# Riddle, old but good.

beetlebomb
Posers and Puzzles 28 Jun '10 19:10
1. 28 Jun '10 19:10
A man is on an island in which half the population always lie and the other half always tell the truth.
On his way to town he comes to a fork in the road and doesn't know which way to go.
How can this man word his question of which road to take so that whoever he asks, truth teller or liar will tell him the same right way to go?
2. forkedknight
Defend the Universe
28 Jun '10 21:103 edits
Which way would a liar tell me to go?

*edit* no nvm

It's actually
Which way would a liar say you would tell me to go?
3. wolfgang59
Mr. Wolf
28 Jun '10 22:39
Originally posted by beetlebomb
A man is on an island in which half the population always lie and the other half always tell the truth.
On his way to town he comes to a fork in the road and doesn't know which way to go.
How can this man word his question of which road to take so that whoever he asks, truth teller or liar will tell him the same right way to go?
Its not a riddle ... but a very old logic problem.

4. 18 Jul '10 01:32
The traveler could ask "If I asked someone from the other group which is the correct road to take, what would their answer be?"

A liar, knowing that the truth tellers always tell the truth, would lie, and name the wrong road.

A truth teller, knowing that the liars always lie, would 'truthfully' tell the lie that the liars would say...again, naming the wrong road.

In either case, the traveler would know he had been misdirected and would take the OPPOSITE road from the road that either a liar or truth teller would name....which would put him on the right road.

One slight variation I heard on this problem involved two brothers who lived by the fork. One brother always lies, the other is always truthful. So the question asked would be "if I asked your brother which road leads to my destination, what would his answer be?". And then, of course, the traveler would take the OTHER road.
5. wolfgang59
Mr. Wolf
18 Jul '10 10:55
Originally posted by TheBloop
The traveler could ask "If I asked someone from the other group which is the correct road to take, what would their answer be?"

A liar, knowing that the truth tellers always tell the truth, would lie, and name the wrong road.

A truth teller, knowing that the liars always lie, would 'truthfully' tell the lie that the liars would say...again, naming the ...[text shortened]... hat would his answer be?". And then, of course, the traveler would take the OTHER road.
This doesnt work.

You have demonstrated what the truth-teller would say.
The liar using the same logic as yourself would also know what the truth-teller would say and therefore say the opposite.
6. 18 Jul '10 11:361 edit
Originally posted by beetlebomb
A man is on an island in which half the population always lie and the other half always tell the truth.
On his way to town he comes to a fork in the road and doesn't know which way to go.
How can this man word his question of which road to take so that whoever he asks, truth teller or liar will tell him the same right way to go?
This problem is more advanced than we might think at first.

The liar lies because he doesn't give the correct information to the man. If he knew that his proper lie would be interpreted in such a way that the correct information would be delivered, he wouldn't lie, would he? If anyone knew he always was lying, he is not interested to lie anymore. He would say something that sounded as a lie, that everyone would take as a lie, and furthermore act upon it in a way as if anyone would believe was a lie.

If I ask a man who is known to always lie, and he kows himself his reputation as a constant liar, the question "Do you speak the truth now?" Then the answer "Yes" wouldn't be trustworthy, and therefore to lie would be pointless.
But if he flipped a coin behind his back and answer accordingly the outcome of the coin, then the answer, a "Yes!" or a "No!" would be without any information, whatsoever.

If a lie means an answer that we can trust that it is a lie, it is not really a lie, is it? It gives reliable information.
But if the answer couldn't be trusted upon if it really is a lie or the truth, then we cannot trust it at all, can we?
So a real liar would give an answer that really is desinformation, to really make the one asking to act in a wrong way, then he would tell the truth if he knew himself that the answer would send the man who asks in the wrong direction.

So a good liar should always give an answer that makes the most harm. A chronic liar isn't a good liar if you can rely that he lies everytime.
So what kind of a liar would we have here? A good liar that we can never rely upon, or a chronic liar that we always can trust that he gives a false answer?

...assuming, of course, that we only asks question that can produce a 'yes' or a 'no'.
A liar that produces any kind of answer, we call a politician.
7. 18 Jul '10 16:52
Originally posted by wolfgang59
This doesnt work.

You have demonstrated what the truth-teller would say.
The liar using the same logic as yourself would also know what the truth-teller would say and therefore say the opposite.
No, I think that method should work... when I say "from the other group", I mean that a truther would refer to what a liar would say, and a liar would refer to what a truther would say.

Not knowing if I'm speaking to a truther or a liar, and asking the person "If I asked someone from the other group which is the correct road to take, what would their answer be?" should work, because:

1) The truther would know that the liars always lie, and so would truthfully tell the lie... in which case, the truther would name the wrong road.

