# On the road to Truth

JS357
Posers and Puzzles 29 May '11 22:12
1. 29 May '11 22:12
You are on a road and reach a three-way fork. One way leads to the village of Truth, where everyone always tells the truth, which is where you want to go. The second way leads to the village of Falsehood, where everyone always lies, and the third way leads to the village of Wavering, where everyone tells a truth, and then tells a lie, then tells a truth, then tells a lie, and so on. A man from one of the villages is waiting for you at the fork. You don't know which village he is from. You know he will answer only the minimum number of questions that are necessary to reveal the correct way to go, and if your questions do not reveal the answer by the time that minimum is reached, too bad for you. What question(s) do you ask?
2. 30 May '11 12:13
what is 1+1, twice.
3. 30 May '11 17:04
Originally posted by Banana King
what is 1+1, twice.
The man's answers will be either 2, 2, 2, 3 (say), 3, 2, or 3, 3. So now you have asked two questions to find out whether his next sequential answers will be truthful.

Can you find out that information using one question? Can that question be framed to discover which way to go, or at least to narrow it down?

Don't forget you have to ask the fewest needed questions.
4. 01 Jun '11 00:47
so all you have to do is discover if he is a liar, truther or wanderer?
5. AThousandYoung
01 Jun '11 09:17
6. sonhouse
Fast and Curious
01 Jun '11 22:27
Originally posted by JS357
The man's answers will be either 2, 2, 2, 3 (say), 3, 2, or 3, 3. So now you have asked two questions to find out whether his next sequential answers will be truthful.

Can you find out that information using one question? Can that question be framed to discover which way to go, or at least to narrow it down?

Don't forget you have to ask the fewest needed questions.
That whole line of logic about asking what is 1 and 1 is predicated on the idea he knows how to count. He could just guess, 1+1 is 34 just as easily. Of course that might not matter, if he gives an answer he THINKS is correct.
7. 02 Jun '11 15:014 edits
Originally posted by JS357
You are on a road and reach a three-way fork. One way leads to the village of Truth, where everyone always tells the truth, which is where you want to go. The second way leads to the village of Falsehood, where everyone always lies, and the third way leads to the village of Wavering, where everyone tells a truth, and then tells a lie, then tells a truth, then l the answer by the time that minimum is reached, too bad for you. What question(s) do you ask?
(assuming the waverer tells the truth first since that is what you stated)

You just point down a path and ask if is the way to the truth village.

if it isn't the liar will say yes the truther and the waverer will say no. (opposite if it is)

You point down the next path and ask if it is the way to the truth village.

If it isn't this time the liar will say yes, the truther will say no and the waverer will say yes. (once again if it is then opposite answers)

You point down the third path and ask if it is the way to the truth village

if it isn't this time the truther will say no, the waverer will say no, and the liar will say yes. (opposite answers if it is)

I could list the answers and which way would be correct to go but it would take too much typing but you can figure out which way to go with this information.
8. 02 Jun '11 15:092 edits
EDIT: after tomtom's edit this post became irrelevant.
9. 06 Jun '11 07:39
Originally posted by tomtom232
(assuming the waverer tells the truth first since that is what you stated)

You just point down a path and ask if is the way to the truth village.

if it isn't the liar will say yes the truther and the waverer will say no. (opposite if it is)

You point down the next path and ask if it is the way to the truth village.

