Here is the labeling of the 9 positions from before.

A  B  C
D  E  F
G  H  I

After utilizing the hints 1 through 5, we find that there are only 7 ways of going from the center back to the center. They are:

1)  E-B-C-F-E           works if x is 1 (mod 4),  produces (3x + 29)/4 

2)  E-B-A-D-G-H-E       works if x is 2 (mod 6),  produces (2x + 71)/3

3)  E-D-A-B-C-F-E       works if x is 0 (mod 4),  produces (3x + 32)/4

4)  E-D-G-H-E           works if x is 0 (mod 6),  produces (x + 96)/6

5)  E-H-G-D-E           works if x is 2 (mod 6),  produces (x + 16)/6

6)  E-H-G-D-A-B-C-F-E   works if x is 2 (mod 6),  produces (2x + 64)/4

7)  E-F-C-B-E           works if x is 0 (mod 4),  produces (3x + 60)/4

There are also (theoretically) 3 ways to get out of the maze:

8)  E-D-G-H-I           works if x is 24 (mod 36)

9)  E-H-I               works if x is 4 (mod 6)

10) E-F-I               works if x is 0 (mod 12)

With this information, it is not hard to determine which values are possible in the center. We can now chart a course through this maze, and the chart will be fairly small. Note that the 10 moves above cannot be done in any order, since we have the "no 180 degree turn" rule. For example, we cannot do sequence 7, and then do sequence 2. None-the-less, the maze is easy to follow using nothing but the above chart.

Back to the maze.

Still need another hint? Click here.