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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 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 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 TOM IS THE KILLER AND BILL SPOKE THE TRUTH. IF BILL WAS THE KILLER, BOTH TOM AND HARRY WILL BE TELLING THE TRUTH. IF HARRY WAS THE KILLER, NONE OF THE STATEMENTS WILL BE TRUE. IF MIKE WAS THE KILLER, NONE OF THE STATEMENTS WILL BE TRUE