Posted by Mensen at mathoverflow.net
Very interesting problem (Very difficult actually)
Let's say that I have a one-dimensional line of finite length 'L' that I populate with a set of 'N' random points. What is the probability 'p' that the minimum distance between any pair of these points is larger than some value 'k' or an expression for the mean minimum distance (MMD) for a pair of points in the set - referring to the smallest distance between any two points that can be found, not the mean minimum/shortest distance between all possible pairs of points.
Good problem :D ... I am happy!!!
Update (11/12/09): Solution in comments!!