Originally posted by JS357Edit: this means, also without waver town.
A clue, maybe:
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
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Originally posted by finnegana) Why do the waverers switch from lying to telling the truth and vice versa mid question? There is only one question.
I may be missing it or I may hear what you are saying and think you are mistaken.
"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 Waverin ...[text shortened]... TruthTown, but now I have to tell a lie, so I will say I would have pointed to WaveringTown.
b) The liar could have pointed to wavering town when asked the way to truth town, so if he points to wavering town now, he is telling the truth.
Originally posted by finneganVery close I think, But not quite because of the same reason my solution fails.
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 ...[text shortened]... n the requested form of pointing at roads. I have edited the question accordingly. )[/b]
A liar could say 'sure, that way' and point to liar town. This is as much of a lie as pointing out two incorrect paths.
sorry
still thinking on this occasionally... maybe 2 questions?... I'd like to solve it with 1.
-jenn
Originally posted by Jenn1482I don't have a huge stake in this one but I was trying to find a better version of the one by iamatiger. I think it ought to be wrong but I did not want to dismiss that suggestion without giving it a fair crack.
Very close I think, But not quite because of the same reason my solution fails.
A liar could say 'sure, that way' and point to liar town. This is as much of a lie as pointing out two incorrect paths.
sorry
still thinking on this occasionally... maybe 2 questions?... I'd like to solve it with 1.
-jenn
My one earlier is correct in my opinion after a lot of thinking. In the worst scenario it does require 5 questions (with a clever liar) but at least I am confident I have tested all the risks and survived them. So the challenge is to find an equally robust solution with fewer questions and I feel that so far the proposals are not convincing.
Trouble is this has taken up an awful lot of good chess time! 🙁
Originally posted by JS357Riddle #3 has two paths and two speakers, Truth and Lie. This puzzle has four possibilities (Truth, Lie, Truth-then-Lie, Lie-Then Truth) and three destinations. I see no logical reason why we should discover one single question that distinguishes those variables. Nice if we can but I doubt it.
A clue, maybe:
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
Originally posted by finneganA venn diagram would be a good way to look at this.
. I see no logical reason why we should discover one single question that distinguishes those variables.
Our question(s) would determine the subsets of answers until we have the correct (sought after) combation.
So atleast 3 questions may be required to be certain. . . .Something just came to me this instant: we could reduce the quesions required to two iff we can word our question to group the two incorrect answers together (in a form to have 1 right way and 2 wrong ways). Hmm, it seems THAT would require us knowing the aspect of the speaker, which would require 1 more question. Doh!
1. e4
-Jenn
Originally posted by JS357I am still intrigued by the other approaches, but am responding to finagen's suggestion to see if 5 questions are the most needed. So OK let's try for at most four questions:
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?
1. Does 1 equal 1?
2. Does 1 equal 1?
Now you know, based on the answers, whether you have T-man (yes, yes), L-man (no, no), W-man set to lie to your next question (no, yes), or W-man set to truth next (yes, no).
Question 3 for T-man or W-Man set to truth next:
3. Which way is to T-Ville? (answers with truth)
Go the way indicated.
Question 3 and 4 for W-man set to lie next:
3. Does 1 equal 1? (answers no)
4. Which way is to T-ville? (answers with truth)
Go the way indicated.
Question 3 and 4 for L-man:
3. Which is the way to T-ville? (answers with lie)
4. Of the two ways you did not indicate, which is the way to T-ville? (answers with lie)
Go the way NOT indicated.
This is a little clumsy and it may be possible to customize a question 3 for whichever villager you have, that eliminates the need for question 4. But it's on the track that has been discussed, of winnowing down the questions.
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This is still the right answer:
"If, instead of asking you this question, I had asked you which way it was to truth town, which way could you have pointed?"
Read it very carefully
A lying waverer thinks: "I would have lied and, could have pointed to one of the non-true towns", so he lies about what he would have done, and points to truth town.
A Truthful waverer thinks "I would have pointed to truth town", so he points to truth town.
The liar works like the lying waverer, and the truth teller works like the true waverer, so they all point to truth town.
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Originally posted by JS357The dissenters amongs us might claim the liar could say "He won't point anywhere, if you ask him, he is deaf!" or something.
A clue, maybe:
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
Originally posted by iamatigerAll things considered, I have to agree...until someone disproves it. But I haven't been able to do that. It seems to have all of the elements of secondary hypotheticality needed to drive the villager no matter which he is, to speak what is actually true. Congrads!
This is still the right answer:
[b]"If, instead of asking you this question, I had asked you which way it was to truth town, which way could you have pointed?"
