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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 72x72 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (186660)

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 72 by 72 magic square shown below has a magic sum equal to 186660.
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 72x72 Magic Square
with a Magic Sum of 186660

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

Steps:

Draw a 72x72 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 72x72 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 5184 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 5184, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 72x72 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 (5184).

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

This time, you can either

Start counting backward, starting with 5184 (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 5184 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 5184 is already written in that square), write down 2 and 3, then skip 4, etc.

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A 72-by-72 Magic Square

(Magic Sum = 186660)

1	5183	5182	4	5	5179	5178	8	9	5175	5174	12	13	5171	5170	16	17	5167	5166	20	21	5163	5162	24	25	5159	5158	28	29	5155	5154	32	33	5151	5150	36	37	5147	5146	40	41	5143	5142	44	45	5139	5138	48	49	5135	5134	52	53	5131	5130	56	57	5127	5126	60	61	5123	5122	64	65	5119	5118	68	69	5115	5114	72
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2233	2951	2950	2236	2237	2947	2946	2240	2241	2943	2942	2244	2245	2939	2938	2248	2249	2935	2934	2252	2253	2931	2930	2256	2257	2927	2926	2260	2261	2923	2922	2264	2265	2919	2918	2268	2269	2915	2914	2272	2273	2911	2910	2276	2277	2907	2906	2280	2281	2903	2902	2284	2285	2899	2898	2288	2289	2895	2894	2292	2293	2891	2890	2296	2297	2887	2886	2300	2301	2883	2882	2304
2305	2879	2878	2308	2309	2875	2874	2312	2313	2871	2870	2316	2317	2867	2866	2320	2321	2863	2862	2324	2325	2859	2858	2328	2329	2855	2854	2332	2333	2851	2850	2336	2337	2847	2846	2340	2341	2843	2842	2344	2345	2839	2838	2348	2349	2835	2834	2352	2353	2831	2830	2356	2357	2827	2826	2360	2361	2823	2822	2364	2365	2819	2818	2368	2369	2815	2814	2372	2373	2811	2810	2376
2808	2378	2379	2805	2804	2382	2383	2801	2800	2386	2387	2797	2796	2390	2391	2793	2792	2394	2395	2789	2788	2398	2399	2785	2784	2402	2403	2781	2780	2406	2407	2777	2776	2410	2411	2773	2772	2414	2415	2769	2768	2418	2419	2765	2764	2422	2423	2761	2760	2426	2427	2757	2756	2430	2431	2753	2752	2434	2435	2749	2748	2438	2439	2745	2744	2442	2443	2741	2740	2446	2447	2737
2736	2450	2451	2733	2732	2454	2455	2729	2728	2458	2459	2725	2724	2462	2463	2721	2720	2466	2467	2717	2716	2470	2471	2713	2712	2474	2475	2709	2708	2478	2479	2705	2704	2482	2483	2701	2700	2486	2487	2697	2696	2490	2491	2693	2692	2494	2495	2689	2688	2498	2499	2685	2684	2502	2503	2681	2680	2506	2507	2677	2676	2510	2511	2673	2672	2514	2515	2669	2668	2518	2519	2665
2521	2663	2662	2524	2525	2659	2658	2528	2529	2655	2654	2532	2533	2651	2650	2536	2537	2647	2646	2540	2541	2643	2642	2544	2545	2639	2638	2548	2549	2635	2634	2552	2553	2631	2630	2556	2557	2627	2626	2560	2561	2623	2622	2564	2565	2619	2618	2568	2569	2615	2614	2572	2573	2611	2610	2576	2577	2607	2606	2580	2581	2603	2602	2584	2585	2599	2598	2588	2589	2595	2594	2592
