Books about
Magic Squares
at Amazon.Canada

Amazing Math Whiz
products available:

Buttons, Magnets,
t-shirts, Tote bags,
Teddy bears, & more
Books about Magic Squares at Amazon.com

Be sure to visit the
Magic Squares Main Menu
for other topics including Irregular Squares, Algebraic Squares and more.

Other 4N+0 Magic Square Sizes:
Detailed Directions for: 4x4 * 8x8 * 12x12 *
and many more examples
* 16 * 20 * 24 * 28 * 32 * 36 * 40 * 44 * 48 * 52 * 56 *
* 60 * 64 * 68 * 72 * 76 * 80 * 84 * 88 * 92 * 96 *

A 84x84 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (296394)

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 84 by 84 magic square shown below has a magic sum equal to 296394.
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.

Read more about Magic Squares
If you'd like to read more about magic squares, click one of these links to look for books about Magic Squares at Amazon.com, at Amazon.canada, and at Amazon.co.UK.

Books about
Magic Squares
at Amazon.co.UK

Support Our Site
by purchasing our
Amazing Math Whiz
products

and other
Amazing Messages

How to Create a 84x84 Magic Square
with a Magic Sum of 296394

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

Steps:

Draw a 84x84 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 84x84 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 7056 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 7056, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 84x84 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 (7056).

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

This time, you can either

Start counting backward, starting with 7056 (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 7056 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 7056 is already written in that square), write down 2 and 3, then skip 4, etc.

We have many
Amazing Message
stores.

Click each image to see
other amazing product choices

(each product imprinted
with an actual
solvable maze puzzle

Amazing Teacher

Amazing Student

Amazing Reader

Amazing Artist

See our choices @
www.mazes.com/cp

Please
Support Our Site

buy
Amazing Math Whiz
products from
our online store

Many other
Amazing Messages
are available

Please visit
www.MAZES.com/cp/
for details

A 84-by-84 Magic Square

(Magic Sum = 296394)

