On a certain island, there are only knights, who always tell the truth, knaves, who always lie, and jokers who can do either. You come across 3 of them, Al, Bo and Cat. They each say the following:
Al: Bo always lies.
Bo: Cat is a knave.
Cat: Al is a knave but Bo is not.
Later, Al adds: Exactly one of us is a knight.
What is the maximum possible number of jokers?
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If Cat is a knave, then Bo is a knave. Then Cat is not a knave. This is impossible. If Cat is a knight, then Al is a knave, Bo is not a knave but Bo still lies. But this means that exactly one of them is a knight contrary to Al being a knave. Then Cat is a joker.
Suppose that Cat is a joker but did not lied. Then Bo is not a knave but he lied. Since Al would be a knave, this brings us up to 2 jokers. Let's suppose that Cat lied. Then either Al is not a knave, or Bo is a knave. If Al is not a knave, let’s assume that he’s a joker. Then Bo doesn’t always lie but he did this time. Since this fits, its possible to have 3 jokers.