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 The way to Normalville (Posted on 2012-10-05)
In Normalville, every inhabitant is either a knight, a liar, or a normal. Knights always tell the truth. Liars always lie. Normals tell the truth and lie completely at random. You are going to Normalville when you see a fork in the road. There are two ways to go. One of them leads to Normalville. You see three inhabitants by the fork, A, B, and C. You know that only one of them is a normal, but you are not sure who it is. In two "yes" or "no" questions, how do you find the way to Normalville? (Each question can only be addressed to one person, but it can be a different person for each question.)

 See The Solution Submitted by Math Man Rating: 3.7500 (4 votes)

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 re(2): no cigar | Comment 3 of 13 |
(In reply to re: no cigar by Math Man)

Oh, Oh, pick me!  I can do it with that hint!

Question 1:

Ask A "Is B is more likely to tell the truth than C?".  If the answer is Yes, then C is not Normal, and you will ask C question 2. Otherwise, then B is not Normal, and you will ask B question 2.

(This works because if A is a knight, and B is Normal, A will answer "Yes", as B is more likely to tell the truth than C.  If A is a Liar, and B is Normal, A will also answer "Yes", as B is less likely to tell the truth than C, and A will lie about it.  And this also works if A is Normal, because then both B and C are not Normal.)

Question 2:

"If you were going to Normalville, would you take the left fork?".  If he says yes, take the left fork.  Otherwise, go right.

 Posted by Steve Herman on 2012-10-06 10:10:52

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