What would the other villager tell me to do in order to reach my destination?

[Mr Davis 97]

Homework Statement

Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a "yes or a "no" response to a question a tourist asks. Suppose that you are a tourist visiting this are and come to a fork in the road. One branch leads to where you want to go, and the other leads to the deep jungle. A villager is standing at a fork in the road. What question can you ask the villager to determine which branch to take?

Homework Equations

The Attempt at a Solution

I am not sure where to start. For these types of logic puzzles, I am not sure if there exists some systematic way to deduce a question to ask based on propositional logic and truth tables, or if you just have to come up with one through trial and error.

 

[phinds]

I am not sure where to start. For these types of logic puzzles, I am not sure if there exists some systematic way to deduce a question to ask based on propositional logic and truth tables, or if you just have to come up with one through trial and error.

I agree. I know the answer to this one but I didn't get it, had to be told (about 50 years ago --- it's an oldie). Once you know the trick, many such become easy.

There may BE a way, but if so, I've never figured it out. Hope someone else has and will post it.

 

[Ray Vickson]

Homework Statement

Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a "yes or a "no" response to a question a tourist asks. Suppose that you are a tourist visiting this are and come to a fork in the road. One branch leads to where you want to go, and the other leads to the deep jungle. A villager is standing at a fork in the road. What question can you ask the villager to determine which branch to take?

Homework Equations

The Attempt at a Solution

I am not sure where to start. For these types of logic puzzles, I am not sure if there exists some systematic way to deduce a question to ask based on propositional logic and truth tables, or if you just have to come up with one through trial and error.

This is one of those standard puzzles (a real "oldie") whose solution is blindingly obvious once somebody tells you the answer, but is almost un-doable otherwilse. It is also one of those question for which the PF rules about supplying hints only (not complete solutions) is so restrictive that even giving a hint seems impossible---the whole solution, or nothing.

 

[phinds]

I think I did come up with a way to give a hint without giving away the answer. It may be too close to the answer but as Ray just said, it is almost undo-able if you don't know the trick. Think of how you can embed two questions in one such that the end result will be the same for the liar and the truther.

 

[haruspex]

There is also the approach which guarantees at least a moral victory. "Please lead me to the village, where I hear there is free beer today"

 

[Battlemage!]

It might help to ask a hypothetical question rather than a direct question about the roads.