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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 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 YOU WILL HAVE TO SAY SOMETHING SO THAT I CAN'T KEEP MY WORD. SO, YOU WILL HAVE TO SAY, "YOU'LL CHOP MY HEAD OFF." IF THE STATEMENT IS TRUE, YOU WILL BE STRANGLED, BUT THEN THE STATEMENT WILL BECOME FALSE. IF THE STATEMENT IS FALSE, YOUR HEAD WILL BE CHOPPED OFF, BUT THEN THE STATEMENT WILL BECOME TRUE A LIE, BECAUSE THE STATEMENT ITSELF SAYS THAT EVERYTHING TOLD WILL BE A LIE