A Special Order 13 Magic Square

A Special Order 13 Magic Square:

This is an order 13 magic square with the normal “magic square properties”, but it also has some special additions. 

157	13	23	147	109	31	111	138	36	66	102	100	72
145	25	17	153	61	139	59	32	134	104	68	98	70
16	154	144	26	57	56	30	112	136	99	105	60	110
22	148	156	14	113	114	140	58	34	65	71	133	37
97	73	94	76	151	18	21	89	146	135	35	29	141
79	91	78	92	27	82	150	155	11	63	107	33	137
74	96	75	95	143	159	15	20	88	115	55	101	69
90	80	93	77	19	24	81	149	152	54	116	103	67
164	6	3	167	85	142	158	12	28	64	106	108	62
7	163	168	86	1	132	44	39	125	50	48	118	124
162	8	84	2	169	38	126	131	45	120	122	52	46
5	83	161	10	166	129	43	40	128	123	117	49	51
87	165	9	160	4	41	127	130	42	47	53	121	119

The square has 169 spaces for number, and contains all of the numbers from 1 to 169 (13 squared) one time each.  All of the rows have the same sum (1105), all of the columns have the same sum (1105), and both of the main diagonals have the same sum. 

What makes it special?  It also contains 12 smaller magic squares (well, one of them is only semi-magic because only one of its diagonals adds up to the magic constant for that square) ranging in size from 3 x 3 to 11 x 11.  So this magic square is really a total of 13 magic squares.

A 3 x3 semi-magic square with 3 in the upper left corner.  All rows and columns, but only 1 main diagonal have a magic constant of 255.

Four 4 x 4 magic squares with 157, 97, 132 or 50 in the upper left corner of each square.  All rows, columns and the two main diagonals sum to 340.

Two 5 x 5 magic squares with 164 or 151 in the upper left corner.  All rows, columns and the two main diagonals sum to 425.

Two 7 x 7 magic squares with 94 or 57 in the upper left corner.  All rows, columns, and the two main diagonals sum to 595.

Two 9 x 9 magic squares with 109 and 97 in the upper left corner.  Their magic constant is 765.

An 11 x 11 magic square with 23 in the upper left corner.  Its magic constant is 935.

And finally, a 13 x 13 magic square with 157 in the upper left corner (the entire array).  Its magic constant is 1105.

My daughter was born on the 13th of the month, turned 13 (became a teenager) on a Friday the 13th (with 12 friends attending a sleepover, all 13 dressed in black).  The last time I warned her about a Friday the 13th coming up (so that she could avoid hospital duty that nigh) she said "Why?  That's when all the fun stuff happens."  What can I say - she has a thing for the number 13.

David