Okay, I think the general problem requires 2 questions. Here would be my revised solution.
You ask "If I were to ask 'what is an example of one path that does not lead to truth town?', what would be one path that you might point out to me?"
The truth teller points either to liar town or to waverer town.
The waverer (true) points either to liar town or to waverer town.
The waverer (false) points either to liar town or to waverer town.
The liar points either to liar town or to waverer town.
Note that in each case, the path to truth town is one of the remaining two paths not specified.
You ask "If I were to ask 'of the two paths you did not just specify, which leads to truth town?' which path would you point out to me?"
The truth teller will point to truth town.
The waverer (initially true, now false) will point to truth town.
The waverer (initially false, now true) will point to truth town.
The liar will point to truth town.
So go in the direction specified in response to the 2nd question.
Originally posted by LemonJelloActually on second thought I think this fails according to a counter that is similar to one I already gave out. I need at least to be consistent.
Okay, I think the general problem requires 2 questions. Here would be my revised solution.
You ask "If I were to ask 'what is an example of one path that does not lead to truth town?', what would be one path that you might point out to me?"
The truth teller points either to liar town or to waverer town.
The waverer (true) points either to liar tow ...[text shortened]... oint to truth town.
So go in the direction specified in response to the 2nd question.
So I revise again:
First question: "If I were to ask 'what is an example of one path that does not lead to truth town?', what would be one path that you might point out to me?"
Second question: "If I were to ask 'out of the two remaining paths that you did not just specify, what is an example of one path that leads to truth town?', which one path would you point out to me?"
Then go in the direction specified in response to the second question.
Originally posted by Jenn1482By the way, why would you say that you think the initial truth of the waverer is crucial? If the waverer is on a truth-telling moment, then he will function like your truth teller, which according to your analysis you claim will point to two villages. If, on the other hand, the waverer is on a falsehood-telling moment, then he will function like a liar, which according to your analysis you claim will point to only one village. Either way, it seems your strategy still follows (if he points to two, go the third way; if he points only to one, go that way).
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
But, regardless, I do not think your analysis of the liar is correct. You are assuming that in answering your particular question the liar cannot point in part to any roads X such that the statement "Road X leads to a village that contains persons who lie at least some of the time" is true. But that seems false to me. If the truthful answer to your question is the set {road to liar town, road to waverer town}, then why cannot the liar give you the set {road to liar town, road to truth town} or the set {road to waverer town, road to truth town}? These are both lies. The liar or waverer (false) should be able to point to two directions, one of which will be truth town.
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Originally posted by Jenn1482I like that one!
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
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Originally posted by LemonJelloGenerally, in these questions, the liars are not "cunning". They tell the maximum lie, which is the opposite of what would be a truthful answer. They do not give out information which is partially true (such as shrugging their shoulders and saying "everyone tells the truth round here" ).
By the way, why would you say that you think the initial truth of the waverer is crucial? If the waverer is on a truth-telling moment, then he will function like your truth teller, which according to your analysis you claim will point to two villages. If, on the other hand, the waverer is on a falsehood-telling moment, then he will function like a liar, or waverer (false) should be able to point to two directions, one of which will be truth town.
Ok interesting analysis of the solution. I still think mine posted is the right path (tee hee) logically to follow.
Q: Which of these villages contain liars?
Move: if the villager points one way, go that way. If he points two ways, go the other way.
The initial truth of the waver is not important. I realized this about 30 minutes after posting a while ago but decided against pointing it out, fell asleep knowing it actually works either way and didnt fail the solution. Thanks 🙂
But yea, if I say "which of these villages contain liars" the liar could point to any combination of two, and I could end up going to liar town. that would suck.
How to word this question to exclude the T village from the subset of false answers to the question? We need a questoin that the only way to lie is to point to the village of truth... This gets into maximum lies and such. Confounding the issue more than intended I'm sure. I'm thinking on this one and will repost.
-Jenn
EDIT: (+30min, as usual): could our solution be the simple question
"which of these roads is not the way to the village of truth?"...
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Originally posted by Jenn1482Given that one, the truth teller points to the true village, and the liar points to a lying village, so it doesn't help.
Ok interesting analysis of the solution. I still think mine posted is the right path (tee hee) logically to follow.
Q: Which of these villages contain liars?
