One says we are all knaves, another says exactly one is a knight
On an island everyone is a knight (always tells the truth) or a knave (always lies). You meet three islanders, A, B and C.
- A says: "We are all knaves."
- B says: "Exactly one of us is a knight."
- C says nothing.
Which of them are knights and which are knaves?
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Can a knight ever say "we are all knaves"? Once you settle A, test B's sentence under each of the two possibilities for B.
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