87 of 100: One Question

Probability Level 2

The road you are traveling on splits, with one fork heading to the City of Lies, and the other to the City of Truth, but you don't know which is which. You want to go to the City of Truth. A person who lives in one of the cities stands at the fork.

We know that

  • People who live in the City of Lies always lie.
  • People who live in the City of Truth always tell the truth.

What one question could you ask the person to determine which way to go?

Those darn liars!

Will the road to the right take me to the City of Truth? Which city do you live in? Which road do you take to go home? None of these questions would help you know which way to go

Janae Pritchett by Janae Pritchett

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12 solutions

  • The first question (Will the road to the right take me to the City of Truth?) is not going to help you. In case the City of Truth is to the right and the person standing there is from the City of Truth, he will say "yes". But if the person is from the City of Lies he will say "yes" also. You don't know where the person is coming from so you don't know if the answer is true or false.
  • The second question (Which city do you live in?) is not going to help you either. It doesn't matter where the person is coming from, they both will answer "the City of Truth". And then you still don't know in which direction the City of Truth will be.
  • The third question (Which road do you take to go home?) will help you. If the person is coming from the City of Truth, he will show you the road to the City of Truth. If the person is coming from the City of Lies, he will also show you the road to the City of Truth.
54 Helpful 1 Interesting 1 Brilliant 2 Confused

A very good solution which gives a CLEAR and PRECISE explanation! Thank you!

William Huang - 3 years, 9 months ago

The third question might help, provided he doesn't point down the road you were travelling on!

Jeff Capbell - 3 years, 9 months ago

Two things about this problem. First it doesn't state what the traveler's desired destination is. Given that number 3 is the official answer, it actually doesn't matter. Second, as @Jeff Capbell points out, the liar could point done the road you were just traveling on. This means that number 4 is actually the correct answer.

Sridev Humphreys - 3 years, 9 months ago

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Thank you @Sridev Humphreys. I got the answer right according to this site, by making restrictions on the answer set available. I find this an interesting area of study where we believe we are being logical, but in reality are conforming to unexpressed "norms". I suspect many people saw this possibility but somehow "knew" what the questioner was after. No matter how we justify this, it isn't pure logic.

Jeff Capbell - 3 years, 9 months ago

Thanks! About the first remark, it doesn't really matter where you, the traveller, want to go. With the answer on question 3 you know which road goes which direction. After that you can decide where you want to go. About the second remark, I thought of that but I also assumed that a lying person doesn't want to be revealed as one. He also can point right up in the sky or give an answer that doesn't make any sense like "peanutbutter". In both cases you know he's a liar.

Michel van den Heuvel - 3 years, 9 months ago

Nice explanation! I wanted to write one, but turns out you already wrote a perfect solution!

Hannah Park - 3 years, 9 months ago

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You never know what solution people like the best...maybe it's your's...

William Huang - 3 years, 9 months ago

In first point, if person is from city of lies then he will say "No" not "Yes" because if he says then he is telling the truth. btw nice explanation :-)

Divyanshu Bansal - 3 years, 9 months ago

I'm confused about the first question. Let's say the City of Truth is to the right. If the person is from the City of Truth, they will tell the truth and say the road on the right leads to the City of Truth. If the person is from the City of Lies, they will lie and say the road on the right does not lead to the City of Truth. This way you will have two conflicting answers and not know which way leads to the City of Truth.

I'm confused because you said the person from the City of Lies will say yes. However, this will mean the person from the City of Lies will be telling the truth and both answers agree.

Akaash Thao - 3 years, 9 months ago

But suppose he's a liar. He won't want you to find the City of Truth. None of the questions will work. There is only one question that does work. You should ask, "Which road will the other person tell me to take?" They will always say it's the one that leads to the City of Lies. Thus you should take the opposite road.

Sara Flint - 3 years, 9 months ago
Tri Nguyen
Aug 25, 2017

If the person is a truth teller, they will give you direction toward the City of Truth as it is their home.

If the person is a liar, they will also give you direction toward the City of Truth as it is NOT their home.