2593	2591	2590	2596	2597	2587	2586	2600	2601	2583	2582	2604	2605	2579	2578	2608	2609	2575	2574	2612	2613	2571	2570	2616	2617	2567	2566	2620	2621	2563	2562	2624	2625	2559	2558	2628	2629	2555	2554	2632	2633	2551	2550	2636	2637	2547	2546	2640	2641	2543	2542	2644	2645	2539	2538	2648	2649	2535	2534	2652	2653	2531	2530	2656	2657	2527	2526	2660	2661	2523	2522	2664
2520	2666	2667	2517	2516	2670	2671	2513	2512	2674	2675	2509	2508	2678	2679	2505	2504	2682	2683	2501	2500	2686	2687	2497	2496	2690	2691	2493	2492	2694	2695	2489	2488	2698	2699	2485	2484	2702	2703	2481	2480	2706	2707	2477	2476	2710	2711	2473	2472	2714	2715	2469	2468	2718	2719	2465	2464	2722	2723	2461	2460	2726	2727	2457	2456	2730	2731	2453	2452	2734	2735	2449
2448	2738	2739	2445	2444	2742	2743	2441	2440	2746	2747	2437	2436	2750	2751	2433	2432	2754	2755	2429	2428	2758	2759	2425	2424	2762	2763	2421	2420	2766	2767	2417	2416	2770	2771	2413	2412	2774	2775	2409	2408	2778	2779	2405	2404	2782	2783	2401	2400	2786	2787	2397	2396	2790	2791	2393	2392	2794	2795	2389	2388	2798	2799	2385	2384	2802	2803	2381	2380	2806	2807	2377
2809	2375	2374	2812	2813	2371	2370	2816	2817	2367	2366	2820	2821	2363	2362	2824	2825	2359	2358	2828	2829	2355	2354	2832	2833	2351	2350	2836	2837	2347	2346	2840	2841	2343	2342	2844	2845	2339	2338	2848	2849	2335	2334	2852	2853	2331	2330	2856	2857	2327	2326	2860	2861	2323	2322	2864	2865	2319	2318	2868	2869	2315	2314	2872	2873	2311	2310	2876	2877	2307	2306	2880
2881	2303	2302	2884	2885	2299	2298	2888	2889	2295	2294	2892	2893	2291	2290	2896	2897	2287	2286	2900	2901	2283	2282	2904	2905	2279	2278	2908	2909	2275	2274	2912	2913	2271	2270	2916	2917	2267	2266	2920	2921	2263	2262	2924	2925	2259	2258	2928	2929	2255	2254	2932	2933	2251	2250	2936	2937	2247	2246	2940	2941	2243	2242	2944	2945	2239	2238	2948	2949	2235	2234	2952
2232	2954	2955	2229	2228	2958	2959	2225	2224	2962	2963	2221	2220	2966	2967	2217	2216	2970	2971	2213	2212	2974	2975	2209	2208	2978	2979	2205	2204	2982	2983	2201	2200	2986	2987	2197	2196	2990	2991	2193	2192	2994	2995	2189	2188	2998	2999	2185	2184	3002	3003	2181	2180	3006	3007	2177	2176	3010	3011	2173	2172	3014	3015	2169	2168	3018	3019	2165	2164	3022	3023	2161
2160	3026	3027	2157	2156	3030	3031	2153	2152	3034	3035	2149	2148	3038	3039	2145	2144	3042	3043	2141	2140	3046	3047	2137	2136	3050	3051	2133	2132	3054	3055	2129	2128	3058	3059	2125	2124	3062	3063	2121	2120	3066	3067	2117	2116	3070	3071	2113	2112	3074	3075	2109	2108	3078	3079	2105	2104	3082	3083	2101	2100	3086	3087	2097	2096	3090	3091	2093	2092	3094	3095	2089
3097	2087	2086	3100	3101	2083	2082	3104	3105	2079	2078	3108	3109	2075	2074	3112	3113	2071	2070	3116	3117	2067	2066	3120	3121	2063	2062	3124	3125	2059	2058	3128	3129	2055	2054	3132	3133	2051	2050	3136	3137	2047	2046	3140	3141	2043	2042	3144	3145	2039	2038	3148	3149	2035	2034	3152	3153	2031	2030	3156	3157	2027	2026	3160	3161	2023	2022	3164	3165	2019	2018	3168
3169	2015	2014	3172	3173	2011	2010	3176	3177	2007	2006	3180	3181	2003	2002	3184	3185	1999	1998	3188	3189	1995	1994	3192	3193	1991	1990	3196	3197	1987	1986	3200	3201	1983	1982	3204	3205	1979	1978	3208	3209	1975	1974	3212	3213	1971	1970	3216	3217	1967	1966	3220	3221	1963	1962	3224	3225	1959	1958	3228	3229	1955	1954	3232	3233	1951	1950	3236	3237	1947	1946	3240
