This myriad of numbers hides 7 pathways that each link a sequence of numbers.

aaa	1	2	3	4	5	6	7	8	9	10	11	12	13
a	55	92	34	28	225	55	12	256	45	89	70	361	144
b	55	169	47	89	196	233	53	225	66	144	256	233	289
c	34	67	21	61	66	16	8	45	35	53	51	225	47
d	53	276	13	59	21	253	15	13	231	169	28	196	2
e	324	256	35	361	225	89	22	256	13	289	253	324	233
f	128	22	35	64	71	32	253	28	210	15	64	351	325
g	210	16	35	15	21	22	231	92	55	35	70	92	43
h	47	12	43	2	2	4	4	45	4	28	45	51	70
i	324	289	8	92	253	12	59	324	22	8	231	35	4
j	61	59	16	61	67	233	71	153	120	22	210	117	12
k	289	53	47	128	256	300	53	276	21	253	34	276	300
l	351	8	325	91	4	300	8	66	91	233	66	276	325
m	361	59	51	70	61	64	59	210	35	231	61	253	67

Each sequence is exactly a consecutive series of 7 numerals in length. The numerals are connected orthogonally, and usually in a perpendicular direction. The path connecting numerals within a sequence may not be intersected or crossed by itself or any other path, and numerals are unique to a particular sequence.

The sequences are:
Prime, Triangle, Square, Pentagonal, Hexagonal, Fibonnacci and Powers of 2, and obviously, do not expect every sequence to begin with its first term.

Hints:
1. Use your "prt sc" function to make a print-out of the page.
2. Determine the range of each sequence within the numeric range of the table.
3. Be aware that some full length sequences exist but would impinge on others.

Note: the three numbers bold and underlined are not part of a solution sequence but demonstrate how a Power of 2 trail might begin.

(In reply to computer visualization aid by Charlie)

Charlie, I admire how you work "your magic".  You have firstly extracted the positions of where numbers of a sequence group resides within the table.

Yes, there a clearly some potential conflicts which could not be helped (nature of numbers); 36 for instance is both a square and a triangle, hexagonal numbers are a subset of the triangles.

Those and similar thoughts were in mind  when taking  into account in this problem's development. 

It seems from Dej Mar's comment that in "padding" the grid with false leads I erroneously placed a number which voided what I expected was a unique solution.

Posted by brianjn on 2009-05-15 10:53:58