Here is the labeling of the 9 positions from before.
A B C D E F G H I
Let us determine the first couple of moves in the maze. One begins with 1 at A, and has a choice to go left to B, or down to D. If one goes down to D, he again has a choice as to go left to E, or down to G. But if he goes left to E, he will have a value of 3, which we saw in the last hint is doomed. So he must go down to G, and then right to H. He will then be at H with a value of 10, so is forced to go up to E.
At this point, he again has a choice of going up to B, or left to D. But going up to B gives a value of 27, and since x+1 is not a multiple of 3, he can't go left, and since x+2 is not a multiple of 4, he can't go right. Thus, going up to B is a mistake, and hence he is forced to go to D.
Once again, there is a choice of going up to A, or down to G. Going up to A, and then right to B gives a value of 28. Since this is not odd, he cannot go down, and since x+2 is not a multiple of 4, he can't go left either. So once again he is stuck. Hence, the only choice is to go down to G, and then to H.
Now he is at H with a value of 11, and so must go up to E, giving a value of 19.But this is one less than a multiple of 4, so even this is doomed.
Looking back, we find that going down for the first move dooms us to fail. Thus, the first move is to go right to B, giving a value of 2. Since this is not odd, we must go right again to C, and then to F, and finally to E, giving a value in the center of 2.
In summary, the first few moves are A-B-C-F-E, giving a value of 2 in the center. Thus, we can treat this as the starting point, and ask which paths go from the center to the center are possible? Can you find conditions (using modular arithmetic notation) as to when these paths can be taken? This is the key to solving the maze.
Still need another hint? Click here.