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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 *
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A 60x60 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (108030)

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 60 by 60 magic square shown below has a magic sum equal to 108030.
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 60x60 Magic Square
with a Magic Sum of 108030

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

Steps:

Draw a 60x60 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 60x60 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 3600 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 3600, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 60x60 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 (3600).

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

This time, you can either

Start counting backward, starting with 3600 (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 3600 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 3600 is already written in that square), write down 2 and 3, then skip 4, etc.

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A 60-by-60 Magic Square

(Magic Sum = 108030)

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2341	1259	1258	2344	2345	1255	1254	2348	2349	1251	1250	2352	2353	1247	1246	2356	2357	1243	1242	2360	2361	1239	1238	2364	2365	1235	1234	2368	2369	1231	1230	2372	2373	1227	1226	2376	2377	1223	1222	2380	2381	1219	1218	2384	2385	1215	1214	2388	2389	1211	1210	2392	2393	1207	1206	2396	2397	1203	1202	2400
2401	1199	1198	2404	2405	1195	1194	2408	2409	1191	1190	2412	2413	1187	1186	2416	2417	1183	1182	2420	2421	1179	1178	2424	2425	1175	1174	2428	2429	1171	1170	2432	2433	1167	1166	2436	2437	1163	1162	2440	2441	1159	1158	2444	2445	1155	1154	2448	2449	1151	1150	2452	2453	1147	1146	2456	2457	1143	1142	2460
1140	2462	2463	1137	1136	2466	2467	1133	1132	2470	2471	1129	1128	2474	2475	1125	1124	2478	2479	1121	1120	2482	2483	1117	1116	2486	2487	1113	1112	2490	2491	1109	1108	2494	2495	1105	1104	2498	2499	1101	1100	2502	2503	1097	1096	2506	2507	1093	1092	2510	2511	1089	1088	2514	2515	1085	1084	2518	2519	1081
1080	2522	2523	1077	1076	2526	2527	1073	1072	2530	2531	1069	1068	2534	2535	1065	1064	2538	2539	1061	1060	2542	2543	1057	1056	2546	2547	1053	1052	2550	2551	1049	1048	2554	2555	1045	1044	2558	2559	1041	1040	2562	2563	1037	1036	2566	2567	1033	1032	2570	2571	1029	1028	2574	2575	1025	1024	2578	2579	1021
2581	1019	1018	2584	2585	1015	1014	2588	2589	1011	1010	2592	2593	1007	1006	2596	2597	1003	1002	2600	2601	999	998	2604	2605	995	994	2608	2609	991	990	2612	2613	987	986	2616	2617	983	982	2620	2621	979	978	2624	2625	975	974	2628	2629	971	970	2632	2633	967	966	2636	2637	963	962	2640
2641	959	958	2644	2645	955	954	2648	2649	951	950	2652	2653	947	946	2656	2657	943	942	2660	2661	939	938	2664	2665	935	934	2668	2669	931	930	2672	2673	927	926	2676	2677	923	922	2680	2681	919	918	2684	2685	915	914	2688	2689	911	910	2692	2693	907	906	2696	2697	903	902	2700
900	2702	2703	897	896	2706	2707	893	892	2710	2711	889	888	2714	2715	885	884	2718	2719	881	880	2722	2723	877	876	2726	2727	873	872	2730	2731	869	868	2734	2735	865	864	2738	2739	861	860	2742	2743	857	856	2746	2747	853	852	2750	2751	849	848	2754	2755	845	844	2758	2759	841
840	2762	2763	837	836	2766	2767	833	832	2770	2771	829	828	2774	2775	825	824	2778	2779	821	820	2782	2783	817	816	2786	2787	813	812	2790	2791	809	808	2794	2795	805	804	2798	2799	801	800	2802	2803	797	796	2806	2807	793	792	2810	2811	789	788	2814	2815	785	784	2818	2819	781
2821	779	778	2824	2825	775	774	2828	2829	771	770	2832	2833	767	766	2836	2837	763	762	2840	2841	759	758	2844	2845	755	754	2848	2849	751	750	2852	2853	747	746	2856	2857	743	742	2860	2861	739	738	2864	2865	735	734	2868	2869	731	730	2872	2873	727	726	2876	2877	723	722	2880
