harder fork in road puzzle

THE LOGIC PUZZLE

Upon your death you find yourself walking along a road in search of heaven. You come to a fork in the road and instinctively know that one road leads to heaven and the other leads to hell, but you do not know which is which.

At the fork are a devout truth teller (resident of heaven), a devout liar (resident of hell), and a resident of limbo who randomly tells the truth (sometimes he lies, sometimes he tells the truth, but with no regularity for either).

Although you know these characteristics of the individuals, you do not know who is which. You are allow two questions (non-compound type without 'and', 'or', 'but', etc.) and may direct these two questions to any individual (either both questions to one individual or one question to one individual and the other question to a different individual).

What two questions would you ask so that you would positively find heaven? NOTE: A question cannot be asked which will cause the respondent to reply 'I do not know'.

This is probably in the archive - I didn't check though.

Let's call the three guys A, B and C.

Firstly you need two questions because the first question could be asked to the random guy - and since we don't know which is which (of the three) we must use the first question to try to discover someone that is not the random guy.

FIRST QUESTION, addressed to A: 'Is B more likely to tell the truth than C?'

His response can only be Yes or No.

YES: IF A is the truth-teller, THEN B is random and C is the liar. IF A is the liar, THEN B is random and C is the truth-teller. IF A is random, THEN C must be a truth-teller or liar.

NO: IF A is the truth-teller, THEN B is the liar and C is random. IF A is the liar, THEN B is the truth-teller and C is random. IF A is random, THEN B must be a truth-teller or liar.

Thus, a YES would mean that C must always be either 'a truth-teller or liar' & a NO would mean that B must always be either 'a truth-teller or liar'.

We still don't know which oC or B may be, but we have now reduced the problem to how we usually find it; we know we have someone that either always lies or always tells the truth.

If he answered YES, address the second question to C. If he answered NO, address the second question to B.

SECOND QUESTION: 'If I were to ask you if the left fork leads to Heaven, would you say 'yes'?'

The response could be YES or NO, and we know the person either always lies or always tells the truth.

Thus we have four possibilities: Yes from a truth-teller No from a truth-teller Yes from a liar No from a liar

Response = YES: If a truth-teller were asked 'Is the left fork the path to Heaven' and it is the path to Heaven, he would say YES. Therefore, he would also say YES to our second question - because he tells the truth.

If a liar were asked 'Is the left fork the path to Heaven' and it is the path to Heaven, he would say NO. Therefore, he would lie about his answer to our second question, and say YES.

Either case, indicates that YES = Left Fork.

Response = NO: If a truth-teller were asked 'Is the left fork the path to Heaven' and it wasn't the correct path, he would say NO. Therefore, he would also say NO to our second question - because he tells the truth.

If a liar were asked 'Is the left fork the path to Heaven' and it wasn't the correct path, he would YES. Therefore, he would then lie about his response to answer our second question, and say NO.

Either case, indicates that NO = Right Fork.

Apologies to all for not using a spoiler space...

I have wondered before somewhat about a variation on this puzzle where you meet up with:

*Truth teller *Lie teller *Zealot

Now the zealot is (keeping with the tone of the original post) a resident of Earth. (And he is a zealot of whatever philosophy the reader of this post is opposed to...) Whatever the zealot believes is completely wrong. In other words, whatever he actually believes is true (or false), he will tell you is true (or false), but he is inaccurate in his assumptions.

As with the original puzzle, you know not which person is which.

Can this puzzle be solved with only one question? I have not tried to solve this at all, so it may be really easy or really impossible.

Thanks, Leroy Quet

This stumped me, so I cheated and Googled.
http://www.creativepuzzels.nl/spel/speel1/puzzel55- 2.htm

[spoiler space]

Without loss of generality, label the individuals A, B, and C.

1) Ask A 'Is B more likely than C to tell the truth?'

Suppose A answers 'yes'.

* If A is the truth-teller, then B is from limbo and C is the liar. * If A is the liar, then B is from limbo and C is the truth-teller. * If A is from limbo, then either B is the truth-teller and C is the liar, or B is the liar and C is the truth-teller.

* In any case, C is not from limbo.

If A answers 'no', then a similar analysis shows that B is not from limbo.

Either way, you now know someone who is not from limbo. Without loss of generality, label them X.

We have now reduced the puzzle to the classic fork-in-the-road puzzle, with one person who is either a truth-teller or a liar.

2) Ask X 'If I asked you whether the left fork goes to heaven, would you say yes?'

If the left fork goes to heaven, then both the truth-teller and the liar would answer 'yes'. If the right fork goes to heaven, then both the truth-teller and the liar would answer 'no'.

I believe the following question will work.

[spoiler space]

'If I asked you 'If I asked you 'If I asked you 'Is this the road to heaven?', would you say yes?', would you say yes?', would you say yes?'

An ambiguous spoiler:

V

V

V

V

V

This whole thing is ambiguous. Assume that the zealot at least knows that there is a truth teller, lie teller, and a zealot (but is completely wrong about who is whom). Then I think a question that can be asked is: 'What would the other person who is not the zealot say is the way to heaven?' The zealot thinks he is the truth-teller (of course....). He is wrong about who is the liar, so he thinks that the liar must be the zealot. And so he thinks that the truth teller is the liar. (Again, this is EXTREMELY ambiguous, and assumes a lot.) So, the puzzle is as it is traditionally if you were to ask the liar or the truther