Primer Part 2 (Best Franklin Squares)

Franklin Squares Primer

Part 2

Franklin square features

	Franklin's original 8x8
	#3	260				260			292			#3A						130
	52	61	4	13	20	29	36	45	260		130	52	61	4	13	20	29	36	45
	14	3	62	51	46	35	30	19	260			14	3	62	51	46	35	30	19
	53	60	5	12	21	28	37	44	260			53	60	5	12	21	28	37	44
	11	6	59	54	43	38	27	22	260			11	6	59	54	43	38	27	22
	55	58	7	10	23	26	39	42	260			55	58	7	10	23	26	39	42
	9	8	57	56	41	40	25	24	260			9	8	57	56	41	40	25	24
	50	63	2	15	18	31	34	47	260			50	63	2	15	18	31	34	47
	16	1	64	49	48	33	32	17	260			16	1	64	49	48	33	32	17
	260	260	260	260	260	260	260	260	228			130


	#4 Franklin's original 16x16																2168
2040	199	216	231	248	7	24	39	56	71	88	103	120	135	152	167	184	2040
	57	38	25	6	249	230	217	198	185	166	153	134	121	102	89	70	2040
	197	218	229	250	5	26	37	58	69	90	101	122	133	154	165	186	2040
	59	36	27	4	251	228	219	196	187	164	155	132	123	100	91	68	2040
	200	215	232	247	8	23	40	55	72	87	104	119	136	151	168	183	2040
	54	41	22	9	246	233	214	201	182	169	150	137	118	105	86	73	2040
	202	213	234	245	10	21	42	53	74	85	106	117	138	149	170	181	2040
	52	43	20	11	244	235	212	203	180	171	148	139	116	107	84	75	2040
	204	211	236	243	12	19	44	51	76	83	108	115	140	147	172	179	2040
	50	45	18	13	242	237	210	205	178	173	146	141	114	109	82	77	2040
	206	209	238	241	14	17	46	49	78	81	110	113	142	145	174	177	2040
2040	48	47	16	15	240	239	208	207	176	175	144	143	112	111	80	79	2040
	195	220	227	252	3	28	35	60	67	92	99	124	131	156	163	188	2040
	61	34	29	2	253	226	221	194	189	162	157	130	125	98	93	66	2040
	193	222	225	254	1	30	33	62	65	94	97	126	129	158	161	190	2040
	63	32	31	0	255	224	223	192	191	160	159	128	127	96	95	64	2040
	2040	2040	2040	2040	2040	2040	2040	2040	2040	2040	2040	2040	2040	2040	2040	2040	1912

In squares #3 and #4, Franklin’s original 8x8 and 16x16, diagonals have the wrong totals. These squares are not true magic squares. However they have many features that make them interesting. I think three of them are necessary in a Franklin type square.

What we call “bent diagonals” he called “bent rows”. In square #4 the highlighted feature from 57 to 70 is a bent diagonal and totals 2040, the same as the rows. The wrapped around bent diagonal from 195 to 188 totals the same. Square #3 shows bent diagonals that also have proper totals. All bent diagonals in these two squares, V up, V down, V right, and V left, have the same totals as the rows. This is Franklin’s trademark feature.

Two other features are shown in #3a. Every half row and half column starting at an outside edge totals half a row total. In each square every 2x2, wherever placed, totals the same.

Best Franklin Squares

Navigation

Primer Part 2