May 17th, 2017, 12:53 PM  #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, 01:22 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,681 Thanks: 438 
Does this involve goats?

May 17th, 2017, 02:44 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,119 Thanks: 2369 Math Focus: Mainly analysis and algebra  
May 17th, 2017, 03:05 PM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,476 Thanks: 495 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, 07:02 AM  #5  
Newbie Joined: May 2017 From: England Posts: 13 Thanks: 0  Quote:
 
May 19th, 2017, 12:15 AM  #6 
Senior Member Joined: Apr 2014 From: UK Posts: 794 Thanks: 295 
The answer is of course, no.

May 19th, 2017, 02:29 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,445 Thanks: 1462 
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, 05:21 AM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,402 Thanks: 731  Quote:
It's automatic that he's also only allowed to tell truth once, since ONLY one question is asked...  
May 20th, 2017, 02:53 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, 12:27 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 18,445 Thanks: 1462 
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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