1944	3242	3243	1941	1940	3246	3247	1937	1936	3250	3251	1933	1932	3254	3255	1929	1928	3258	3259	1925	1924	3262	3263	1921	1920	3266	3267	1917	1916	3270	3271	1913	1912	3274	3275	1909	1908	3278	3279	1905	1904	3282	3283	1901	1900	3286	3287	1897	1896	3290	3291	1893	1892	3294	3295	1889	1888	3298	3299	1885	1884	3302	3303	1881	1880	3306	3307	1877	1876	3310	3311	1873
1872	3314	3315	1869	1868	3318	3319	1865	1864	3322	3323	1861	1860	3326	3327	1857	1856	3330	3331	1853	1852	3334	3335	1849	1848	3338	3339	1845	1844	3342	3343	1841	1840	3346	3347	1837	1836	3350	3351	1833	1832	3354	3355	1829	1828	3358	3359	1825	1824	3362	3363	1821	1820	3366	3367	1817	1816	3370	3371	1813	1812	3374	3375	1809	1808	3378	3379	1805	1804	3382	3383	1801
3385	1799	1798	3388	3389	1795	1794	3392	3393	1791	1790	3396	3397	1787	1786	3400	3401	1783	1782	3404	3405	1779	1778	3408	3409	1775	1774	3412	3413	1771	1770	3416	3417	1767	1766	3420	3421	1763	1762	3424	3425	1759	1758	3428	3429	1755	1754	3432	3433	1751	1750	3436	3437	1747	1746	3440	3441	1743	1742	3444	3445	1739	1738	3448	3449	1735	1734	3452	3453	1731	1730	3456
3457	1727	1726	3460	3461	1723	1722	3464	3465	1719	1718	3468	3469	1715	1714	3472	3473	1711	1710	3476	3477	1707	1706	3480	3481	1703	1702	3484	3485	1699	1698	3488	3489	1695	1694	3492	3493	1691	1690	3496	3497	1687	1686	3500	3501	1683	1682	3504	3505	1679	1678	3508	3509	1675	1674	3512	3513	1671	1670	3516	3517	1667	1666	3520	3521	1663	1662	3524	3525	1659	1658	3528
1656	3530	3531	1653	1652	3534	3535	1649	1648	3538	3539	1645	1644	3542	3543	1641	1640	3546	3547	1637	1636	3550	3551	1633	1632	3554	3555	1629	1628	3558	3559	1625	1624	3562	3563	1621	1620	3566	3567	1617	1616	3570	3571	1613	1612	3574	3575	1609	1608	3578	3579	1605	1604	3582	3583	1601	1600	3586	3587	1597	1596	3590	3591	1593	1592	3594	3595	1589	1588	3598	3599	1585
1584	3602	3603	1581	1580	3606	3607	1577	1576	3610	3611	1573	1572	3614	3615	1569	1568	3618	3619	1565	1564	3622	3623	1561	1560	3626	3627	1557	1556	3630	3631	1553	1552	3634	3635	1549	1548	3638	3639	1545	1544	3642	3643	1541	1540	3646	3647	1537	1536	3650	3651	1533	1532	3654	3655	1529	1528	3658	3659	1525	1524	3662	3663	1521	1520	3666	3667	1517	1516	3670	3671	1513
3673	1511	1510	3676	3677	1507	1506	3680	3681	1503	1502	3684	3685	1499	1498	3688	3689	1495	1494	3692	3693	1491	1490	3696	3697	1487	1486	3700	3701	1483	1482	3704	3705	1479	1478	3708	3709	1475	1474	3712	3713	1471	1470	3716	3717	1467	1466	3720	3721	1463	1462	3724	3725	1459	1458	3728	3729	1455	1454	3732	3733	1451	1450	3736	3737	1447	1446	3740	3741	1443	1442	3744
3745	1439	1438	3748	3749	1435	1434	3752	3753	1431	1430	3756	3757	1427	1426	3760	3761	1423	1422	3764	3765	1419	1418	3768	3769	1415	1414	3772	3773	1411	1410	3776	3777	1407	1406	3780	3781	1403	1402	3784	3785	1399	1398	3788	3789	1395	1394	3792	3793	1391	1390	3796	3797	1387	1386	3800	3801	1383	1382	3804	3805	1379	1378	3808	3809	1375	1374	3812	3813	1371	1370	3816
1368	3818	3819	1365	1364	3822	3823	1361	1360	3826	3827	1357	1356	3830	3831	1353	1352	3834	3835	1349	1348	3838	3839	1345	1344	3842	3843	1341	1340	3846	3847	1337	1336	3850	3851	1333	1332	3854	3855	1329	1328	3858	3859	1325	1324	3862	3863	1321	1320	3866	3867	1317	1316	3870	3871	1313	1312	3874	3875	1309	1308	3878	3879	1305	1304	3882	3883	1301	1300	3886	3887	1297
