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$ 1 5
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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 THE CORRECT COMBINATION IS 65292. SINCE THE THIRD DIGIT IS THREE LESS THAN THE SECOND, AND THE FOURTH IS FOUR GREATER THAN THE SECOND, THERE ARE ONLY THREE POSSIBLE COMBINATIONS FOR THE SECOND, THIRD AND FOURTH DIGITS. THESE ARE -307-, -418-, AND -529-. WITH THE FIRST DIGIT THREE TIMES THE FIFTH, THE ONLY POSSIBLE COMBINATIONS FOR THE FIRST AND FIFTH DIGITS ARE 0 0,3 1, 6 2, AND 9 3. THE SOLUTION ARISES FROM COMBINING THESE TWO SETS OF POSSIBILITIES, WITH THE ADDED CRITERIA THAT THERE ARE THREE COMBINATIONS OF TWO DIGITS THAT THAT EACH SUM TO 11 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