246: Labyrinth Puzzle

Explain xkcd: It's 'cause you're dumb.
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| number    = 246
 
| number    = 246
 
| date      = April 9, 2007
 
| date      = April 9, 2007
| title    = Labryinth Puzzle
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| title    = Labyrinth Puzzle
| image    = labyrinth puzzle.png
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| image    = labyrinth_puzzle.png
| titletext = And the whole setup is just a trap to capture escaping logicians. None of the doors actually lead out
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| titletext = And the whole setup is just a trap to capture escaping logicians. None of the doors actually lead out.
 
}}
 
}}
  
 
==Explanation==
 
==Explanation==
This comic alludes to a famous {{w|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 spoiling next paragraph.
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This comic alludes to a famous {{w|Knights and Knaves}} logic puzzle, and specifically to the version featured in the Jim Henson movie {{w|Labyrinth (film)|Labyrinth}}, with ''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 tricky question indeed. If you want to give the original puzzle a try for yourself, don't read the spoiler below.
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*Solution 1: Ask one guard (it doesn't matter which one) which door the other guard would say leads out. The door indicated does not lead out.
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*Solution 2: Ask any guard what answer he would give if you asked him the question "Which door leads out ?". The door indicated leads out.
  
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.
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[[Black Hat]] added a third guard here who would stab his spear to [[Cueball]] on every tricky question. But even if the questions from before are not tricky enough to get stabbed there would be no helpful answer. And if Cueball asks one of the other guards the answers can't help to find the correct door.
  
==Transcript==
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The title text presents a typical behavior of Black Hat — no door in fact does lead out of this labyrinth.
:Black Hat: And here we have the labrinth guards. One always lies, one always tells the truth, and one stabs people who ask tricky questions.
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{{comic discussion}}
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==Transcript==
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:[Three guards with spears stand in front of three doors. Black Hat and Cueball stand in front of the guards.]
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:Black Hat: And over 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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{{comic discussion}}
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Black Hat]]
 
[[Category:Comics featuring Black Hat]]
 
[[Category:Logic]]
 
[[Category:Logic]]

Revision as of 20:57, 26 May 2014

Labyrinth Puzzle
And the whole setup is just a trap to capture escaping logicians. None of the doors actually lead out.
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 logic puzzle, and specifically to the version featured in the Jim Henson movie Labyrinth, with 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 tricky question indeed. If you want to give the original puzzle a try for yourself, don't read the spoiler below.

  • Solution 1: Ask one guard (it doesn't matter which one) which door the other guard would say leads out. The door indicated does not lead out.
  • Solution 2: Ask any guard what answer he would give if you asked him the question "Which door leads out ?". The door indicated leads out.

Black Hat added a third guard here who would stab his spear to Cueball on every tricky question. But even if the questions from before are not tricky enough to get stabbed there would be no helpful answer. And if Cueball asks one of the other guards the answers can't help to find the correct door.

The title text presents a typical behavior of Black Hat — no door in fact does lead out of this labyrinth.

Transcript

[Three guards with spears stand in front of three doors. Black Hat and Cueball stand in front of the guards.]
Black Hat: And over 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)

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)

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 ~~~~)
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