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.)
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?