# 246: Labyrinth Puzzle

Labyrinth Puzzle |

Title text: And the whole setup is just a trap to capture escaping logicians. None of the doors actually lead out |

## Explanation

This comic alludes to a famous Knights and Knaves-type logic puzzle, in which there are *two* doors and *two* guards. One guard always lies, and the other always tells the truth. One of the doors leads to freedom, and you can only ask one guard one question. The solution to this riddle involves a very tricky question indeed, and one would in the xkcd-version risk a stabbing from the third guard. If you want to give the original puzzle a try for yourself, don't read the spoiler in the next paragraph.

Solution: Ask one guard (it doesn't matter which one) which door the other guard would say leads out. The door indicated doesn't lead out.

## Transcript

- Black Hat: And here we have the labyrinth guards. One always lies, one always tells the truth, and one stabs people who ask tricky questions.

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# Discussion

Just ask which color is the sky.. -- 175.110.37.200 (talk) *(please sign your comments with ~~~~)*

- Oh, although the strip doesn't explicitly say so; in those riddles you can normally only ask one question. --St.nerol (talk) 23:00, 27 January 2013 (UTC)
- There's another (more traditional) three-guard variation where one guard always tells the truth, one guard always tells a lie and the third alternates between pure truth and pure lie (and you don't know which flip they're currently flopped upon). But you
*still*only get to ask one question of one guard. Have fun with that one. My personal solution certainly has a degree of convolution, but I've heard other workable answers. 178.98.31.27 02:24, 21 June 2013 (UTC)- @175.110.37.200, you would know which one lies but you would not know which door leads out. Tharkon (talk) 23:13, 10 October 2013 (UTC)
- Eh, well, even if you had a perfect question to ask in this case, a lot of good would that do you: it'd only reveal the truth behind the setup, that
*none*of the doors lead out. :p -- 173.245.51.210 08:20, 8 November 2013 (UTC)- Well yes it says that in the title-text. But good pick-up. 108.162.219.58 02:31, 6 February 2014 (UTC)

- Eh, well, even if you had a perfect question to ask in this case, a lot of good would that do you: it'd only reveal the truth behind the setup, that

- @175.110.37.200, you would know which one lies but you would not know which door leads out. Tharkon (talk) 23:13, 10 October 2013 (UTC)

- There's another (more traditional) three-guard variation where one guard always tells the truth, one guard always tells a lie and the third alternates between pure truth and pure lie (and you don't know which flip they're currently flopped upon). But you

One question, of one guard. I really like the original form of this riddle. It's a bit of a trick, though. It is crucial that the guards "know" each other's rules, but this is not even implied. And if it was stated in the question, that would probably be a good enough clue to get you to the answer. Of course, once you know the answer it seems trivial, but I wonder what percentage of people actually worked it out for themselves? Another good one is Monty Hall, even though that is pure, straightforward probability. 108.162.219.223 18:11, 17 January 2014 (UTC)

- With two guards, they wouldn't need to know each others role. If they know their own role - which they do - each can infer the role of the other. 162.158.34.137 13:01, 21 April 2016 (UTC)

- I think somebody needs a hug! 108.162.219.223 18:11, 17 January 2014 (UTC)

The whole problem with this entire riddle is that if they are both liars you are screwed! Nothing in the riddle establishes a fact that they aren't liars. Now if there was a known truth teller in the riddle that explains the nature of the guards or the narrator does it, then the above solution works. 108.162.216.28 (talk) *(please sign your comments with ~~~~)*

As you aren't given a limit to the number of questions, you can just ask each guard if they're the stabby guard. If two say yes, the third one is the truthful guard and you can ask him which way the exit is. If two say no, the third one is the lying guard and you can ask him where the exit isn't. No tricky questions so the stabby guard shouldn't stab you.162.158.255.195 18:14, 14 August 2015 (UTC)

I have a solution, but you need to ask multiple questions:

*If the Stab Guard tells the truth:*

Ask each guard, firstly, "Are you the Stab Guard?"

Truth Guard will answer "No."

Stab Guard will answer "Yes."

Liar Guard knows the answer is no, but, because he lies, will answer "Yes."

The one who said no is the Truth Guard, so you can ask him which door leads to freedom.

*If the Stab Guard lies:*

Point to the guard on the left, and ask each guard, "Does that guard lie?"

If that guard is Truth Guard, then Truth Guard will answer "No," while Stab Guard and Liar Guard answer "Yes."

If that guard is a liar, then Truth Guard will answer "Yes," while Stab Guard and Liar Guard answer "No."

Whichever guard gives a unique answer is Truth Guard, so you can ask him which door leads to freedom. NickOfFørvania (talk) 23:37, 3 November 2015 (UTC)

- It's been solved on puzzling.stackexchange.com (given a specific definition of a tricky question): http://puzzling.stackexchange.com/questions/43092/xkcd-inspired-logic-puzzle 141.101.98.130 12:14, 24 September 2016 (UTC)

I remember a book where the main character kicked one guard in the face and asked if it hurt. 162.158.252.137 (talk) *(please sign your comments with ~~~~)*

There's another unspoken rule: That the lie is either a yes or a no. If you asked the liar something, he could lie and say, "I don't know," which would leave you with nothing. Also, as Stabby MacStabberson does not appear to have any restrictions on what he tells you (that is, he has the choice between truth or falsehood,) there's no sure way out even if he wasn't tasked with stabbing you.162.158.255.69 05:32, 30 April 2016 (UTC)