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mistermickster Thou detestable maw
Joined: 19 Feb 2004 Posts: 1414 Location: Nottingham, England

Posted: Mon Oct 18, 2004 5:53 pm Post subject: Old riddle, new variation 


Hi all,
I guess everybody knows the old riddle:
There are two doors. One leads to certain death, the other leads to ultimate wealth. There is a guard in front of each door. One guard always tells the truth, the other always lies, but you don't know which is which. You can ask one guard one question only, what do you ask to determine the door to wealth? And of course you ask either guard, "If I asked the other guard which was the door to wealth, what would he say?" . You then know it's the other door.
Well one of my work colleagues has asked me a variation on this. There are still two doors, but now there are three guards. One always tells the truth, one always lies and the other gives a random answer. This time you can ask the guards two questions. What questions do you ask to determine the door to wealth?
Any experts care to lend a hand in solving this? _________________ Lead on adventurer, your quest awaits. 

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


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mistermickster Thou detestable maw
Joined: 19 Feb 2004 Posts: 1414 Location: Nottingham, England

Posted: Mon Oct 18, 2004 8:14 pm Post subject: 


Thanks Neil, but the same logic cannot be applied here, as there are only 2 doors but 3 guards. _________________ Lead on adventurer, your quest awaits. 

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

Posted: Tue Oct 19, 2004 10:51 pm Post subject: 


I'd be tempted to ask the question as in the old puzzle, to the same guard twice. If he doesn't change his answer, you know he's not the random one and you've found your door. But then I'm not tempted by riches, or scared of dying, so you don't want to take my advice 

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ckmcheetah Lets meet as little as we can
Joined: 21 Sep 2003 Posts: 1157 Location: Grand Canyon State

Posted: Tue Oct 19, 2004 10:59 pm Post subject: 


theandygrant wrote:  I'd be tempted to ask the question as in the old puzzle, to the same guard twice. If he doesn't change his answer, you know he's not the random one and you've found your door. But then I'm not tempted by riches, or scared of dying, so you don't want to take my advice 
You can't say this because the random guy can pick the same answer twice, and since there are only two choices, wealth or death, each is equally likely to be picked _________________ Everyone is different, no two people are not on fire... 

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

Posted: Tue Oct 19, 2004 11:03 pm Post subject: 


1) Is this the door to great riches?
2) Would you like to go first? 

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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: Thu Dec 30, 2004 2:31 pm Post subject: 


Question) Raise your hand if you're the guard who answers randomly.
If one guard raises his hand you know that's the liar. So you ask him which is the door that leads to certain death and take it.
If two guards raise their hand you know the one that didn't is the truth teller. So you ask him which is the door to certain death and take the other door.
If that's not the right answer then I'm really stuck.
Clare 

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mistermickster Thou detestable maw
Joined: 19 Feb 2004 Posts: 1414 Location: Nottingham, England

Posted: Thu Dec 30, 2004 2:43 pm Post subject: 


That sounds very feasible Clare. I'll put it to the test.
Thanks _________________ Lead on adventurer, your quest awaits. 

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

Posted: Fri Dec 31, 2004 11:04 am Post subject: 


I'm impressed! That one's been bugging me since it was posted. Nice one Claire. _________________ 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: Fri Dec 31, 2004 11:56 am Post subject: 


Yes it does work quite nicely, but unfortunately I'm not sure that it counts as an answer to this particular puzzle. I read 'question' as meaning something which is addressed to one specific guard.
Having said that, I haven't yet managed to come up with a solution which does satisfy this criterion 

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

Posted: Mon Jan 03, 2005 1:04 am Post subject: 


I think its definitely the right approach.
The first question needs to isolate either the truth teller or the liar. 

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

Posted: Mon Jan 03, 2005 10:13 pm Post subject: 


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.
Then ask the guard whom we know more about some variation of the following: "If I were to ask YOU if the left door leads to wealth, 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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thalichan Thy mother's name is ominous to children
Joined: 25 Oct 2004 Posts: 27 Location: Nevada

Posted: Mon Jan 03, 2005 11:45 pm Post subject: 


With a single response from Moe, how can you determine whether that is a random answer or not, though? 

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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 2:28 am Post subject: 


thalichan wrote:  With a single response from Moe, how can you determine whether that is a random answer or not, though? 
The first question isolates one of the other two as either a fulltime liar or a fulltime truthteller. (If we ask the right second questiona variant of MisterMickster's originalof a nonrandom guard, then we can find out if a door is good or not. So all we need to do in the first question is to find a nonrandom knight).
If Moe is the random one, then we can ask either of the other two the seond question.
If Moe is the liar, then his Yes implies Curly is always truthful; if he is the truthteller, then his Yes implies Curly always lies.
And if Moe is the liar, then his No implies Larry is always truthful; if Moe is the truthteller, then his No implies Larry always lies. _________________ 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 2:58 am Post subject: 


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. 

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