1	7055	7054	4	5	7051	7050	8	9	7047	7046	12	13	7043	7042	16	17	7039	7038	20	21	7035	7034	24	25	7031	7030	28	29	7027	7026	32	33	7023	7022	36	37	7019	7018	40	41	7015	7014	44	45	7011	7010	48	49	7007	7006	52	53	7003	7002	56	57	6999	6998	60	61	6995	6994	64	65	6991	6990	68	69	6987	6986	72	73	6983	6982	76	77	6979	6978	80	81	6975	6974	84
6972	86	87	6969	6968	90	91	6965	6964	94	95	6961	6960	98	99	6957	6956	102	103	6953	6952	106	107	6949	6948	110	111	6945	6944	114	115	6941	6940	118	119	6937	6936	122	123	6933	6932	126	127	6929	6928	130	131	6925	6924	134	135	6921	6920	138	139	6917	6916	142	143	6913	6912	146	147	6909	6908	150	151	6905	6904	154	155	6901	6900	158	159	6897	6896	162	163	6893	6892	166	167	6889
6888	170	171	6885	6884	174	175	6881	6880	178	179	6877	6876	182	183	6873	6872	186	187	6869	6868	190	191	6865	6864	194	195	6861	6860	198	199	6857	6856	202	203	6853	6852	206	207	6849	6848	210	211	6845	6844	214	215	6841	6840	218	219	6837	6836	222	223	6833	6832	226	227	6829	6828	230	231	6825	6824	234	235	6821	6820	238	239	6817	6816	242	243	6813	6812	246	247	6809	6808	250	251	6805
253	6803	6802	256	257	6799	6798	260	261	6795	6794	264	265	6791	6790	268	269	6787	6786	272	273	6783	6782	276	277	6779	6778	280	281	6775	6774	284	285	6771	6770	288	289	6767	6766	292	293	6763	6762	296	297	6759	6758	300	301	6755	6754	304	305	6751	6750	308	309	6747	6746	312	313	6743	6742	316	317	6739	6738	320	321	6735	6734	324	325	6731	6730	328	329	6727	6726	332	333	6723	6722	336
337	6719	6718	340	341	6715	6714	344	345	6711	6710	348	349	6707	6706	352	353	6703	6702	356	357	6699	6698	360	361	6695	6694	364	365	6691	6690	368	369	6687	6686	372	373	6683	6682	376	377	6679	6678	380	381	6675	6674	384	385	6671	6670	388	389	6667	6666	392	393	6663	6662	396	397	6659	6658	400	401	6655	6654	404	405	6651	6650	408	409	6647	6646	412	413	6643	6642	416	417	6639	6638	420
6636	422	423	6633	6632	426	427	6629	6628	430	431	6625	6624	434	435	6621	6620	438	439	6617	6616	442	443	6613	6612	446	447	6609	6608	450	451	6605	6604	454	455	6601	6600	458	459	6597	6596	462	463	6593	6592	466	467	6589	6588	470	471	6585	6584	474	475	6581	6580	478	479	6577	6576	482	483	6573	6572	486	487	6569	6568	490	491	6565	6564	494	495	6561	6560	498	499	6557	6556	502	503	6553
6552	506	507	6549	6548	510	511	6545	6544	514	515	6541	6540	518	519	6537	6536	522	523	6533	6532	526	527	6529	6528	530	531	6525	6524	534	535	6521	6520	538	539	6517	6516	542	543	6513	6512	546	547	6509	6508	550	551	6505	6504	554	555	6501	6500	558	559	6497	6496	562	563	6493	6492	566	567	6489	6488	570	571	6485	6484	574	575	6481	6480	578	579	6477	6476	582	583	6473	6472	586	587	6469
589	6467	6466	592	593	6463	6462	596	597	6459	6458	600	601	6455	6454	604	605	6451	6450	608	609	6447	6446	612	613	6443	6442	616	617	6439	6438	620	621	6435	6434	624	625	6431	6430	628	629	6427	6426	632	633	6423	6422	636	637	6419	6418	640	641	6415	6414	644	645	6411	6410	648	649	6407	6406	652	653	6403	6402	656	657	6399	6398	660	661	6395	6394	664	665	6391	6390	668	669	6387	6386	672
673	6383	6382	676	677	6379	6378	680	681	6375	6374	684	685	6371	6370	688	689	6367	6366	692	693	6363	6362	696	697	6359	6358	700	701	6355	6354	704	705	6351	6350	708	709	6347	6346	712	713	6343	6342	716	717	6339	6338	720	721	6335	6334	724	725	6331	6330	728	729	6327	6326	732	733	6323	6322	736	737	6319	6318	740	741	6315	6314	744	745	6311	6310	748	749	6307	6306	752	753	6303	6302	756
6300	758	759	6297	6296	762	763	6293	6292	766	767	6289	6288	770	771	6285	6284	774	775	6281	6280	778	779	6277	6276	782	783	6273	6272	786	787	6269	6268	790	791	6265	6264	794	795	6261	6260	798	799	6257	6256	802	803	6253	6252	806	807	6249	6248	810	811	6245	6244	814	815	6241	6240	818	819	6237	6236	822	823	6233	6232	826	827	6229	6228	830	831	6225	6224	834	835	6221	6220	838	839	6217
6216	842	843	6213	6212	846	847	6209	6208	850	851	6205	6204	854	855	6201	6200	858	859	6197	6196	862	863	6193	6192	866	867	6189	6188	870	871	6185	6184	874	875	6181	6180	878	879	6177	6176	882	883	6173	6172	886	887	6169	6168	890	891	6165	6164	894	895	6161	6160	898	899	6157	6156	902	903	6153	6152	906	907	6149	6148	910	911	6145	6144	914	915	6141	6140	918	919	6137	6136	922	923	6133
925	6131	6130	928	929	6127	6126	932	933	6123	6122	936	937	6119	6118	940	941	6115	6114	944	945	6111	6110	948	949	6107	6106	952	953	6103	6102	956	957	6099	6098	960	961	6095	6094	964	965	6091	6090	968	969	6087	6086	972	973	6083	6082	976	977	6079	6078	980	981	6075	6074	984	985	6071	6070	988	989	6067	6066	992	993	6063	6062	996	997	6059	6058	1000	1001	6055	6054	1004	1005	6051	6050	1008
1009	6047	6046	1012	1013	6043	6042	1016	1017	6039	6038	1020	1021	6035	6034	1024	1025	6031	6030	1028	1029	6027	6026	1032	1033	6023	6022	1036	1037	6019	6018	1040	1041	6015	6014	1044	1045	6011	6010	1048	1049	6007	6006	1052	1053	6003	6002	1056	1057	5999	5998	1060	1061	5995	5994	1064	1065	5991	5990	1068	1069	5987	5986	1072	1073	5983	5982	1076	1077	5979	5978	1080	1081	5975	5974	1084	1085	5971	5970	1088	1089	5967	5966	1092
