A remote village in the mountains is difficult to access and has few inhabitants. Because of their long isolation, they have split into three groups with strange behavior patterns. The truth tellers always tell the truth, the liars always lie, and the “mixers” sometimes tell the truth and sometimes lie. A hiker who has lost their way comes across three people sitting on a bench under the village’s linden tree. Each belongs to a different group. The first person claims, “I am not a truth teller.” The second person claims, “I am not a mixer.” And the third person says, “I am not a liar.” Which groups do the three people belong to?
If the first person were a truth teller, they would not claim that they are not one. If they were a liar, their claim that they are not a truth teller would be true. But that is a contradiction. Thus, they are a mixer. Because the first person is a mixer, the second cannot be one. So they are a truth-teller. The third person is therefore a liar.
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.