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1 / 3 .
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H _ G H _ R Clue
VINCE DID IT. JOYCE'S STATEMENTS 1 AND 3 MUST BE TRUE. IF SHE HAD BROKEN THE WINDOW, BOTH STATEMENTS WOULD HAVE BEEN FALSE. BUT SINCE EACH CHILD TOLD ONLY ONE LIE, THESE TWO STATEMENTS MUST BE TRUE. THEREFORE, JOYCE'S STATEMENT 2 IS THE ONE THAT IS FALSE. THE STATEMENT OF ALL THE OTHER CHILDREN CAN THEN BE PROVEN TRUE OR FALSE USING THIS INFORMATION. SINCE WE KNOW THAT JOYCE'S STATEMENT 2 IS FALSE, SALLY'S STATEMENT 1 AND MATT'S STATEMENT 1 HAVE TO BE FALSE. JOE'S STATEMENT 2 HAS TO BE FALSE, SINCE SALLY DID NOT TELL WHO DID IT. NOW WE ARE LEFT ONLY WITH VINCE PETE TOLD THEM TO FORM A CIRCLE AROUND HIM. ALL THE SQUAD WAS FACING IN AT PETE, READY TO SHOOT, WHEN THEY REALIZED THAT EVERYONE WHO MISSED WOULD LIKELY END UP SHOOTING ANOTHER SQUAD MEMBER. SO NO ONE DARED TO FIRE, KNOWING THE RISK. THUS AT SUNDOWN HE WAS RELEASED 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 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