A native, either a knight or a liar, once pointed to a man sitting below a tree and told me "If asked, that man would say I'm not the same type as he is."
What can you deduce about the native or the man?
Call the first native A and the man under the tree B. Suppose A is a knight. Then, B would say that he is not the same type as A. If B was a knight, then they would be the same type, so B would not say that they are different types. If B was a liar, then they would be of different types, so B would say that they are the same type. That is a contradiction, so A is a liar.
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Since A is a liar, B would say that they are of the same type. If B was a knight, then he would not say that they are of the same type. If B was a liar, then they would be the same type, so he would not say that. Therefore, the problem is a paradox!

Posted by Math Man
on 20110910 17:01:25 