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THE ELDEST IS 8 YEARS OLD AND THE 2 YOUNGER ONES ARE 3 YEARS OLD. LET'S BREAK IT DOWN. THE PRODUCT OF THEIR AGES IS 72. SO THE POSSIBLE CHOICES ARE: 2, 2, 18 - SUM(2, 2, 18) = 22 2, 4, 9 - SUM(2, 4, 9) = 15 2, 6, 6 - SUM(2, 6, 6) = 14 2, 3, 12 - SUM(2, 3, 12) = 17 3, 4, 6 - SUM(3, 4, 6) = 13 3, 3, 8 - SUM(3, 3, 8 ) = 14 1, 8, 9 - SUM(1,8,9) = 18 1, 3, 24 - SUM(1, 3, 24) = 28 1, 4, 18 - SUM(1, 4, 18) = 23 1, 2, 36 - SUM(1, 2, 36) = 39 1, 6, 12 - SUM(1, 6, 12) = 19 THE SUM OF THEIR AGES IS THE SAME AS YOUR BIRTH DATE. THAT COULD BE ANYTHING FROM 1 TO 31 BUT THE FACT THAT JACK WAS UNABLE TO FIND OUT THE AGES, IT MEANS THERE ARE TWO OR MORE COMBINATIONS WITH THE SAME SUM. FROM THE CHOICES ABOVE, ONLY TWO OF THEM ARE POSSIBLE NOW. 2, 6, 6 - SUM(2, 6, 6) = 14 3, 3, 8 - SUM(3, 3, 8 ) = 14 SINCE THE ELDEST KID IS TAKING PIANO LESSONS, WE CAN ELIMINATE COMBINATION 1 SINCE THERE ARE TWO ELDEST ONES. THE ANSWER IS 3, 3 AND 8 DAUGHTER-IN-LAW. HER DAUGHTER'S FATHER IS HER HUSBAND. THIS MEANS JOHN'S SON IS HER HUSBAND, SO JOHN IS HER FATHER-IN-LAW, MAKING HER THE DAUGHTER-IN-LAW 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 THE SILVER BOX CONTAINED ANNA'S PICTURE. IF HER PICTURE HAD BEEN IN THE GOLD BOX, THE STATEMENTS ON THE GOLD BOX AND SILVER BOX WOULD HAVE BEEN TRUE. IF HER PICTURE HAD BEEN IN THE BRONZE BOX, THE STATEMENTS ON THE BRONZE BOX AND SILVER BOX WOULD HAVE BEEN TRUE. IF HER PICTURE IS IN THE SILVER BOX, THE STATEMENT ON THE BRONZE BOX WOULD BE TRUE AND THE STATEMENTS ON THE GOLD AND SILVER BOXES WOULD NOT BE TRUE