2229	2228	78	79	2225	2224	82	83	2221	2220	86	87	2217	2216	90	91	2213	2212	94	95	2209
2208	98	99	2205	2204	102	103	2201	2200	106	107	2197	2196	110	111	2193	2192	114	115	2189	2188	118	119	2185	2184	122	123	2181	2180	126	127	2177	2176	130	131	2173	2172	134	135	2169	2168	138	139	2165	2164	142	143	2161
145	2159	2158	148	149	2155	2154	152	153	2151	2150	156	157	2147	2146	160	161	2143	2142	164	165	2139	2138	168	169	2135	2134	172	173	2131	2130	176	177	2127	2126	180	181	2123	2122	184	185	2119	2118	188	189	2115	2114	192
193	2111	2110	196	197	2107	2106	200	201	2103	2102	204	205	2099	2098	208	209	2095	2094	212	213	2091	2090	216	217	2087	2086	220	221	2083	2082	224	225	2079	2078	228	229	2075	2074	232	233	2071	2070	236	237	2067	2066	240
2064	242	243	2061	2060	246	247	2057	2056	250	251	2053	2052	254	255	2049	2048	258	259	2045	2044	262	263	2041	2040	266	267	2037	2036	270	271	2033	2032	274	275	2029	2028	278	279	2025	2024	282	283	2021	2020	286	287	2017
2016	290	291	2013	2012	294	295	2009	2008	298	299	2005	2004	302	303	2001	2000	306	307	1997	1996	310	311	1993	1992	314	315	1989	1988	318	319	1985	1984	322	323	1981	1980	326	327	1977	1976	330	331	1973	1972	334	335	1969
337	1967	1966	340	341	1963	1962	344	345	1959	1958	348	349	1955	1954	352	353	1951	1950	356	357	1947	1946	360	361	1943	1942	364	365	1939	1938	368	369	1935	1934	372	373	1931	1930	376	377	1927	1926	380	381	1923	1922	384
385	1919	1918	388	389	1915	1914	392	393	1911	1910	396	397	1907	1906	400	401	1903	1902	404	405	1899	1898	408	409	1895	1894	412	413	1891	1890	416	417	1887	1886	420	421	1883	1882	424	425	1879	1878	428	429	1875	1874	432
1872	434	435	1869	1868	438	439	1865	1864	442	443	1861	1860	446	447	1857	1856	450	451	1853	1852	454	455	1849	1848	458	459	1845	1844	462	463	1841	1840	466	467	1837	1836	470	471	1833	1832	474	475	1829	1828	478	479	1825
1824	482	483	1821	1820	486	487	1817	1816	490	491	1813	1812	494	495	1809	1808	498	499	1805	1804	502	503	1801	1800	506	507	1797	1796	510	511	1793	1792	514	515	1789	1788	518	519	1785	1784	522	523	1781	1780	526	527	1777
529	1775	1774	532	533	1771	1770	536	537	1767	1766	540	541	1763	1762	544	545	1759	1758	548	549	1755	1754	552	553	1751	1750	556	557	1747	1746	560	561	1743	1742	564	565	1739	1738	568	569	1735	1734	572	573	1731	1730	576
577	1727	1726	580	581	1723	1722	584	585	1719	1718	588	589	1715	1714	592	593	1711	1710	596	597	1707	1706	600	601	1703	1702	604	605	1699	1698	608	609	1695	1694	612	613	1691	1690	616	617	1687	1686	620	621	1683	1682	624
1680	626	627	1677	1676	630	631	1673	1672	634	635	1669	1668	638	639	1665	1664	642	643	1661	1660	646	647	1657	1656	650	651	1653	1652	654	655	1649	1648	658	659	1645	1644	662	663	1641	1640	666	667	1637	1636	670	671	1633
1632	674	675	1629	1628	678	679	1625	1624	682	683	1621	1620	686	687	1617	1616	690	691	1613	1612	694	695	1609	1608	698	699	1605	1604	702	703	1601	1600	706	707	1597	1596	710	711	1593	1592	714	715	1589	1588	718	719	1585
721	1583	1582	724	725	1579	1578	728	729	1575	1574	732	733	1571	1570	736	737	1567	1566	740	741	1563	1562	744	745	1559	1558	748	749	1555	1554	752	753	1551	1550	756	757	1547	1546	760	761	1543	1542	764	765	1539	1538	768
769	1535	1534	772	773	1531	1530	776	777	1527	1526	780	781	1523	1522	784	785	1519	1518	788	789	1515	1514	792	793	1511	1510	796	797	1507	1506	800	801	1503	1502	804	805	1499	1498	808	809	1495	1494	812	813	1491	1490	816
1488	818	819	1485	1484	822	823	1481	1480	826	827	1477	1476	830	831	1473	1472	834	835	1469	1468	838	839	1465	1464	842	843	1461	1460	846	847	1457	1456	850	851	1453	1452	854	855	1449	1448	858	859	1445	1444	862	863	1441
1440	866	867	1437	1436	870	871	1433	1432	874	875	1429	1428	878	879	1425	1424	882	883	1421	1420	886	887	1417	1416	890	891	1413	1412	894	895	1409	1408	898	899	1405	1404	902	903	1401	1400	906	907	1397	1396	910	911	1393
