Truth City

Logic Level 1

You reach a fork in a road: one path leads to Truth City while the other leads to Lies City.

You encounter a man who you know is either from Truth City or Lies City. If he is from Truth City, he will tell the truth, and if he from Lies City, he will lie.

What question will make him point to Truth City?

"Which way is Truth City?" "Which way is Lies City?" "Which city is that way?" "Which way is your hometown?"

10 solutions

Terry Yu
May 3, 2017

Which way is your hometown because if he was born in lies city, he would point to truth city, and if he was born in truth city, he would point toward truth city.

Moderator note:

Technically speaking, a complete answer needs to indicate that the other choices don't work, as diagrammed below:

	Truthteller indicates:	Liar indicates:
Which way is Truth City?	Truth City	Liar City
Which way is Lies City?	Lies City	Truth City
Which city is that way?	Truth or Lies (depending)	Truth or Lies (depending)
Which way is your hometown?	Truth City	Truth City

The man that you meet is an UNKNOWN truth teller or an UNKNOWN liar. Therefore 3 questions will INDICATE 3 directions and one question will indicate 1 direction. This therefore leaves a nagging doubt as to which way Truth City really is. Too many other comments have the word IF in the answer.

Mark Rhodes - 4 years ago

You have to combine the answer you would get from either the person from Truth City or Lie City. You ask something like the following question, "If I were to ask someone who is from the city you are NOT from, 'Which path leads to Truth City?', what answer would THEY give me?"

This way, the answer will ALWAYS come out to be a lie. The answer will actually tell you which path leads to 'Lies City.' If the person you are talking to is from Truth City, then he would have to tell you the answer a person from 'Lies City' would give you. He would have to do this because he always tells the truth and he knows a person from Lies City, would lie.

If the person you are talking to is from 'Lies City', he would know a person from 'Truth City' would tell you the truth. He, on the other hand, would have to LIE about the answer. So, because the person from Truth City would give the true answer, the person from Lie City would have to lie and tell you the other answer...

So, you combine their answers and always get a lie...

Timothy Tolentino - 4 years ago

Nice explanation. This way we are guaranteed to know the way to Truth city.

Pranshu Gaba - 4 years ago

IF he was born in truth city, he would point toward truth city. Why would he tell the truth?

Waqas Khan - 4 years ago

Because he is born in truth city.

Terry Yu - 4 years ago

Plot twist: he is allowed to point to your city instead if he is a liar.

Cheng Wei Chang - 4 years ago

Wrong. If he is from Lies City he could point anywhere except there. That includes pointing back where you came from or up at the sky.

Anthony Cutler - 4 years ago

That is true, and I agree with you.

Diana Bradish - 1 year, 2 months ago

Abidur Rahman
May 15, 2017

If the person lies when asked "which way is your hometown?", then they must be from lie town, but as they lied about where they are from, they will point you towards truth town. If the person tells the truth, then they will point to truth town, thus "which way is your hometown" is the correct answer.

Good explanation for why "Which way is your hometown?" works. Why do other choices not work?

Pranshu Gaba - 4 years ago

First off, the questions says "point". Only answer four would cause the person to to "point". Also, having two choices does not solve the problem, especially when there are only two possibilities to begin with.

Brenda Gaines Hunter - 4 years ago

Thanks for explaining :)

Pranshu Gaba - 4 years ago

All of the other choices lead to two possible answers.

Brenda Gaines Hunter - 4 years ago

Programiranje Srbija
May 15, 2017

Answer is: Witch way is your hometown?

Reason: If he is from Truth city will point to Truth city because he doesn't lie. Also if he is from Lies city he will point to truth city because he lies and will not point to Lies city. So either way he will point to Truth city.

you still don't know if he lies or not so that doesn't force a correct answer

Patrick Rosborough - 4 years ago

Does it matter if he lies or not? In either case, he is pointing to the Truth City.

Pranshu Gaba - 4 years ago

The assumption seems to be that his hometown, where he was born, is the city he is currently "from." Not necessarily true. There is really not enough information given, not to mention if it is a one-time question/answer. Not a good logic question. BTW, the logical "safe" answer is your "correct" one, but I submit the provided information does not necessarily lead to that response.

Joseph Bogo - 4 years ago

The main quis have indicate to four quies.

Dinesh Dahal - 4 years ago

The qtion is right.

Dinesh Dahal - 4 years ago

@Programiranje Srbija - It's which not witch

Terry Yu - 4 years ago

Ishwar Karthik
May 15, 2017

If he is from Lies city, he'll lie and say Truth city, and if he is from Truth city, he will tell the truth and say he's from Truth city.

Nicely explained. What question could we ask them if we want them to point to the Lies City instead of Truth City?

