Out of Gas

[bill_bright]

You are driving north on an old country road, late at night with only enough gas to go one more mile. You approach an intersection where you see an old, faded, poorly lit sign that says

[Ruff_Hi]

Ok, giving that the rules ...

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> then, the question to ask is "which road would your brother indicate was the road to the gas station?" Assume that the RIGHT road is to the gas station, if you are talking to the truth teller, he will say the LEFT because his brother would lie. If you are talking to the false teller, his brother would say RIGHT, but he is going to lie and say LEFT".

So, you go the opposite way regardless if you are talking to the truth teller or the false teller.
</font color=yellow></span hi>

[AlanMiller]

Somewhat more difficult variation - the farmhouse is home to a large family, some of whom always tell the truth, others who always lie. Same problem, same constraints - what should the question be?

Alan

[StuartR]

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> If I came here tomorrow and asked you which way to go to the petrol station, what would you say? </font color=yellow></span hi>

StuartR

[bill_bright]

StuartR - Sorry - don't see how that would get you the truth.

[AlanMiller]

The answer would probably be "no idea", since they wouldn't know that petrol was "gas" (funny name for a liquid); but yes, such a question would do the trick.

Alan

[AlanMiller]

Same situation as before - <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>you don't know if you're talking to a liar or not</font color=yellow></span hi>.
Think about the possibilities in the same way as before, and I think you'll see that <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>you'll get the correct direction without knowing who you're asking.</font color=yellow></span hi>

Alan

[StuartR]

Whether or not they understand the English language presumably depends on where this country road is. I was assuming that it is in the heart of Transylvania where everyone uses the Kings English as spoken by Bram Stoker.

StuartR

[Bowlie]

... and probably drives on the wrong (i.e. not the right) side of the road ....

[bill_bright]

Now that I work it out, your solution might work, StuartR - if the liar does answer by pointing to a direction. If he answers with "the same as today" then you would be out of luck.

Still looking for a lock tight answer - Like Timbo's.

[Ruff_Hi]

This all assumes that the liar always lies and the truth teller always tells the truth. What happens if we free up this constain by making the liar a 'logical' liar - that is, he can see through any cunning logical question and give such an answer such that you are left with a false-hood.

In this situation, there is no logical answer, so the best you can do is <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> ask the person who comes to the door if they knew that they were giving away free beer at the gas / petrol station? Then they either say yes or no - doesn't matter. After then close the door, you get back in the car and drive 1/8 mile back the way you have come, stop, get out of your car and watch which way the brothers go. Then you follow them. Now, this doesn't guarantee that you will get to the station, because the brother could see through your ruse. If that is the case, then at least you have a moral victory in that you have left that brother with the feeling that, while they have outsmarted you, they have missed out on free beer.</font color=yellow></span hi>

[AlanMiller]

Well think about this: <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>The liar must lie about everything. This includes lying about the hypothetical answer he/she would give to a hypothetical question. It's all just boolean algebra really.</font color=yellow></span hi>

Alan

[Jezza]

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> Bill, is this a variation of an old theme. Would you not ask this question to either brother, doesn't matter which:

" If I ask your brother, which was the right way to the petrol (gas) station, which way would he point to?"

Whatever way he points to, you will always take the opposite direction.

Reason, if you are speaking to the truthful one, he would point in the wrong direction because the liar would always lie. If you were talking to the liar, he would always state the opposite of the truth.</font color=yellow></span hi>

Jerry

[bill_bright]

Jerry - You got it - but I think StuartR might be on to something.