Knights, knaves, and the fork in the road

Question

You reach a fork in the road: one path leads to freedom, the other to doom. Two guards stand there. One is a knight who always tells the truth; the other is a knave who always lies. You don't know which guard is which. You may ask one yes/no question to one guard to determine the safe path. What single question guarantees you find the road to freedom?

Accepted Answer

The classic solution asks one guard what the other guard would say, then does the opposite. Ask either guard: "If I asked the other guard whether the left path leads to freedom, would they say yes?" Then: - If the answer is "yes", take the right path. - If the answer is "no", take the left path. Why it works. The answer passes through both guards, the one you ask plus the one they describe, so exactly one lie is always applied, regardless of whom you asked. Suppose the left path really does lead to freedom. - You ask the knight (truth-teller) about the knave. The knave, asked directly, would …

Knights, knaves, and the fork in the road

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