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Who gets a free dinner?


Best Answer James33, 23 March 2013 - 12:17 AM

Spoiler for A Third Way

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15 replies to this topic

#1 bonanova

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Posted 22 March 2013 - 10:48 PM

You're out with friends at Chuck's Steak House and decide to flip a coin to select one person get a free dinner. The bill will be split n-1 ways instead of n ways. Since I was not invited, I don't know how many are in the group. (Maybe next time you'll include me; I love Chuck's place.) So anyway, your selection method has to work for an arbitrary numbers of participants.

You have only a fair coin, and the method has to treat everyone equally.
It must be absolutely fair and unbiased.

There might be many ways; bonus points await methods with originality, flair, and minimization of flips.

Pick one person out of n, fairly, with a sequence of fair coin tosses.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 James33

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Posted 22 March 2013 - 11:19 PM

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#3 Rob_Gandy

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Posted 23 March 2013 - 12:01 AM

Spoiler for Another method


Edited by Rob_Gandy, 23 March 2013 - 12:02 AM.

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#4 bonanova

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Posted 23 March 2013 - 12:04 AM

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OK, that works. Any others? What if n was large? Like 100.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 James33

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Posted 23 March 2013 - 12:04 AM

Thought about it some more I I think I have an algorithm that would do it more efficiantly

 

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#6 James33

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Posted 23 March 2013 - 12:17 AM   Best Answer

Spoiler for A Third Way


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#7 bonanova

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Posted 23 March 2013 - 12:25 AM

Spoiler for A Third Way


I'll take that.
Very nice.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#8 bushindo

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Posted 23 March 2013 - 12:49 AM

Spoiler for A Third Way

 

Question

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#9 bushindo

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Posted 23 March 2013 - 05:18 AM

You're out with friends at Chuck's Steak House and decide to flip a coin to select one person get a free dinner. The bill will be split n-1 ways instead of n ways. Since I was not invited, I don't know how many are in the group. (Maybe next time you'll include me; I love Chuck's place.) So anyway, your selection method has to work for an arbitrary numbers of participants.

You have only a fair coin, and the method has to treat everyone equally.
It must be absolutely fair and unbiased.

There might be many ways; bonus points await methods with originality, flair, and minimization of flips.

Pick one person out of n, fairly, with a sequence of fair coin tosses.

 

 

I'm trying to go for the minimum expected number of flips here. This is my best attempt so far

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#10 Prime

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Posted 23 March 2013 - 08:20 AM

I want to be a party pooper.

 

Thought about it some more I I think I have an algorithm that would do it more efficiantly

 

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This one is unfair.

Spoiler for explanation

 

Spoiler for A Third Way

Nice. However, as Bushindo has noticed this one may require replay for number of participants other than power of 2. So there is no ceiling on how many coin throws decide the winner.

 

You're out with friends at Chuck's Steak House and decide to flip a coin to select one person get a free dinner. The bill will be split n-1 ways instead of n ways. Since I was not invited, I don't know how many are in the group. (Maybe next time you'll include me; I love Chuck's place.) So anyway, your selection method has to work for an arbitrary numbers of participants.

You have only a fair coin, and the method has to treat everyone equally.
It must be absolutely fair and unbiased.

There might be many ways; bonus points await methods with originality, flair, and minimization of flips.

Pick one person out of n, fairly, with a sequence of fair coin tosses.

 

 

I'm trying to go for the minimum expected number of flips here. This is my best attempt so far

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Awesome. Same problem though – no ceiling. And it seems fair, but not in an obvious way. A proof of fairness would be nice.


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Past prime, actually.





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