Puzzle | Truth and Lie

There are two tribes, “Lie tribe” and “Truth Tribe”. “Lie tribe”, as per the name, always lie and “Truth tribe” always speak the truth. You meet three of the persons from these tribes and ask the first person: “Which tribe do you belong to ?”. He replies something in his language which you don’t understand. Second person translates to you that, he is saying that he belongs to the “Lie Tribe”. Third person says that second person is lying.
Which tribe does the third person belong to?


Solution: Truth Tribe
Explanation: Since we don’t know to which tribe the first person belong to, let us assume that the first person is from “Truth tribe”, then he will claim that he is from the “truth tribe” (because he won’t lie), in which case the second person must be lying.
Now, assume that the first person is from “Lie tribe”. Even then, he will say that he belongs to the truth tribe (as he is a liar), so second person is lying again in this case as well.
Thus, third person is correct in both the scenarios, hence he belongs to “Truth Tribe”.

Reference: https://brilliant.org/problems/1truth-tribe-or-2-lie-tribe/

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