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SuperGrover Lets meet as little as we can
Joined: 12 Nov 2004 Posts: 1165 Location: USA

Posted: Tue Jan 04, 2005 5:56 am Post subject: 


theandygrant wrote:  Yes, but since we don't know from Moe's answer of "yes" whether he is lying or telling the truth, we don't know whether to ask Larry or Curly the second question. 
Remember that the goal here is to find a guard who either always lies or always tells the truth. Then we can ask him the trick question mentioned up in the thread.
If Moe answers randomly, then we can ask the second question of either Larry or Curly, because exactly one of them is the liar and the other is the truthteller. As we will see, a Yes answer means we will ask Curly and a No answer means we will ask Larry.
So let's examine the other two cases. If Moe is the liar, then a Yes answer (that Larry tells the truth more often than Curly) means that Curly is the truthteller. So Yes means ask Curly. And a No answer (that Larry lies more often than Curly) means that Larry is the truthteller. So No means ask Larry.
If Moe is the truthteller, then his answer to the first question is truthful. A Yes answer means that Curly is the liar. So Yes means ask Curly. A No answer means that Larry is the liar. So No means ask Larry. _________________ There are only 10 kinds of people in the worldthose who know binary, and those who don't. 

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theandygrant This is the foul fiend Flibbertigibbet
Joined: 07 Feb 2004 Posts: 1264 Location: The Lethargic Dodecahedron

Posted: Tue Jan 04, 2005 6:22 am Post subject: 


SuperGrover wrote: 
Remember that the goal here is to find a guard who either always lies or always tells the truth. Then we can ask him the trick question mentioned up in the thread.

We can't use the same question.
"If I asked the other guard, what would he say?" only works because the guards were polar opposites.
If we successfully identify the randomanswerer with the first question, then we could indeed use the original question again.
Its not a case of "If Moe tells the truth" or "If Moe answers randomly".
It's a case of "If Moe says Yes" and "If Moe says No"
Say you ask Moe "Is Larry more likely to tell the truth than Curly?" and he says "Yes."
The four possible outcomes are:
1. Moe always tells the truth; Larry answers randomly; Curly always lies.
2. Moe always lies; Larry answers randomly; Curly always tells the truth.
3. Moe answers randomly; Larry always tells the truth; Curly always lies.
4. Moe answers randomly; Larry always lies; Curly always tells the truth.
We know now that Curly is not the randomspeaker, which is useful, but not useful enough, since we still don't know who the opposite guard to Curly is.
It may be possible to construct some sort of doublenegative trap question to ask Curly.... 

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theandygrant This is the foul fiend Flibbertigibbet
Joined: 07 Feb 2004 Posts: 1264 Location: The Lethargic Dodecahedron

Posted: Tue Jan 04, 2005 6:50 am Post subject: 


From what I can see, there are three generic solutions to this riddle.
Solution A:
Use the first question to identify the Truthteller.
Use the second question to ask the Truthteller which door leads to riches.
Go through that door.
Solution B:
Use the first question to identify the Liar.
Use the second question to ask the Liar which door leads to riches.
Go through the other door.
Solution C:
Use the first question to identify the Randomanswerer.
Use the second question to ask the second guard what the third guard would say.
Go through the other door.
Now, I notice that the wording of the riddle says "You may ask the guards two questions", with guards in plural. This may be ambiguous, but I don't think this outlaws asking the questions to all three guards at the same time. Solutions to riddles have lain in more pedantic interpretations than that, I'm sure. So it may be that Clare's solution is indeed an acceptable one. 

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SuperGrover Lets meet as little as we can
Joined: 12 Nov 2004 Posts: 1165 Location: USA

Posted: Tue Jan 04, 2005 5:10 pm Post subject: 


theandygrant wrote:  SuperGrover wrote: 
Remember that the goal here is to find a guard who either always lies or always tells the truth. Then we can ask him the trick question mentioned up in the thread.

We can't use the same question.
"If I asked the other guard, what would he say?" only works because the guards were polar opposites.
The four possible outcomes are:
1. Moe always tells the truth; Larry answers randomly; Curly always lies.
2. Moe always lies; Larry answers randomly; Curly always tells the truth.
3. Moe answers randomly; Larry always tells the truth; Curly always lies.
4. Moe answers randomly; Larry always lies; Curly always tells the truth.
We know now that Curly is not the randomspeaker, which is useful, but not useful enough, since we still don't know who the opposite guard to Curly is.
It may be possible to construct some sort of doublenegative trap question to ask Curly.... 
I thought that the trick question would be "If I were to ask you if Door A were the door to riches, what would you say?" _________________ There are only 10 kinds of people in the worldthose who know binary, and those who don't. 

