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?

The man under the tree is either a knave, a mute, deaf, unsociable, does not speak the local language or does not know the native.

The native is a knight or maybe a liar.

Explanation: If both are knights the statement would not be made. Likewise any combination of knight-liar, liar-knight, liar-liar would create a situation where the statement would not be made.

We are restricted to have the native as a knight or a liar.  This means the man under the tree is neither a knight nor a liar and thus sometimes tells the truth and sometimes lies.  Though I cannot prove that the man is true knave (alternating lies and truths), I will label the man as such.

If the native is a knight, then he could make the statement if he knew the knave had just lied. If the native is a liar, then he could make the statement if he knew the knave had just told the truth.

Posted by Leming on 2006-09-26 08:48:00