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You are in the intersection of two roads, there is a troll in the beginning of each road.

One of them is liar (always lies), and one of them always tells the truth.

One of the roads, ends to your destination and one of them ends to death :) .

The trolls know which way is the right one and which one ends to death.

How can you find the way if you can ask only one question?

it's your choice who to ask from and you don't know who tells the truth and who lies.

klm123
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Alireza Fallah
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    A harder question involves each of them always lying or telling the truth, but you don't know whether it's one, both, or none that tells the truth. –  Jun 10 '14 at 14:00
  • that will be easy too, What would you tell me if I ask you whether this road ends to death? ( the exact answer of klm's) : the answer is always true. – Alireza Fallah Jun 11 '14 at 04:43
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    That's true; however, most people only know the "other guard" solution, and would be totally flummoxed by that formulation. –  Jun 11 '14 at 05:45

9 Answers9

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The idea is to ask question about question.
In that case Lie about Lie = Truth about Truth = Truth (if you ask person about question to himself)
or Lie about Truth = Truth about Lie = Lie (if you ask person about question to his antipode).
Therefore it won't be matter who you are asking.

An example of such a question is:

What would you tell me if I ask you whether this road ends to death?

If answer is "yes" you better do not take this road. If answer is "No" you should take this road.

Proof/explanation:

  1. If we ask a liar whether this road ends in death and the road ends in death, he must answer "No". Therefore to our question the liar must lie about his answer and say "Yes".
  2. If we ask a liar whether this road ends in death and the road doesn't end in death, he must answer "Yes". Therefore to our question the liar must lie about his answer and say "No".
  3. If we ask a truth-teller whether this road ends in death, then he must answer truthfully; he will answer the same truth to our question.
Andrew
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klm123
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  • yes, it's correct, but there is at least one more right answer – Alireza Fallah Jun 10 '14 at 11:51
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    @AlirezaFallah, there are millions of right answers:) But all should you the same idea. For example, you can ask "How your friend would answer if I ask him whether this road ends to death?". If you have different idea (without question about question) just make your own answer, it would be interesting to see. – klm123 Jun 10 '14 at 11:59
  • I've been looking for a way to formulate the problem so that you can't use "the other person" and would have to go with klm123's answer. I asked about it in this math.SE post. –  Jun 10 '14 at 13:55
  • How this will help if, I asked the question to person who always lies? – PM. Jun 11 '14 at 10:22
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    @PM., lie+lie = truth. Do you know the basic mechanics of such type of puzzles? The liar finds the correct answer and then answers the opposite. – klm123 Jun 11 '14 at 10:26
  • @PM., I added the detailed explanation. – klm123 Jun 11 '14 at 10:32
  • change ends to death to leads to my destination and yes is the road you want to take. It's fun to try to make the answers different too. – Justin Jun 12 '14 at 18:01
  • @Quincunx, I like it more my way. Why should troll know what my destination is. – klm123 Jun 12 '14 at 18:06
  • @Quincunx, yes, but in general my question is valid: Why should he know such a thing? I prefer to make answer more general and independent from small details of the formualtion. – klm123 Jun 12 '14 at 18:09
  • @Quincunx, why should I? – klm123 Jun 12 '14 at 18:12
  • @klm123 Sorry for causing a misunderstanding. Even from my first comment, I meant "changing it to like this changes the answers correspond with the right and wrong words." Just an observation, not telling you to do anything. – Justin Jun 12 '14 at 18:18
  • This answer has a defect in that the question asked is not a yes/no question. What would you do if the answer was "I would tell you that it's almost time for dinner."? We have learned that the troll you asked is the troll that always lies (If we assume that the answers are always on topic), but we have not learned anything about the roads. – Taemyr Nov 11 '14 at 08:23
  • @Taemyr, "Does this road end to death?" is yes/no question. Therefore my example question is also yes/no question I think. Anyway, this is small things, which anyone can change/improve if he likes and nothing is perfect:) – klm123 Nov 11 '14 at 08:53
  • @klm123 No "what would you tell me if..." is not a yes/no question. As the inner question is a yes/no question yes and no are the only potentially true answers. – Taemyr Nov 11 '14 at 09:12
  • Could a lying troll not answer "I don't know"? – Weckar E. Aug 24 '16 at 12:00
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    @WeckarE., no. It is common agreement, that in such puzzles the only possible answers are yes or no. Otherwise a puzzle would have no sence. – klm123 Aug 24 '16 at 12:05
  • @klm123 This puzzle in particular stipulates no such limitation, while many other similar ones on here do. Would it be too late to propose an edit to rectify this? – Weckar E. Aug 24 '16 at 12:06
  • @WeckarE. it really does. It's just doesn't state it explicitly. But you can always add your own answer, which considers any possibilities you want. – klm123 Aug 24 '16 at 13:28
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Here's a solution without meta-questions:

Ask the left troll: "Does the liar guard the destination?" Iff yes, go right.

