If you remember the awesome movie Labyrinth by Jim Henson, you’ll probably remember three things from the movie:
- A young Jennifer Connelly led the movie as a curious adventurer
- David Bowie starred as a creepy crystal ball-holding madman
- The weird double-headed guards with the weird life or death, truth or lie puzzle
It turns out, the simple but somehow complicated riddle that many children didn’t stop to think about for longer than 5 minutes was a variation of an old logic puzzle called Knights and Knaves.
The same puzzle has even been featured in fun mystery shows like Doctor Who and Samurai Jack. The basic riddle has built up a bit of a fan base over the years.
Here’s how it goes.
Explaining Labyrinth’s Liar’s Paradox Riddle
The premise of the puzzle is somewhat basic. The young adventurer Sarah approaches a fork in the road of a labyrinth where there are two guards waiting in front of two doors.
- One of the doors leads to her freedom and the other door leads to certain death.
- One guard is red and the other is blue.
- One can only tell lies and the other can only tell the truth.
- Sarah is also only allowed to ask a yes or no question and to only one of the guards.
- The lying guard kind of wants you to die (by taking the death door).
What question does she ask the guards so she can know for certain she won’t be walking into a certain deathtrap and the viewers can keep watching the awesome movie?
Take a moment to think about the problem and we’ll get to the answer shortly.
Now I’ll fill up some space so you don’t see the answer inadvertently.
Hmm, what to put here?
How about some fun trivia for the movie Labyrinth?
- The owl in the opening credits was one of the first uses of CGI in a movie (it came out in 1986)
- All the fun rolling around and juggling of the crystal ball by David Bowie’s character was actually a professional juggler crouched and hidden behind him
- Michael Jackson, Prince, and Mick Jagger were also considered for the role of the Goblin King Jareth (David Bowie’s character)
Or what about a sexy clown?
Beauty is in the eye of the balloon holder, after all.
Anyway, now that you’ve thought of the answer, we can test your knowledge and see!
The Solution to Labyrinth’s Two Door Riddle
Essentially, there are two different scenarios.
Let’s say for the sake of argument you want to ask the red guard about which door to take. Furthermore, let’s say he’s the one that can only ever tell the truth.
Now, our first thought as simple simians would be to ask him if one of the doors is the right one.
“Should I take this door?”
The problem is, of course, we have no idea if he’s the liar or the truther. So, that leaves us with a clever answer and the one used in the movie, albeit with a bit different wording.
“Would the blue guard want me to take this door?”
If you pointed at the good door — the one where you’ll live — the red truth-telling guard would say “No!” because the blue lying guard wouldn’t want you to go through that door.
If you pointed at the bad door — where you’d die — the red truth-telling guard would say “Yes!” because the blue lying guard wants you to venture off to a fiery death.
Let’s flip the equation now and talk to the blue lying guard.
We’d want to ask him the same question, of course. But remember, here’s the trick; he has to lie — it’s not optional!
“Would the red guard want me to take this door?”
If you pointed at the good door, the blue lying guard would say “No!” because he knows the red truthful guard would say “Yes!”, but he has to lie and say the opposite.
Similarly, if you pointed at the wrong door, the blue lying guard would say “Yes!”, because he knows the red truthful guard would say “No!”, and again, he has to say a lie.
Still sound a bit confusing?
Perhaps this last part can help tie it all together.
Since you phrase the question this way, both guards will give you the same answer!
If you point at the good door where you’ll live, both guards will say “No!” because of how the logic is phrased. If you point at the bad door where you’ll die, both guards would say “Yes!”.
And all you need to do is simply choose the opposite of what they say.
The double negative of manipulating the liar guard kind of cancels out, allowing Sarah to pass through the correct door and…well, I won’t spoil the rest of the movie.
Another way to think about it is like multiplying two negatives together, they cancel out.
Yet another way to grasp this is to remember the lying guard can only ever lie. So, by asking him what the truth-telling guard would say, you catch him in a form of liar’s paradox.
So, the next time you find yourself in an elaborate labyrinth meant to either kill you or reward you, perhaps something built by Elon Musk in the near future, then you’ll know exactly how to survive.
Just remember to thank me later.
Unless you’re still confused and end up falling into a death trap — in which case you won’t be around to thank me later — so that cancels out too.
Head over here for more of my written shenanigans.