A 17x17 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 *
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A 17x17 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (2465)

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 17 by 17 magic square shown below has a magic sum equal to 2465.
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 17-by-17 Magic Square

(Magic Sum = 2465)

Books about
Magic Squares
at Amazon.co.UK

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155	174	193	212	231	250	269	288	1	20	39	58	77	96	115	134	153
173	192	211	230	249	268	287	17	19	38	57	76	95	114	133	152	154
191	210	229	248	267	286	16	18	37	56	75	94	113	132	151	170	172
209	228	247	266	285	15	34	36	55	74	93	112	131	150	169	171	190
227	246	265	284	14	33	35	54	73	92	111	130	149	168	187	189	208
245	264	283	13	32	51	53	72	91	110	129	148	167	186	188	207	226
263	282	12	31	50	52	71	90	109	128	147	166	185	204	206	225	244
281	11	30	49	68	70	89	108	127	146	165	184	203	205	224	243	262
10	29	48	67	69	88	107	126	145	164	183	202	221	223	242	261	280
28	47	66	85	87	106	125	144	163	182	201	220	222	241	260	279	9
46	65	84	86	105	124	143	162	181	200	219	238	240	259	278	8	27
64	83	102	104	123	142	161	180	199	218	237	239	258	277	7	26	45
82	101	103	122	141	160	179	198	217	236	255	257	276	6	25	44	63
100	119	121	140	159	178	197	216	235	254	256	275	5	24	43	62	81
118	120	139	158	177	196	215	234	253	272	274	4	23	42	61	80	99
136	138	157	176	195	214	233	252	271	273	3	22	41	60	79	98	117
137	156	175	194	213	232	251	270	289	2	21	40	59	78	97	116	135

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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 (9) and (10) 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 17 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 (153) 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.

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155	174	193	212	231	250	269	288	1	20	39	58	77	96	115	134	153
173	192	211	230	249	268	287	17	19	38	57	76	95	114	133	152	154
191	210	229	248	267	286	16	18	37	56	75	94	113	132	151	170	172
209	228	247	266	285	15	34	36	55	74	93	112	131	150	169	171	190
227	246	265	284	14	33	35	54	73	92	111	130	149	168	187	189	208
245	264	283	13	32	51	53	72	91	110	129	148	167	186	188	207	226
263	282	12	31	50	52	71	90	109	128	147	166	185	204	206	225	244
281	11	30	49	68	70	89	108	127	146	165	184	203	205	224	243	262
10	29	48	67	69	88	107	126	145	164	183	202	221	223	242	261	280
28	47	66	85	87	106	125	144	163	182	201	220	222	241	260	279	9
46	65	84	86	105	124	143	162	181	200	219	238	240	259	278	8	27
64	83	102	104	123	142	161	180	199	218	237	239	258	277	7	26	45
82	101	103	122	141	160	179	198	217	236	255	257	276	6	25	44	63
100	119	121	140	159	178	197	216	235	254	256	275	5	24	43	62	81
118	120	139	158	177	196	215	234	253	272	274	4	23	42	61	80	99
136	138	157	176	195	214	233	252	271	273	3	22	41	60	79	98	117
137	156	175	194	213	232	251	270	289	2	21	40	59	78	97	116	135

155	174	193	212	231	250	269	288	1	20	39	58	77	96	115	134	153
173	192	211	230	249	268	287	17	19	38	57	76	95	114	133	152	154
191	210	229	248	267	286	16	18	37	56	75	94	113	132	151	170	172
209	228	247	266	285	15	34	36	55	74	93	112	131	150	169	171	190
227	246	265	284	14	33	35	54	73	92	111	130	149	168	187	189	208
245	264	283	13	32	51	53	72	91	110	129	148	167	186	188	207	226
263	282	12	31	50	52	71	90	109	128	147	166	185	204	206	225	244
281	11	30	49	68	70	89	108	127	146	165	184	203	205	224	243	262
10	29	48	67	69	88	107	126	145	164	183	202	221	223	242	261	280
28	47	66	85	87	106	125	144	163	182	201	220	222	241	260	279	9
46	65	84	86	105	124	143	162	181	200	219	238	240	259	278	8	27
64	83	102	104	123	142	161	180	199	218	237	239	258	277	7	26	45
82	101	103	122	141	160	179	198	217	236	255	257	276	6	25	44	63
100	119	121	140	159	178	197	216	235	254	256	275	5	24	43	62	81
118	120	139	158	177	196	215	234	253	272	274	4	23	42	61	80	99
136	138	157	176	195	214	233	252	271	273	3	22	41	60	79	98	117
137	156	175	194	213	232	251	270	289	2	21	40	59	78	97	116	135

A 17x17 Magic Square

Scroll down to see a magic squarein which all rows, columns, and both diagonalsadd up to the same magic sum (2465)

Read more about Magic Squares

A 17-by-17 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 (2465)

155	174	193	212	231	250	269	288	1	20	39	58	77	96	115	134	153
173	192	211	230	249	268	287	17	19	38	57	76	95	114	133	152	154
191	210	229	248	267	286	16	18	37	56	75	94	113	132	151	170	172
209	228	247	266	285	15	34	36	55	74	93	112	131	150	169	171	190
227	246	265	284	14	33	35	54	73	92	111	130	149	168	187	189	208
245	264	283	13	32	51	53	72	91	110	129	148	167	186	188	207	226
263	282	12	31	50	52	71	90	109	128	147	166	185	204	206	225	244
281	11	30	49	68	70	89	108	127	146	165	184	203	205	224	243	262
10	29	48	67	69	88	107	126	145	164	183	202	221	223	242	261	280
28	47	66	85	87	106	125	144	163	182	201	220	222	241	260	279	9
46	65	84	86	105	124	143	162	181	200	219	238	240	259	278	8	27
64	83	102	104	123	142	161	180	199	218	237	239	258	277	7	26	45
82	101	103	122	141	160	179	198	217	236	255	257	276	6	25	44	63
100	119	121	140	159	178	197	216	235	254	256	275	5	24	43	62	81
118	120	139	158	177	196	215	234	253	272	274	4	23	42	61	80	99
136	138	157	176	195	214	233	252	271	273	3	22	41	60	79	98	117
137	156	175	194	213	232	251	270	289	2	21	40	59	78	97	116	135