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. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd@netcom.com $ via Finger. $