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S H _ T Clue
THE PROBLEM IS THAT THE QUESTION IS CLEVERLY PHRASED TO CONCEAL WHAT IS REALLY GOING ON. LET'S LOCATE ALL THAT MONEY. THERE ARE TWO WAYS TO THINK ABOUT HOW MUCH MONEY IS OUT THERE TO BE FOUND.THE WAY THAT THIS QUESTION IS TRICKY IS THAT IT COMBINES THAT TWO WAYS. THE FIRST WAY IS THIS. HOW MUCH MONEY DID THE THREE MEN PAY ORIGINALLY? THE SECOND WAY IS THIS. HOW MUCH MONEY DID THEY END UP PAYING? SO IF IT IS THE FIRST WAY, THEN CLEARLY THE TOTAL WE NEED TO ACCOUNT FOR IS THE $15. SO LET'S SEE WHAT HAPPENS TO THAT $15. THE CHEF GETS $10, THE WAITER GETS $2 AND THE GUYS GET $3 BACK. THAT ADDS UP FINE. NOW LET'S LOOK AT THE SECOND WAY. HOW MUCH MONEY DID THEY END UP PAYING? WELL $12, AND $10 OF IT WENT TO THE CHEF AND $2 TO THE WAITER. NOW, THAT ADDS UP TOO. THE PROBLEM WITH THE QUESTION IS THAT THE THE $2 THAT THE WAITER TOOK IS CONTAINED IN THE $12 THAT THEY END UP PAYING SO WE SHOULDN'T EXPECT THEM TO ADD TO ANYTHING MEANINGFUL SHE NEEDS TO GIVE YOU 5 APPLES. YOU BOTH NEED AT LEAST 5 APPLES TO BEGIN WITH, BUT APART FROM THAT IT DOESN'T MATTER EXACTLY HOW MANY YOU EACH HAVE. WHEN SHE GIVES YOU 5 YOU WILL HAVE 10 MORE THAN HER BECAUSE SHE WILL LOSE 5 AND YOU WILL GAIN 5, RESULTING IN A NET DIFFERENCE OF 10. FOR EXAMPLE, IF BOTH OF YOU HAVE 20 APPLES AND SHE GIVES YOU 5 OF HERS, SHE WILL BE LEFT WITH 15 AND YOU WILL NOW HAVE 25, PRECISELY 10 MORE THAN SHE HAS 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 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