Explanation:

1. The left troll says the truth and guards the deathtrap:
The correct answer is yes. The troll will answer yes.
2. The left troll lies and guards the deathtrap:
The correct answer is no. The troll will answer yes.
3. The left troll says the truth and guards the destination:
The correct answer is no. The troll will answer no.
4. The left troll lies and guards the destination:
The correct answer is yes. The troll will answer no.

Anon
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  • you still don't know which is which. if the liar is guarding the destination and you ask the liar you get "No" and if you ask the truth teller you get a "Yes", but you don't know who's the liar. – Marius Apr 08 '16 at 14:26
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    So what? Your goal is to find the correct road, not who's lying. This method finds the correct road. In fact, you can't actually simultaneously find out the correct road and who's lying with a single yes/no question, since the two possible answers you can receive aren't enough to distinguish between the four possible combinations of road and liar. – Anon Apr 08 '16 at 14:30
  • @Kate Gregory I did so. – Anon Apr 08 '16 at 19:04
2

Select a random road and...

Ask either one of the trolls:

Would the other troll point me on this road in order for me to live?

Expanation:

1. You chose the wrong road and asked the liar.
He would answer Yes. Because the truth teller would tell you "No" when asked if this is the right road.
2. You chose the wrong road and asked the truth teller.
He would answer Yes. Because the liar would say "No" when asked if this is the right road.
3. You chose the right road and asked the liar.
He would answer No. Because the truth teller would tell you "Yes" when asked if this is the right road.
4. You chose the right road and asked the truth teller.
He would answer No. Because the liar would say "No" when asked if this is the right road.

Conclusion:

The answer is Yes from either one of the trolls: take the other road.
The answer is No from either one of the trolls: take the road you selected.

Marius
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2

The open questions in the other answers create loopholes that can lead to the answer not being discernable. - We have little assurances about what the lying troll answers to "what would you tell me if...". The only thing we know is that the lying troll would not say "I would say yes" (if the truthfull answer to the containeed question was no) or "I would say no" (if the truthfull answer to the containeed question was no).

By explicitly making the question a yes or no question you can avoid this;

If I asked you, does this road lead to death, would you answer yes?
Taemyr
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1

Question I'd ask: "What would the other troll tell me is the road to my destination?"

Liar would tell me truth-teller would guide to death.
Truth teller would tell me liar would guide me to death.

I go the on the opposite road and reach my destination.

Gusto
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The Troll that speaks and says, "IF Truthful Troll I be, then go though east, and be thou free. " that is the liar in my opinion. Because IF he were the Truthful Troll, he would always be Truthful so he would respond with, "Truthful Troll I am", instead of "IF Truthful Troll I be."

izzie
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    You seem to be misunderstanding what lying means in the context of these logic puzzles. See also this meta post. It's perfectly valid for a truthful person to make a statement beginning with "If I'm truthful, ..." – Rand al'Thor Feb 15 '17 at 01:01
  • This is a cool puzzle to work with...it gets your mind ticking..We are dealing with 2 absolutes which we already have the answer for...1 is an absolute liar and 1 is an absolute truth teller...so there is no room for "IF" at this part of puzzle because each one "IS" an absolute that has already been established from the onset..so then you can eliminate the liar and go on to the next part..which can include the "IF" statement..."IF the troll you choose = Truthful Troll, then You be set free IF the troll you choose = Lying Troll, you will go to your death" – izzie Feb 15 '17 at 17:20
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"Which road would the other troll tell me to go to for this destination?"
Then take the opposite road.

mmking
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AwesomeGoddess22
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what is 2+2? Whichever one says 4 is the one that is telling the truth. the one that says fifty billion or something like that is lying.

Grandpa Brick
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    But then you've used up your question, and you still don't know which road is the right one. – f'' Apr 08 '16 at 04:11
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Why not just ask a general question you already know the answer to so you can determine if the guard you ask is telling truth or lies e.g "Am I human?"

Or would that be against the rules :)

Shane Hsu
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Jan Ottestad
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    How do you then find out the correct road after you've wasted your one and only question on determining which Troll is which? – Jaap Scherphuis Mar 31 '18 at 05:08