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Mar 5, 2013 at 13:20 comment added Anthony Quas @Douglas: Just saw your answer (almost identical to the above) to a previous incarnation of this question (on which I commented).
Mar 5, 2013 at 12:56 comment added Douglas Zare For other distributions, the logarithm of the probability is either $0$ or $\Theta(n^2)$ by essentially the same argument.
Mar 5, 2013 at 11:56 comment added Joel David Hamkins The lower bound argument works also if all distances are in $[\frac13,\frac23]$, or more generally in $[a,2a]$; perhaps one can find a better bound this way?
Mar 4, 2013 at 16:52 history answered Anthony Quas CC BY-SA 3.0