Asking The Right Question
Help! I'm lost! Luckily, I have found two paths with 1 of the Wilson twins on each path.
One of the twins always lies and the other always tells the truth, but I can't tell who's who!
They are both telling me to go on their own path.
I can only ask them 1 question, so what would it be?
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If you ask "Do you know anyone else that can help me?" or "Is there another path I can take?", the answers will not be helpful. (For example, if they both know someone/some path or both don't know someone/some path, then one will say yes and one will say no, so you get no information about the paths.)
If you ask "Which one of you tells the truth?", they will both say "me"! So this isn't helpful.
If you ask "Which path do I take", you get no additional information beyond what you already have (they will both say to take their path).
If you ask "If I asked the other person where to go, which path would he tell me to go to", you will know which path to take. Here's why:
The twin who is telling the truth is standing on the path you should take (because he doesn't lie, and they both say to come to their path). When asked this question, the truth teller will tell you that the other twin will tell you to go to his own (the liar's) path, because he tells the truth that his twin will lie. On the other hand, the liar will say that the truth-twin will tell you to go to the liars path, because he knows that the truth teller will tell you to go to the truth tellers path. Both people will tell you that the other person will tell you to go down the liar's path, so go to the other path!