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J _ K _ R Clue
BERTIE IS THE MOLE. BOTH ALBERT AND CEDRIC ARE TELLING THE TRUTH. WHEN ALBERT SAID, "BERTIE IS A MOLE," HE WAS TELLING THE TRUTH, AND GIVING THE CORRECT ANSWER. WHEN BERTIE SAID, "CEDRIC IS A MOLE," HE WAS LYING, AS HE HIMSELF IS A LYING MOLE. WHEN CEDRIC RESPONDED, "BERTIE IS LYING," HE WAS TELLING THE TRUTH, AND ALSO AFFIRMING THAT BERTIE WAS LYING 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 ON THURSDAY. THEY CAN ONLY MAKE THIS STATEMENT DURING THE BORDER DAYS - ON THE BORDER DAY THEY TELL THE TRUTH AND ON THE NEXT DAY THEY LIE, OR VICE VERSE. FOR JAMES, HIS BORDER DAYS ARE ON THURSDAYS AND SUNDAYS. FOR JONATHAN, HIS BORDER DAYS ARE ON MONDAYS AND THURSDAYS. SO, ONLY ON THURSDAYS CAN THEY BOTH MAKE THE STATEMENT