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janbb's avatar

Can you help me remember the solution to this riddle?

Asked by janbb (60949points) 1 month ago

It went something like this. You are in a new country where there are liars and truth tellers. How can you find out which a new person is with just asking them one question?

I know there is a solution that went something like. “What would you say if I asked you if you were a liar?” But I’m not sure that’s it exactly and if so, why does the answer prove whether the person is a liar or a truth teller.

The logic escapes me.

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15 Answers

filmfann's avatar

What would you say if I asked if you were a liar?

If they were a liar, they would say they would say they were a liar.
That, of course, would be a lie. They would have lied and said they told the truth.

HP's avatar

Here is the version I recall. There’s a land populated with missionaries, beggars and the king. The beggars always lie and the missionaries always tell the truth. The king summons 2 men before him, and asks the first man are you a beggar or a missionary. The man answers too softly for the king to hear. So the king asks the second man “what did the first man say? The second man replies
“the first man says he’s a missionary”. The king then asks the first man “is the second man telling the truth?” The first man says no. Which if either man is a missionary or a beggar?

Zissou's avatar

The key idea is that you ask one guy what the other guy would say if asked the relevant question. The question is one that both the liar and the truth-teller would answer the same way.

The version I know goes like this:

1. You are imprisoned in a cell with two unlocked doors and and two jailers.
2. One door leads to freedom, one door leads to death, you don’t know which is which.
3. One jailer always tells the truth, one always lies, you don’t know which is which.
4. You can ask only one question of only one jailer before opening a door. (If you do not open a door, you will remain in the cell for the rest of your life.)

If you want to leave the prison, what question should you ask before opening a door?
Solution: Ask either jailer, “If I ask the other jailer to point to the door that leads to freedom, which door would he point to?”

ragingloli's avatar

You grab a random person, kill them, and ask the other if the corpse is dead or alive.

HP's avatar

@ZissouYes that’s another version. The riddle’s the same. In mine there’s only one possible answer to the question “are you a missionary?” In yours the jailers are aware to begin with of the liar (if any) so the second question is unnecessary. Yours is more succinct.

Zissou's avatar

Addendum to my above response: and then you open the other door, not the one indicated.

HP's avatar

Yes! That’s implied. Yours begins with one man being a liar and the other truthful. In mine that stipulation is missing— thus the requirement for the second question.

gorillapaws's avatar

It reminded me of this.

Zaku's avatar

First, realize you are in a hell universe created in the imagination of a logician. They are thinking of people as if they were logical machines compelled to always do something, because this is a logic problem.

Try asking them about something that you and they both know the truthful answer to.

The truthful person will tell you the true answer.

According to the excessive logical story-problem writer, the liar will always lie about everything, so they’ll lie about something you know whether it is a lie, and reveal themselves.

“Are most cats usually born with four legs and a tail?”
Logic-problem-compelled liar: “No.”

But maybe even that is outside the bounds of whatever the typical problems are worded as.

HP's avatar

Here’s another one that requires a bit more thought. Three men are brought into a room and seated single file in chairs such that the man in the rear can see the heads of the 2 in front of him, the man in the middle can only see the head of the man in front of him, and the man in the front sees no one at all. The moderator informs the men that there are a total of 5 hats, 3 black and 2 white. He then places a hat on the head of each man. The 3 men are then quizzed on whether they can determine which color hat is on their own head. The man in the back looks at the 2 men in front of him and says I don’t know what color my hat is. The man in the middle hears this, looks at the man in front of him and says I don’t know what color my hat is. The man in the front who can see no one, hears the other 2 but declares I know what color my hat is. How does he know? What color is his hat and why?

Response moderated (Unhelpful)
Pandora's avatar

An honest person would admit to lying because we all tell white lies. Best way is to ask them what lies have they ever told. If they say none, you know they are a liar.

NovDel's avatar

@HP He’s wearing a black hat. The rearmost guy would only know what colour he himself was wearing if the two in front of him were both wearing white. He doesn’t know, so they obviously aren’t. The middle guy would then know that if the front guy is wearing white, then he himself must be wearing black. He doesn’t know, so the front guy must be wearing black.

HP's avatar

well done.

LostInParadise's avatar

That problem generalizes. For example, if there were ten people in a line with 9 white hats and 10 black hats, if none of the 9 people in the back know the color of their hat then the first person knows that their hat is black.

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