Re: Twenty Beautiful Women

[ichudov@algebra.com (Igor Chudov @ home)]

Timothy C. May wrote:
> >Twenty beautiful women are to pass before you, one by one (or 20 handsome
> >men). You see only one at a time. You cannot speak to them. After seeing
> >any one, you must pick her or reject her. If you reject her, you cannot
> >change your mind. If you pick her the exercise terminates.
> >
> >What is the optimal strategy for insuring you get the most beautiful woman
> >possible under the circumstances?
> 
> Look at the first 1/e of them, or about the first 36.8% of them. In this
> case, the first 7 of them. Then pick the first one after this group which
> is better than any of the first group.
> 
> While there is some chance that one will get to #20 and find that none of
> #8-20 were better than #1-7, this strategy is the best compromise between
> "committing too early" and "waiting too long."

This "some chance" is 1/e (for a very large number of women), obviously.

There is 1/e chance that the best woman will be in the first 1/e 
fraction of women.

Also, I would appreciate if someone specified what exactly the goal 
function is.

	- Igor.