Solution to Problem 3: No U-turn Maze

	From the start square, label with a 1 every legal space that can be reached from the start square.  Then, from each square labeled 1, put a 2 on every space that can be legally reached from that square.  The label indicates the number of moves in the shortest path from the start square.
	Continue in this manner until the start square has a label.  We find that the shortest path back to start has 13 moves.
	To recreate the path, circle the spot with label 13, then circle a spot with label 12 that points to it, then circle a spot with label 11 that points to the circled 12 spot, and so on.  This will give us the shortest path.
	The lengths of each of the moves in order is 3 2 4 4 1 2 2 4 3 2 5 4 1.

Notes: This was the first puzzle that I solved, which took less than five minutes.  I wound up checking it several times, though, to make sure that the path was correct and the answer I would be submitting was the one I intended.  All in all, I think it was the cheapest 15 points in the contest.

It has been pointed out from several solvers that it is easier yet to solve the puzzle "backwards" since there is a very small number of options at each step and most of them can be immediately ruled out.  It does seem to me that if you circle every arrow that is pointing to the start hex or another circled arrow (unless the circled arrow in question is pointing toward the arrow), and cross out any circled hexes that have no arrows pointing to it that it is not pointing to, the circled uncrossed hexes would be exactly the highlighted hexes in the last grid that I've got here, and much more easily generated.