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A 52x52 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (70330)

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 52 by 52 magic square shown below has a magic sum equal to 70330.
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 52x52 Magic Square
with a Magic Sum of 70330

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

Steps:

Draw a 52x52 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 52x52 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 2704 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 2704, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 52x52 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 (2704).

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

This time, you can either

Start counting backward, starting with 2704 (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 2704 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 2704 is already written in that square), write down 2 and 3, then skip 4, etc.

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A 52-by-52 Magic Square

(Magic Sum = 70330)

1	2703	2702	4	5	2699	2698	8	9	2695	2694	12	13	2691	2690	16	17	2687	2686	20	21	2683	2682	24	25	2679	2678	28	29	2675	2674	32	33	2671	2670	36	37	2667	2666	40	41	2663	2662	44	45	2659	2658	48	49	2655	2654	52
2652	54	55	2649	2648	58	59	2645	2644	62	63	2641	2640	66	67	2637	2636	70	71	2633	2632	74	75	2629	2628	78	79	2625	2624	82	83	2621	2620	86	87	2617	2616	90	91	2613	2612	94	95	2609	2608	98	99	2605	2604	102	103	2601
2600	106	107	2597	2596	110	111	2593	2592	114	115	2589	2588	118	119	2585	2584	122	123	2581	2580	126	127	2577	2576	130	131	2573	2572	134	135	2569	2568	138	139	2565	2564	142	143	2561	2560	146	147	2557	2556	150	151	2553	2552	154	155	2549
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2444	262	263	2441	2440	266	267	2437	2436	270	271	2433	2432	274	275	2429	2428	278	279	2425	2424	282	283	2421	2420	286	287	2417	2416	290	291	2413	2412	294	295	2409	2408	298	299	2405	2404	302	303	2401	2400	306	307	2397	2396	310	311	2393
2392	314	315	2389	2388	318	319	2385	2384	322	323	2381	2380	326	327	2377	2376	330	331	2373	2372	334	335	2369	2368	338	339	2365	2364	342	343	2361	2360	346	347	2357	2356	350	351	2353	2352	354	355	2349	2348	358	359	2345	2344	362	363	2341
365	2339	2338	368	369	2335	2334	372	373	2331	2330	376	377	2327	2326	380	381	2323	2322	384	385	2319	2318	388	389	2315	2314	392	393	2311	2310	396	397	2307	2306	400	401	2303	2302	404	405	2299	2298	408	409	2295	2294	412	413	2291	2290	416
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989	1715	1714	992	993	1711	1710	996	997	1707	1706	1000	1001	1703	1702	1004	1005	1699	1698	1008	1009	1695	1694	1012	1013	1691	1690	1016	1017	1687	1686	1020	1021	1683	1682	1024	1025	1679	1678	1028	1029	1675	1674	1032	1033	1671	1670	1036	1037	1667	1666	1040
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1196	1510	1511	1193	1192	1514	1515	1189	1188	1518	1519	1185	1184	1522	1523	1181	1180	1526	1527	1177	1176	1530	1531	1173	1172	1534	1535	1169	1168	1538	1539	1165	1164	1542	1543	1161	1160	1546	1547	1157	1156	1550	1551	1153	1152	1554	1555	1149	1148	1558	1559	1145
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1665	1039	1038	1668	1669	1035	1034	1672	1673	1031	1030	1676	1677	1027	1026	1680	1681	1023	1022	1684	1685	1019	1018	1688	1689	1015	1014	1692	1693	1011	1010	1696	1697	1007	1006	1700	1701	1003	1002	1704	1705	999	998	1708	1709	995	994	1712	1713	991	990	1716
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936	1770	1771	933	932	1774	1775	929	928	1778	1779	925	924	1782	1783	921	920	1786	1787	917	916	1790	1791	913	912	1794	1795	909	908	1798	1799	905	904	1802	1803	901	900	1806	1807	897	896	1810	1811	893	892	1814	1815	889	888	1818	1819	885
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2445	259	258	2448	2449	255	254	2452	2453	251	250	2456	2457	247	246	2460	2461	243	242	2464	2465	239	238	2468	2469	235	234	2472	2473	231	230	2476	2477	227	226	2480	2481	223	222	2484	2485	219	218	2488	2489	215	214	2492	2493	211	210	2496
2497	207	206	2500	2501	203	202	2504	2505	199	198	2508	2509	195	194	2512	2513	191	190	2516	2517	187	186	2520	2521	183	182	2524	2525	179	178	2528	2529	175	174	2532	2533	171	170	2536	2537	167	166	2540	2541	163	162	2544	2545	159	158	2548
156	2550	2551	153	152	2554	2555	149	148	2558	2559	145	144	2562	2563	141	140	2566	2567	137	136	2570	2571	133	132	2574	2575	129	128	2578	2579	125	124	2582	2583	121	120	2586	2587	117	116	2590	2591	113	112	2594	2595	109	108	2598	2599	105
104	2602	2603	101	100	2606	2607	97	96	2610	2611	93	92	2614	2615	89	88	2618	2619	85	84	2622	2623	81	80	2626	2627	77	76	2630	2631	73	72	2634	2635	69	68	2638	2639	65	64	2642	2643	61	60	2646	2647	57	56	2650	2651	53
2653	51	50	2656	2657	47	46	2660	2661	43	42	2664	2665	39	38	2668	2669	35	34	2672	2673	31	30	2676	2677	27	26	2680	2681	23	22	2684	2685	19	18	2688	2689	15	14	2692	2693	11	10	2696	2697	7	6	2700	2701	3	2	2704

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 52x52 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (70330)

Read more about Magic Squares

How to Create a 52x52 Magic Square with a Magic Sum of 70330

Step One: Draw a 52x52 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 52-by-52 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (70330)

How to Create a 52x52 Magic Square
with a Magic Sum of 70330

Step One: Draw a 52x52 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