Move: if the villager points one way, go that way. If he points two ways, go the other way.
The initial truth of the waver is not important. I realized this about 30 minutes after posti be the simple question
"which of these roads is not the way to the village of truth?"...
Let's go back to my suggestion:
"If, instead of asking you this question, I had asked you which way it was to truth town, which way could you have pointed?"
The liar and the lying waverer think "I could have pointed to either of the lying towns", so they point to the truth town.
The truth teller and the true waverer think "I could only have pointed to the true town", so they point to the true town.
Originally posted by sonhouseActually, it's not dependant on counting. It's dependant on the ability to add. That said, I think it must surely be a fairly safe assumption. Otherwise, we might also wonder if he speaks the same language as us.
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.
We may find we get there and ask, "What is 1 + 1" to which he answers "Ke?" ........ but then again, maybe he's lying!
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Originally posted by SmaugarooHe might say "Bal" or "Da". And be a sane vampire.
Otherwise, we might also wonder if he speaks the same language as us.
We may find we get there and ask, "What is 1 + 1" to which he answers "Ke?" ........ but then again, maybe he's lying!
*Waves at Raymond Smullyan*
Richard
I have worked hard to arrive at this answer.
a) There are 3 towns, T, L and W, but 4 categories of local:
T: always tells the truth
L: always tells a lie
W t/l : tells first a truth, then a lie
W l/t : tells first a lie, then a truth.
b) I need five questions as follows:
1. Where is WaverTown?
2. Are you from WaverTown?
3. Where is Liar Town?
4. Where is Truthtown?
5. Does this path lead to Truthtown? (see explanation below. for this one).
c) I have a table of all possible answers but set out answers here for each local in turn. Remember that we do not ever know which local is answering our questions and we will, in fact, only hear one answer to each question. Also the task is NOT to identify the local’s status, but to find the right path to TruthTown.
Also when I say they point to T, the questioner knows only that he is pointing to a path, not where the path really does go. Obviously it does go to the destination I mention, but we do not know this. If we did there would be no problem.
d) T: always tells the truth
Q1: must answer correctly.
Q2: must say NO
Q3: will give the right answer.
e) W t/l : tells first a truth, then a lie
Q1: must answer correctly (must say WaveringTown)
Q2: must say NO (deny that he is from Wavering Town: the best way I could find to force him into a clear lie and use the information)
Q3 will give the right answer.
f) W l/t : tells first a lie, then a truth.
Q1: must point falsely to L or to T
Q2: must answer YES (which is true, he is from W)
Q3: Must point falsely to W or T
g) L: always tells a lie
Q1: must point falsely to L or T
Q2: must answer YES
Q3: must point falsely to W or T.
h) Now if the answer to Q 2 is a NO we know that we must have correct answers to Q 1 (W) and Q 3 (L). So we therefore know the correct locations of two towns (W and L) and can see that Truthtown has to be the third and only remaining path. SOLVED
i) If the answer to Q2 is YES, then the answers to Q1 and Q3 must both be false.
j) If the answer to Q1 is the same as the answer to Q 3 (ie they point down the same path) then that can ONLY be the path to TruthTown. SOLVED
k) If the answers are different, then I do not see a logical solution without one more question.
l) Q4: Where is Truthtown?
W l/t will point correctly to T as this is his turn to be truthful.
L will point falsely to either L or W.
REMEMBER I do not know if he is a W or a L, only one or the other.
m) If the answers to Q 1, 3 and 4 are identical this can only mean he is pointing at T and we have solved the problem. (The local must be a W l/t by the way.)
n) If not, but the answer to Q4 matches Q1, then this must be pointing to Liartown. But we have two unknowns, T and W.
o) If not and Q4 matches Q3, then this must point to WaverTown. But we have two unknowns, T and L.
p) In each case, to decide which one is T, we have to ask a final question, knowing that the waverer will lie and the liar will lie. So that is easy.
q) Q5: Will this path - which of course is one of the two unkowns - lead to Truthtown?
If the lying local says "No", it does. Solved.
If "yes", it does not, so the other one does. Solved.
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Originally posted by iamatigerWhat was wrong with this, single question?
Let's go back to my suggestion:
"If, instead of asking you this question, I had asked you which way it was to truth town, which way could you have pointed?"
