Peter and Paul are twin brothers. One of them always lies (we don't know which). The other one always tells the truth. I ask one of them: "Is Paul the one that lies?" "Yes." he answers. Did I speak to Paul or Peter?
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I spoke to Peter. If a person always lies or alternately, always tells the truth, he cannot admit he is lying (if this person were a liar, he would be telling the truth and if this person were honest, he would be lying). Therefore Paul couldn't have answered my question. Peter could answer about Paul without contradicting himself. What we don't know is who the liar is.