Given K points in a N-dimensional (hyper-)cube with all edges length 1. What is the expected minimal distance between 2 points. I found the 1-dimensional case in this topic: http://mathoverflow.net/questions/1294/mean-minimum-distance-for-n-random-points-on-a-one-dimensional-line and I wonder if this can be generalized into multiple dimensions in general. I don't seem to succeed in extending the card analogy in the other topic. Does anyone have any hints as to proceed with this?