The liar and the lying waverer think "I could have pointed to either of the lying towns", so they point to the truth town.
The truth teller and the true waverer think "I could only have pointed to the true town", so they point to the true town.
Originally posted by iamatigerPart of your question is redundant.
What was wrong with this, single question?
"If, instead of asking you this question, I had asked you which way it was to truth town, which way could you have pointed?"
The liar and the lying waverer think "I could have pointed to either of the lying towns", so they point to the truth town.
The truth teller and the true waverer think "I could only have pointed to the true town", so they point to the true town.
"If, [ instead of asking you this question, ] I had asked you which way it was to truth town, which way could you have pointed?"
Is not different to "If I had asked you which way it was to truth town, which way could you have pointed?"
Is not different to asking "Which is the way to TruthTown".
So the liar and the lying waverer will both lie and point the way to another town, while the Truth teller and the truthful Waverer will point correctly. Now knowing if the person you adddress is lying or truthful means you cannot get a solution with this single question.
It is essential to know if each answer is true or false, and for that you need at least two questions. The one I discovered was my question two, as set out above. But even though I know that the Waverer has to be telling a lie in order to answer No, I do not know if the person speaking is a Waverer or a Truth Teller, who would also answer No. What I do know, however, is that the Truth Teller and the Waverer who answers No BOTH must have told the truth on the first and third questions.
THEN AGAIN, Maybe you would succeed if you required the local to point to all of the roads that lead to Truth Town, so that liars would be forced (by the rules of the game) to point to two roads, while the truthful locals would only point to one road. Then you would know where TruthTown is either from the single truthful answer or by inference from the two false answers (the two roads they point to being wrong, there is only one other road available which is the correct one).
THIS MIGHT BE RIGHT!
"I am told that two roads lead to TruthTown: would you please point me to any road or roads leading there."
True Answer - "I can only point to one road which is that one."
False answer - "Delighted to oblige ,my dear friend - they are that one and that one."
( BUT could the True answer be - "Sorry but there is only one road." This leaves a headache which is going to head down a slope to trouble. It needs more questions unless we can force an anambigous reply in the requested form of pointing at roads. I have edited the question accordingly. )
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You are missing how it works. I am not asking the person to point to truth town I am asking "where would you have pointed if I had asked...", this cancels out a liar because he knows he would have lied and pointed somewhere else, so he would be telling the truth if he points somewhere else now.
It like saying: "If there was another person here, with exactly the same inclination to lie or not as you have now, and I asked him to point to truth town, which way might he point?". The idea is to create a double negative with a single question in a way that does not flip the waverer.
Originally posted by iamatigerI may be missing it or I may hear what you are saying and think you are mistaken.
You are missing how it works. I am not asking the person to point to truth town I am asking "where would you have pointed if I had asked...", this cancels out a liar because he knows he would have lied and pointed somewhere else, so he would be telling the truth if he points somewhere else now.
It like saying: "If there was another person here, with ...[text shortened]... create a double negative with a single question in a way that does not flip the waverer.
"If [ x ] what would you have said?" invites a lie in response but which lie?
You say if [I had asked you to point at TruthTown] where would you have pointed?
Now if [ I had asked you to point to TruthTown] then [ you would have pointed to either LieTown or WaveringTown BUT NOT BOTH].
To push this to extremes:
LIAR: If you had asked me to point to TruthTown I would have pointed to Wavering Town, but I want to lie in response to that clever question, so I will say I would have pointed to LieTown.
1st WAVERER: If you had asked me to point to TruthTown I would have lied and pointed to Wavering Town, but now I have to tell the truth, so I will say I would have pointed to WaveringTown.
2nd Waverer: If you had asked me to point to TruthTown I would have been truthful and pointed to TruthTown, but now I have to tell a lie, so I will say I would have pointed to WaveringTown.
Originally posted by JS357A clue, maybe:
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 ...[text shortened]... l the answer by the time that minimum is reached, too bad for you. What question(s) do you ask?
Without the waverer, this is the solution:
Ask, "If I asked the _other_ guard, which door would he indicate
leads to truth town?" Take the door _opposite_ to what's indicated!
Regardless of whom you ask, they'll point to the wrong door.
This is based on riddle #3 at:
http://www.calpoly.edu/~mcarlton/riddles.html