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posted by  tokio on 8/25/2008 5:00:55 PM  |  status: Live  

Logic question

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Question Details:
Four friends have been identified as suspects for an unauthorized access into a computer system. They have made statements to the investigating authorities. “Alice said Carlos did it.” John said “I did not do it.” Carlos said “Diana did it.” Diana said “Carlos lied when he said that I did it.”

a)      If authorities also know that exactly one of the four suspects is telling the truth, who sis it? Explain your reasoning.

b)      If the authorities also know that exactly one is lying, who did it? Explain your reasoning.
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posted by Gatorfan on 8/25/2008 7:39:26 PM  |  status: Live
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Response Details:

a)

Possibility 1.
 Alice  Carlos did it.
  truth  
 John  I didn't do it.
  lie  If Carlos did it and John is lying then they both did it, logic break
 Carlos  Diana did it.
  lie  
 Diana  Carlos lied
  lie  

2.
Alice  Carlos did it
  lie  
 John  I didn't do it
  truth  
 Carlos  Diana did it
  lie  
 Diana  Carlos lied
  lie  If Carlos lied then Diana is telling truth, logic break

3.
Alice  Carlos did it
 lie
 
 John  I didn't do it
  lie  If he is lying then he did it, logic break since Diana did it according to Carlos
 Carlos  Diana did it
  truth  
 Diana  Carlos lied
  lie  

4...no logic breaks
Alice  Carlos did it
 lie
 John  I didn't do it
  lie
 Carlos  Diana did it
  lie
 Diana  Carlos lied
  truth




b)

1.
Alice  Carlos did it
  lie  
 John  I didn't do it
  truth  
 Carlos  Diana did it
  truth  
 Diana  Carlos lied
  truth  logic break, Carlos didn't lie

2.
Alice  Carlos did it
  truth  
 John  I didn't do it
  lie  
 Carlos  Diana did it
  truth  
 Diana  Carlos lied
  truth  logic break, Carlos didn't lie

3. no logic breaks
Alice  Carlos did it
  truth
 John  I didn't do it
  truth
 Carlos  Diana did it
  lie
 Diana  Carlos lied
  truth

4.
Alice  Carlos did it
  truth  
 John  I didn't do it
  truth  
 Carlos  Diana did it
  truth  logic break, only 1 person did it
 Diana  Carlos lied
  lie  

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