FOR EXAMPLE You meet three islanders named Ellis, Farin, and Gobi. They all know what each other is (a knight, knave or joker) and make the following statements:If exactly one of them is a joker then One of them is a knight
Since exactly one of them is a joker, and they all accuse different people of being jokers, then the joker is lying. If the joker were telling the truth, then they would claim that they themselves are the joker, which none of these three are doing.
Given this, one of them is telling the truth. For instance, suppose that Ellis is the Joker, then Gobi is telling the truth. Or you can suppose that Farin is the joker, in which case Ellis is telling the truth. Same thing with Gobi.
This person telling the truth can't be a joker since all the statements accuse other people of being jokers and, again, a joker telling the truth this once would say that they, themselves, are the joker. So the truth-teller must be a knight.
So one person is a joker, and at least one is a knight. The third person can't be a knight (they must be a knave), because the knight and the third person are saying that different people are jokers, which is impossible with only one joker. For instance, if Ellis is the joker, then Gobi is telling the truth (and is a knight), and Farin is lying (and is a knave.
So, since there is only one truth-teller there must be only one knight