5964	1094	1095	5961	5960	1098	1099	5957	5956	1102	1103	5953	5952	1106	1107	5949	5948	1110	1111	5945	5944	1114	1115	5941	5940	1118	1119	5937	5936	1122	1123	5933	5932	1126	1127	5929	5928	1130	1131	5925	5924	1134	1135	5921	5920	1138	1139	5917	5916	1142	1143	5913	5912	1146	1147	5909	5908	1150	1151	5905	5904	1154	1155	5901	5900	1158	1159	5897	5896	1162	1163	5893	5892	1166	1167	5889	5888	1170	1171	5885	5884	1174	1175	5881
5880	1178	1179	5877	5876	1182	1183	5873	5872	1186	1187	5869	5868	1190	1191	5865	5864	1194	1195	5861	5860	1198	1199	5857	5856	1202	1203	5853	5852	1206	1207	5849	5848	1210	1211	5845	5844	1214	1215	5841	5840	1218	1219	5837	5836	1222	1223	5833	5832	1226	1227	5829	5828	1230	1231	5825	5824	1234	1235	5821	5820	1238	1239	5817	5816	1242	1243	5813	5812	1246	1247	5809	5808	1250	1251	5805	5804	1254	1255	5801	5800	1258	1259	5797
1261	5795	5794	1264	1265	5791	5790	1268	1269	5787	5786	1272	1273	5783	5782	1276	1277	5779	5778	1280	1281	5775	5774	1284	1285	5771	5770	1288	1289	5767	5766	1292	1293	5763	5762	1296	1297	5759	5758	1300	1301	5755	5754	1304	1305	5751	5750	1308	1309	5747	5746	1312	1313	5743	5742	1316	1317	5739	5738	1320	1321	5735	5734	1324	1325	5731	5730	1328	1329	5727	5726	1332	1333	5723	5722	1336	1337	5719	5718	1340	1341	5715	5714	1344
1345	5711	5710	1348	1349	5707	5706	1352	1353	5703	5702	1356	1357	5699	5698	1360	1361	5695	5694	1364	1365	5691	5690	1368	1369	5687	5686	1372	1373	5683	5682	1376	1377	5679	5678	1380	1381	5675	5674	1384	1385	5671	5670	1388	1389	5667	5666	1392	1393	5663	5662	1396	1397	5659	5658	1400	1401	5655	5654	1404	1405	5651	5650	1408	1409	5647	5646	1412	1413	5643	5642	1416	1417	5639	5638	1420	1421	5635	5634	1424	1425	5631	5630	1428
5628	1430	1431	5625	5624	1434	1435	5621	5620	1438	1439	5617	5616	1442	1443	5613	5612	1446	1447	5609	5608	1450	1451	5605	5604	1454	1455	5601	5600	1458	1459	5597	5596	1462	1463	5593	5592	1466	1467	5589	5588	1470	1471	5585	5584	1474	1475	5581	5580	1478	1479	5577	5576	1482	1483	5573	5572	1486	1487	5569	5568	1490	1491	5565	5564	1494	1495	5561	5560	1498	1499	5557	5556	1502	1503	5553	5552	1506	1507	5549	5548	1510	1511	5545
5544	1514	1515	5541	5540	1518	1519	5537	5536	1522	1523	5533	5532	1526	1527	5529	5528	1530	1531	5525	5524	1534	1535	5521	5520	1538	1539	5517	5516	1542	1543	5513	5512	1546	1547	5509	5508	1550	1551	5505	5504	1554	1555	5501	5500	1558	1559	5497	5496	1562	1563	5493	5492	1566	1567	5489	5488	1570	1571	5485	5484	1574	1575	5481	5480	1578	1579	5477	5476	1582	1583	5473	5472	1586	1587	5469	5468	1590	1591	5465	5464	1594	1595	5461
1597	5459	5458	1600	1601	5455	5454	1604	1605	5451	5450	1608	1609	5447	5446	1612	1613	5443	5442	1616	1617	5439	5438	1620	1621	5435	5434	1624	1625	5431	5430	1628	1629	5427	5426	1632	1633	5423	5422	1636	1637	5419	5418	1640	1641	5415	5414	1644	1645	5411	5410	1648	1649	5407	5406	1652	1653	5403	5402	1656	1657	5399	5398	1660	1661	5395	5394	1664	1665	5391	5390	1668	1669	5387	5386	1672	1673	5383	5382	1676	1677	5379	5378	1680
1681	5375	5374	1684	1685	5371	5370	1688	1689	5367	5366	1692	1693	5363	5362	1696	1697	5359	5358	1700	1701	5355	5354	1704	1705	5351	5350	1708	1709	5347	5346	1712	1713	5343	5342	1716	1717	5339	5338	1720	1721	5335	5334	1724	1725	5331	5330	1728	1729	5327	5326	1732	1733	5323	5322	1736	1737	5319	5318	1740	1741	5315	5314	1744	1745	5311	5310	1748	1749	5307	5306	1752	1753	5303	5302	1756	1757	5299	5298	1760	1761	5295	5294	1764
5292	1766	1767	5289	5288	1770	1771	5285	5284	1774	1775	5281	5280	1778	1779	5277	5276	1782	1783	5273	5272	1786	1787	5269	5268	1790	1791	5265	5264	1794	1795	5261	5260	1798	1799	5257	5256	1802	1803	5253	5252	1806	1807	5249	5248	1810	1811	5245	5244	1814	1815	5241	5240	1818	1819	5237	5236	1822	1823	5233	5232	1826	1827	5229	5228	1830	1831	5225	5224	1834	1835	5221	5220	1838	1839	5217	5216	1842	1843	5213	5212	1846	1847	5209
5208	1850	1851	5205	5204	1854	1855	5201	5200	1858	1859	5197	5196	1862	1863	5193	5192	1866	1867	5189	5188	1870	1871	5185	5184	1874	1875	5181	5180	1878	1879	5177	5176	1882	1883	5173	5172	1886	1887	5169	5168	1890	1891	5165	5164	1894	1895	5161	5160	1898	1899	5157	5156	1902	1903	5153	5152	1906	1907	5149	5148	1910	1911	5145	5144	1914	1915	5141	5140	1918	1919	5137	5136	1922	1923	5133	5132	1926	1927	5129	5128	1930	1931	5125
1933	5123	5122	1936	1937	5119	5118	1940	1941	5115	5114	1944	1945	5111	5110	1948	1949	5107	5106	1952	1953	5103	5102	1956	1957	5099	5098	1960	1961	5095	5094	1964	1965	5091	5090	1968	1969	5087	5086	1972	1973	5083	5082	1976	1977	5079	5078	1980	1981	5075	5074	1984	1985	5071	5070	1988	1989	5067	5066	1992	1993	5063	5062	1996	1997	5059	5058	2000	2001	5055	5054	2004	2005	5051	5050	2008	2009	5047	5046	2012	2013	5043	5042	2016
2017	5039	5038	2020	2021	5035	5034	2024	2025	5031	5030	2028	2029	5027	5026	2032	2033	5023	5022	2036	2037	5019	5018	2040	2041	5015	5014	2044	2045	5011	5010	2048	2049	5007	5006	2052	2053	5003	5002	2056	2057	4999	4998	2060	2061	4995	4994	2064	2065	4991	4990	2068	2069	4987	4986	2072	2073	4983	4982	2076	2077	4979	4978	2080	2081	4975	4974	2084	2085	4971	4970	2088	2089	4967	4966	2092	2093	4963	4962	2096	2097	4959	4958	2100
4956	2102	2103	4953	4952	2106	2107	4949	4948	2110	2111	4945	4944	2114	2115	4941	4940	2118	2119	4937	4936	2122	2123	4933	4932	2126	2127	4929	4928	2130	2131	4925	4924	2134	2135	4921	4920	2138	2139	4917	4916	2142	2143	4913	4912	2146	2147	4909	4908	2150	2151	4905	4904	2154	2155	4901	4900	2158	2159	4897	4896	2162	2163	4893	4892	2166	2167	4889	4888	2170	2171	4885	4884	2174	2175	4881	4880	2178	2179	4877	4876	2182	2183	4873