1296	3890	3891	1293	1292	3894	3895	1289	1288	3898	3899	1285	1284	3902	3903	1281	1280	3906	3907	1277	1276	3910	3911	1273	1272	3914	3915	1269	1268	3918	3919	1265	1264	3922	3923	1261	1260	3926	3927	1257	1256	3930	3931	1253	1252	3934	3935	1249	1248	3938	3939	1245	1244	3942	3943	1241	1240	3946	3947	1237	1236	3950	3951	1233	1232	3954	3955	1229	1228	3958	3959	1225
3961	1223	1222	3964	3965	1219	1218	3968	3969	1215	1214	3972	3973	1211	1210	3976	3977	1207	1206	3980	3981	1203	1202	3984	3985	1199	1198	3988	3989	1195	1194	3992	3993	1191	1190	3996	3997	1187	1186	4000	4001	1183	1182	4004	4005	1179	1178	4008	4009	1175	1174	4012	4013	1171	1170	4016	4017	1167	1166	4020	4021	1163	1162	4024	4025	1159	1158	4028	4029	1155	1154	4032
4033	1151	1150	4036	4037	1147	1146	4040	4041	1143	1142	4044	4045	1139	1138	4048	4049	1135	1134	4052	4053	1131	1130	4056	4057	1127	1126	4060	4061	1123	1122	4064	4065	1119	1118	4068	4069	1115	1114	4072	4073	1111	1110	4076	4077	1107	1106	4080	4081	1103	1102	4084	4085	1099	1098	4088	4089	1095	1094	4092	4093	1091	1090	4096	4097	1087	1086	4100	4101	1083	1082	4104
1080	4106	4107	1077	1076	4110	4111	1073	1072	4114	4115	1069	1068	4118	4119	1065	1064	4122	4123	1061	1060	4126	4127	1057	1056	4130	4131	1053	1052	4134	4135	1049	1048	4138	4139	1045	1044	4142	4143	1041	1040	4146	4147	1037	1036	4150	4151	1033	1032	4154	4155	1029	1028	4158	4159	1025	1024	4162	4163	1021	1020	4166	4167	1017	1016	4170	4171	1013	1012	4174	4175	1009
1008	4178	4179	1005	1004	4182	4183	1001	1000	4186	4187	997	996	4190	4191	993	992	4194	4195	989	988	4198	4199	985	984	4202	4203	981	980	4206	4207	977	976	4210	4211	973	972	4214	4215	969	968	4218	4219	965	964	4222	4223	961	960	4226	4227	957	956	4230	4231	953	952	4234	4235	949	948	4238	4239	945	944	4242	4243	941	940	4246	4247	937
4249	935	934	4252	4253	931	930	4256	4257	927	926	4260	4261	923	922	4264	4265	919	918	4268	4269	915	914	4272	4273	911	910	4276	4277	907	906	4280	4281	903	902	4284	4285	899	898	4288	4289	895	894	4292	4293	891	890	4296	4297	887	886	4300	4301	883	882	4304	4305	879	878	4308	4309	875	874	4312	4313	871	870	4316	4317	867	866	4320
4321	863	862	4324	4325	859	858	4328	4329	855	854	4332	4333	851	850	4336	4337	847	846	4340	4341	843	842	4344	4345	839	838	4348	4349	835	834	4352	4353	831	830	4356	4357	827	826	4360	4361	823	822	4364	4365	819	818	4368	4369	815	814	4372	4373	811	810	4376	4377	807	806	4380	4381	803	802	4384	4385	799	798	4388	4389	795	794	4392
792	4394	4395	789	788	4398	4399	785	784	4402	4403	781	780	4406	4407	777	776	4410	4411	773	772	4414	4415	769	768	4418	4419	765	764	4422	4423	761	760	4426	4427	757	756	4430	4431	753	752	4434	4435	749	748	4438	4439	745	744	4442	4443	741	740	4446	4447	737	736	4450	4451	733	732	4454	4455	729	728	4458	4459	725	724	4462	4463	721
720	4466	4467	717	716	4470	4471	713	712	4474	4475	709	708	4478	4479	705	704	4482	4483	701	700	4486	4487	697	696	4490	4491	693	692	4494	4495	689	688	4498	4499	685	684	4502	4503	681	680	4506	4507	677	676	4510	4511	673	672	4514	4515	669	668	4518	4519	665	664	4522	4523	661	660	4526	4527	657	656	4530	4531	653	652	4534	4535	649
