When I visited the Knights and Liars Archipelago, one island I visited was called Liontruth. The tourism had a great influence on the island, so much that the knaves on the island spoke differently from most knaves. They didn't have to follow an alternating pattern, but could tell truths (like knights always do) and lie (like liars always do) in whatever pattern they wanted. The three types of inhabitants are indistinguishable by eye.
If a tourist thinks the local knaves alternate truths and lies how can a knave convince the tourist that he is not a knave?
How can a knave from this island prove himself in one statement without revealing whether he is lying or not?
How can a knight prove himself in one statement?
How can a liar prove himself in one statement?
What single statement can be said by either a knight or liar but not a knave?
Abe has to be a liar, because if his statement is true, then rex and jack are liars. However, this cannot work because Dan would then speak the truth, which would mean Abe couldn't also be telling truth. Now that he know that Abe is a liar, we know that Dan's statement is true and thus we've reached a paradox, because now we have two liars, as Dan says there is a second in either Rex or Jack, but there would have to be a third in Earl, who contradicts Dan.
If we scratch this paradox by assuming that Dan's full statement is not entirely true, then we can call dan the second liar. Now everyone else is speaking truth and since we know the culprits were either Rex or Abe, and Rex is protected by his knight's honor, Abe is the one who stole the candy bar.
Actually, I did it.
Solution
