Knights, Knaves & Spies
On the island of Knights and Knaves, I met three people A, B, and C, one of whom is a knight, another is a knave, and the other is a spy. The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.
A says, "I am the knight."
B says, "I am the knave."
C says, "I am the spy."
Who is the spy?
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A knight can only say "I am a knight," hence A is the knight.
A knave cannot say "I am a knave," hence C is the knave.
Hence, B is the spy. □