Philosophy Discussion Forums | A Humans-Only Club for Open-Minded Discussion & Debate

[Alan Masterman]

Catching up after an absence of many moons from this forum, I was so taken with Alan McDougall's "Odd-ball Puzzle" (a genuine test of scientific reasoning) that I was motivated to post this variant of the Prisoner Dilemma (courtesy of Dr Who). I can't immediately trace any reference to it in previous posts, so forgive me if it isn't new.

You are confined in a prison cell. There are two doors, both of which are unlocked. One leads to freedom, one leads to certain death, but you don't know which is which. Each door is guarded. One guard always tells the truth, one always lies, but again, you don't know which is which.

You are allowed to ask ONE question to identify the door which leads to freedom. You may put your question to either of the guards, bearing in mind that you don't know which one will tell the truth.

What question will you ask?

[Eckhart Aurelius Hughes]

I'm assuming the guards know which door is which. I'm assuming the the guard whose asked the question will have to answer. I'm assuming, for all intents and purposes, each guard is omnipotent, meaning any meaningful question I can come up with will be answered according to whether the guard is the liar or truth-teller.

If I ask one guard if his own door leads to leads to freedom or death, and regardless of whether he says life or death, I cannot know whether he is telling the truth or lying. If I ask one guard if the other guard's door leads to freedom or death, I have the same problem.

Perhaps I can ask him does the guard of the door to freedom tell the truth which leaves 4 options:

1. He says yes, and he is lying, in which case the answer is no, and thus his door is the one to freedom.

2. He says no, and he is lying, in which case the answer is yes, and thus his is the one to death.

3. He says yes, and he is telling the truth, in which case the answer is yes and his door leads to freedom.

4. He says no, and he is telling the truth, in which case the answer is no, and his door leads to death.

Assuming I have not made a miscalculation, this means if his answer is yes his door leads to freedom and if his answer is no it leads to death and the other door leads to freedom regardless of whether he is the liar or not. I won't know whether he is the liar or not, until I go through the door, but I'll know which door leads to freedom. Correct me if I'm wrong.

[Half-Six]

Scott, that seems right. I've heard this before, but the answer I know is slightly different, and a bit more convoluted! So there is another way, if folk want to keep playing

I don't think though you know who the liar is, even once you've gone through the door, not without asking another question.

[Grecorivera5150]

Do you understand that if you are lying to me that and I am facing certain death that I am going to make every effort to take you with me?

Perhaps I can create enough nervous energy or self doubt to vary the outcome of an interaction with the guard either before or after going through the door.

-- Updated June 26th, 2012, 10:46 pm to add the following --

My brother figured this out very quickly and it was very impressive IMO. I gave him the scenario and he had an answer in under 5 minutes. He has been falsely accused of a crime for which he was imprisoned and has also been imprisoned for his own mistakes. His life experience has honed his ability to meticulously evaluate systems and rules and to try and find ways to exploit the.

He said he would simply choose a door an ask 1 absurd question of the guard that could not be true such as are you wearing a Santa Suit and a tutu or perhaps are you a purple dinosaur. If the guard answers yes to the absurd question he is lying and so you choose the other door if he says no he is telling the truth and you go through that door.

This was a great lesson for me in humility and patience as I have a tendency to sometimes rush to judgement and prepare for a fight when I am presented with an emotional struggle.

Perhaps this says something about my own psychology or maybe I am just not used to being represented with scenarios that lack such simple answers.

The scenario itself invoked an emotional response immediately because I had to imagine myself trapped and that my life was being threatened.

-- Updated June 26th, 2012, 11:09 pm to add the following --

So after some rumination we see now that just because a guard lied about the absurd question does not mean he was designated to guard the door to freedom. Here we defaulted to psychology and assumed the guard that was to be the liar would be guarding the door to freedom.

So this brings me back to want to elaborate on my original answer. My answer was just a ploy to try and create an emotional stress in the guard outside of the door that I was going through just in case it was supposed to lead to certain death and just in case I had a chance to fight.

My brothers choice here would be to try and kill who ever was on the other side of the door regardless of what question he asked or what answer he was given to gain the initiative and perhaps a better chance at surviving a physical altercation.

[Partinobodycular]

Okay, I'll take a crack at it. But to make it a little less convoluted I'll call them door "A" and door "B", and I'll assume that the door to freedom is door "B', just to make the explanation simpler.

I would simply ask the guard at door "A" which door the guard at door "B" would say is the door to freedom.

(Remember, in this example door "B" is the door to freedom)

If the guard at door "A" is the liar, then he will say that the guard at door "B" will say that the door to freedom is door "A" (The guard at door "B" would actually say door "B")

If the guard at door "A" tells the truth, then he will say that the guard at door "B" will say that the door to freedom is door "A" (Which is of course exactly what the guard at door "B" would say)

So no matter what the guard at door "A" says, I would know that the door to freedom is the other door. This works even if we do not assume which door is the door to freedom. It's just much easier to explain this way. No matter what, you simply go through the opposite door of what guard "A" says.

[Half-Six]

Partinobodycular - that's the answer I know.

[chazwyman]

This one is as old as the hills. Does anyone know its origin?

The solution is to ask each guard what the other guard will tell you to go down to save yourself. In theory you can get the solution with one question, as the answer will be the same door from each guard - You have to take the door neither indicates.

The truthful guard will always tell you that the lying guard will tell you to go down the door of doom. The lying guard will always tell you that the truthful guard will send you down the door of doom.

Thus, as they both know which door, then you have to choose the door they did not say.

Thus one question to either guard will solve the problem.

[Eckhart Aurelius Hughes]

To toot my own horn, I already solved the dilemma in post #2.

[chazwyman]

To toot my own horn, I already solved the dilemma in post #2.

Sorry but due to the lack of elegance, I missed it

Do you know what is the origin of this puzzle?

[Misty]

I would ask one guard to come into my cell for help, then watch which door he uses to leave my cell.

[Grecorivera5150]

chazwyman-the directions say that you can ask either of the guards one question not both of them one question.

[Partinobodycular]

To toot my own horn, I already solved the dilemma in post #2.

Sorry Scott, you were of course the first to solve the puzzle correctly, and I pay you due homage.

But Half-Six asked if anyone could give the alternate solution, and so I thought that I would tackle that one.

I do love puzzles, and if anyone knows of something a bit more challenging, I for one would love to give it a go.

[Grecorivera5150]

http://www.brainbashers.com/

[chazwyman]

chazwyman-the directions say that you can ask either of the guards one question not both of them one question.

Please have the curtesy to read my solution.

As both guards render the same answer, then there would be no point asking them both.

-- Updated Sun Jul 01, 2012 2:45 am to add the following --

Can anyone suggest the origin of this age-old puzzle?

[Misty]

A more simple question: Guard, will you stop me if I go through the door you are guarding? The liar will say no even though it is his job to stop him.