4872	2186	2187	4869	4868	2190	2191	4865	4864	2194	2195	4861	4860	2198	2199	4857	4856	2202	2203	4853	4852	2206	2207	4849	4848	2210	2211	4845	4844	2214	2215	4841	4840	2218	2219	4837	4836	2222	2223	4833	4832	2226	2227	4829	4828	2230	2231	4825	4824	2234	2235	4821	4820	2238	2239	4817	4816	2242	2243	4813	4812	2246	2247	4809	4808	2250	2251	4805	4804	2254	2255	4801	4800	2258	2259	4797	4796	2262	2263	4793	4792	2266	2267	4789
2269	4787	4786	2272	2273	4783	4782	2276	2277	4779	4778	2280	2281	4775	4774	2284	2285	4771	4770	2288	2289	4767	4766	2292	2293	4763	4762	2296	2297	4759	4758	2300	2301	4755	4754	2304	2305	4751	4750	2308	2309	4747	4746	2312	2313	4743	4742	2316	2317	4739	4738	2320	2321	4735	4734	2324	2325	4731	4730	2328	2329	4727	4726	2332	2333	4723	4722	2336	2337	4719	4718	2340	2341	4715	4714	2344	2345	4711	4710	2348	2349	4707	4706	2352
2353	4703	4702	2356	2357	4699	4698	2360	2361	4695	4694	2364	2365	4691	4690	2368	2369	4687	4686	2372	2373	4683	4682	2376	2377	4679	4678	2380	2381	4675	4674	2384	2385	4671	4670	2388	2389	4667	4666	2392	2393	4663	4662	2396	2397	4659	4658	2400	2401	4655	4654	2404	2405	4651	4650	2408	2409	4647	4646	2412	2413	4643	4642	2416	2417	4639	4638	2420	2421	4635	4634	2424	2425	4631	4630	2428	2429	4627	4626	2432	2433	4623	4622	2436
4620	2438	2439	4617	4616	2442	2443	4613	4612	2446	2447	4609	4608	2450	2451	4605	4604	2454	2455	4601	4600	2458	2459	4597	4596	2462	2463	4593	4592	2466	2467	4589	4588	2470	2471	4585	4584	2474	2475	4581	4580	2478	2479	4577	4576	2482	2483	4573	4572	2486	2487	4569	4568	2490	2491	4565	4564	2494	2495	4561	4560	2498	2499	4557	4556	2502	2503	4553	4552	2506	2507	4549	4548	2510	2511	4545	4544	2514	2515	4541	4540	2518	2519	4537
4536	2522	2523	4533	4532	2526	2527	4529	4528	2530	2531	4525	4524	2534	2535	4521	4520	2538	2539	4517	4516	2542	2543	4513	4512	2546	2547	4509	4508	2550	2551	4505	4504	2554	2555	4501	4500	2558	2559	4497	4496	2562	2563	4493	4492	2566	2567	4489	4488	2570	2571	4485	4484	2574	2575	4481	4480	2578	2579	4477	4476	2582	2583	4473	4472	2586	2587	4469	4468	2590	2591	4465	4464	2594	2595	4461	4460	2598	2599	4457	4456	2602	2603	4453
2605	4451	4450	2608	2609	4447	4446	2612	2613	4443	4442	2616	2617	4439	4438	2620	2621	4435	4434	2624	2625	4431	4430	2628	2629	4427	4426	2632	2633	4423	4422	2636	2637	4419	4418	2640	2641	4415	4414	2644	2645	4411	4410	2648	2649	4407	4406	2652	2653	4403	4402	2656	2657	4399	4398	2660	2661	4395	4394	2664	2665	4391	4390	2668	2669	4387	4386	2672	2673	4383	4382	2676	2677	4379	4378	2680	2681	4375	4374	2684	2685	4371	4370	2688
2689	4367	4366	2692	2693	4363	4362	2696	2697	4359	4358	2700	2701	4355	4354	2704	2705	4351	4350	2708	2709	4347	4346	2712	2713	4343	4342	2716	2717	4339	4338	2720	2721	4335	4334	2724	2725	4331	4330	2728	2729	4327	4326	2732	2733	4323	4322	2736	2737	4319	4318	2740	2741	4315	4314	2744	2745	4311	4310	2748	2749	4307	4306	2752	2753	4303	4302	2756	2757	4299	4298	2760	2761	4295	4294	2764	2765	4291	4290	2768	2769	4287	4286	2772
4284	2774	2775	4281	4280	2778	2779	4277	4276	2782	2783	4273	4272	2786	2787	4269	4268	2790	2791	4265	4264	2794	2795	4261	4260	2798	2799	4257	4256	2802	2803	4253	4252	2806	2807	4249	4248	2810	2811	4245	4244	2814	2815	4241	4240	2818	2819	4237	4236	2822	2823	4233	4232	2826	2827	4229	4228	2830	2831	4225	4224	2834	2835	4221	4220	2838	2839	4217	4216	2842	2843	4213	4212	2846	2847	4209	4208	2850	2851	4205	4204	2854	2855	4201
4200	2858	2859	4197	4196	2862	2863	4193	4192	2866	2867	4189	4188	2870	2871	4185	4184	2874	2875	4181	4180	2878	2879	4177	4176	2882	2883	4173	4172	2886	2887	4169	4168	2890	2891	4165	4164	2894	2895	4161	4160	2898	2899	4157	4156	2902	2903	4153	4152	2906	2907	4149	4148	2910	2911	4145	4144	2914	2915	4141	4140	2918	2919	4137	4136	2922	2923	4133	4132	2926	2927	4129	4128	2930	2931	4125	4124	2934	2935	4121	4120	2938	2939	4117
2941	4115	4114	2944	2945	4111	4110	2948	2949	4107	4106	2952	2953	4103	4102	2956	2957	4099	4098	2960	2961	4095	4094	2964	2965	4091	4090	2968	2969	4087	4086	2972	2973	4083	4082	2976	2977	4079	4078	2980	2981	4075	4074	2984	2985	4071	4070	2988	2989	4067	4066	2992	2993	4063	4062	2996	2997	4059	4058	3000	3001	4055	4054	3004	3005	4051	4050	3008	3009	4047	4046	3012	3013	4043	4042	3016	3017	4039	4038	3020	3021	4035	4034	3024
3025	4031	4030	3028	3029	4027	4026	3032	3033	4023	4022	3036	3037	4019	4018	3040	3041	4015	4014	3044	3045	4011	4010	3048	3049	4007	4006	3052	3053	4003	4002	3056	3057	3999	3998	3060	3061	3995	3994	3064	3065	3991	3990	3068	3069	3987	3986	3072	3073	3983	3982	3076	3077	3979	3978	3080	3081	3975	3974	3084	3085	3971	3970	3088	3089	3967	3966	3092	3093	3963	3962	3096	3097	3959	3958	3100	3101	3955	3954	3104	3105	3951	3950	3108
3948	3110	3111	3945	3944	3114	3115	3941	3940	3118	3119	3937	3936	3122	3123	3933	3932	3126	3127	3929	3928	3130	3131	3925	3924	3134	3135	3921	3920	3138	3139	3917	3916	3142	3143	3913	3912	3146	3147	3909	3908	3150	3151	3905	3904	3154	3155	3901	3900	3158	3159	3897	3896	3162	3163	3893	3892	3166	3167	3889	3888	3170	3171	3885	3884	3174	3175	3881	3880	3178	3179	3877	3876	3182	3183	3873	3872	3186	3187	3869	3868	3190	3191	3865
