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$ 2 0 Clue
THE BARBER LOST $5 IN CASH. THE LADY FROM THE FLOWER SHOP GAVE $20 TO THE BARBER AND EVENTUALLY GOT HER $20 BACK. THE MAN WHO GOT THE HAIRCUT, GAVE NOTHING EXCEPT THE COUNTERFEIT MONEY AND GOT $5 BACK. SO THE BARBER LOST $5 IN CASH BUT LOST $15 IN REVENUE AS HE GOT COUNTERFEIT MONEY FOR THE HAIRCUT. LET'S SAY THE BARBER HAD $20 INITIALLY. HE GOT A $20 BILL FOR THE HAIRCUT AND AFTER PAYING THE MAN THE $5 CHANGE, HE HAD A BALANCE OF $35. THE BARBER THEN GAVE $20 TO THE LADY FROM THE FLOWER SHOP IN EXCHANGE FOR THE COUNTERFEIT MONEY WHICH BROUGHT HIS BALANCE TO $15. SO, THE BARBER MADE A LOSS OF $5, SINCE HIS BALANCE AFTER THE HAIRCUT WAS $15 FROM THE INITIAL AMOUNT OF $20 THE CONTENTS OR THE TEN ENVELOPES (IN DOLLAR BILLS) SHOULD BE AS FOLLOWS: $1, 2, 4, 8, 16, 32, 64, 128, 256, 489. THE FIRST NINE NUMBERS ARE IN GEOMETRICAL PROGRESSION, AND THEIR SUM, DEDUCTED FROM 1,000, GIVES THE CONTENTS OF THE TENTH ENVELOPE A HALF DOLLAR, A QUARTER, AND FOUR DIMES. YOU OBVIOUSLY CAN'T HAVE ANY PENNIES, BECAUSE YOU COULDN'T HAVE 1-4 PENNIES, SINCE $1.15 IS A MULTIPLE OF 5, AND IF YOU HAD 5 PENNIES OR MORE YOU COULD CHANGE A NICKEL. YOU CAN'T HAVE MORE THAN 1 NICKEL, OTHERWISE YOU COULD CHANGE A DIME. AND IF YOU HAD 1 NICKEL YOU COULDN'T HAVE BUT 1 DIME, OTHERWISE YOU COULD CHANGE A QUARTER. THEN IF YOU HAD 1 NICKEL AND 1 DIME YOU'D HAVE 15 CENTS. THAT WOULD LEAVE $1.00 AND YOU COULDN'T MAKE THAT REMAINING $1.00 WITH QUARTERS AND HALVES WITHOUT EITHER BEING ABLE TO CHANGE A HALF OR A DOLLAR. SO YOU CAN'T HAVE ANY PENNIES OR NICKELS. SINCE YOU CAN'T HAVE ANY PENNIES OR NICKELS, YOU CAN'T POSSIBLY MAKE $1.15 WITH DIMES AND HALVES ONLY, SO YOU MUST HAVE AT LEAST 1 QUARTER. YOU CAN'T HAVE MORE THAT ONE QUARTER, OTHERWISE YOU COULD CHANGE A HALF. SO YOU MUST HAVE EXACTLY 1 QUARTER. THAT LEAVES 90 CENTS, TO MAKE WITH A HALF DOLLAR AND DIMES. SO THAT'S 1 HALF AND 4 DIMES. AND WITH ONLY 4 DIMES YOU CAN'T CHANGE A HALF DOLLAR 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