My Math Forum Logic question: knights, jesters, tourists

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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 time-related 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
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Quote:
 Originally Posted by mjsilverfly 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?
The first sentence says that M, J, and K are islanders so they are not tourists. Either M is a knight or he is a jester. If he is a knight he would tell the truth- he would NOT say he is a liar. But if he is a jester then he would lie and again would NOT say he is a liar- neither a knight nor a jester can say of himself that he is a liar.

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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