Benjamin Franklin's Magic Square

Benjamin Franklin, an 18th-century American printer, politician, diplomat, scientist, inventor, etc., etc., enjoyed creating magic squares in his free time.

52	61	4	13	20	29	36	45
14	3	62	51	46	35	30	19
53	60	5	12	21	28	37	44
11	6	59	54	43	38	27	22
55	58	7	10	23	26	39	42
9	8	57	56	41	40	25	24
50	63	2	15	18	31	34	47
16	1	64	49	48	33	32	17

In Franklin's autobiography, he mentions that in his youth he had created an 8×8 semi-magic square with a magic sum of 260, which also had the properties that each half-row sums to 130, and that each "bent row", as Franklin described it, summed to 260. An example "bent row" is illustrated in red in the magic square on the right.

Later on in his life, Franklin created a 16×16 semi-magic square with similar properties; in other words, each row or column sums to the magic sum, 2056, each half-row sums to half of 2056, and each "bent row" sums to 2056. In addition, the numbers in any 4×4 square drawn within the magic square sum to 2056. Here is the square tha Franklin created:

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

You may also be interested in Euler's Knight's Tour Magic Square.

Sources used (see bibliography page for titles corresponding to numbers): 33.

More information on Franklin's magic squares