A logic puzzle by MIT mathematician Tanya Khovanova: You’re visiting an island on which every resident is either a knight or a knave. Knights always tell the truth, and knaves always lie. All the islanders know one another. You meet three islanders, Alice, Bob, and Charlie, and ask each one, “Of the two other islanders here, how many are knights?” Alice says, “Zero.” Bob says, “One.” What will Charlie say?
If Alice is speaking the truth, then Bob and Charlie are liars. But in that case Bob would be uttering a true statement, which is a contradiction. So Alice is a knave. If that’s the case, then either Bob or Charlie (or both) is a knight. If Bob is a knave, then he’s lying when he says that there’s exactly one truth-teller among the other two. But that’s another contradiction: In that circumstance his statement would be right, since Alice is a knave and Charlie would be a knight. So Bob must be a knight, which means that we can trust what he says and Charlie is a knight too. So Charlie says, “One.”
(Khovanova’s students pointed out that the very question in the puzzle implies that Charlie makes a predictable answer, which wouldn’t be the case if he were a liar. The result follows from there.)
