This is a tough game to diagram in general, and nearly impossible to do so on a keyboard, so I'm not sure how helpful I can be. Our rules are fairly general before the last two, and we already have a picture of the initial setup. We know that we can make any path with five segments, as long as it connects all six, does not cross itself, and no chalet is connected with three other chalets.
With this, I would probably draw their diagram on my paper, and put in two lines for JN and KL. From there, I would maybe make up one or two scenarios of viable paths, but that is probably where I would stop. This is a very atypical game, and when you see as weird a game as this, sometimes the best you can do is understand the rules, the setup, and how your scenarios (if you choose to do them) help, and move onto the questions.