913	1391	1390	916	917	1387	1386	920	921	1383	1382	924	925	1379	1378	928	929	1375	1374	932	933	1371	1370	936	937	1367	1366	940	941	1363	1362	944	945	1359	1358	948	949	1355	1354	952	953	1351	1350	956	957	1347	1346	960
961	1343	1342	964	965	1339	1338	968	969	1335	1334	972	973	1331	1330	976	977	1327	1326	980	981	1323	1322	984	985	1319	1318	988	989	1315	1314	992	993	1311	1310	996	997	1307	1306	1000	1001	1303	1302	1004	1005	1299	1298	1008
1296	1010	1011	1293	1292	1014	1015	1289	1288	1018	1019	1285	1284	1022	1023	1281	1280	1026	1027	1277	1276	1030	1031	1273	1272	1034	1035	1269	1268	1038	1039	1265	1264	1042	1043	1261	1260	1046	1047	1257	1256	1050	1051	1253	1252	1054	1055	1249
1248	1058	1059	1245	1244	1062	1063	1241	1240	1066	1067	1237	1236	1070	1071	1233	1232	1074	1075	1229	1228	1078	1079	1225	1224	1082	1083	1221	1220	1086	1087	1217	1216	1090	1091	1213	1212	1094	1095	1209	1208	1098	1099	1205	1204	1102	1103	1201
1105	1199	1198	1108	1109	1195	1194	1112	1113	1191	1190	1116	1117	1187	1186	1120	1121	1183	1182	1124	1125	1179	1178	1128	1129	1175	1174	1132	1133	1171	1170	1136	1137	1167	1166	1140	1141	1163	1162	1144	1145	1159	1158	1148	1149	1155	1154	1152
1153	1151	1150	1156	1157	1147	1146	1160	1161	1143	1142	1164	1165	1139	1138	1168	1169	1135	1134	1172	1173	1131	1130	1176	1177	1127	1126	1180	1181	1123	1122	1184	1185	1119	1118	1188	1189	1115	1114	1192	1193	1111	1110	1196	1197	1107	1106	1200
1104	1202	1203	1101	1100	1206	1207	1097	1096	1210	1211	1093	1092	1214	1215	1089	1088	1218	1219	1085	1084	1222	1223	1081	1080	1226	1227	1077	1076	1230	1231	1073	1072	1234	1235	1069	1068	1238	1239	1065	1064	1242	1243	1061	1060	1246	1247	1057
1056	1250	1251	1053	1052	1254	1255	1049	1048	1258	1259	1045	1044	1262	1263	1041	1040	1266	1267	1037	1036	1270	1271	1033	1032	1274	1275	1029	1028	1278	1279	1025	1024	1282	1283	1021	1020	1286	1287	1017	1016	1290	1291	1013	1012	1294	1295	1009
1297	1007	1006	1300	1301	1003	1002	1304	1305	999	998	1308	1309	995	994	1312	1313	991	990	1316	1317	987	986	1320	1321	983	982	1324	1325	979	978	1328	1329	975	974	1332	1333	971	970	1336	1337	967	966	1340	1341	963	962	1344
1345	959	958	1348	1349	955	954	1352	1353	951	950	1356	1357	947	946	1360	1361	943	942	1364	1365	939	938	1368	1369	935	934	1372	1373	931	930	1376	1377	927	926	1380	1381	923	922	1384	1385	919	918	1388	1389	915	914	1392
912	1394	1395	909	908	1398	1399	905	904	1402	1403	901	900	1406	1407	897	896	1410	1411	893	892	1414	1415	889	888	1418	1419	885	884	1422	1423	881	880	1426	1427	877	876	1430	1431	873	872	1434	1435	869	868	1438	1439	865
864	1442	1443	861	860	1446	1447	857	856	1450	1451	853	852	1454	1455	849	848	1458	1459	845	844	1462	1463	841	840	1466	1467	837	836	1470	1471	833	832	1474	1475	829	828	1478	1479	825	824	1482	1483	821	820	1486	1487	817
1489	815	814	1492	1493	811	810	1496	1497	807	806	1500	1501	803	802	1504	1505	799	798	1508	1509	795	794	1512	1513	791	790	1516	1517	787	786	1520	1521	783	782	1524	1525	779	778	1528	1529	775	774	1532	1533	771	770	1536
1537	767	766	1540	1541	763	762	1544	1545	759	758	1548	1549	755	754	1552	1553	751	750	1556	1557	747	746	1560	1561	743	742	1564	1565	739	738	1568	1569	735	734	1572	1573	731	730	1576	1577	727	726	1580	1581	723	722	1584
720	1586	1587	717	716	1590	1591	713	712	1594	1595	709	708	1598	1599	705	704	1602	1603	701	700	1606	1607	697	696	1610	1611	693	692	1614	1615	689	688	1618	1619	685	684	1622	1623	681	680	1626	1627	677	676	1630	1631	673
672	1634	1635	669	668	1638	1639	665	664	1642	1643	661	660	1646	1647	657	656	1650	1651	653	652	1654	1655	649	648	1658	1659	645	644	1662	1663	641	640	1666	1667	637	636	1670	1671	633	632	1674	1675	629	628	1678	1679	625
