One question to find the right road from two dwarfs
Question
At a fork, one road leads to a sage and the other into the jungle. Two dwarfs stand there: one always tells the truth and one always lies, and you cannot tell which is which. Can you learn the road to the sage with a single yes/no question to one dwarf? If so, what do you ask?
Short answer
Yes. Ask either dwarf: "If I asked the other dwarf whether the left road leads to the sage, would he say yes?" The answer passes through exactly one lie either way, so it is always the opposite of the truth: take the left road on "no" and the right road on "yes".
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Open the worked solutionLessons behind this question
- Sample Spaces, Events, and the Probability Axioms
- Conditional Probability, Total Probability, and Bayes' Rule
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