Number of shortest paths? please help?

Only ONE path can be SHORTEST, by definition. If you have two, then your means of measurement are not precise enough. Of course, by Heisenberg's uncertainty principle, it is impossible to know both the position and momentum of an electron at a given time, so it is possible that you are incapable of determining the shortest path, but that by no means indicates that there is not one, only that you can never determine it.