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16 10 There are $69$ people in a room, of which $42$ are truth-tellers (they always tell the truth) and the rest are liars (they can lie or tell the truth). You are allowed to ask any person $A$ whether any person $B$ is a liar or not. What is the minimum number of questions needed to reliably identify at least one truth-teller? I was asked to try to solve this problem on logic. Unfortunately, this is way above my level and I couldn't even attempt solving it. Would somebody please guide me on how to solve this problem? Thank you very much in advance. discrete-mathematics logic puzzle combinatorial-game-theory extremal-combinatorics share | cite | improve this question