Lately, I have introduced the classic eighties film Labyrinth to Emilia. Even at four months old she is eminently capable of realising that, despite it's original Box Office failure, it remains one of the best movies of its type and a testament to the late great Jim Henson. Of course, that is not just my opinion, but verifiable fact so there...Now, those of you who have seen the film will recall that halfway through, Sarah is faced with "the riddle of the two doors" - something that I believe took its inspiration from the work of Raymond Smulluan's "Knights and Knaves" logic puzzles - in order to avoid certain death.
The challenge is presented by these talking doors thus: "One of us leads to the castle, one of us leads to certain death. One of us always tells the truth; the other always lies."
Now, Sarah successfully guesses correctly (she actually ends up falling down a hole through a chasm of bizarre talking hands, before descending into an oubliette, but this is down to the goblin king punishing her for claiming it is "a piece of cake", rather than her own poor choice) - but I have always found it a very optimistic viewpoint that she could solve this for the first time under the pressure of having to save her baby brother in the space of thirteen hours...
Yes, I know it's a fantasy film - I promise I'm not taking it that seriously. It's just that the only way to answer the riddle correctly is to ask a certain question in a manner structured in mathematical logic, rather than intuition or cunning. The solution is not to find out which door is lying and which one is telling the truth, but to find a way of them both giving you the same answer. So - if you ask either door, as Sarah does: "If I asked the other door would he lead to the castle?" then whatever answer they give you is the opposite of the truth as follows:
1. You are either asking a truthful door what a lying door would say, OR
2. You are asking a lying door what a truthful door would say
Door one happens to be the correct door, so given that she asked door two the question, in scenario one from above, if he says YES, then door one IS the correct door (as he is truthful). In scenario two, if he says NO then door one IS STILL the right door (as he is a liar)
The point here is that the roles are such that the scenario remains the same when switched around - the two variables don't remain consistent, so therefore, providing you ask the correct question, you will determine the outcome by definition.
Now, it took me several views to even understand what the hell Sarah was on about - the reason being that to solve this by pure logic would require either a working understanding of this problem, or a pen and paper to map out the process. She had neither and was considerably up against it (what with only a few hours to get to the center armed with nothing other than a temperamental dwarf and a big hairy orange creature whose only friends are rocks. Also - with the choice as being life or death, I fine it hard to imagine that you would be content to rush through to a decision on the spot...
I'm taking it too seriously again, I know, I know... and I'm really just jealous because a fictional character played by a fifteen-year-old Jennifer Connolly is able to do what I cannot. Having said all that, if you want to have matters re-balanced by reality, there is always Karl Pilkington's approach to consider. Here's how he approached a similar puzzle when quizzed by Ricky Gervais...
Actually your question is incorrect. She asks "Would he tell me if this door leads to the castle?"
ReplyDeleteEither way you are correct in that a fourteen year old hot chick with size C/D cups who hasn't slept/eaten in a while and has a kidnapped brother would probably not also coincidentally be extremely good at on the spot life versus death logic puzzles. If that was the case in our world I think I'd shoot myself.
If you are ever presented with this scenario I suggest you just hold up your midle finger to one and ask 'am I holding up one finger?' Then you'll know the liar. Or beat one until submissive then force them to walk through one of the doors. Even a liar will choose self preservation.
IIRC she could only ask one question so although 'am I holding up one finger?' would tell her which one lies it wouldn't help choose the right door.
DeleteHer cup size makes her bad at riddles? How many fedoras do you own?
DeleteThanks for the correction.
ReplyDeleteI have a feeling that there were some unwritten rules that prevented any question from being asked - I think it had to be in reference to the doors themselves...
could you stop using "right"
ReplyDeletethe "right" door
is that the "correct" door or the one that is not on the left?
it makes things a bit more confusing.
My apologies - Ive updated as per the suggestion...
ReplyDeleteAlthough Sarah's reasoning is a step in the correct direction, her question does not actually help her at all. Simply because if her question to the left door guard is "Would he(referring to the right door guard) tell me that this door leads to the castle?" and the left door guard said yes, then if the left door guard is lying then then that means the right door guard wouldn't tell her that meaning the right door leads to the castle. If the left door guard was telling the truth then that means the other would lie meaning the right door leads to the castle. However, the only problem with her logic is what if she asked the right door guard the same question? Then all roles would be reversed meaning that the left door would lead to the castle. So, really she is very lucky, because even after falling into the oubliette you really don't know whether that door led to certain death or not:
ReplyDelete1) because she said "this is a piece of cake" then it could have been just a simple punishment from Jareth meaning the door she chose was the correct door
2)because the hands that caught her ask her which way she wants to go, therefore she could have gone back up which also suggests that she chose the correct door
3)because she fell into the oubliette where most people probably die, then that suggests that it wasn't the correct door, and that she only survived because Hogle got her out
So in the end, we really don't know which door was correct or not, and Sarah's question did not help anyone in figuring that out.
It does, because by referencing to what the "other" guard would say she knew that she would be guaranteed a lie. Use a piece of paper but to try and help I will explain below. Firstly replace left and right with Door A and B. We will say Door A is correct.
ReplyDelete"Would HE (referring to the other door) tell me this door leads to the castle"
If we are at Door A the answer given would be "No";
-Liar because the Truth teller would say Yes so Liar says No.
-Truth teller because the Liar would say "No" so he says "No"
If we are at Door B the answer given would be (as in the movie) "Yes";
-Liar because the Truth teller would say No so he says Yes.
-Truth teller because the Liar would say Yes so he does too.
There is always one and only one lie if you ask what the other would say, as such because one knows the answer is a lie it can be solved.
Break this down easy. Misconception about being in front of door A and B because there is a fundamental error people are actually making. There are 4 possibles total and doesn't matter if you are in front of A or B door. Going to use A and B as the Doors, T and L as truth and lie, and c for the correct door.
ReplyDeleteEach scenario we will be in front of Door A but is exactly the same for Door B.
cAT and BL - No. The T will tell you the L will say no
cAL and BT - No. The L will tell you the T will say no
AT and cBL - Yes. The T will tell you the L will say yes
AL and cBT - Yes. The L will tell you the T will say yes
So a "no" means you're in front of the correct door. A "yes" means you are in front of the wrong door.
Each one shows the L trying to get you to go into the wrong door because if you don't go no then you die and if you go yes you die. So No is Yes and Yes is No :O