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Other 4N+0 Magic Square Sizes:
Detailed Directions for: 4x4 * 8x8 * 12x12 *
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* 16 * 20 * 24 * 28 * 32 * 36 * 40 * 44 * 48 * 52 * 56 *
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A 56x56 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (87836)

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 56 by 56 magic square shown below has a magic sum equal to 87836.
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 56x56 Magic Square
with a Magic Sum of 87836

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

Steps:

Draw a 56x56 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 56x56 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 3136 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 3136, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 56x56 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 (3136).

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

This time, you can either

Start counting backward, starting with 3136 (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 3136 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 3136 is already written in that square), write down 2 and 3, then skip 4, etc.

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A 56-by-56 Magic Square

(Magic Sum = 87836)

1	3135	3134	4	5	3131	3130	8	9	3127	3126	12	13	3123	3122	16	17	3119	3118	20	21	3115	3114	24	25	3111	3110	28	29	3107	3106	32	33	3103	3102	36	37	3099	3098	40	41	3095	3094	44	45	3091	3090	48	49	3087	3086	52	53	3083	3082	56
3080	58	59	3077	3076	62	63	3073	3072	66	67	3069	3068	70	71	3065	3064	74	75	3061	3060	78	79	3057	3056	82	83	3053	3052	86	87	3049	3048	90	91	3045	3044	94	95	3041	3040	98	99	3037	3036	102	103	3033	3032	106	107	3029	3028	110	111	3025
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784	2354	2355	781	780	2358	2359	777	776	2362	2363	773	772	2366	2367	769	768	2370	2371	765	764	2374	2375	761	760	2378	2379	757	756	2382	2383	753	752	2386	2387	749	748	2390	2391	745	744	2394	2395	741	740	2398	2399	737	736	2402	2403	733	732	2406	2407	729
2409	727	726	2412	2413	723	722	2416	2417	719	718	2420	2421	715	714	2424	2425	711	710	2428	2429	707	706	2432	2433	703	702	2436	2437	699	698	2440	2441	695	694	2444	2445	691	690	2448	2449	687	686	2452	2453	683	682	2456	2457	679	678	2460	2461	675	674	2464
2465	671	670	2468	2469	667	666	2472	2473	663	662	2476	2477	659	658	2480	2481	655	654	2484	2485	651	650	2488	2489	647	646	2492	2493	643	642	2496	2497	639	638	2500	2501	635	634	2504	2505	631	630	2508	2509	627	626	2512	2513	623	622	2516	2517	619	618	2520
616	2522	2523	613	612	2526	2527	609	608	2530	2531	605	604	2534	2535	601	600	2538	2539	597	596	2542	2543	593	592	2546	2547	589	588	2550	2551	585	584	2554	2555	581	580	2558	2559	577	576	2562	2563	573	572	2566	2567	569	568	2570	2571	565	564	2574	2575	561
560	2578	2579	557	556	2582	2583	553	552	2586	2587	549	548	2590	2591	545	544	2594	2595	541	540	2598	2599	537	536	2602	2603	533	532	2606	2607	529	528	2610	2611	525	524	2614	2615	521	520	2618	2619	517	516	2622	2623	513	512	2626	2627	509	508	2630	2631	505
2633	503	502	2636	2637	499	498	2640	2641	495	494	2644	2645	491	490	2648	2649	487	486	2652	2653	483	482	2656	2657	479	478	2660	2661	475	474	2664	2665	471	470	2668	2669	467	466	2672	2673	463	462	2676	2677	459	458	2680	2681	455	454	2684	2685	451	450	2688
2689	447	446	2692	2693	443	442	2696	2697	439	438	2700	2701	435	434	2704	2705	431	430	2708	2709	427	426	2712	2713	423	422	2716	2717	419	418	2720	2721	415	414	2724	2725	411	410	2728	2729	407	406	2732	2733	403	402	2736	2737	399	398	2740	2741	395	394	2744
392	2746	2747	389	388	2750	2751	385	384	2754	2755	381	380	2758	2759	377	376	2762	2763	373	372	2766	2767	369	368	2770	2771	365	364	2774	2775	361	360	2778	2779	357	356	2782	2783	353	352	2786	2787	349	348	2790	2791	345	344	2794	2795	341	340	2798	2799	337
336	2802	2803	333	332	2806	2807	329	328	2810	2811	325	324	2814	2815	321	320	2818	2819	317	316	2822	2823	313	312	2826	2827	309	308	2830	2831	305	304	2834	2835	301	300	2838	2839	297	296	2842	2843	293	292	2846	2847	289	288	2850	2851	285	284	2854	2855	281
2857	279	278	2860	2861	275	274	2864	2865	271	270	2868	2869	267	266	2872	2873	263	262	2876	2877	259	258	2880	2881	255	254	2884	2885	251	250	2888	2889	247	246	2892	2893	243	242	2896	2897	239	238	2900	2901	235	234	2904	2905	231	230	2908	2909	227	226	2912
2913	223	222	2916	2917	219	218	2920	2921	215	214	2924	2925	211	210	2928	2929	207	206	2932	2933	203	202	2936	2937	199	198	2940	2941	195	194	2944	2945	191	190	2948	2949	187	186	2952	2953	183	182	2956	2957	179	178	2960	2961	175	174	2964	2965	171	170	2968
168	2970	2971	165	164	2974	2975	161	160	2978	2979	157	156	2982	2983	153	152	2986	2987	149	148	2990	2991	145	144	2994	2995	141	140	2998	2999	137	136	3002	3003	133	132	3006	3007	129	128	3010	3011	125	124	3014	3015	121	120	3018	3019	117	116	3022	3023	113
112	3026	3027	109	108	3030	3031	105	104	3034	3035	101	100	3038	3039	97	96	3042	3043	93	92	3046	3047	89	88	3050	3051	85	84	3054	3055	81	80	3058	3059	77	76	3062	3063	73	72	3066	3067	69	68	3070	3071	65	64	3074	3075	61	60	3078	3079	57
3081	55	54	3084	3085	51	50	3088	3089	47	46	3092	3093	43	42	3096	3097	39	38	3100	3101	35	34	3104	3105	31	30	3108	3109	27	26	3112	3113	23	22	3116	3117	19	18	3120	3121	15	14	3124	3125	11	10	3128	3129	7	6	3132	3133	3	2	3136

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
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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 56x56 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (87836)

Read more about Magic Squares

How to Create a 56x56 Magic Square with a Magic Sum of 87836

Step One: Draw a 56x56 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 56-by-56 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (87836)

How to Create a 56x56 Magic Square
with a Magic Sum of 87836

Step One: Draw a 56x56 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