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HE HAS TO JUGGLE THEM. AT ANY ONE POINT, THE MAN WILL ONLY BE CARRYING 2 GOLD BARS AND THE OTHER GOLD BAR WILL BE AIRBORNE, MEANING A MAXIMUM OF 95KG TOTAL AT ANY GIVEN TIME 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 THE TWO SONS GET ON THE BOAT AND ROW BACK TO SHORE. ONE JUMPS OUT AND THE OTHER ROWS BACK TO THE ISLAND AND GETS OUT. THE DAD GETS IN AND RIDES BACK TO SHORE WHERE HE JUMPS OUT AND THE OTHER SON GETS BACK IN. THE SON GOES BACK TO THE ISLAND, FETCHES THE OTHER SON AND TOGETHER THE TWO OF THEM ROW BACK TO THE SHORE WHEN THE FIRST SERVANT COMES IN, THE KING SHOULD WRITE DOWN HIS NUMBER. FOR EACH OTHER SERVANT THAT REPORTS IN, THE KING SHOULD ADD THAT SERVANT'S NUMBER TO THE CURRENT NUMBER WRITTEN ON THE PAPER, AND THEN WRITE THIS NEW NUMBER ON THE PAPER. LET X BE THE NUMBER OF THE MISSING SERVANT AND Y BE THE NUMBER THAT THE KING HAS WRITTEN. ONCE THE FINAL SERVANT HAS REPORTED IN, THE NUMBER ON THE PAPER SHOULD EQUAL: Y = (1 + 2 + 3 + ... + 99 + 100) - X (1 + 2 + 3 + ... + 99 + 100) = 5050, SO WE CAN REPHRASE THIS TO SAY THAT THE NUMBER ON THE PAPER SHOULD EQUAL: Y = 5050 - X SO TO FIGURE OUT THE MISSING SERVANT'S NUMBER, THE KING SIMPLY NEEDS TO SUBTRACT THE NUMBER WRITTEN ON HIS PAPER FROM 5050: 5050 - Y = X