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S H _ T Clue
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 YOU SHOULD NOT SPIN THE BARREL. THERE ARE 2 CONSECUTIVE BULLETS AND 4 CONSECUTIVE EMPTY SLOTS, SO WE LET IT BE EEEEBB. THE PROBABILITY THAT YOU GET A BULLET AFTER SPINNING THE BARREL IS 2/6 = 1/3. YOU GAINED SOME KNOWLEDGE AFTER THE FIRST SHOT. SINCE YOU DIDN'T HIT YOURSELF YOU KNOW YOU GOT ONE OF THE 4 EMPTY BULLET SLOTS. THE SEQUENCE IS EEEEBB, SO IF YOU GOT THE LAST E FOR THE 1ST SHOT, YOU WILL HIT BY A BULLET IN THE 2ND SHOT. IF YOU GOT ANY OF THE 1ST THREE ES, YOU WILL NOT GET A BULLET IN THE 2ND SHOT. THE CHANCES OF GETTING THE 1ST THREE ES IS 3/4. IT'S SAFER TO NOT SPIN THE BARREL AGAIN AS THE PROBABILITY OF MISSING THE BULLET IS HIGHER 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 THE OPTION TO PULL THE TRIGGER AGAIN WILL GIVE A HIGHER PROBABILITY OF NOT BEING SHOT. THE KEY HINT HERE IS THAT THE BULLETS WERE LOADED ADJACENT TO EACH OTHER. THERE ARE 4 WAYS TO ARRANGE THE REVOLVER WITH CONSECUTIVE BULLETS SO THAT THE FIRST SHOT IS BLANK. THESE ARE THE POSSIBLE SCENARIOS: (XBBXXX) (XXBBXX) (XXXBBX) (XXXXBB) THE OTHER TWO SCENARIOS WOULD HAVE MEANT YOU GOT SHOT ON THE FIRST ATTEMPT. (BBXXXX) OR (BXXXXB). NOW LOOK AT THE SECOND SLOT IN THE 4 POSSIBLE SCENARIOS ABOVE. THE ODDS OF GETTING SHOT ARE 1⁄4 OR 25% (ONLY THE FIRST SCENARIO WOULD GET YOU SHOT). BUT IF YOU RESPIN, THERE ARE 2 BULLETS REMAINING AND A TOTAL OF 6 SLOTS, WHICH GIVES A PROBABILITY OF 2⁄6 OR 33% OF BEING SHOT