A 29x29 Magic Square

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Other Magic Square Sizes: 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19 *
21 * 23 * 25 * 27 * 29 * 31 * 33 * 35 * 37 * 39 * 41 * 43 * 45 * 47 * 49 * 51 * 53 * 55 * 57 * 59 *
61 * 63 * 65 * 67 * 69 * 71 * 73 * 75 * 77 * 79 * 81 * 83 * 85 * 87 * 89 * 91 * 93 * 95 * 97 * 99 *
A 29x29 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (12209)

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 29 by 29 magic square shown below has a magic sum equal to 12209.
Though magic squares can be made with non-consecutive and non-regular sequences, they are usually seen made up of consecutive numbers. To the best of my knowledge, the middle number in the sequence must be in the center square, and the magic sum will be equal to this middle number times the number of rows in the square. (In the case of 3x3 squares, I have proved that the middle number MUST be equal to one-third of the sum. See proof here.)
All odd-size Magic Squares can be made with the method shown below, which can be summarized as "start in the middle of the top and keep moving up and to the right except when you get blocked, in which case drop down and continue." The more detailed directions about creating these squares can be found further below. There are other methods for creating magic squares, but this is the easiest to learn. (There are basically only two methods of creating a 3x3 square but the larger squares have a large number of irregular variants, and probably other regular methods.)
Read more about Magic Squares
If you'd like to read more about magic squares, click one of these links to look for books about Magic Squares at Amazon.com, at Amazon.canada, and at Amazon.co.UK.

A 29-by-29 Magic Square

(Magic Sum = 12209)

Books about
Magic Squares
at Amazon.co.UK

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

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How to Make Your Own Odd-Size Magic Square

Draw a square with any odd number of rows and columns.
Put your first number in the MIDDLE square of the TOP row.
Move UP and to the RIGHT to find the position for your next number, but ...
- if the next "position" is ABOVE a column, go to BOTTOM of that column (you can see a sample of this movement by looking at how we moved from 1 to 2 in the square above).
- if the next "position" is to the RIGHT of a row, go to LEFT of that row (you can see this movement between (15) and (16) above).
- if the next cell is already filled in, drop down to the cell below the number you just filled in for the next number (you can see this when you look at how we moved from 29 to the next number above).
- if the next cell is both ABOVE and to the RIGHT of the entire square, drop down to the cell below the number you just filled in for your next number (you can see this if you look at (435) and the next number).
Print your NEXT number into the new square you just moved to.
Repeat steps 3-4 until the entire square is full.
You can see how it works by printing this page and drawing arrows to see how it worked when I created this magic square

This Magic Square was created by John Knoderer, a webmaster and computer programmer who is available to telecommute to your location.

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.

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

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

A 29x29 Magic Square

Scroll down to see a magic squarein which all rows, columns, and both diagonalsadd up to the same magic sum (12209)

Read more about Magic Squares

A 29-by-29 Magic Square

How to Make Your Own Odd-Size Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (12209)

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