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Truth/Lies Logic Puzzles

Instructions: Someone committed a crime, and the police have gathered statements from everyone. Use logic and the fact that each person either always lies or always tells the truth to figure out who is the guilty party!

See the answer for last week's puzzle

Carol said:

Patrick is truthful.
Robert didn't murder the policeman.
Jessica said:
Paul is not telling the truth
Mark didn't murder the policeman.
Joshua said:
Exactly one of Carol and Patrick tells the truth..
Carol didn't murder the policeman.
Mark said:
Carol and Jessica both tell the truth.
Paul didn't murder the policeman.
Patrick said:
Exactly one person, Paul or Carol, lies.
I didn't murder the policeman.
Paul said:
Both Patrick and Carol lie.
Joshua murdered the policeman.
Robert said:
Carol is truthful
I didn't murder the policeman.

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