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Officer X was entrusted with the duty of investigating a murder. The dead body was found in the living room. Preliminary investigation suggested that four of the six suspects were liars (at least one of each of their statements is a lie). Upon further interrogation, Officer X succeeded in extracting the following responses:

  • A: “P and I were in the 2nd bedroom and M was in the bathroom.”
  • O: “I agree with A. M was in the bathroom and P in the second bedroom, but A was in the living room.”
  • P: “As far as I remember, O and J were in the kitchen and I was in the bathroom.”
  • M: “P was in the second bedroom and C was in the bathroom. I saw A in the 1st bedroom.”
  • C: “P and J were in the bathroom and O was in the kitchen.”
  • J: “M was in the kitchen. P and I were in the second bedroom.”

From these replies Officer X immediately deduced who the murderer was. Who was the murderer and what line of reasoning led him to his conclusion?

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O is the murderer

Reasoning:

We can see that for each person, if they are telling the truth, some others are lying. These are A:O,P,M,C,J; O:A,P,M,C,J; P:A,O,M,C,J, M:A,O,P,C; C:A,O,P,M,J; J:A,O,P,C. Since we know that there are only four liars, M and J have to be truthful. This means that P,C,A,M and J were not in the living room, leaving O as the only remaining suspect.

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