Prisoner standing next to 2 doors and 2 guards

[EternityMech]

This is really old but some of you might not know it, if you heard it before dont answer.

Prisoner is put in a room with 2 doors. 1 door leads to freedom, the other to excecution.
Next to the doors are 2 guards. One of the guards always lies, the other always tells the truth. The prisoner is allowed to ask one of the guards one question to figure out what door leads where. What does he ask?

[Vectus]

I've heard this before but I've never seen the solution or worked out the answer. At first glance, it seems to be unsolvable, as you need two pieces of information. You must determine which door is the one that leads to freedom and which guard is which, but either guard you ask has a 50% chance to be either:

If you ask, "Are you the liar?" the liar would say no, truth teller would say no, and you've gotten nowhere.

If you ask, "Which door leads to freedom?" the liar would point to execution, the truth-teller would point to freedom, and you've gotten nowhere.


What's interesting is that nearly every question you ask to either guard about the doors will have opposite answers, but any question you ask about the truth-content of their answer will have an identical answer. So you must ask a question about the door that would make the liar lie about lying, and thus give an identical answer to that of the truth-teller who would tell the truth about telling the truth.


So you ask, "If I asked you which door leads to freedom, what would your answer be?"

The liar would lie about the lie he would have given (execution), and point to freedom.
The truth teller would tell the truth about the answer he would have given (freedom), and point to freedom.

[i.neu]

I thought a little about this,and my best shot for now would be the question:

"If you were the other guard, which door would you say leads to freedom?"

They will both point towards the door that leads to an execution, so you pick the other one.

How?
The guard that always tells the truth, will be truthful/honest and say what the guard that always lies would have said, so he will point towards the execution door (that would be the answer of the "dishonest" guard).
The guard that always lies, will lie this time as well, and won't answer what the other guard would answer, so he would also point towards the execution door (that wouldn't be the answer of the "honest" guard, and hence a lie).

Is this reasoning correct? :)

[Vectus]

Is this reasoning correct? :)

Yeah that's correct. It goes along the same lines as getting the liar to lie about lying.

Although, it would potentially fail if the two guards didn't have knowledge of the other (the truth guard doesn't know the other always lies and the lie guard doesn't know the other always tells the truth).

I'd venture that any hypothetical question that asks about a guard's answer in regards to which door is which would be a valid solution. The truth teller would always tell the truth, and the liar would always flip his response. No matter what their answer would be, you could infer which door was which by the answer given, as long as your question was meaningful with respect to the doors.

[i.neu]

Although, it would potentially fail if the two guards didn't have knowledge of the other (the truth guard doesn't know the other always lies and the lie guard doesn't know the other always tells the truth)

well, these details are usually implied in any riddle.

but if the 2 guards wouldn't have knowledge of the other, then I think the same type of question will work again, because the honest guard will say "I don't know what the other guard would answer" and the dishonest guard would point towards the wrong door...

[archis]

So you ask, "If I asked you which door leads to freedom, what would your answer be?"
The liar would lie about the lie he would have given (execution), and point to freedom.
The truth teller would tell the truth about the answer he would have given (freedom), and point to freedom.
Call me stupid but why the question "If I asked you which door leads to freedom, what would your answer be?" from question "Which door leads to freedom". If he points the bad doors in first question doesnt he lie? Why must he lie about lie ? its not he's job.

In the answer ''If you were the other guard, which door would you say leads to freedom'' i see also some paradox. ''The guard that always tells the truth, will be truthful/honest and say what the guard that always lies would have said'' So truth teller would give the same answer as liar? So if you give the same answer as a liar doednt it make you a liar too, both you say wrong fact? And if you are forced to quate other person and you quete him where did you lie? For me, the person says a lie and says the truth in the same time. What answer would you get if you asked truth teller ''lie to me''? Same thing.