bonanova Posted February 6, 2009 Report Share Posted February 6, 2009 While the Breakfast Club was detained in the school library, one of them started a small fire. When Mr. Vernon questioned them, he heard the following replies: Allison Reynolds: It was Andrew or Brian Andrew Clark: Neither John nor I did it. Brian Johnson: Both of you are lying. Claire Standish: No, Brian; Allison or Andrew is telling the truth. John Bender: No, Claire; that is not true. Mr. Vernon knows that two of them cannot be trusted. Believing the others, who does he conclude is the fire-starter? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 6, 2009 Report Share Posted February 6, 2009 While the Breakfast Club was detained in the school library, one of them started a small fire. When Mr. Vernon questioned them, he heard the following replies: Allison Reynolds: It was Andrew or Brian Andrew Clark: Neither John nor I did it. Brian Johnson: Both of you are lying. Claire Standish: No, Brian; Allison or Andrew is telling the truth. John Bender: No, Claire; that is not true. Mr. Vernon knows that two of them cannot be trusted. Believing the others, who does he conclude is the fire-starter? Brian Johnson. If he is truthful, then Allison, Andrew and Claire are all lying. However, we are working under the assumption that three of the five are truthful, so Brian is lying. John agrees with Brian, so he must also be lying. Therefore, Allison and Andrew are both truthful, implying that Brian started the fire. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 6, 2009 Report Share Posted February 6, 2009 Claire is lying, it's obvious. Ignore John. Among Allison, Andrew and Brian, only one is supposed to be lying, But Brains says two of them are lying, he is false. So Allison and Andrew are saying truth, according to them the arsonist is Brian. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 6, 2009 Report Share Posted February 6, 2009 I agree with everyone's solution, but for another reason. Alison claims that either Andrew or Brian are the arsonist. Andrew says it is not him nor John. Brian says they both lie - which cannot be true, because then Andrew would be, according to his lie, the arsonist - and Alison's truth would be that Andrew is NOT the arsonist, which cannot be. So definitely, Brian is lying. Of course, John is not telling the truth, because he is saying that Claire is lying and hence is making the same conclusion as Brian, contradicting himself. So, with the two liers eliminated, it leaves Alison telling the truth - it was Andrew or Brian. Andrew is also telling the truth when he states that it was NOT him. Which leaves: BRIAN! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 6, 2009 Report Share Posted February 6, 2009 Brian Here are what the five are really saying: Andrew Brian Allison Brian, Claire John Andrew, Brian, Allison, Claire John We are looking for a name stated by 3 only. That one is Brian. Quote Link to comment Share on other sites More sharing options...
0 Prime Posted February 7, 2009 Report Share Posted February 7, 2009 Brian started the fire. Brian and John are liars. Reasoning: If Brian were telling the truth, that would make Allison, Andrew, and Claire liars; but we know there were only two liars. So Brian is a liar, which makes Claire's statement 100% truthful, which, in turn, makes John a liar. Then from the truthful statements made by Allison and Andrew, we can tell it was Brian, who started the fire. Quote Link to comment Share on other sites More sharing options...
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bonanova
While the Breakfast Club was detained in the school library, one of them started a small fire.
When Mr. Vernon questioned them, he heard the following replies:
Allison Reynolds: It was Andrew or Brian
Andrew Clark: Neither John nor I did it.
Brian Johnson: Both of you are lying.
Claire Standish: No, Brian; Allison or Andrew is telling the truth.
John Bender: No, Claire; that is not true.
Mr. Vernon knows that two of them cannot be trusted.
Believing the others, who does he conclude is the fire-starter?
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