The Fork in the Road

Question

A fork: one road leads to the village of truth-tellers, the other to the village of liars. A local stands at the fork, truth-tellers always tell the truth, liars always lie, and you can't tell which this one is. With one yes/no question, find the road to the truth-tellers' village.

Accepted Answer

Point at a road and ask: "Does this road lead to your village?" Case check with the left road: - Left goes to the truth village: the truth-teller (whose village it is) truthfully says yes; the liar (whose village it isn't) lies about the true answer "no" and says yes. - Left goes to the liars' village: the truth-teller truthfully says no; the liar, whose village it is, lies and says no. Either type answers yes iff the road leads to the truth-tellers' village. Take the road on "yes." Why it works: the question entangles the speaker's identity with the road, liar + liar-village produces a double negative. The equivalent classic construction: "If I asked you whether this is the way, would you say yes?", forcing the liar to lie about their own lie. The general principle: when a channel may invert your signal, ask about the channel's own output; inversion composed with itself is the identity. (Same trick as XOR-ing out an unknown bit.)

The Fork in the Road

Problem

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