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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 THE ANSWER IS 3, 3 AND 8 OLD PASSWORD: OUT OF DATE NEW PASSWORD: DIFFERENT HE SAID: MY PASSWORD IS "OUT OF DATE." AND THE BOSS TOLD HIM THE NEW ONE WHEN HE SAID: "THE PASSWORD IS DIFFERENT." THE WEIGHT OF THE 5 RINGS ARE 1, 2, 4, 8 AND 16 GRAMS. USING THE COMBINATION OF THE 5 TYPE OF WEIGHTS YOU CAN REWARD FROM 1 TO 31 GRAMS IN WEIGHT TO THE WISE MAN. FOR EXAMPLE: FOR THE 3RD DAY, YOU CAN GIVE HIM THE 1 AND 2 GRAM RINGS. FOR THE 15TH DAY, YOU CAN GIVE HIM THE 1, 2, 4, 8 GRAM RINGS. FOR THE 30TH DAY, YOU CAN GIVE HIM THE 2, 4, 8, 16 GRAMS 2 CAKES. AT EACH BRIDGE YOU ARE REQUIRED TO GIVE HALF OF YOUR CAKES, AND YOU RECEIVE ONE BACK. WHICH LEAVES YOU WITH 2 CAKES AFTER EVERY BRIDGE