You are in a popular tourist town in the land of Liars and Knights. You happen to overhear a conversation another tourist is having with three of the locals: Alex, Bert and Carl. Each of the three could be a knight, a knave or a liar. You know that for each question the tourist asks, Alex, Bert and Carl each give one response, but you don't know who said what. The conversation is as follows:
- What type are each of you?
- I am a knight.
- I am a knave.
- I am a liar.
- How many of you are the same type?
- We are all the same type.
- We are all different types.
- Exactly two of us are the same type.
- What type is Alex?
- A knave.
- A liar.
- Different from Bert.
Can you determine which type Alex, Bert and Carl are?
As to the 2nd statement's answers, it's obvious only one is true.
As to the 1st statement's answers, only a lying knave could claim to be a liar, and he would have to tell the truth the next time around, so he's the one who tells the truth when answering the 2nd statement, so there are no knights.
The one who answered "I am a knight" must be a liar; if he was a knave, he would have had to tell the truth the next time. The one who answered "I am a knave" can either be a truthful knave or a liar.
A must be either a knave or a liar, so one of the answers to the 3rd question is true. It cannot either come from the lying knave who claimed to be a liar, or from the liar who claimed to be a knight, so it must come from a truth telling knave, who claimed to be a knave.
Thus, only ONE answer to the 3rd question is true, and it must be either the 1st or the 2nd, so the 3rd is false, and Alex and Bert are the same type (knaves) so Carl is the liar.
Posted by e.g.
on 2007-05-17 17:52:31