Which Fork
Written on 10:30 am by Vja Students
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?
Ans: 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.
I'll ask :
Could you please ask the guy next to you to go ask the guy next to him what the right road is, and let me know of it?
And then I will rather choose the other road rather than the one I have been told.
Having said that, the role of the guy who is unreliable in his truth/false response leaves the whole exercise a bit ambiguous. Because we can't conclude that out of two times he'll lie once & tell the truth once.