1681	623	622	1684	1685	619	618	1688	1689	615	614	1692	1693	611	610	1696	1697	607	606	1700	1701	603	602	1704	1705	599	598	1708	1709	595	594	1712	1713	591	590	1716	1717	587	586	1720	1721	583	582	1724	1725	579	578	1728
1729	575	574	1732	1733	571	570	1736	1737	567	566	1740	1741	563	562	1744	1745	559	558	1748	1749	555	554	1752	1753	551	550	1756	1757	547	546	1760	1761	543	542	1764	1765	539	538	1768	1769	535	534	1772	1773	531	530	1776
528	1778	1779	525	524	1782	1783	521	520	1786	1787	517	516	1790	1791	513	512	1794	1795	509	508	1798	1799	505	504	1802	1803	501	500	1806	1807	497	496	1810	1811	493	492	1814	1815	489	488	1818	1819	485	484	1822	1823	481
480	1826	1827	477	476	1830	1831	473	472	1834	1835	469	468	1838	1839	465	464	1842	1843	461	460	1846	1847	457	456	1850	1851	453	452	1854	1855	449	448	1858	1859	445	444	1862	1863	441	440	1866	1867	437	436	1870	1871	433
1873	431	430	1876	1877	427	426	1880	1881	423	422	1884	1885	419	418	1888	1889	415	414	1892	1893	411	410	1896	1897	407	406	1900	1901	403	402	1904	1905	399	398	1908	1909	395	394	1912	1913	391	390	1916	1917	387	386	1920
1921	383	382	1924	1925	379	378	1928	1929	375	374	1932	1933	371	370	1936	1937	367	366	1940	1941	363	362	1944	1945	359	358	1948	1949	355	354	1952	1953	351	350	1956	1957	347	346	1960	1961	343	342	1964	1965	339	338	1968
336	1970	1971	333	332	1974	1975	329	328	1978	1979	325	324	1982	1983	321	320	1986	1987	317	316	1990	1991	313	312	1994	1995	309	308	1998	1999	305	304	2002	2003	301	300	2006	2007	297	296	2010	2011	293	292	2014	2015	289
288	2018	2019	285	284	2022	2023	281	280	2026	2027	277	276	2030	2031	273	272	2034	2035	269	268	2038	2039	265	264	2042	2043	261	260	2046	2047	257	256	2050	2051	253	252	2054	2055	249	248	2058	2059	245	244	2062	2063	241
2065	239	238	2068	2069	235	234	2072	2073	231	230	2076	2077	227	226	2080	2081	223	222	2084	2085	219	218	2088	2089	215	214	2092	2093	211	210	2096	2097	207	206	2100	2101	203	202	2104	2105	199	198	2108	2109	195	194	2112
2113	191	190	2116	2117	187	186	2120	2121	183	182	2124	2125	179	178	2128	2129	175	174	2132	2133	171	170	2136	2137	167	166	2140	2141	163	162	2144	2145	159	158	2148	2149	155	154	2152	2153	151	150	2156	2157	147	146	2160
144	2162	2163	141	140	2166	2167	137	136	2170	2171	133	132	2174	2175	129	128	2178	2179	125	124	2182	2183	121	120	2186	2187	117	116	2190	2191	113	112	2194	2195	109	108	2198	2199	105	104	2202	2203	101	100	2206	2207	97
96	2210	2211	93	92	2214	2215	89	88	2218	2219	85	84	2222	2223	81	80	2226	2227	77	76	2230	2231	73	72	2234	2235	69	68	2238	2239	65	64	2242	2243	61	60	2246	2247	57	56	2250	2251	53	52	2254	2255	49
2257	47	46	2260	2261	43	42	2264	2265	39	38	2268	2269	35	34	2272	2273	31	30	2276	2277	27	26	2280	2281	23	22	2284	2285	19	18	2288	2289	15	14	2292	2293	11	10	2296	2297	7	6	2300	2301	3	2	2304

This Magic Square was created by John Knoderer, a webmaster and computer programmer who is available to telecommute to your location. (In other words, John would be delighted to create puzzles for your website or do other amazing work for you on a contract basis.)

If you found this page useful, and especially if you printed this page to distribute to students, we invite you to send a suitable donation to John (address below) or PayPal your donation to Donations (at) Mazes.com.

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A 48x48 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (55320)

Read more about Magic Squares

How to Create a 48x48 Magic Square with a Magic Sum of 55320

Step One: Draw a 48x48 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 48-by-48 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (55320)

How to Create a 48x48 Magic Square
with a Magic Sum of 55320

Step One: Draw a 48x48 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