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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

Dennis said:

Exactly one of Dennis and Jessica tells the truth..
Michelle didn't murder the mailman.
Jessica said:
Pamela is not telling the truth
Dennis murdered the mailman.
Michelle said:
At least one of us, Patrick or I, is telling the truth.
I didn't murder the mailman.
Pamela said:
Patrick is not telling the truth
I didn't murder the mailman.
Patrick said:
Michelle isn't telling the truth.
Jessica murdered the mailman.

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