4537	647	646	4540	4541	643	642	4544	4545	639	638	4548	4549	635	634	4552	4553	631	630	4556	4557	627	626	4560	4561	623	622	4564	4565	619	618	4568	4569	615	614	4572	4573	611	610	4576	4577	607	606	4580	4581	603	602	4584	4585	599	598	4588	4589	595	594	4592	4593	591	590	4596	4597	587	586	4600	4601	583	582	4604	4605	579	578	4608
4609	575	574	4612	4613	571	570	4616	4617	567	566	4620	4621	563	562	4624	4625	559	558	4628	4629	555	554	4632	4633	551	550	4636	4637	547	546	4640	4641	543	542	4644	4645	539	538	4648	4649	535	534	4652	4653	531	530	4656	4657	527	526	4660	4661	523	522	4664	4665	519	518	4668	4669	515	514	4672	4673	511	510	4676	4677	507	506	4680
504	4682	4683	501	500	4686	4687	497	496	4690	4691	493	492	4694	4695	489	488	4698	4699	485	484	4702	4703	481	480	4706	4707	477	476	4710	4711	473	472	4714	4715	469	468	4718	4719	465	464	4722	4723	461	460	4726	4727	457	456	4730	4731	453	452	4734	4735	449	448	4738	4739	445	444	4742	4743	441	440	4746	4747	437	436	4750	4751	433
432	4754	4755	429	428	4758	4759	425	424	4762	4763	421	420	4766	4767	417	416	4770	4771	413	412	4774	4775	409	408	4778	4779	405	404	4782	4783	401	400	4786	4787	397	396	4790	4791	393	392	4794	4795	389	388	4798	4799	385	384	4802	4803	381	380	4806	4807	377	376	4810	4811	373	372	4814	4815	369	368	4818	4819	365	364	4822	4823	361
4825	359	358	4828	4829	355	354	4832	4833	351	350	4836	4837	347	346	4840	4841	343	342	4844	4845	339	338	4848	4849	335	334	4852	4853	331	330	4856	4857	327	326	4860	4861	323	322	4864	4865	319	318	4868	4869	315	314	4872	4873	311	310	4876	4877	307	306	4880	4881	303	302	4884	4885	299	298	4888	4889	295	294	4892	4893	291	290	4896
4897	287	286	4900	4901	283	282	4904	4905	279	278	4908	4909	275	274	4912	4913	271	270	4916	4917	267	266	4920	4921	263	262	4924	4925	259	258	4928	4929	255	254	4932	4933	251	250	4936	4937	247	246	4940	4941	243	242	4944	4945	239	238	4948	4949	235	234	4952	4953	231	230	4956	4957	227	226	4960	4961	223	222	4964	4965	219	218	4968
216	4970	4971	213	212	4974	4975	209	208	4978	4979	205	204	4982	4983	201	200	4986	4987	197	196	4990	4991	193	192	4994	4995	189	188	4998	4999	185	184	5002	5003	181	180	5006	5007	177	176	5010	5011	173	172	5014	5015	169	168	5018	5019	165	164	5022	5023	161	160	5026	5027	157	156	5030	5031	153	152	5034	5035	149	148	5038	5039	145
144	5042	5043	141	140	5046	5047	137	136	5050	5051	133	132	5054	5055	129	128	5058	5059	125	124	5062	5063	121	120	5066	5067	117	116	5070	5071	113	112	5074	5075	109	108	5078	5079	105	104	5082	5083	101	100	5086	5087	97	96	5090	5091	93	92	5094	5095	89	88	5098	5099	85	84	5102	5103	81	80	5106	5107	77	76	5110	5111	73
5113	71	70	5116	5117	67	66	5120	5121	63	62	5124	5125	59	58	5128	5129	55	54	5132	5133	51	50	5136	5137	47	46	5140	5141	43	42	5144	5145	39	38	5148	5149	35	34	5152	5153	31	30	5156	5157	27	26	5160	5161	23	22	5164	5165	19	18	5168	5169	15	14	5172	5173	11	10	5176	5177	7	6	5180	5181	3	2	5184

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 72x72 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (186660)

Read more about Magic Squares

How to Create a 72x72 Magic Square with a Magic Sum of 186660

Step One: Draw a 72x72 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 72-by-72 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (186660)

How to Create a 72x72 Magic Square
with a Magic Sum of 186660

Step One: Draw a 72x72 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