Doesn't this problem basically take the Feynman restaurant problem and replaces meal with woman?
http://www.feynmanlectures.info/exercises/Feynmans_restauran...
http://www.feynmanlectures.info/exercises/Feynmans_restauran...
In short : maximum likelihood soultion is to pass on (1/e)*N, minimum mean squared error solution is to pass on sqrt(N). This of course assumes you can estimate N well.