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J _ K _ R Clue
THE ISLANDER IS A JOKER. A KNIGHT CANNOT LIE AND SAY THEY ARE A KNAVE, A KNAVE CANNOT TELL THE TRUTH AND SAY THEY ARE A KNAVE AND A JOKER IS FREE TO LIE AND SAY THEY ARE A KNAVE. THE ISLANDER HAS TO BE A JOKER A LIE, BECAUSE THE STATEMENT ITSELF SAYS THAT EVERYTHING TOLD WILL BE A LIE THE SALESMAN IS A VISITOR AND HE IS TELLING THE TRUTH. IF THE WOMAN IS A VISITOR, AND ASKED IF SHE IS A VISITOR, SHE WILL ANSWER TRUTHFULLY: "YES". IF THE WOMAN IS A NATIVE, AND ASKED IF SHE IS A VISITOR, SHE WILL ANSWER FALSELY: "YES". IN EITHER CASE, THE WOMAN WILL ANSWER, "YES." SINCE THE SALESMAN DID NOT LIE, HE HAS TO BE A VISITOR ALEX IS A KNIGHT, CODY IS A KNAVE, AND BROOK IS A SPY. BROOK IS NOT THE KNIGHT, SINCE IF HE IS, THEN ALEX WOULD ALSO BE THE KNIGHT. CODY IS NOT THE KNIGHT, SINCE HIS STATEMENT WOULD THEN BE A LIE. THEREFORE ALEX IS THE KNIGHT, CODY IS THE KNAVE, AND BROOK IS THE SPY