3864	3194	3195	3861	3860	3198	3199	3857	3856	3202	3203	3853	3852	3206	3207	3849	3848	3210	3211	3845	3844	3214	3215	3841	3840	3218	3219	3837	3836	3222	3223	3833	3832	3226	3227	3829	3828	3230	3231	3825	3824	3234	3235	3821	3820	3238	3239	3817	3816	3242	3243	3813	3812	3246	3247	3809	3808	3250	3251	3805	3804	3254	3255	3801	3800	3258	3259	3797	3796	3262	3263	3793	3792	3266	3267	3789	3788	3270	3271	3785	3784	3274	3275	3781
3277	3779	3778	3280	3281	3775	3774	3284	3285	3771	3770	3288	3289	3767	3766	3292	3293	3763	3762	3296	3297	3759	3758	3300	3301	3755	3754	3304	3305	3751	3750	3308	3309	3747	3746	3312	3313	3743	3742	3316	3317	3739	3738	3320	3321	3735	3734	3324	3325	3731	3730	3328	3329	3727	3726	3332	3333	3723	3722	3336	3337	3719	3718	3340	3341	3715	3714	3344	3345	3711	3710	3348	3349	3707	3706	3352	3353	3703	3702	3356	3357	3699	3698	3360
3361	3695	3694	3364	3365	3691	3690	3368	3369	3687	3686	3372	3373	3683	3682	3376	3377	3679	3678	3380	3381	3675	3674	3384	3385	3671	3670	3388	3389	3667	3666	3392	3393	3663	3662	3396	3397	3659	3658	3400	3401	3655	3654	3404	3405	3651	3650	3408	3409	3647	3646	3412	3413	3643	3642	3416	3417	3639	3638	3420	3421	3635	3634	3424	3425	3631	3630	3428	3429	3627	3626	3432	3433	3623	3622	3436	3437	3619	3618	3440	3441	3615	3614	3444
3612	3446	3447	3609	3608	3450	3451	3605	3604	3454	3455	3601	3600	3458	3459	3597	3596	3462	3463	3593	3592	3466	3467	3589	3588	3470	3471	3585	3584	3474	3475	3581	3580	3478	3479	3577	3576	3482	3483	3573	3572	3486	3487	3569	3568	3490	3491	3565	3564	3494	3495	3561	3560	3498	3499	3557	3556	3502	3503	3553	3552	3506	3507	3549	3548	3510	3511	3545	3544	3514	3515	3541	3540	3518	3519	3537	3536	3522	3523	3533	3532	3526	3527	3529
3528	3530	3531	3525	3524	3534	3535	3521	3520	3538	3539	3517	3516	3542	3543	3513	3512	3546	3547	3509	3508	3550	3551	3505	3504	3554	3555	3501	3500	3558	3559	3497	3496	3562	3563	3493	3492	3566	3567	3489	3488	3570	3571	3485	3484	3574	3575	3481	3480	3578	3579	3477	3476	3582	3583	3473	3472	3586	3587	3469	3468	3590	3591	3465	3464	3594	3595	3461	3460	3598	3599	3457	3456	3602	3603	3453	3452	3606	3607	3449	3448	3610	3611	3445
3613	3443	3442	3616	3617	3439	3438	3620	3621	3435	3434	3624	3625	3431	3430	3628	3629	3427	3426	3632	3633	3423	3422	3636	3637	3419	3418	3640	3641	3415	3414	3644	3645	3411	3410	3648	3649	3407	3406	3652	3653	3403	3402	3656	3657	3399	3398	3660	3661	3395	3394	3664	3665	3391	3390	3668	3669	3387	3386	3672	3673	3383	3382	3676	3677	3379	3378	3680	3681	3375	3374	3684	3685	3371	3370	3688	3689	3367	3366	3692	3693	3363	3362	3696
3697	3359	3358	3700	3701	3355	3354	3704	3705	3351	3350	3708	3709	3347	3346	3712	3713	3343	3342	3716	3717	3339	3338	3720	3721	3335	3334	3724	3725	3331	3330	3728	3729	3327	3326	3732	3733	3323	3322	3736	3737	3319	3318	3740	3741	3315	3314	3744	3745	3311	3310	3748	3749	3307	3306	3752	3753	3303	3302	3756	3757	3299	3298	3760	3761	3295	3294	3764	3765	3291	3290	3768	3769	3287	3286	3772	3773	3283	3282	3776	3777	3279	3278	3780
3276	3782	3783	3273	3272	3786	3787	3269	3268	3790	3791	3265	3264	3794	3795	3261	3260	3798	3799	3257	3256	3802	3803	3253	3252	3806	3807	3249	3248	3810	3811	3245	3244	3814	3815	3241	3240	3818	3819	3237	3236	3822	3823	3233	3232	3826	3827	3229	3228	3830	3831	3225	3224	3834	3835	3221	3220	3838	3839	3217	3216	3842	3843	3213	3212	3846	3847	3209	3208	3850	3851	3205	3204	3854	3855	3201	3200	3858	3859	3197	3196	3862	3863	3193
3192	3866	3867	3189	3188	3870	3871	3185	3184	3874	3875	3181	3180	3878	3879	3177	3176	3882	3883	3173	3172	3886	3887	3169	3168	3890	3891	3165	3164	3894	3895	3161	3160	3898	3899	3157	3156	3902	3903	3153	3152	3906	3907	3149	3148	3910	3911	3145	3144	3914	3915	3141	3140	3918	3919	3137	3136	3922	3923	3133	3132	3926	3927	3129	3128	3930	3931	3125	3124	3934	3935	3121	3120	3938	3939	3117	3116	3942	3943	3113	3112	3946	3947	3109
3949	3107	3106	3952	3953	3103	3102	3956	3957	3099	3098	3960	3961	3095	3094	3964	3965	3091	3090	3968	3969	3087	3086	3972	3973	3083	3082	3976	3977	3079	3078	3980	3981	3075	3074	3984	3985	3071	3070	3988	3989	3067	3066	3992	3993	3063	3062	3996	3997	3059	3058	4000	4001	3055	3054	4004	4005	3051	3050	4008	4009	3047	3046	4012	4013	3043	3042	4016	4017	3039	3038	4020	4021	3035	3034	4024	4025	3031	3030	4028	4029	3027	3026	4032
4033	3023	3022	4036	4037	3019	3018	4040	4041	3015	3014	4044	4045	3011	3010	4048	4049	3007	3006	4052	4053	3003	3002	4056	4057	2999	2998	4060	4061	2995	2994	4064	4065	2991	2990	4068	4069	2987	2986	4072	4073	2983	2982	4076	4077	2979	2978	4080	4081	2975	2974	4084	4085	2971	2970	4088	4089	2967	2966	4092	4093	2963	2962	4096	4097	2959	2958	4100	4101	2955	2954	4104	4105	2951	2950	4108	4109	2947	2946	4112	4113	2943	2942	4116
2940	4118	4119	2937	2936	4122	4123	2933	2932	4126	4127	2929	2928	4130	4131	2925	2924	4134	4135	2921	2920	4138	4139	2917	2916	4142	4143	2913	2912	4146	4147	2909	2908	4150	4151	2905	2904	4154	4155	2901	2900	4158	4159	2897	2896	4162	4163	2893	2892	4166	4167	2889	2888	4170	4171	2885	2884	4174	4175	2881	2880	4178	4179	2877	2876	4182	4183	2873	2872	4186	4187	2869	2868	4190	4191	2865	2864	4194	4195	2861	2860	4198	4199	2857