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Shiz Pernicious and indubitate beggar
Joined: 10 Jun 2004 Posts: 366 Location: Middle of England, Expat Scotland

Posted: Tue Jan 04, 2005 6:26 pm Post subject: 


There's also the version of question which goes 'If I had asked you yesterday which door was the door to riches, which door would you have pointed to?'
With this question both the liar and the truth teller must point to the door to riches, but I still can't work out how to apply that to the random guard. _________________ Banging one's head against the wall seldom results in the answer falling out. 

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Robin Scurvy, old, filthy, scurry lord
Joined: 06 Mar 2004 Posts: 501 Location: Durham, England

Posted: Tue Jan 04, 2005 9:39 pm Post subject: 


I can't be bothered right now to wade through the labyrinthine logic of all these replies, but I did read SuperGrover's answer, and it quite clearly works. There is quite clearly no way, in one question, to work out who is the liar, or who is the truthteller (since the other guard can always answer anything to any question), but all you need is to identify one person who definitely isn't the randomanswerer. SuperGrover's question, as far as I can see, achieves that. Nice one 

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Hatfielder A great lubberly boy
Joined: 19 May 2004 Posts: 233 Location: The beautiful city of Durham, well a nearby village anyway

Posted: Wed Jan 05, 2005 2:58 pm Post subject: 


That took a lot of wading through.
I still like my answer and was shocked I came up with it as I'm ususally dreadful at answering these kinds of problems.
Reading the resulting chat you do seem to have come up with a workable answer between you all.
Quote:  Ask one of the guards (Moe) if the second (Larry) is more likely to tell the truth than the third (Curly). If Moe answers Yes, then we actually know something about Curly:
If Moe always tells the truth, then Curly is the liar;
If Moe always lies, then Curly is the truthteller;
If Moe answers randomly, then Curly is either the liar or the truthteller (we don't know which, but that's okay).
And if Moe answers No, then we know something about Larry:
If Moe always tells the truth, then Larry is the liar;
If Moe always lies, then Larry is the truthteller;
If Moe answers randomly, then Larry is either the liar or the truthteller.

SuperGrover allows us to be certain that we are addressing the second question to either the liar or the truth teller. If we got an answer of No we can be sure that larry is not the random speeker, and if we got an answer of yes we can be sure that Curly is not the random speeker.
Quote:  There's also the version of question which goes 'If I had asked you yesterday which door was the door to riches, which door would you have pointed to?'
With this question both the liar and the truth teller must point to the door to riches.

Shiz's post gives us a question that both the liar and the truth teller will point to the door to riches, but which importantly doesn't rely on the guards polarity with another guard.
There now. Noone can argue with that combined solution.
But then I liked my simple one better, working through the possibilities of this one made my brain spin.
Clare 

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theandygrant This is the foul fiend Flibbertigibbet
Joined: 07 Feb 2004 Posts: 1264 Location: The Lethargic Dodecahedron

Posted: Wed Jan 05, 2005 3:27 pm Post subject: 


Yep. I like all that.


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SparkPlug Because I can
Joined: 30 Jan 2004 Posts: 11763 Location: Here!

Posted: Wed Jan 05, 2005 5:29 pm Post subject: 


Why don't you all go together  then you'll have loads of questions 

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theandygrant This is the foul fiend Flibbertigibbet
Joined: 07 Feb 2004 Posts: 1264 Location: The Lethargic Dodecahedron

Posted: Wed Jan 05, 2005 8:50 pm Post subject: 


Or we could just not ask any questions and send Shiz through one of the doors first 

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Rosie Ragdoll Drunkenness is thy best virtue
Joined: 28 Sep 2004 Posts: 2426 Location: Hove actually

Posted: Wed Jan 05, 2005 9:42 pm Post subject: 


theandygrant wrote:  Or we could just not ask any questions and send Shiz through one of the doors first 
That's just cruel but of course if there were any gentlemen out there they'd offer to go first
Rosie _________________ The Lady Rosie has been ensorcelled. 

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theandygrant This is the foul fiend Flibbertigibbet
Joined: 07 Feb 2004 Posts: 1264 Location: The Lethargic Dodecahedron

Posted: Wed Jan 05, 2005 9:58 pm Post subject: 


Which is why Gentlemen make poor adventurers.
I can't quite see Harrison Ford offering to go first
Gentlemen are all well and good,
but rogues and rapscalions are where it's at 

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Rosie Ragdoll Drunkenness is thy best virtue
Joined: 28 Sep 2004 Posts: 2426 Location: Hove actually

Posted: Wed Jan 05, 2005 10:52 pm Post subject: 


But the bad guy never gets the girl, so it looks like you are going to be whisked away to a life of luxury by a real gentleman Shiz.
Rosie _________________ The Lady Rosie has been ensorcelled. 

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Shiz Pernicious and indubitate beggar
Joined: 10 Jun 2004 Posts: 366 Location: Middle of England, Expat Scotland

Posted: Thu Jan 06, 2005 2:24 am Post subject: 


Real Gentlemen? Suddenly beginning to think they no longer exist!
Shiz _________________ Banging one's head against the wall seldom results in the answer falling out. 

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