Four pins are randomly nailed to a square board (according to a uniform probability distribution), and a rubber band is stretched completely around them to form a convex shape. What is the probability that the rubber band is in the shape of a triangle?

This puzzle has a rating of 4.75 as of my composing this comment.  Why is David Shin apologizing (in the official solution) for submitting it? It was good food for thought.  A Monte Carlo method of getting the probability was found; that was interesting to do.  And we got to look at the solution in the Wolfram site.

Posted by Charlie on 2005-02-20 16:35:28