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This is yet another question I found on the Internet.


During a recent police investigation, Chief Inspector Stone was interviewing five local villains to try and identify who stole Mrs Archer's cake from the mid-summers fayre. Below is a summary of their statements:

Arnold: it wasn't Edward. It was Brian

Brian: it wasn't Charles. It wasn't Edward

Charles: it was Edward. It wasn't Arnold

Derek: it was Charles. It was Brian

Edward: it was Derek. It wasn't Arnold

It was well known that each suspect told exactly one lie. Can you determine who stole the cake?

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Brian's and Derek's statements give the answer

Charles

because

if exactly one of Brian's statements is a lie, then the culprit must be either Charles or Edward; if exactly one of Derek's statements is a lie, then the culprit must be either Charles or Brian.

So Arnold, Charles, and Edward's answers (we can check each one told exactly one lie) aren't actually necessary to solve the puzzle.

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  • $\begingroup$ Arnold lied saying it was Brian. Brian lied saying it was not Charles. Charles lied saying it was Edward. Derek lied saying it was Brian. Edward lied saying it was Derek. $\endgroup$ – Kritixi Lithos Jun 7 '15 at 16:33
  • $\begingroup$ @KritixiLithos Sorry! I got confused. Not sure what my problem was there. You're right of course. +1 to the question. $\endgroup$ – Rand al'Thor Jun 7 '15 at 16:36
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    $\begingroup$ Sorry, I accidentally turned a comment into an answer. $\endgroup$ – Kritixi Lithos Jun 7 '15 at 17:07
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    $\begingroup$ We can also get the answer with just Arnold and Brian's clues. $\endgroup$ – Carl Jun 9 '15 at 0:13
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If one of Brian's statements was a lie, than either Charles or Edward did the crime. If one of Derek's statements was a lie, that either Charles or Brian did the crime. Charles is included in both statements, proving that he is the one who committed the crime.

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First two statements give the answer i.e. Arnold's and Brian's.

Arnold: it wasn't Edward. It was Brian.

Looking at Arnold's statement one can be say that second part of his statement is lie ,because if it wasn't, the first one would be true, which would make Edward and Brian both culprits. Both Edward and Brian couldn't have stolen the cake. Therefore, "It wasn't Edward" is true.

Brian: it wasn't Charles. It wasn't Edward.

Coming to Brian's statement. We know Edward isn't culprit, so secont part is true making first statement a lie. This means Charles is the thief.

That's it.

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  • $\begingroup$ Good explanation! $\endgroup$ – Kritixi Lithos Jun 20 '15 at 7:00

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