Read it very carefully
A lying waverer thinks: "I would have lied and, could have pointed to one of the non-true towns", so he lies about what he would have done, and points to truth to ...[text shortened]... averer, and the truth teller works like the true waverer, so they all point to truth town.[/b]
As far as I can tell, from my internet research, my creation of this riddle is its first instance {buffs fingernails}. At least, I have no other source. But there was a lot of time before there was an internet, when people were making up riddles. I did not have much of a clue to the right answer when I thought it up, except that the minimal answer would probably begin with "If I ...".
Originally posted by JS357I find aspects of this solution inelegant.
I am still intrigued by the other approaches, but am responding to finagen's suggestion to see if 5 questions are the most needed. So OK let's try for at most four questions:
1. Does 1 equal 1?
2. Does 1 equal 1?
Now you know, based on the answers, whether you have T-man (yes, yes), L-man (no, no), W-man set to lie to your next question (no, yes), or W- ...[text shortened]... r question 4. But it's on the track that has been discussed, of winnowing down the questions.
1. Are there no truthful ways to say that 1 is not equal to 1? 1 bunch of bananas is not equal to 1 flock of birds for instance. This 1 on the left is not that 1 on the right so in some essential sense they are not equal as each is uniquely itself. I know you could remove that extreme scepticism by defining your terms even more precisely but I think you might have to.
2. If you can test for lies by repeating an unambiguous question to which you know the answer (instead of 1=1?) then it does seem you get the solution in four questions at most. But can the villager refuse to respond after answering once? e.g. "you have already asked that question - if you want you may ask another question but this is not another question." We already know that the villager can refuse to respond to questions on the grounds there are too many so we know they are truculent yokels.
3. If my solution was also able to settle things finally with four questions, then I would prefer mine to yours on the aesthetic ground that it does not step outside the story (so to speak). I have battered my brains to achieve that without success but using your venn diagram concept, I wonder if there is a solution. I already know that the order in which the questions are asked has a big effect and there are a fair few permutations available. It is easier to analyse with a table instead of just prose by the way but we can't do that here. My account looks far more complicated as set out than in a table, with squiggles and lines to join things up.
Originally posted by iamatigerNo.
This is still the right answer:
[b]"If, instead of asking you this question, I had asked you which way it was to truth town, which way could you have pointed?"
Read it very carefully
A lying waverer thinks: "I would have lied and, could have pointed to one of the non-true towns", so he lies about what he would have done, and points to truth to ...[text shortened]... averer, and the truth teller works like the true waverer, so they all point to truth town.[/b]
A liar MIGHT think that way but does not have to.
A liar could think: "I would have lied and would have pointed to one of the non-true towns", so he lies about what he would have done, and points to the other one, also non-true.
Your argument is that, because he would have lied and wishes to lie about what he would have done, he would certainly say he would have told the truth. But that is not equivalent to saying he would point at Truthtown. He has at least two lies available, not one.
However maybe your question is designed to mean that the liar could have pointed to one of two roads, both non-true, so a truthful answer this time would be to point at both non-true roads again, and the only way to lie is to point at the remaining road which is true. However I do not think that is the only way to lie. For example he could point to two roads, one of which is true and one false, or point to one false road, which is not identical to two false roads, so again lies about what the earlier answer could have been. Because there are several ways to lie, you cannot infer what you wish from this one answer.
A waverer is more complicated but your agument has already failed on the liar.
MAY BE you could work on an alternative version based on:
"I wish to avoid taking the wrong road to TruthTown - please point out to me the wrong roads." [then build in your formula "If, instead of.... "
I don't think it will work out though for the same reasons.
Originally posted by finneganI am seeing a difference between iam's "could" and your "would". L thinks, "I could have pointed to either Lt or Wt. I know that is true. So I must lie about that, by not revealing either of the two towns I could have pointed to. So if I point to Tt, I will have fulfilled my duty to lie. It is not my duty to keep him from getting to Ttown."
No.
A liar MIGHT think that way but does not have to.
A liar could think: "I would have lied and would have pointed to one of the non-true towns", so he lies about what he would have done, and points to [b] the other one, also non-true.
Your argument is that, because he would have lied and wishes to lie about what he would have done, he wou ...[text shortened]... mula "If, instead of.... "
I don't think it will work out though for the same reasons.[/b]
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Originally posted by JS357Thanks Js, yes, the could is important (and is partly why I needed several edits the first time I posted this answer). If the liar thinks "I would have pointed to the lying town", so he points ot the wavering town, he is telling the truth, because he could have pointed to that wavering town if he had liked. The only town he couldn't point to is the true town, so he points there, see?
I am seeing a difference between iam's "could" and your "would". L thinks, "I could have pointed to either Lt or Wt. I know that is true. So I must lie about that, by not revealing either of the two towns I could have pointed to. So if I point to Tt, I will have fulfilled my duty to lie. It is not my duty to keep him from getting to Ttown."