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A 32x32 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (16400)

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 32 by 32 magic square shown below has a magic sum equal to 16400.
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 32x32 Magic Square
with a Magic Sum of 16400

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

Steps:

Draw a 32x32 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 32x32 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 1024 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 1024, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 32x32 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 (1024).

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

This time, you can either

Start counting backward, starting with 1024 (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 1024 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 1024 is already written in that square), write down 2 and 3, then skip 4, etc.

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A 32-by-32 Magic Square

(Magic Sum = 16400)

1	1023	1022	4	5	1019	1018	8	9	1015	1014	12	13	1011	1010	16	17	1007	1006	20	21	1003	1002	24	25	999	998	28	29	995	994	32
992	34	35	989	988	38	39	985	984	42	43	981	980	46	47	977	976	50	51	973	972	54	55	969	968	58	59	965	964	62	63	961
960	66	67	957	956	70	71	953	952	74	75	949	948	78	79	945	944	82	83	941	940	86	87	937	936	90	91	933	932	94	95	929
97	927	926	100	101	923	922	104	105	919	918	108	109	915	914	112	113	911	910	116	117	907	906	120	121	903	902	124	125	899	898	128
129	895	894	132	133	891	890	136	137	887	886	140	141	883	882	144	145	879	878	148	149	875	874	152	153	871	870	156	157	867	866	160
864	162	163	861	860	166	167	857	856	170	171	853	852	174	175	849	848	178	179	845	844	182	183	841	840	186	187	837	836	190	191	833
832	194	195	829	828	198	199	825	824	202	203	821	820	206	207	817	816	210	211	813	812	214	215	809	808	218	219	805	804	222	223	801
225	799	798	228	229	795	794	232	233	791	790	236	237	787	786	240	241	783	782	244	245	779	778	248	249	775	774	252	253	771	770	256
257	767	766	260	261	763	762	264	265	759	758	268	269	755	754	272	273	751	750	276	277	747	746	280	281	743	742	284	285	739	738	288
736	290	291	733	732	294	295	729	728	298	299	725	724	302	303	721	720	306	307	717	716	310	311	713	712	314	315	709	708	318	319	705
704	322	323	701	700	326	327	697	696	330	331	693	692	334	335	689	688	338	339	685	684	342	343	681	680	346	347	677	676	350	351	673
353	671	670	356	357	667	666	360	361	663	662	364	365	659	658	368	369	655	654	372	373	651	650	376	377	647	646	380	381	643	642	384
385	639	638	388	389	635	634	392	393	631	630	396	397	627	626	400	401	623	622	404	405	619	618	408	409	615	614	412	413	611	610	416
608	418	419	605	604	422	423	601	600	426	427	597	596	430	431	593	592	434	435	589	588	438	439	585	584	442	443	581	580	446	447	577
576	450	451	573	572	454	455	569	568	458	459	565	564	462	463	561	560	466	467	557	556	470	471	553	552	474	475	549	548	478	479	545
481	543	542	484	485	539	538	488	489	535	534	492	493	531	530	496	497	527	526	500	501	523	522	504	505	519	518	508	509	515	514	512
513	511	510	516	517	507	506	520	521	503	502	524	525	499	498	528	529	495	494	532	533	491	490	536	537	487	486	540	541	483	482	544
480	546	547	477	476	550	551	473	472	554	555	469	468	558	559	465	464	562	563	461	460	566	567	457	456	570	571	453	452	574	575	449
448	578	579	445	444	582	583	441	440	586	587	437	436	590	591	433	432	594	595	429	428	598	599	425	424	602	603	421	420	606	607	417
609	415	414	612	613	411	410	616	617	407	406	620	621	403	402	624	625	399	398	628	629	395	394	632	633	391	390	636	637	387	386	640
641	383	382	644	645	379	378	648	649	375	374	652	653	371	370	656	657	367	366	660	661	363	362	664	665	359	358	668	669	355	354	672
352	674	675	349	348	678	679	345	344	682	683	341	340	686	687	337	336	690	691	333	332	694	695	329	328	698	699	325	324	702	703	321
320	706	707	317	316	710	711	313	312	714	715	309	308	718	719	305	304	722	723	301	300	726	727	297	296	730	731	293	292	734	735	289
737	287	286	740	741	283	282	744	745	279	278	748	749	275	274	752	753	271	270	756	757	267	266	760	761	263	262	764	765	259	258	768
769	255	254	772	773	251	250	776	777	247	246	780	781	243	242	784	785	239	238	788	789	235	234	792	793	231	230	796	797	227	226	800
224	802	803	221	220	806	807	217	216	810	811	213	212	814	815	209	208	818	819	205	204	822	823	201	200	826	827	197	196	830	831	193
192	834	835	189	188	838	839	185	184	842	843	181	180	846	847	177	176	850	851	173	172	854	855	169	168	858	859	165	164	862	863	161
865	159	158	868	869	155	154	872	873	151	150	876	877	147	146	880	881	143	142	884	885	139	138	888	889	135	134	892	893	131	130	896
897	127	126	900	901	123	122	904	905	119	118	908	909	115	114	912	913	111	110	916	917	107	106	920	921	103	102	924	925	99	98	928
96	930	931	93	92	934	935	89	88	938	939	85	84	942	943	81	80	946	947	77	76	950	951	73	72	954	955	69	68	958	959	65
64	962	963	61	60	966	967	57	56	970	971	53	52	974	975	49	48	978	979	45	44	982	983	41	40	986	987	37	36	990	991	33
993	31	30	996	997	27	26	1000	1001	23	22	1004	1005	19	18	1008	1009	15	14	1012	1013	11	10	1016	1017	7	6	1020	1021	3	2	1024

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.)

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A 32x32 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (16400)

Read more about Magic Squares

How to Create a 32x32 Magic Square with a Magic Sum of 16400

Step One: Draw a 32x32 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 32-by-32 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (16400)

How to Create a 32x32 Magic Square
with a Magic Sum of 16400

Step One: Draw a 32x32 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