This is a question from Enderton.
You are in a land inhabited by people who either always tell the truth or always tell falsehoods. You come to a fork in the road and you need to know which fork leads to the capital. There is a native nearby but he has time only to reply to one yes-or-no question. What would you ask him to learn which way to take?
This is what I came up with and would be grateful if someone could verify if it's right and maybe provide alternate/better solutions.
I would ask him "Is the statement: 'You are a truth-teller if and only if the road to your left leads to the capital', true ?"
Yes
If the bloke is a truth-teller then he points to the right road. If he is a liar then he lied about the statement too. So the statement is false. Then the two sub-statements must have opposite truth values. The first is false since he is a liar. So the road to his left does lead to the capital.
No
If the bloke is a truth-teller then the road does not lead to the capital. If he is a liar then he lied about the statement too. So the incorporated statement is actually true. But then it follows the road does not lead to the capital.
So a Yes answer means the pointed road is the correct one and a No answer means I should take the other one.
Your solution appears to work. A somewhat simpler question would be "If I asked you which road leads to the capital, would you have answered that it was the left road?". Yes means it is to the left, no means to the right.