If it isn't this time the lia ...[text shortened]... t it would take too much typing but you can figure out which way to go with this information.
I don't think that this method will work because you'll have 2 Yes's and 1 No from the liar, 2 No's and 1 Yes from thruther and either one of the above from the waverer and you'll never know which is which.
With three questions there is an easier way which was suggested above (1+1). The third Q will determine the right path after who is who part is determined.
Yet for this question to be nontrivial the minimum # of questions should be 2. (1 question is not possible due to the existence of the waverer). But I don't have the answer to that
10. 15 Jun '11 20:154 edits
Originally posted by JS357
You are on a road and reach a three-way fork. One way leads to the village of Truth, where everyone always tells the truth, which is where you want to go. The second way leads to the village of Falsehood, where everyone always lies, and the third way leads to the village of Wavering, where everyone tells a truth, and then tells a lie, then tells a truth, then l the answer by the time that minimum is reached, too bad for you. What question(s) do you ask?
"If my third question is 'which path leads to truth town?', which way might you point?"
11. 16 Jun '11 20:07
Originally posted by iamatiger
"If my third question is 'which path leads to truth town?', which way might you point?"
Are you proposing that this one question will reveal the way to Truth town?
12. 16 Jun '11 21:446 edits
Originally posted by JS357
Are you proposing that this one question will reveal the way to Truth town?
Yes:
Liar thinks "I would point to lie or wavering", so he points to true town.
Truth sayer thinks "I would point to true town", so he points to true town.
Waverer (false) thinks "I would point to lie or wavering", so he points to true town.
Waverer (true) thinks "I would point to true town", so he points to true town.

The only problem is if he thinks "hmm, I would not point anywhere because it would be too many questions". If you rule it out because of that then I propose:

"If, instead of asking you this question, I had asked you which way it was to truth town, which way could you have pointed?"
13. 17 Jun '11 09:35
Originally posted by iamatiger
"If my third question is 'which path leads to truth town?', which way might you point?"
I like this suggestion, but I can see multiple counter-arguments against your analysis of both the liar and the waverer (false).

As far as I can tell (correct me if I am wrong), your analysis basically assumes that such a person would think of the following disjunction: "I might point to lie or I might point to wavering". Then, your analysis assumes that in order to lie to you here, he has to basically give you the negation of the disjunction which is "It is not the case that I might point to lie and it is not the case that I might point to wavering", which translates here to his pointing only to truth town.

I can think of at least 2 counters to this analysis:

(1) In order to lie to you, it is not necessary that they give you the full negation of the disjunction. The point is that these persons function as deceivers, and they can try to deceive you in multiple ways. One way is simply to withhold one part of the disjunction and thereby not give you the full truth. In this case "I might point to lie" does not give you the full truth, and neither does "I might point to wavering". Both can be deceptive, just as "I might point to truth town" is deceptive. Then, under this construal, the liar or the waverer (false) can point to ANY of the towns in response to your question. (Or, else, it can be countered that your question presupposes only one way they might point, whereas there are multiple ways they might point.)

(2) The liar or waverer (false) would not think the above disjunction but rather would think the following conjunction: "I might point to lie and I might point to wavering". Then the negation of the conjunction is "It is not the case that I might point to lie or it is not the case that I might point to wavering". But, in this case, again in order to lie to you, it seems he can point to ANY of the towns in response to your question. (Or, else, it can be countered that your question presupposes only one way they might point, whereas there are multiple ways they might point.)
14. 18 Jun '11 08:36
Originally posted by JS357
the third way leads to the village of Wavering, where everyone tells a truth, and then tells a lie, then tells a truth, then tells a lie, and so on. What question(s) do you ask?
I think that only ONE question is required. Given the nature of truth/lie/truth/lie of the wayfarers of the 'wavering' town (the crucial point is the initial truth)

My question is: "Which of these roads leads to villages that contain liars?"

The truth teller and the waver guy will point to two villages.
Go the the other way.
The liar will only point to one.
Go that way.

-Jenn
15. 18 Jun '11 19:478 edits
Originally posted by Jenn1482
I think that only ONE question is required. Given the nature of truth/lie/truth/lie of the wayfarers of the 'wavering' town (the crucial point is the initial truth)

My question is: "Which of these roads leads to villages that contain liars?"

The truth teller and the waver guy will point to two villages.
Go the the other way.
The liar will only point to one.
Go that way.

-Jenn
I do not think the problem is actually supposed to read as though you know a waverer will always tell a truth on the initial question you pose (although I could be wrong about that). And, even if that were the way the initial problem is supposed to read, I do not think your proposed solution works. For example, the liar can just point to all 3 ways if he wants. After all, "All of them" constitutes a lie with regard to your question.

EDIT: Drat, my proposed solution I put here also fails.