Echoing what was said here - it took a while to understand how to approach it. Maybe an animation of a simple problem being solved would be useful.
BTW, are you making sure somehow there's only a single solution or do you accept any solution?
Regarding the second question. I've developed an algorithm, that traverses a dictionary of English words and makes sure that only certain set of words (2 or more) fits the given dots and lines. It is possible to find conditions under which only one word is possible, or words of different lengths.
So there is more than one solution, got it. Either way is fine just wanted to know if everybody's searching for the same answer or any answer.