2) The liar, knowing that truthers always tell the truth, would again lie... knowing that a truther would name the correct road, the liar would answer the question by naming the wrong road.

So in either case, the key here is to take the OPPOSITE road from the road that either side directed me to.
8. 18 Jul '10 17:26
Originally posted by TheBloop
No, I think that method should work... when I say "from the other group", I mean that a truther would refer to what a liar would say, and a liar would refer to what a truther would say.

Not knowing if I'm speaking to a truther or a liar, and asking the person "If I asked someone from the other group which is the correct road to take, what would their an ...[text shortened]... e, the key here is to take the OPPOSITE road from the road that either side directed me to.
....unless the liar wants you to take the wrong route. Then he gives you the correct information and thus fooling you to go the wrong direction.
9. wolfgang59
Mr. Wolf
19 Jul '10 11:54
Originally posted by TheBloop
No, I think that method should work... when I say "from the other group", I mean that a truther would refer to what a liar would say, and a liar would refer to what a truther would say.

Not knowing if I'm speaking to a truther or a liar, and asking the person "If I asked someone from the other group which is the correct road to take, what would their an ...[text shortened]... e, the key here is to take the OPPOSITE road from the road that either side directed me to.
But using this argument the liar tells you what the truth-teller tells you ... he doesnt lie!
10. 19 Jul '10 11:57
i think that the liar knows the answer to the question u ask him but doesnt tell u the rite 1. hes not smart enough to figure out a method to trick u.
11. 22 Jul '10 02:19
Originally posted by FabianFnas
....unless the liar wants you to take the wrong route. Then he gives you the correct information and thus fooling you to go the wrong direction.
The liar always lies. And since my question is "if I asked a person from the other group (i.e. a truther) which is the right road to take, what would his answer be?".

The liar knows that the truthers always tell the truth. If a truther was asked which road to take, he would name the correct road. The liar knows this, and therefore the liar names the wrong road.

The wrong road would be named regardless of whether you asked a truther or a liar...the key then, is to take the OTHER road from the one that either person directed you to take...which will put you on the correct road.

But the problem has nothing to do with whether the liar wants me to take the wrong route. The liar always lies, and the truthers always tell the truth. Therefore, my question would work no matter who you asked, as long as I then proceeded to take the opposite road than the one indicated (because both truthers and liars would each direct me to the incorrect road).
12. 22 Jul '10 02:23
Originally posted by wolfgang59
But using this argument the liar tells you what the truth-teller tells you ... he doesnt lie!
Yes, the liar does lie...because he always lies. A liar will not tell me what a truther will tell me.

Remember, I'm asking the person "if I asked someone in the OTHER group (i.e. if I'm talking to a truther, I'm asking which road a liar would recommend, and if I'm taking to a liar, I'm asking which road a truther would recommend).

The liar knows that the truther always tells the truth, and would name the correct road. Knowing this, the liar then names the wrong road, because he's lying (as he always does).
13. 22 Jul '10 05:29
Originally posted by TheBloop
The liar always lies. And since my question is "if I asked a person from the other group (i.e. a truther) which is the right road to take, what would his answer be?".

The liar knows that the truthers always tell the truth. If a truther was asked which road to take, he would name the correct road. The liar knows this, and therefore the liar names the w ...[text shortened]... he one indicated (because both truthers and liars would each direct me to the incorrect road).
Yes I know. The standard problem is that the liar always lies. My point he is not a good liar.

A good liar is anyone whose answsers you cannot ever trust. Where a 'yes' sometimes means yes and sometimes no, and you cannot ever know when. He lies at a erratic unforeseeable way. The only thing you know about this liar is that he maximize the harm done by his lies.

I understand the original problem. I just take this problem to an higher level.
14. forkedknight
Defend the Universe
22 Jul '10 14:49
Originally posted by FabianFnas
Yes I know. The standard problem is that the liar always lies. My point he is not a good liar.

A good liar is anyone whose answsers you cannot ever trust. Where a 'yes' sometimes means yes and sometimes no, and you cannot ever know when. He lies at a erratic unforeseeable way. The only thing you know about this liar is that he maximize the harm done by his lies.

I understand the original problem. I just take this problem to an higher level.
And I think that you fully understand that makes it no longer a logic problem, nor solvable.
15. 09 Aug '10 14:18
Originally posted by beetlebomb
A man is on an island in which half the population always lie and the other half always tell the truth.
On his way to town he comes to a fork in the road and doesn't know which way to go.
How can this man word his question of which road to take so that whoever he asks, truth teller or liar will tell him the same right way to go?
http://xkcd.com/246/

HTH; HANPuzzle.

Richard