Re: Twenty Beautiful Women

[mpd@netcom.com (Mike Duvos)]

Lucky Green writes:

> For clarification, the problem is often stated in textbooks similar like this:
> 
> You ask someone to write one number each on ten pieces of paper without you
> being able to see the numbers. The person may use any number from 1 to
> 10^99, but may not use a number twice. The person turns over the ten
> papers.
> 
> You goal is to determine the paper with the highest number [rules apply as
> described in the original post]
> 
> The general solution is to flip over 1/e papers and choose the paper that
> has a higher number on it than any of the 1/e papers turned over at first.

Stated this way, I suppose strategy A is better than strategy B if after
an arbitrarily large number of trials, N(A>B) > N(B>A).

It is still unclear that such a notion translates smoothly into notions
like "lowest gas price", where buying once at a station that is half
the price beats buying a dozen times at a station that is only one 
cent less.  

It does translate perfectly well into the original problem of picking
subjectively beautiful women, however, which is also non-parametric in
a similar way.  It would be nice to see a short proof that for the
optimal solution, the threshold is the max of the first 1/e elements, 
and is not a function of how many steps have been taken. 

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     Mike Duvos         $    PGP 2.6 Public Key available     $
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