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Truth, lies and pot luck


Best Answer araver, 30 January 2013 - 09:39 PM

Spoiler for perhaps
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17 replies to this topic

#1 bonanova

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Posted 30 January 2013 - 04:53 PM

You already know the story.

Monty Hall has two doors, concealing in some order a valuable prize and a bag of garbage. But when Regis Philbin learns that the prize is $1 million, he runs onto stage and has security throw Monty out, claiming Monty has stolen his show. Regis then asks if you want to be a millionaire. Since you haven't answered any questions so far and thus have nothing to lose, you agree. He tells you that the contents behind the door of your choice are yours to keep. Which door do you choose? As an unadvertised bonus, you may use one of the standard lifelines for assistance.

You reason that since none of your friends has any useful knowledge, a phone call is useless. Accordingly, you ask the computer to eliminate half of the answers. Unfortunately the computer has been programmed to eliminate precisely two answers. This is useful when there are four choices. But with only two options, it also is not useful. That leaves the audience call-out.

The good news is that the audience was shown the winning door before you arrived. Every person in the audience has the information that you need to win the money. The bad news is that the audience comprises unknown numbers of truth-tellers, liars, and persons who randomly tell the truth or lie.

Regis senses your sadness and offers you a choice. You may ask a single yes/no question of your choosing, either to the audience as a whole, after which you will see a tabulation of their answers, or to a single audience member, whom you may select by pointing out, from where you sit on stage.

I know. This plot is worn pretty thin. But if something isn't clear, ask..

Otherwise, just tell me how much money you go home with, and how. Enjoy!
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#2 k-man

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Posted 30 January 2013 - 07:42 PM

Spoiler for the best I can think of right now

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#3 bonanova

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Posted 30 January 2013 - 07:48 PM

Spoiler for the best I can think of right now


Nice.
That would get you three points of the star.
But there is a more complete solution.
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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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#4 Yoruichi-san

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Posted 30 January 2013 - 08:20 PM

What kind of 'random' are the random answerers?  Do they, like, flip the coin every time they answer or is there a pre-set random order of truth/lie that they have memorized?  Also what happens when you ask someone a question they cannot answer?

 

Spoiler for My strat...


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#5 k-man

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Posted 30 January 2013 - 08:59 PM

My understanding of the "random answerer" is that he flips a coin every time you ask any question and answers "Yes" for heads and "No" for tails. It doesn't really matter what the question is as the answer will be either a truth or a lie, provided the question eliminates any other kind of answer as valid (yes/no question). There isn't a yes/no question they cannot answer.


Edited by k-man, 30 January 2013 - 09:00 PM.

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#6 bonanova

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Posted 30 January 2013 - 08:59 PM

What kind of 'random' are the random answerers?  Do they, like, flip the coin every time they answer or is there a pre-set random order of truth/lie that they have memorized?  Also what happens when you ask someone a question they cannot answer? 

Spoiler for My strat...


As stated in the OP any audience member who is not a truth-teller or a liar will randomly lie or tell the truth. If you like, s/he could make that decision by coin flip.
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#7 bonanova

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Posted 30 January 2013 - 09:02 PM

My understanding of the "random answerer" is that he flips a coin every time you ask any question and answers "Yes" for heads and "No" for tails. It doesn't really matter what the question is as the answer will be either a truth or a lie, provided the question eliminates any other kind of answer as valid (yes/no question).


The OP does not describe them as randomly answering yes or no.
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#8 araver

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Posted 30 January 2013 - 09:39 PM   Best Answer

Spoiler for perhaps

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#9 bushindo

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Posted 30 January 2013 - 11:54 PM


What kind of 'random' are the random answerers?  Do they, like, flip the coin every time they answer or is there a pre-set random order of truth/lie that they have memorized?  Also what happens when you ask someone a question they cannot answer? 

Spoiler for My strat...

As stated in the OP any audience member who is not a truth-teller or a liar will randomly lie or tell the truth. If you like, s/he could make that decision by coin flip.
 
Clarifications, please
 
1) Does each member of the audience know the type of all remaining audience member?
2) For the audience members that randomly tell the truth or lie, at any moment, do they know whether they will lie or tell the truth to the next question? That is, before hearing a particular question, have they already decided on lying or telling the truth?
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#10 bonanova

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Posted 31 January 2013 - 11:15 AM

Clarifications, please
 
1) Does each member of the audience know the type of all remaining audience member?
2) For the audience members that randomly tell the truth or lie, at any moment, do they know whether they will lie or tell the truth to the next question? That is, before hearing a particular question, have they already decided on lying or telling the truth?


  1. I'm thinking that they do not know much if anything about each other.
    They all got complimentary tickets and just arrived for the show.
    without an evening together to plot a strategy.

     
  2. I'm not sure, but probably not. But hey, do any of us? .
    Specifically, have they already decided? Not necessarily.
    OK. Let's say they have not decided anything prior to hearing the question.

 

An adequate description of the so-called "random" folk is to say that they randomly tell the truth or lie. That choice could be made [a] by coin flip, [b] at any time prior to giving their response, and [c] with or without consultation.


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