1) The Islands of the Crazoes has two types of inhabitants: knights- who always
ID: 3144789 • Letter: 1
Question
1) The Islands of the Crazoes has two types of inhabitants: knights- who always tell the truth and knaves- who always lie.
a) I met Connie and Devon. Connie said at least one of us is a knave." What is Connie and what is Devon?
b) Later I met a couple on the island. The husband says: "My wife and Iare of the same type"
What can be deduced?
c) Later I run into Annie, Bob, and Carlos and I ask Annie: "Are you a knight or a knave?" Annie answers but I do not hear. Bob saysShe said she is a knave". at which Carlos pipes up: Don't believe that, it's a lie". What are Annie, Bob, and Carlos?
2) John, James and William are indistinguishable except that John and James always lie and William always tells the truth. You meet one of them on the road. You want to know if that person is John. What question, answerable by YES or NO, could you ask to de- termine if the person you meet is John
Can some please explain these to me as I am having trouble understanding them. I find using a truth table helpful for the knights and knaves questions but still can't seem to deduce the question to a finals statement. Thanks.
Explanation / Answer
1. a. Connie is a kinght and Devon is a knave.
If Connie is a knave then her statement "Atleast one of us is a knave" would come true. But as she is a knave she can't be telling the truth and we have a contradiction.
If Connie is a knight her statement "Atleast one of us is a knave" is true and Devon is the knave.
b. "My husband and I are of the same type"
If this statement is true then both are knights as only knights speak the truth.
If the statement is wrong then the woman is a knave and her husband is of the opposite type i.e a knight.
It can be deduced that her husband is a knight.
c. (The question appears to be faulty. What does "But I do not hear" mean? The answer below is from an assumption)
Since Annie says she cannot hear she must be lying because if she could not hear, she would not have got the question at all. So she is a knave. Since Bob said she is a knave, he spoke the truth and he is a knight. Since Carlos tried to refute him, he lied and he is a knave.
2. The question is "Are you James?"
William being a knight will say no.
James being a knave will say no.
John being a knave will say yes.
So if the person says yes, he is John.
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