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?

It is given that the native is a knight or liar, but it is not given that the man sitting below a tree is limited to one of the categories of knight or liar.

If the native were a knight, then the tree-shaded stranger would give an answer congruent to "I'm not the same type as he (the knight) is". Thus, the tree-shaded man could not be a knight, yet this does not make the tree-shaded stranger a liar. He could be a knave, normal, or some other type.

Given the native was a liar, if the tree-shaded man were a knight the tree-shaded man would have answered the question with an answer congruent to "I'm not the same type as he (the liar) is". This answer would have the native, a liar, making a true statement -- a contradiction, thus the tree-shaded man could not be a knight.

Given the native was a liar, if the tree-shaded man were a liar the tree-shaded man would answered the question (assuming he would have answered) with an answer NOT congruent to "I'm not the same type as he (the liar) is", i.e., "I'm the same type as he (the liar) is". Such a statement could not have been made by a liar, as it would be a true statement -- a contradiction, thus the tree-shaded man could not be a liar (who provided an answer similar to that given).

In conclusion, nothing new is known of the native. He is either a knight or a liar. What is known is that the tree-shaded man is not a knight and likely not a liar, yet he could be knave, normal, or some other type.

Posted by Dej Mar on 2011-09-11 00:02:41