2881	719	718	2884	2885	715	714	2888	2889	711	710	2892	2893	707	706	2896	2897	703	702	2900	2901	699	698	2904	2905	695	694	2908	2909	691	690	2912	2913	687	686	2916	2917	683	682	2920	2921	679	678	2924	2925	675	674	2928	2929	671	670	2932	2933	667	666	2936	2937	663	662	2940
660	2942	2943	657	656	2946	2947	653	652	2950	2951	649	648	2954	2955	645	644	2958	2959	641	640	2962	2963	637	636	2966	2967	633	632	2970	2971	629	628	2974	2975	625	624	2978	2979	621	620	2982	2983	617	616	2986	2987	613	612	2990	2991	609	608	2994	2995	605	604	2998	2999	601
600	3002	3003	597	596	3006	3007	593	592	3010	3011	589	588	3014	3015	585	584	3018	3019	581	580	3022	3023	577	576	3026	3027	573	572	3030	3031	569	568	3034	3035	565	564	3038	3039	561	560	3042	3043	557	556	3046	3047	553	552	3050	3051	549	548	3054	3055	545	544	3058	3059	541
3061	539	538	3064	3065	535	534	3068	3069	531	530	3072	3073	527	526	3076	3077	523	522	3080	3081	519	518	3084	3085	515	514	3088	3089	511	510	3092	3093	507	506	3096	3097	503	502	3100	3101	499	498	3104	3105	495	494	3108	3109	491	490	3112	3113	487	486	3116	3117	483	482	3120
3121	479	478	3124	3125	475	474	3128	3129	471	470	3132	3133	467	466	3136	3137	463	462	3140	3141	459	458	3144	3145	455	454	3148	3149	451	450	3152	3153	447	446	3156	3157	443	442	3160	3161	439	438	3164	3165	435	434	3168	3169	431	430	3172	3173	427	426	3176	3177	423	422	3180
420	3182	3183	417	416	3186	3187	413	412	3190	3191	409	408	3194	3195	405	404	3198	3199	401	400	3202	3203	397	396	3206	3207	393	392	3210	3211	389	388	3214	3215	385	384	3218	3219	381	380	3222	3223	377	376	3226	3227	373	372	3230	3231	369	368	3234	3235	365	364	3238	3239	361
360	3242	3243	357	356	3246	3247	353	352	3250	3251	349	348	3254	3255	345	344	3258	3259	341	340	3262	3263	337	336	3266	3267	333	332	3270	3271	329	328	3274	3275	325	324	3278	3279	321	320	3282	3283	317	316	3286	3287	313	312	3290	3291	309	308	3294	3295	305	304	3298	3299	301
3301	299	298	3304	3305	295	294	3308	3309	291	290	3312	3313	287	286	3316	3317	283	282	3320	3321	279	278	3324	3325	275	274	3328	3329	271	270	3332	3333	267	266	3336	3337	263	262	3340	3341	259	258	3344	3345	255	254	3348	3349	251	250	3352	3353	247	246	3356	3357	243	242	3360
3361	239	238	3364	3365	235	234	3368	3369	231	230	3372	3373	227	226	3376	3377	223	222	3380	3381	219	218	3384	3385	215	214	3388	3389	211	210	3392	3393	207	206	3396	3397	203	202	3400	3401	199	198	3404	3405	195	194	3408	3409	191	190	3412	3413	187	186	3416	3417	183	182	3420
180	3422	3423	177	176	3426	3427	173	172	3430	3431	169	168	3434	3435	165	164	3438	3439	161	160	3442	3443	157	156	3446	3447	153	152	3450	3451	149	148	3454	3455	145	144	3458	3459	141	140	3462	3463	137	136	3466	3467	133	132	3470	3471	129	128	3474	3475	125	124	3478	3479	121
120	3482	3483	117	116	3486	3487	113	112	3490	3491	109	108	3494	3495	105	104	3498	3499	101	100	3502	3503	97	96	3506	3507	93	92	3510	3511	89	88	3514	3515	85	84	3518	3519	81	80	3522	3523	77	76	3526	3527	73	72	3530	3531	69	68	3534	3535	65	64	3538	3539	61
3541	59	58	3544	3545	55	54	3548	3549	51	50	3552	3553	47	46	3556	3557	43	42	3560	3561	39	38	3564	3565	35	34	3568	3569	31	30	3572	3573	27	26	3576	3577	23	22	3580	3581	19	18	3584	3585	15	14	3588	3589	11	10	3592	3593	7	6	3596	3597	3	2	3600

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 60x60 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (108030)

Read more about Magic Squares

How to Create a 60x60 Magic Square with a Magic Sum of 108030

Step One: Draw a 60x60 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 60-by-60 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (108030)

How to Create a 60x60 Magic Square
with a Magic Sum of 108030

Step One: Draw a 60x60 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