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The way to Normalville (Posted on 2012-10-05) Difficulty: 3 of 5
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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Hints/Tips First question only | Comment 7 of 13 |

As to the first question, it seems to me that the key is that what a normal says can't be predicted in advance.

So just pick any of the three, say A, and ask him  'If I ask B 'Is L the road to Normalville' what will he reply?'

A can only answer the question if either:
(1) A is normal, and B is not (given that only one of them is a normal);
(2) Neither A nor B are normal;
because if B is normal, then he answers randomly, so A (who must then be a knight or a liar) cannot give either a true or a false answer in advance of B's actual answer.

If A cannot answer, then B is normal. We can just ask A the 'second question'.

If A can answer, we just ask B the 'second question', since B cannot be normal.

 

Edited on October 7, 2012, 11:05 am
  Posted by broll on 2012-10-07 06:21:14

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