Thursday, May 30, 2019

The Random Native

You come across a fork with two roads ahead and you want to know which to take. Exactly one leads to destination. Three natives $A$, $B$, and $C$ emerge to help. The truth-teller always tells the truth, the liar always a lie, and randomist tosses a fair coin to decide his answer. Too bad you don't know who is who. Can you ask two yes/no questions, each directed to either $A$, $B$, or $C$, to get your answer?

Solution:

The key is to find one who is not random. Ask $A$ if $B$ is more honest than $C$. Note that no matter what, if the answer is yes, then $C$ is not random. Otherwise $B$ is not random. Then, ask this non-randomist: "If I ask you whether the first road takes me to my destination, would you reply yes?" and take the road indicated by the reply.

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