2856	4202	4203	2853	2852	4206	4207	2849	2848	4210	4211	2845	2844	4214	4215	2841	2840	4218	4219	2837	2836	4222	4223	2833	2832	4226	4227	2829	2828	4230	4231	2825	2824	4234	4235	2821	2820	4238	4239	2817	2816	4242	4243	2813	2812	4246	4247	2809	2808	4250	4251	2805	2804	4254	4255	2801	2800	4258	4259	2797	2796	4262	4263	2793	2792	4266	4267	2789	2788	4270	4271	2785	2784	4274	4275	2781	2780	4278	4279	2777	2776	4282	4283	2773
4285	2771	2770	4288	4289	2767	2766	4292	4293	2763	2762	4296	4297	2759	2758	4300	4301	2755	2754	4304	4305	2751	2750	4308	4309	2747	2746	4312	4313	2743	2742	4316	4317	2739	2738	4320	4321	2735	2734	4324	4325	2731	2730	4328	4329	2727	2726	4332	4333	2723	2722	4336	4337	2719	2718	4340	4341	2715	2714	4344	4345	2711	2710	4348	4349	2707	2706	4352	4353	2703	2702	4356	4357	2699	2698	4360	4361	2695	2694	4364	4365	2691	2690	4368
4369	2687	2686	4372	4373	2683	2682	4376	4377	2679	2678	4380	4381	2675	2674	4384	4385	2671	2670	4388	4389	2667	2666	4392	4393	2663	2662	4396	4397	2659	2658	4400	4401	2655	2654	4404	4405	2651	2650	4408	4409	2647	2646	4412	4413	2643	2642	4416	4417	2639	2638	4420	4421	2635	2634	4424	4425	2631	2630	4428	4429	2627	2626	4432	4433	2623	2622	4436	4437	2619	2618	4440	4441	2615	2614	4444	4445	2611	2610	4448	4449	2607	2606	4452
2604	4454	4455	2601	2600	4458	4459	2597	2596	4462	4463	2593	2592	4466	4467	2589	2588	4470	4471	2585	2584	4474	4475	2581	2580	4478	4479	2577	2576	4482	4483	2573	2572	4486	4487	2569	2568	4490	4491	2565	2564	4494	4495	2561	2560	4498	4499	2557	2556	4502	4503	2553	2552	4506	4507	2549	2548	4510	4511	2545	2544	4514	4515	2541	2540	4518	4519	2537	2536	4522	4523	2533	2532	4526	4527	2529	2528	4530	4531	2525	2524	4534	4535	2521
2520	4538	4539	2517	2516	4542	4543	2513	2512	4546	4547	2509	2508	4550	4551	2505	2504	4554	4555	2501	2500	4558	4559	2497	2496	4562	4563	2493	2492	4566	4567	2489	2488	4570	4571	2485	2484	4574	4575	2481	2480	4578	4579	2477	2476	4582	4583	2473	2472	4586	4587	2469	2468	4590	4591	2465	2464	4594	4595	2461	2460	4598	4599	2457	2456	4602	4603	2453	2452	4606	4607	2449	2448	4610	4611	2445	2444	4614	4615	2441	2440	4618	4619	2437
4621	2435	2434	4624	4625	2431	2430	4628	4629	2427	2426	4632	4633	2423	2422	4636	4637	2419	2418	4640	4641	2415	2414	4644	4645	2411	2410	4648	4649	2407	2406	4652	4653	2403	2402	4656	4657	2399	2398	4660	4661	2395	2394	4664	4665	2391	2390	4668	4669	2387	2386	4672	4673	2383	2382	4676	4677	2379	2378	4680	4681	2375	2374	4684	4685	2371	2370	4688	4689	2367	2366	4692	4693	2363	2362	4696	4697	2359	2358	4700	4701	2355	2354	4704
4705	2351	2350	4708	4709	2347	2346	4712	4713	2343	2342	4716	4717	2339	2338	4720	4721	2335	2334	4724	4725	2331	2330	4728	4729	2327	2326	4732	4733	2323	2322	4736	4737	2319	2318	4740	4741	2315	2314	4744	4745	2311	2310	4748	4749	2307	2306	4752	4753	2303	2302	4756	4757	2299	2298	4760	4761	2295	2294	4764	4765	2291	2290	4768	4769	2287	2286	4772	4773	2283	2282	4776	4777	2279	2278	4780	4781	2275	2274	4784	4785	2271	2270	4788
2268	4790	4791	2265	2264	4794	4795	2261	2260	4798	4799	2257	2256	4802	4803	2253	2252	4806	4807	2249	2248	4810	4811	2245	2244	4814	4815	2241	2240	4818	4819	2237	2236	4822	4823	2233	2232	4826	4827	2229	2228	4830	4831	2225	2224	4834	4835	2221	2220	4838	4839	2217	2216	4842	4843	2213	2212	4846	4847	2209	2208	4850	4851	2205	2204	4854	4855	2201	2200	4858	4859	2197	2196	4862	4863	2193	2192	4866	4867	2189	2188	4870	4871	2185
2184	4874	4875	2181	2180	4878	4879	2177	2176	4882	4883	2173	2172	4886	4887	2169	2168	4890	4891	2165	2164	4894	4895	2161	2160	4898	4899	2157	2156	4902	4903	2153	2152	4906	4907	2149	2148	4910	4911	2145	2144	4914	4915	2141	2140	4918	4919	2137	2136	4922	4923	2133	2132	4926	4927	2129	2128	4930	4931	2125	2124	4934	4935	2121	2120	4938	4939	2117	2116	4942	4943	2113	2112	4946	4947	2109	2108	4950	4951	2105	2104	4954	4955	2101
4957	2099	2098	4960	4961	2095	2094	4964	4965	2091	2090	4968	4969	2087	2086	4972	4973	2083	2082	4976	4977	2079	2078	4980	4981	2075	2074	4984	4985	2071	2070	4988	4989	2067	2066	4992	4993	2063	2062	4996	4997	2059	2058	5000	5001	2055	2054	5004	5005	2051	2050	5008	5009	2047	2046	5012	5013	2043	2042	5016	5017	2039	2038	5020	5021	2035	2034	5024	5025	2031	2030	5028	5029	2027	2026	5032	5033	2023	2022	5036	5037	2019	2018	5040
5041	2015	2014	5044	5045	2011	2010	5048	5049	2007	2006	5052	5053	2003	2002	5056	5057	1999	1998	5060	5061	1995	1994	5064	5065	1991	1990	5068	5069	1987	1986	5072	5073	1983	1982	5076	5077	1979	1978	5080	5081	1975	1974	5084	5085	1971	1970	5088	5089	1967	1966	5092	5093	1963	1962	5096	5097	1959	1958	5100	5101	1955	1954	5104	5105	1951	1950	5108	5109	1947	1946	5112	5113	1943	1942	5116	5117	1939	1938	5120	5121	1935	1934	5124
1932	5126	5127	1929	1928	5130	5131	1925	1924	5134	5135	1921	1920	5138	5139	1917	1916	5142	5143	1913	1912	5146	5147	1909	1908	5150	5151	1905	1904	5154	5155	1901	1900	5158	5159	1897	1896	5162	5163	1893	1892	5166	5167	1889	1888	5170	5171	1885	1884	5174	5175	1881	1880	5178	5179	1877	1876	5182	5183	1873	1872	5186	5187	1869	1868	5190	5191	1865	1864	5194	5195	1861	1860	5198	5199	1857	1856	5202	5203	1853	1852	5206	5207	1849
