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mistermickster
Thou detestable maw


Joined: 19 Feb 2004
Posts: 1414
Location: Nottingham, England

PostPosted: Mon Oct 18, 2004 5:53 pm    Post subject: Old riddle, new variation Reply with quote

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?
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SparkPlug
Because I can


Joined: 30 Jan 2004
Posts: 11689
Location: Here!

PostPosted: Mon Oct 18, 2004 6:16 pm    Post subject: Reply with quote

This is what unfolded last time they tried to Razz

http://www.cluckbook.com/murphyz/viewtopic.php?t=1789&start=0
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mistermickster
Thou detestable maw


Joined: 19 Feb 2004
Posts: 1414
Location: Nottingham, England

PostPosted: Mon Oct 18, 2004 8:14 pm    Post subject: Reply with quote

Thanks Neil, but the same logic cannot be applied here, as there are only 2 doors but 3 guards.
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theandygrant
This is the foul fiend Flibbertigibbet


Joined: 07 Feb 2004
Posts: 1264
Location: The Lethargic Dodecahedron

PostPosted: Tue Oct 19, 2004 10:51 pm    Post subject: Reply with quote

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 Smile
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ckmcheetah
Lets meet as little as we can


Joined: 21 Sep 2003
Posts: 1157
Location: Grand Canyon State

PostPosted: Tue Oct 19, 2004 10:59 pm    Post subject: Reply with quote

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 Smile


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
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theandygrant
This is the foul fiend Flibbertigibbet


Joined: 07 Feb 2004
Posts: 1264
Location: The Lethargic Dodecahedron

PostPosted: Tue Oct 19, 2004 11:03 pm    Post subject: Reply with quote

1) Is this the door to great riches?

2) Would you like to go first?
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Hatfielder
A great lubbery boy


Joined: 19 May 2004
Posts: 233
Location: The beautiful city of Durham, well a nearby village anyway

PostPosted: Thu Dec 30, 2004 2:31 pm    Post subject: Reply with quote

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

PostPosted: Thu Dec 30, 2004 2:43 pm    Post subject: Reply with quote

That sounds very feasible Clare. I'll put it to the test. Thumbs up

Thanks
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Shiz
Pernicious and indubitate beggar


Joined: 10 Jun 2004
Posts: 366
Location: Middle of England, Ex-pat Scotland

PostPosted: Fri Dec 31, 2004 11:04 am    Post subject: Reply with quote

I'm impressed! That one's been bugging me since it was posted. Nice one Claire.
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Robin
Scurvy, old, filthy, scurry lord


Joined: 06 Mar 2004
Posts: 501
Location: Durham, England

PostPosted: Fri Dec 31, 2004 11:56 am    Post subject: Reply with quote

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 Sad
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theandygrant
This is the foul fiend Flibbertigibbet


Joined: 07 Feb 2004
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PostPosted: Mon Jan 03, 2005 1:04 am    Post subject: Reply with quote

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

PostPosted: Mon Jan 03, 2005 10:13 pm    Post subject: Reply with 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 truth-teller;
  • If Moe answers randomly, then Curly is either the liar or the truth-teller (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 truth-teller;
  • If Moe answers randomly, then Larry is either the liar or the truth-teller.


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?"
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thalichan
Thy mothers name is ominous to children


Joined: 25 Oct 2004
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PostPosted: Mon Jan 03, 2005 11:45 pm    Post subject: Reply with quote

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


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PostPosted: Tue Jan 04, 2005 2:28 am    Post subject: Reply with quote

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 full-time liar or a full-time truth-teller. (If we ask the right second question--a variant of MisterMickster's original--of a non-random 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 non-random 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 truth-teller, 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 truth-teller, then his No implies Larry always lies.
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theandygrant
This is the foul fiend Flibbertigibbet


Joined: 07 Feb 2004
Posts: 1264
Location: The Lethargic Dodecahedron

PostPosted: Tue Jan 04, 2005 2:58 am    Post subject: Reply with quote

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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