Solution to Problem 22: "Absolutely Dotty"

When we talk about a number, we'll describe it by the label of the four dots around it.   For example, there is a 0 at EF45.

Here are some rules that will be applied without comment:

(A) If a dot has only one line that can be part of the path, then the dot is not part of the path.

(B) If a dot is part of the path and the two lines are allready known, then the other lines connected to the dot are not part of the path.

(C) If a dot has two lines coming out of it, then either both lines are in the path or neither is.  (Two corollaries to this is that if a 3 is surrounded by two lines that are the only things coming out of a dot, then both lines are in the path and if a 1 is in the same situation then neither line is in the path.)

	All of the lines surrounding 0's are out, of course, then we start applying the rules described above indiscriminiately.
	If two 3's are adjacent to one another (like CD23 and CD34), then the line between them must be in the path, and so is the line parallel to it on each side (like C-D3, C-D2, and C-D4).  Also, if two 3's are diagonally adjacent (like BC12 and CD23), then the four lines on the "outside corner" are in the path (like B-C1, B1-2, C-D3, and D2-3). Lots of applications of the rules leads us to....
	The area in the upper right quadrant can only be accessed if E4 and J5 are in the path. If B4-5 were in the path, then there would be no way for the path to complete a circuit. If F5 or G5 were in the path, then it would form an incomplete circuit with the 3 at FG67. If I6 were in the path, then H7 wouldn't be, but then there would be no way to satisfy the 2 at GH67.  So I6 is not in the path. If C-D9 were in the path, then either the lower left quadrant would be an incomplete circuit or there would be no way to satisfy the 2 at EF89.
	The open line around FG67 must be on the left side, because if it were at the bottom there would be a loose end on the right side.
	The code that they're looking for to describe row 6 and column F is OLLILILIOOO LILOOILLLLO.

Comments: I spent a few minutes on this problem, then a few more, then I wished I hadn't.  You need to juggle two different pencil colors to represent edges that are in the path with those that aren't, and it's hard to keep track of exactly what goes where.  It is a lot less cumbersome solving it with a computerized paint package where you can draw in some thin lines at the beginning and then thicken or erase them (as I did here). Did anyone have a more enjoyable strategy?