On your travels, three men stand at a fork in the road. You're not sure
which fork you need to take, but each of the three men do. One of these people
tells the truth, one always lies, and the third tells the truth sometimes and
lies the other times. Each of the three men know each of the others, but you
don't know who is who. If you could ask only one of the men (chosen at random,
since you don't know which man is which) one yes/no question, what question
would you ask to determine the road you wish to take?
Give up?
Drag your cursor between the asterisks for the solution
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Pick one of the men and ask, "If I were to ask
you whether the left fork leads to where I'm going, and you chose to answer
that question with the same degree of truth as you answer this question, would
you then answer 'yes'?"
The truthteller will say "yes" if the left fork leads to where
you're going and "no" otherwise. The liar will answer the same, since
he will lie about where the left fork leads, and he will lie about lying. The
third man may either lie or tell the truth about this one question, but either
way he is behaving like either the truthteller or the liar and thus must
correctly report the road to your destination.
*
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