$N$ points are generated randomly within a unit square, with a uniform distribution. What is the probability that the points form a connected graph, given that two points are connected if the distance between them is less than or equal to $d$? (this should obviously be some function of $N$ and $d$).
If you don't know the answer, but have an idea that may (or may not) lead me a step forward, please let me know as well. I'm will try anything sensible.
Moreover, if you know for sure that this problem is yet unsolved, that's also good news for me. I can then do it through a Monte-Carlo simulation, but my approach would be justified.