prior probability

Your mission, should you choose to accept it, is to find the shortest possible route connecting the three corners or vertices of an equilateral triangle, as shown in the illustration below:

Hint: in searching for the shortest possible route connecting all three points of the triangle, your route may also need to run through or connect to one or more extra points within the boundary of the triangle. So, now, ask yourself a different question: how many extra points would you add to this triangle and where would you place them?

Postscript for my law students: although the geometrical problem above has a correct solution, can we really say the same about problems in law? In short, why is it that some legal problems, especially hard cases, do not necessarily have a “correct” solution? Consider one of the short essay questions on my Torts final: what’s wrong with Judge Cardozo’s opinion in the Palsgraf case? One possible answer is that Cardozo’s “zone of danger” test is too indefinite and indeterminate. That is, how can we say (with any level of certainty) whether Ms. Palsgraf was really in the zone of danger or not when the scale fell on her head; after all, wasn’t she standing on the platform of the train station when the explosion occurred? The larger and more important question, however, is this: how should we approach such hard problems in law?  What should we do when we are confronted with a difficult legal problem, i.e. one with no right answer or correct solution?