Which Way To Go? --- A Challenging Question

You should ask, "If I asked you if I should go (insert direction here), would you say yes?" Both men will answer NO, and then you go the OPPOSITE WAY of the direction you asked. Think about it....

I did and this is equal to eni-mini-mini-mo. Think about it.

How so? If you chose the wrong direction both men say no and you go the opposite way. If you chose the correct direction both would say yes and you go that way. In essence the liar has to lie about lieing...if that makes sense.

First, read exactly what you wrote. It is not the same as you indicate in your second comment. If you are counting on the liar to reverse what he would normally tell you (I think this is the trick you mean to make it work) then the direction is correct if both men say yes and incorrect if both men say no. There will be two possible outcomes and perhaps you didn't intend to only indicate, as you did, that both will say yes, and even then, yes would be the correct way since the non-liar will never reverse himself. But what if the liar only thinks you are asking the simple question of is it correct? Then regardless of which one you pick one man will say yes and one will say no. Read "forks and liars" further down, for the simplest solution.

Further thought leads me to realize that the puzzle as it is strictly stated does not indicate that the men know if the other is a liar or truthful. Strictly speaking, we should not then depend on their ability to report on the other's response. In this event, if we can rely on the liar to lie about what he "would say" then this is the method that is reliable. However, the correct response is to take the "Yes" route or not take the "No" route since you will get a true response from either man (the truth from the non-liar and a lie about a lie from the liar) and you will not need a response from both which violates one of the conditions of the puzzle (only one response allowed).

Ask either man which way the other man would tell him is the "right" path, then take the other path. P.S. This riddle is older than I, and I ain't no spring chicken!

I am curious to know if the original question is an accurate rendition of the puzzle. As stated, we must make an assumption that the two men know that the other is truthful and a liar. Without this unspecified condition the scheme breaks down and becomes indeterminate. Not to be picky it's just the kind of thing by brain pops out when I'm doing something else. Also, you would be stumped (no correct solution) if you didn't read into it the assumption.

What is the basis for the assumption that either, both or neither man actually knows the truth, i.e. the correct direction to take? If the liar doesn't know the correct way can he make his answer untruthful? If the honest man is mistaken in knowing the correct direction is his answer true? What is the outcome if only one or the other knows the correct route, e.g. the liar knows the way but the non-liar doesn't? In this case would it make a difference if the liar answered first or if the non-liar answered first? This has been bothering me on and off now for two days. Has anyone sorted through the remaining possibilities? I must admit I haven't read the Scientific American article cited below. Was any of this covered there?

Well, I'll kill two birds with one stone . . . The original post posing the question was:"rcuplin writes: A man arrives at a fork in the road. At the intersection are two men. One man always tells the truth and one always lies. You do not know which is which, but both know the right path to take. You can ask one question and get one response. What do you ask to determine the right path?"

Exactly correct! It's elementary.

Best discussion I've ever seen was by Martin Gardner in Scientific American; he added more sophisticated liars, whose aim was to mislead, and others. Questions got more complex at each stage. Best final question: "Did you know that they're serving free beer in the village?". Only the misleader, who says "Ugh - I hate beer" and sets off down the wrong path will keep you from getting where you're going. And you'll know that he'll always have the nagging suspicion that he missed out on free beer.

The answer lies in the movie "Labrinth" with David Bowie. The scene is exactly the same as you are asking and the answer is as simple. Enjoy the movie.

I agree with Bill. I heard the riddle about a man in purgatory. ...two "guards", two doors. One leads to "freedom" - the other leads to "hell." One always lies - the other always tells the truth. Only one question allowed - it is: What door would the other guard tell me leads to freedom?

You ask one of the men (doesn't matter which), "Would the other man tell me to take the left path?" If the other man is the liar, he will answer "no" and the man who doesn't lie will tell you "no" and you will know that left is correct. If the other man tells the truth and answers "yes", the liar will tell you "no". Again you will know that left is correct. This may be an oldie, but I have recycled it for you young pips.