Re: Twenty Beautiful Women
At 20:54 7/27/96, Mike Duvos wrote:
ichudov@algebra.com (Igor Chudov @ home) writes:
Also, I would appreciate if someone specified what exactly the goal function is.
Me too.
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. -- Lucky Green <mailto:shamrock@netcom.com> PGP encrypted mail preferred. Defeat the Demopublican Unity Party. Vote no on Clinton/Dole in November. Vote Harry Browne for President.
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. $
At 20:54 7/27/96, Mike Duvos wrote:
ichudov@algebra.com (Igor Chudov @ home) writes:
Also, I would appreciate if someone specified what exactly the goal function is.
Me too.
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.
Can someone explain the theory behind this? -- "Of all tyrannies a tyranny sincerely exercised for the good of its victims may be the most oppressive. It may be better to live under robber barons than under omnipotent moral busybodies, The robber baron's cruelty may sometimes sleep, his cupidity may at some point be satiated; but those who torment us for own good will torment us without end, for they do so with the approval of their own conscience." - C.S. Lewis, _God in the Dock_ +---------------------+--------------------+----------------------------------+ |Julian Assange RSO | PO Box 2031 BARKER | Secret Analytic Guy Union | |proff@suburbia.net | VIC 3122 AUSTRALIA | finger for PGP key hash ID = | |proff@gnu.ai.mit.edu | FAX +61-3-98199066 | 0619737CCC143F6DEA73E27378933690 | +---------------------+--------------------+----------------------------------+
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