On a certain island precisely one-third of the native people are liars who always lie, one-third are knights who always tell the truth, and one-third are knaves who strictly alternate between a truth and a lie (albeit not necessarily in this order) . The chances of encountering any one of the three types on the island are the same.

Frank, who is a traveler comes across three natives-Abe, Ben and Cal. It is known that exactly one of them is a knight, precisely one of them is a liar and the remaining is a knave (albeit not necessarily in this order.)

They say:

Abe: I love cats.
Ben: Cal always tells the truth.
Cal: Abe hates cats.

If someone bets Frank $20 that he can not correctly identify which one of these people is a knight, which of the three natives will be wisest for him to bet on?

Ben can't be a knight, since that would imply Cal is also a knight, which is a contradiction. 

If Cal is a knight, then Ben is a truth-first knave and Abe is a liar (only 1 possibility).

If Abe is a knight, then Ben and Cal are a liar and a lie-first knave, in some order (2 possibilities).

Thus Abe has the greatest probability of being the Knight.

Posted by tomarken on 2014-03-06 10:08:57