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 May 17th, 2017, 11:53 AM #1 Newbie   Joined: May 2017 From: England Posts: 13 Thanks: 0 A REALLY confusing logic problem! If anyone can help me with this problem, that'll be great. I have my own solution, but I need to check it. Problem: There are two doors each labelled A and B respectively. One door leads to treasure whilst the other leads to certain death. A doorkeeper stands in your way and you must ask him only one question to know for certain the door with the treasure. However, the doorkeeper will randomly tell the truth or will randomly lie. He is only allowed to lie once. Is there a way to find the correct door?
 May 17th, 2017, 12:22 PM #2 Senior Member   Joined: Aug 2012 Posts: 2,311 Thanks: 706 Does this involve goats? Thanks from Joppy and Abidur Rahman
May 17th, 2017, 01:44 PM   #3
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Quote:
 Originally Posted by Abidur Rahman … you must ask him only one question … He is only allowed to lie once…
I suspect you've posed the question incorrectly.

 May 17th, 2017, 02:05 PM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,801 Thanks: 636 Math Focus: Yet to find out. I thought it went: each guard keeper either always lies or always tells the truth, but you don't know which. That one you can figure out. But only allowed to lie once, and randomly?
May 18th, 2017, 06:02 AM   #5
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Quote:
 Originally Posted by Abidur Rahman If anyone can help me with this problem, that'll be great. I have my own solution, but I need to check it. Problem: There are two doors each labelled A and B respectively. One door leads to treasure whilst the other leads to certain death. A doorkeeper stands in your way and you must ask him only one question to know for certain the door with the treasure. However, the doorkeeper will randomly tell the truth or will randomly lie. He is only allowed to lie once. Is there a way to find the correct door?
NOTE: I assure you that I did not write the problem incorrectly, this is an alternate version of the original problem. Good luck.

 May 18th, 2017, 11:15 PM #6 Senior Member   Joined: Apr 2014 From: UK Posts: 919 Thanks: 331 The answer is of course, no.
 May 19th, 2017, 01:29 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,640 Thanks: 2082 The answer to what? I would think there is a way. It might require certain minor assumptions, such as that he would answer truthfully if he has previously answered with a lie, and that he understands whatever he is asked, replies in a language that the questioner understands, and replies to questions about what he could reply in hypothetical situations. It might also be necessary to assume that the doorkeeper always uses a direct reply when such a reply is possible.
May 19th, 2017, 04:21 AM   #8
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Quote:
 Originally Posted by Abidur Rahman A doorkeeper stands in your way and you must ask him only one question to know for certain the door with the treasure. However, the doorkeeper will randomly tell the truth or will randomly lie. He is only allowed to lie once.
This makes no sense: "He is only allowed to lie once."
It's automatic that he's also only allowed to tell truth once,
since ONLY one question is asked...

 May 20th, 2017, 01:53 AM #9 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 I guess if you ask him a $2$ part question and force him to lie on the first part , his answer to the second part must be truthfull. Can you force him to lie? I don't know how
 May 20th, 2017, 11:27 AM #10 Global Moderator   Joined: Dec 2006 Posts: 20,640 Thanks: 2082 The question could ask about the replies that would be given to several other questions, or could start with "If you're answering truthfully, what is . . .", etc.

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