Pranshu Gaba - 4 years ago

A Former Brilliant Member
May 15, 2017

"Which way is your hometown?" since the problem now is only if the man was a liar the negation of the question will always lead to the truth city

The correct answer is: If I were to ask you if this were the way to Truth City, would you tell me 'yes'?

Ralph Harnden - 4 years ago

Yes, your question definitely works. Both the truth teller and the liar would give the same response to this question. The truth teller would simply tell the truth, but the liar would have to tell the double negation of the truth, which is the truth.

"Which way is your hometown?" also works. "If I were to ask you if this were the way to Lies City, would you tell me 'yes'" also works. There are might exist other ways of finding out the way to Truth City too.

Pranshu Gaba - 4 years ago

@Ralph Harnden - If you pointed toward truth city, and the guy is from lies city, then he would lie and say no. Then you would go the other way and get to the wrong place.

Terry Yu - 4 years ago

Hi there, perhaps you misunderstood my answer; I am quite sure it is correct.

I ask the liar this: "If I were to ask you if this were the way to Truth City, would you tell me 'yes'?"

If I point to Truth City and simply asked him if that were the way to Truth City, he would have to lie and say 'no'. However, I did not ask that question. I asked how he would respond if I asked that question, so he would have to lie, saying he would NOT say that was not the way to Truth City -- in other words, he would have to say 'yes'.

If instead I point to Lies City and simply asked him if that were the way to Truth City, he would have to lie and say 'yes'. However, I did not ask that question. I asked how he would respond if I asked that question, so he would have to lie, saying he would say that he would NOT say that was the way to Truth City -- in other words, he would have to say 'no'.

This is a classic logic riddle I first encountered as an undergraduate math major almost 45 years ago, and I still remember the answer! ;^)

Ralph Harnden - 4 years ago

Ragini Jain
May 30, 2017

Coz if he was really from truth city he would have pointed towards the truth city and if from lies city then also to the truth city as he lived in the lies city😊

Xylene resha Terminio
May 19, 2017

Thats because a truthteller and a liar can both make this sentence: I come from Truth City and it is this way. The truthteller will tell the truth and he will point , Truth City is this way , while the liar will say , Truth City is that way.A more further explanation is: The truthteller will tell the truth and agrees with his nature that Truth City is that way. The liar will tell a lie and agrees with his nature that Truth City is this way.Also, if you ask the truthteller, Which way is Truth City, its same thing as asking which way is your hometown. But, if you ask the liar, Which way is Truth City, he will lie and who knows: you might believe him and you might think its the same thing as asking which way is your hometown.Thus, which way is your hometown is the correct answer:).

Yes, this is the only question in the choices to which both persons give the same response, so we don't have to care whether we asked the liar or the truth teller.

Pranshu Gaba - 4 years ago

Lee-Ann Conlan
May 18, 2017

The trick here is to go through each situation.. since you cannot tell whether the person is a liar or not.. you can be sure of one thing.. that if he is from truth city he will tell the truth but if he is from lies city he will lie.. with this knowledge you need to assume the person could be a liar. In each scenario the truth teller will point you in the right direction.. but since one cannot be certain if he is a truth teller we hav to assume he could be lying.. assess and compare each answer a liar and truth teller will give you..

which way to truth city.. both outcomes produce different answers.
Which way to lies city.. both outcomes produce different answers.
Which city is that.. both outcomes produce different answers.
Which is your home town.. both outcomes will produce the same answer..

So no. 4 is the answer and the correct question to ask.. If he is from lies city he will lie an say truth city.. if he is from truth city he will tell the truth an say truth city.

Great! In questions 1. 2. 3. both persons give different responses, and since we don't know who is lying and who is telling the truth, it does not give us any helpful information

Pranshu Gaba - 4 years ago

Brenda Gaines Hunter
May 18, 2017

I will commit to the fourth question because the fourth question is the only one that will lead both the liar and the truth teller to point to the same city.

Yup, this is the only question to which the liar and truth teller give the same response.

Pranshu Gaba - 4 years ago

Amartya Harsh Singh
May 16, 2017

A different approach- treat the truth and lie tellers as functions- say that the truthful person is $f(x)=x$ , and the liar is $g(x)=-x$ . The problem essentially asks us to find x such that $f(x)=g(x)$ , forcing $x=0$ . This means that you are forcing your functions to point to the starting point of their domains, which translates to 'hometown' if you bring in the truth-lie claptrap.

While that is an interesting interpretation, it is unfortunately flawed. There is no correlation between "asking a question" and "representing it on the real number line".

It is possible to talk about functions f: { statements } -> {statements}. But it doesn't imply that $f(0)$ has a meaningful interpretation. At best, the conclusion is that "If you ask them no question, you will get the same answer, which is no answer".

Calvin Lin Staff - 4 years ago

You must be a math genius. :D

Parvesh A. Deosarran - 4 years ago

Truth City

10 solutions

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