Wednesday, March 18, 2009

«Flaw With an Old Riddle»

One door leads to safety, the other leads to certain death. Once a door is opened the other becomes locked; so you have to go through the one you choose. There are 2 people standing in front of you. You know that one always tells the truth, and one always lies, but you don't know which person is which. Both people know which door leads to safety and which one to certain death. You are allowed to ask only one of them one question. What is your question?

The riddle is old enough and has been around long enough that you probably remember the answer from the last time you saw it. Of course, the "correct" answer is "If I asked the other person, which door would they say leads to safety?"

There is a flaw in that answer. The idea is if you're talking to the liar, he knows the other one would tell you the correct door, so the liar tells you the wrong door. If you're talking to the truth teller, he knows the other guy would lie, so the truth teller also tells you the wrong door. So you take the opposite door, no matter which person you asked.

Here's the major flaw in the logic of that solution: let's say the liar replies "I don't know." Clearly he is lying, because he does in fact know. If you ask your question of the truth teller, he'd also have to truthfully tell you that the other guy would answer "I don't know." Well, you're screwed now...

There is no way with one single question to determine which door leads to safety if they don't answer like you expected. It comes down to 50/50 whether you ask a question or not.

Don't you just hate it when you over-think a riddle?


  1. It is a rather naive view of the 'liar'. In my experience, the best liars give information that is 100% correct. It is what they leave out that kills.

  2. Ew. Good point Looney. So true.

  3. Ow, my brain hurts! I'd just bribe 'em with money or food. *lol* Nah, I just wouldn't take any door, turn around and walk away.

  4. @ Berni: Walking away is not an option. The path you took to get there is now impassable. Cave-in or something... Who knows.

  5. In that case, I'd just cry myself to death. *lol* Or, better yet, I'd be really annoying, so much so the two dudes wouldn't be able to stand me for any longer and tell me which door to just get rid of me.

    Hmm, they'd probably tell me the door leading to my demise, though. [°¸°]

  6. @ Berni: Yeah, that's what I was going to say... But then you'd still have one of them telling you to take the door to your demise, and one telling you the other door.

    Remember, the liar (however much he hates you) still has to lie. So even though he'd like to send you to your demise, he'd have to tell you he wants you to go through the other door.

  7. Assuming the two people HAVE to answer your question directly, here's how I think it would go.

    If you asked either of them "If I asked the other person, which door would they say leads to safety?", you should take the opposite door that either of them suggests.

    If you've asked the truth teller, then he's going to tell you the door that the liar would pick, hence the wrong door.

    If you've asked the liar, then he's obviously going to suggest the opposite door that the truth teller would have picked.

    Therefore, you can't really go wrong by picking the opposite door that either the truth teller or liar suggested.


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