What could be better than a 16-year-old Jennifer Connelly, David Bowie, and a bunch of muppets all in one movie? Anyway, you know the part where Sarah gets to the castle and has to solve a puzzle to pick the right door in?
Sarah: What am I supposed to do?
Jim: Try one of these doors.
Tim: One of them leads to the castle,
and the other one leads to —
Ralph: Ba Ba Ba Bum!
Tim: Certain death!
Guards: Ooh! Ooh!
Sarah: Which one is which?
Jim: We can’t tell you.
Sarah: Why not?
Jim: Uh… I, uh…
We don’t know.
Tim: But they do.
Sarah: Oh. Then I’ll ask them.
Alph: Uh…
You can only ask one of us.
Ralph: It’s in the rules.
One of us always tells the truth,
And one of us always lies.
He always lies.
Alph: I do not! I tell the truth!
Ralph: Oh, what a lie!
Tim: Ha ha ha!
Alph: He’s the liar!
Sarah: All right, answer yes or no:
Would he tell me
That this door leads to the castle?
Alph: Uh…
What do you think?
Really?
Yes.
Sarah: Then the other door leads to the castle,
and this door leads to certain death.
Alph: He could be telling the truth.
Sarah: But then you wouldn’t be,
so if you said he said yes,
the answer is no
Alph: I could be telling the truth.
Sarah: Then he’d be lying.
The answer would still be no.
Alph: Is that right?
Ralph: I don’t know, I’ve never understood it.
Sarah: No, it’s right. I’ve figured it out.
To recap, Sarah got the answer right. She pointed to a door and asked Alph if Ralph would tell her that it leads to the castle. So we have two options. Either Alph is the truth-teller, or Alph is the liar.
Alph is the truth-teller
Alph’s answer was “yes”, meaning that Ralph would say that door leads to the castle. If Alph’s the truth-teller, than Ralph is the liar. So if Ralph says that door leads to the castle, then it doesn’t, and leads to certain death instead.
Alph is the liar
If Alph is the liar, then Ralph always tells the truth. If he says that Ralph would say that door was the right one, then it must not be.
So, no matter which person is trust-worthy and which isn’t, the door that Sarah pointed to is not the door she wants to be going through. Now here’s the trick: as soon as she goes through the door, she falls into a pit. So did she get the answer wrong? From what I can figure out, there are basically two options: either the pit doesn’t qualify as “certain death”, since after all she doesn’t die, or Sarah’s fallen into the trap of the Liar Paradox. It’s entirely possible that neither Alph nor Ralph ever tells the truth, or that they sometimes lie and sometimes don’t. Just because they said that one tells the truth and one lies doesn’t mean that they weren’t lying when they told her that. Or there could be more rules to the game but only told her the part about the lying. So while she got the correct answer to the game set before her, she could have been playing a different game with different rules that would be undiscoverable.
Did the filmmakers have this in mind when they put a pit inside the “correct” door, or were they just trying to move the story along to its next segment? It seems odd to put in a game, lay out a set of rules, and then set them up so that the rule-givers are themselves untrustworthy, but in a world run by glam-era rock David Bowie, why not?