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June 24th, 2018, 08:12 AM  #1 
Newbie Joined: Feb 2018 From: California Posts: 17 Thanks: 1  Logic question: knights, jesters, tourists
Hello! I am putting this here since there is no section for logic. Can someone please help me figure out the logic/answers to these? I am very stuck and it is bugging me. Knights and Jesters You travel to a magic island with two types of people who live on there: Knights who always tell the truth and Jesters who always lie. Occasionally there are tourists who can either tell the truth or lie. 1) You are having a conversation with a Knight. You ask him the same question twice, and he gave you two diﬀerent answers. Which question did you ask? Think of several such questions. 2) M (Matthew), J (Jake) and K (Kate) are islanders. M is asked who he is. He mumbled so we couldn't hear. We asked J who stood next to M what M said. J said that M said he is a Liar. But K said that we shouldn’t believe J because he is a Liar. What, if anything, can we determine from this scenario? 
June 24th, 2018, 08:36 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,274 Thanks: 1959 
(1) The question could have been "Have I already asked you a question?" or "Is it just before noon?" (asked just before noon and then just after noon) or some other question of a timerelated nature.
Last edited by skipjack; June 24th, 2018 at 08:51 AM. 
June 25th, 2018, 05:56 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988 
Give the Knight a stick of gum. As he's unwrapping it, ask: are you chewing gum? After he pops it in his mouth, ask same question 
June 25th, 2018, 06:25 AM  #4  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896  Quote:
So what J said cannot be true. He must be lying and so is a jester. Since he said M lied, it must not be true that M said he is a liar. He must have said, truthfully, that he is a knight. And, of course, what K said is true. M is a knight, J is a jester, and K is a knight.  
June 25th, 2018, 02:31 PM  #5 
Newbie Joined: Feb 2018 From: California Posts: 17 Thanks: 1 
Yes!! Thank you!! I read the problem with the "which question would get two answers?" as "which question would get opposite answers?", which made me stumped even more, but I eventually came up with one that would work. It could be, "Did you just tell me 'no'?" and the knight would have to say "no" the first time and "yes" the second time. But now I see that it's an easier question in that the reply just has to be different, not opposite. Thank you for the help with the mumbler question. That one hurt my head for a while, but now I see it! 

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jesters, knights, logic, question, tourists 
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