Either way, the person would point you toward the City of Truth.

17 Helpful 0 Interesting 1 Brilliant 0 Confused

almost about to write a solution exactly like yours

Chloe Davis - 3 years, 9 months ago

@Tri Nguyen , please make your solution more clear.

Thanks!

Micah Gadbois - 3 years, 9 months ago
Avik Das
Aug 25, 2017

The answer of both liers and truth tellers will be same.
TRUTH TELLERS WILL INDICATE THE WAY TO TRUTH CITY.
LIERS WILL INDICATE THE WAY TO TRUTH CITY ,as the actual way of their home is the either way. But as they tell lie, they will indicate the way of truth City.
Hence, I can know the way of truth City and can determine my way to go.


4 Helpful 0 Interesting 1 Brilliant 0 Confused

I think you meant to write "the other way" instead of "the either way". Might want to correct that?

Jubayer Matin - 3 years, 9 months ago

@Avik das, please correct "either" to other

Thanks!

Micah Gadbois - 3 years, 9 months ago
Jim Cutts
Aug 27, 2017

Could also ask: "If I asked you which road goes to the City of Truth, which road would you say?" People from either city would indicate the correct road. Then you could go to the City of Truth, instead of to Washington D.C.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Aug 26, 2017

for question-3....which road do you take to go home is the most valid.

cz.....the truth tellers will always say the truth.and the liers will always lie.so the liers will also show the city of truth.

and for the other 2 questions,if the liers lie you will not be able to find the right track.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Randy Marsh
Aug 25, 2017

The only lie I know, is that I lie.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Those that lie tell the truth of their fear.

Randy Marsh - 3 years, 9 months ago

But a solution is a comment;

By definition a comment is -

A verbal or written remark expressing an opinion or reaction. (Credit to Dictionary.com)

Thus everyone who posted a solution, their solution becomes automatically a comment, by reacting towards the problem and expressing their opinion on how to solve the dilemma.

Randy Marsh - 3 years, 9 months ago

I would seriously consider deleting this "solution", because this is a place for solutions, not comments. If you wish to comment, then I would comment on one of the solutions, not post it as a solution. No offence...

William Huang - 3 years, 9 months ago
Abby Titlow
May 26, 2020

Here is what will happen if you ask any of the questions: 1. Lets play out what could happen: 1. It is the right path and they tell the truth, saying "yes" 2. It is the right path and they lie, saying "no" 3. It is the wrong path and they tell the truth saying "no" 4. It is the wrong path and they lie saying "yes" This clearly doesn't get you anywhere because in some cases you get the answer "yes", and sometimes you get the answer "no". You want the answer yes or no from both sides because then you know where to go. 2. In this case it doesn't tell you anything because it has nothing to do with the paths. 3. The lier will point to the path to get to the City Of Truth, because he doesn't live there, and he is lying. If it is the person who tells the truth they will point to their home, the City Of Truth. Both of them will point to the correct path.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Moose Buckley
Sep 27, 2017

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0 Helpful 0 Interesting 0 Brilliant 0 Confused
Syrous Marivani
Aug 26, 2017

If you ask him the third question and he is staying in the city of Lies, then he will be lying and the road he mentions goes to city of Truth. If he lives in City of Truth, then he will be saying the truth and the road he mentions goes to city of truth. So by asking the third question you know the road to Truth and therefore the other road to goes to city of Lies also.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Chris Lee
Aug 26, 2017

The fastest way to solve a problem like this is to see what they would both say, so the first question, a liar would say the exact same of a truth-teller and therefore, this would be confusing. Question 2, either way, the answer is "The city of truth" Question 3, A liar would show you the path to the city of truth, and a truth teller would do the same.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Stefano Gallenda
Aug 26, 2017

Q: Which road do you take to go home?

A: The answer is always the road to go to the City of Truth.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nikita Mahilewets
Aug 25, 2017

There is a question

Both kind of people will answer the same

To find it

Just substitute liar and truth sayer to every question

So the question is how to take home

Both people will point to the Truth city

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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