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THE SMALLEST AMOUNT OF ONE-DOLLAR AND TWO-DOLLAR BILLS THE CASHIER MAY GIVE TO THE OLD MAN IS 1×1 + 10×2 = 21. HE MUST GIVE THE OLD MAN A MULTIPLE OF 21 I.E. 21 OR 42 OR 63 OR 84 OR 105 OR 126 OR 147 OR 168 OR 187 WITHOUT EXCEEDING 200. OUT OF ALL THESE NUMBERS ONLY 105 CAN BE ADDED TO A MULTIPLE OF 5 TO SUM UP TO MAKE 200 ALTOGETHER. SO HE MUST GIVE THE BALANCE OF 95 IN FIVE-DOLLAR BILLS. THEREFORE, THE CASHIER MUST GIVE 5 ONE-DOLLAR BILLS, 50 TWO-DOLLAR BILLS AND 19 FIVE-DOLLAR BILLS 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 PROBLEM IS THAT THE QUESTION IS CLEVERLY PHRASED TO CAUSE CONFUSION. THE BALANCE TOTAL DOES NOT NEED TO BE EQUAL TO THE WITHDRAWAL TOTAL. AND IN THIS CASE, THE BALANCE TOTAL WILL NOT ADD UP TO SOMETHING MEANINGFUL. LET'S SAY YOU HAVE $100 IN YOUR BANK ACCOUNT AND YOU MAKE 2 WITHDRAWALS OF $1 EACH. THE WITHDRAWAL TOTAL IS $2 ($1 + $1). BUT THE BALANCE TOTAL IS $197 ($99 + $98) 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