1848	5210	5211	1845	1844	5214	5215	1841	1840	5218	5219	1837	1836	5222	5223	1833	1832	5226	5227	1829	1828	5230	5231	1825	1824	5234	5235	1821	1820	5238	5239	1817	1816	5242	5243	1813	1812	5246	5247	1809	1808	5250	5251	1805	1804	5254	5255	1801	1800	5258	5259	1797	1796	5262	5263	1793	1792	5266	5267	1789	1788	5270	5271	1785	1784	5274	5275	1781	1780	5278	5279	1777	1776	5282	5283	1773	1772	5286	5287	1769	1768	5290	5291	1765
5293	1763	1762	5296	5297	1759	1758	5300	5301	1755	1754	5304	5305	1751	1750	5308	5309	1747	1746	5312	5313	1743	1742	5316	5317	1739	1738	5320	5321	1735	1734	5324	5325	1731	1730	5328	5329	1727	1726	5332	5333	1723	1722	5336	5337	1719	1718	5340	5341	1715	1714	5344	5345	1711	1710	5348	5349	1707	1706	5352	5353	1703	1702	5356	5357	1699	1698	5360	5361	1695	1694	5364	5365	1691	1690	5368	5369	1687	1686	5372	5373	1683	1682	5376
5377	1679	1678	5380	5381	1675	1674	5384	5385	1671	1670	5388	5389	1667	1666	5392	5393	1663	1662	5396	5397	1659	1658	5400	5401	1655	1654	5404	5405	1651	1650	5408	5409	1647	1646	5412	5413	1643	1642	5416	5417	1639	1638	5420	5421	1635	1634	5424	5425	1631	1630	5428	5429	1627	1626	5432	5433	1623	1622	5436	5437	1619	1618	5440	5441	1615	1614	5444	5445	1611	1610	5448	5449	1607	1606	5452	5453	1603	1602	5456	5457	1599	1598	5460
1596	5462	5463	1593	1592	5466	5467	1589	1588	5470	5471	1585	1584	5474	5475	1581	1580	5478	5479	1577	1576	5482	5483	1573	1572	5486	5487	1569	1568	5490	5491	1565	1564	5494	5495	1561	1560	5498	5499	1557	1556	5502	5503	1553	1552	5506	5507	1549	1548	5510	5511	1545	1544	5514	5515	1541	1540	5518	5519	1537	1536	5522	5523	1533	1532	5526	5527	1529	1528	5530	5531	1525	1524	5534	5535	1521	1520	5538	5539	1517	1516	5542	5543	1513
1512	5546	5547	1509	1508	5550	5551	1505	1504	5554	5555	1501	1500	5558	5559	1497	1496	5562	5563	1493	1492	5566	5567	1489	1488	5570	5571	1485	1484	5574	5575	1481	1480	5578	5579	1477	1476	5582	5583	1473	1472	5586	5587	1469	1468	5590	5591	1465	1464	5594	5595	1461	1460	5598	5599	1457	1456	5602	5603	1453	1452	5606	5607	1449	1448	5610	5611	1445	1444	5614	5615	1441	1440	5618	5619	1437	1436	5622	5623	1433	1432	5626	5627	1429
5629	1427	1426	5632	5633	1423	1422	5636	5637	1419	1418	5640	5641	1415	1414	5644	5645	1411	1410	5648	5649	1407	1406	5652	5653	1403	1402	5656	5657	1399	1398	5660	5661	1395	1394	5664	5665	1391	1390	5668	5669	1387	1386	5672	5673	1383	1382	5676	5677	1379	1378	5680	5681	1375	1374	5684	5685	1371	1370	5688	5689	1367	1366	5692	5693	1363	1362	5696	5697	1359	1358	5700	5701	1355	1354	5704	5705	1351	1350	5708	5709	1347	1346	5712
5713	1343	1342	5716	5717	1339	1338	5720	5721	1335	1334	5724	5725	1331	1330	5728	5729	1327	1326	5732	5733	1323	1322	5736	5737	1319	1318	5740	5741	1315	1314	5744	5745	1311	1310	5748	5749	1307	1306	5752	5753	1303	1302	5756	5757	1299	1298	5760	5761	1295	1294	5764	5765	1291	1290	5768	5769	1287	1286	5772	5773	1283	1282	5776	5777	1279	1278	5780	5781	1275	1274	5784	5785	1271	1270	5788	5789	1267	1266	5792	5793	1263	1262	5796
1260	5798	5799	1257	1256	5802	5803	1253	1252	5806	5807	1249	1248	5810	5811	1245	1244	5814	5815	1241	1240	5818	5819	1237	1236	5822	5823	1233	1232	5826	5827	1229	1228	5830	5831	1225	1224	5834	5835	1221	1220	5838	5839	1217	1216	5842	5843	1213	1212	5846	5847	1209	1208	5850	5851	1205	1204	5854	5855	1201	1200	5858	5859	1197	1196	5862	5863	1193	1192	5866	5867	1189	1188	5870	5871	1185	1184	5874	5875	1181	1180	5878	5879	1177
1176	5882	5883	1173	1172	5886	5887	1169	1168	5890	5891	1165	1164	5894	5895	1161	1160	5898	5899	1157	1156	5902	5903	1153	1152	5906	5907	1149	1148	5910	5911	1145	1144	5914	5915	1141	1140	5918	5919	1137	1136	5922	5923	1133	1132	5926	5927	1129	1128	5930	5931	1125	1124	5934	5935	1121	1120	5938	5939	1117	1116	5942	5943	1113	1112	5946	5947	1109	1108	5950	5951	1105	1104	5954	5955	1101	1100	5958	5959	1097	1096	5962	5963	1093
5965	1091	1090	5968	5969	1087	1086	5972	5973	1083	1082	5976	5977	1079	1078	5980	5981	1075	1074	5984	5985	1071	1070	5988	5989	1067	1066	5992	5993	1063	1062	5996	5997	1059	1058	6000	6001	1055	1054	6004	6005	1051	1050	6008	6009	1047	1046	6012	6013	1043	1042	6016	6017	1039	1038	6020	6021	1035	1034	6024	6025	1031	1030	6028	6029	1027	1026	6032	6033	1023	1022	6036	6037	1019	1018	6040	6041	1015	1014	6044	6045	1011	1010	6048
6049	1007	1006	6052	6053	1003	1002	6056	6057	999	998	6060	6061	995	994	6064	6065	991	990	6068	6069	987	986	6072	6073	983	982	6076	6077	979	978	6080	6081	975	974	6084	6085	971	970	6088	6089	967	966	6092	6093	963	962	6096	6097	959	958	6100	6101	955	954	6104	6105	951	950	6108	6109	947	946	6112	6113	943	942	6116	6117	939	938	6120	6121	935	934	6124	6125	931	930	6128	6129	927	926	6132
924	6134	6135	921	920	6138	6139	917	916	6142	6143	913	912	6146	6147	909	908	6150	6151	905	904	6154	6155	901	900	6158	6159	897	896	6162	6163	893	892	6166	6167	889	888	6170	6171	885	884	6174	6175	881	880	6178	6179	877	876	6182	6183	873	872	6186	6187	869	868	6190	6191	865	864	6194	6195	861	860	6198	6199	857	856	6202	6203	853	852	6206	6207	849	848	6210	6211	845	844	6214	6215	841
