This month's problem is a variation on the Buffon Needle Problem.

A needle of length 2 is bent at its midpoint forming a right angle. It is then dropped onto a floor on which a family of parallel lines spaced Sqrt[2] units apart have been drawn. What is the probability that the needle lands on one of the lines? Assume that where the midpoint of the needle lands and with what orientation are both uniformly distributed. What if the lines are spaced 2 units apart? 1 unit?