840	6218	6219	837	836	6222	6223	833	832	6226	6227	829	828	6230	6231	825	824	6234	6235	821	820	6238	6239	817	816	6242	6243	813	812	6246	6247	809	808	6250	6251	805	804	6254	6255	801	800	6258	6259	797	796	6262	6263	793	792	6266	6267	789	788	6270	6271	785	784	6274	6275	781	780	6278	6279	777	776	6282	6283	773	772	6286	6287	769	768	6290	6291	765	764	6294	6295	761	760	6298	6299	757
6301	755	754	6304	6305	751	750	6308	6309	747	746	6312	6313	743	742	6316	6317	739	738	6320	6321	735	734	6324	6325	731	730	6328	6329	727	726	6332	6333	723	722	6336	6337	719	718	6340	6341	715	714	6344	6345	711	710	6348	6349	707	706	6352	6353	703	702	6356	6357	699	698	6360	6361	695	694	6364	6365	691	690	6368	6369	687	686	6372	6373	683	682	6376	6377	679	678	6380	6381	675	674	6384
6385	671	670	6388	6389	667	666	6392	6393	663	662	6396	6397	659	658	6400	6401	655	654	6404	6405	651	650	6408	6409	647	646	6412	6413	643	642	6416	6417	639	638	6420	6421	635	634	6424	6425	631	630	6428	6429	627	626	6432	6433	623	622	6436	6437	619	618	6440	6441	615	614	6444	6445	611	610	6448	6449	607	606	6452	6453	603	602	6456	6457	599	598	6460	6461	595	594	6464	6465	591	590	6468
588	6470	6471	585	584	6474	6475	581	580	6478	6479	577	576	6482	6483	573	572	6486	6487	569	568	6490	6491	565	564	6494	6495	561	560	6498	6499	557	556	6502	6503	553	552	6506	6507	549	548	6510	6511	545	544	6514	6515	541	540	6518	6519	537	536	6522	6523	533	532	6526	6527	529	528	6530	6531	525	524	6534	6535	521	520	6538	6539	517	516	6542	6543	513	512	6546	6547	509	508	6550	6551	505
504	6554	6555	501	500	6558	6559	497	496	6562	6563	493	492	6566	6567	489	488	6570	6571	485	484	6574	6575	481	480	6578	6579	477	476	6582	6583	473	472	6586	6587	469	468	6590	6591	465	464	6594	6595	461	460	6598	6599	457	456	6602	6603	453	452	6606	6607	449	448	6610	6611	445	444	6614	6615	441	440	6618	6619	437	436	6622	6623	433	432	6626	6627	429	428	6630	6631	425	424	6634	6635	421
6637	419	418	6640	6641	415	414	6644	6645	411	410	6648	6649	407	406	6652	6653	403	402	6656	6657	399	398	6660	6661	395	394	6664	6665	391	390	6668	6669	387	386	6672	6673	383	382	6676	6677	379	378	6680	6681	375	374	6684	6685	371	370	6688	6689	367	366	6692	6693	363	362	6696	6697	359	358	6700	6701	355	354	6704	6705	351	350	6708	6709	347	346	6712	6713	343	342	6716	6717	339	338	6720
6721	335	334	6724	6725	331	330	6728	6729	327	326	6732	6733	323	322	6736	6737	319	318	6740	6741	315	314	6744	6745	311	310	6748	6749	307	306	6752	6753	303	302	6756	6757	299	298	6760	6761	295	294	6764	6765	291	290	6768	6769	287	286	6772	6773	283	282	6776	6777	279	278	6780	6781	275	274	6784	6785	271	270	6788	6789	267	266	6792	6793	263	262	6796	6797	259	258	6800	6801	255	254	6804
252	6806	6807	249	248	6810	6811	245	244	6814	6815	241	240	6818	6819	237	236	6822	6823	233	232	6826	6827	229	228	6830	6831	225	224	6834	6835	221	220	6838	6839	217	216	6842	6843	213	212	6846	6847	209	208	6850	6851	205	204	6854	6855	201	200	6858	6859	197	196	6862	6863	193	192	6866	6867	189	188	6870	6871	185	184	6874	6875	181	180	6878	6879	177	176	6882	6883	173	172	6886	6887	169
168	6890	6891	165	164	6894	6895	161	160	6898	6899	157	156	6902	6903	153	152	6906	6907	149	148	6910	6911	145	144	6914	6915	141	140	6918	6919	137	136	6922	6923	133	132	6926	6927	129	128	6930	6931	125	124	6934	6935	121	120	6938	6939	117	116	6942	6943	113	112	6946	6947	109	108	6950	6951	105	104	6954	6955	101	100	6958	6959	97	96	6962	6963	93	92	6966	6967	89	88	6970	6971	85
6973	83	82	6976	6977	79	78	6980	6981	75	74	6984	6985	71	70	6988	6989	67	66	6992	6993	63	62	6996	6997	59	58	7000	7001	55	54	7004	7005	51	50	7008	7009	47	46	7012	7013	43	42	7016	7017	39	38	7020	7021	35	34	7024	7025	31	30	7028	7029	27	26	7032	7033	23	22	7036	7037	19	18	7040	7041	15	14	7044	7045	11	10	7048	7049	7	6	7052	7053	3	2	7056

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.

You can find more of John's puzzling materials at www.MAZES.com and at www.GodLovesEveryone.org. You can reach John at Webmaster (at) Mazes.com.

Fine Print: If you print and duplicate these magic squares for classroom use or other multiple copy use, please send a payment of $(however much you think this is worth) to the author. John puts a GREAT DEAL of time into creating and posting materials to the internet for you to use (and enjoy). Your donations will help pay bills and keep new materials coming your way.

Send your donations to:

John Knoderer
www.MAZES.com
P O Box 235
Sulphur Springs, AR 72768 USA

www.MAZES.com
www.GodLovesEveryone.org
www.DriverExam.org

E-mail the webmaster: webmaster (at) mazes.com

The contents of this page are copyright 2005 by the author. However, we recognize that teachers may wish to download and use our materials with their students. We give that permission, as long as the teacher sends what they believe to be a fair donation to the author each time the material is used.

A 84x84 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (296394)

Read more about Magic Squares

How to Create a 84x84 Magic Square with a Magic Sum of 296394

Step One: Draw a 84x84 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 84-by-84 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (296394)

How to Create a 84x84 Magic Square
with a Magic Sum of 296394

Step One: Draw a 84x84 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