August 17th, 2005

odd baud skins (pic by Waywind)

Riddle: The Paradox Dragon

Wow, I've been on an unusual mathematical kick lately. Must be the aftereffects of all the good news I'll mention in my next post, or something.

First amthrax came up with the river-crossing riddle I posted here two days ago; I not only solved it, but came up with a proof for why the given solution is optimal.

Now, by chance I've stumbled upon the PartiallyClips strip (LJ: partiallyclips) named "Paradox Dragon". And the logic circuits of my brain kicked in.

Right off the bat, the third panel contains a fairly obvious paradox. (Warm-up puzzle: What?) I'm going to assume that it was put in there intentionally, to give the strip its title; or maybe it simply drifted in as part of the punchline. However, if you discard the third panel entirely ... the first two panels are a self-consistent logic puzzle. I've reprinted the dialogue below, modified to clarify it for problem-solving purposes:

NARRATOR: On the hundredth day of my quest, I faced the Paradox Dragon. I knew that one of its three heads always lied, one always told the truth, and the other head would alternate [back and forth between telling the truth and lying].
FIRST HEAD: You may ask us one question, then you must guess which head is which.
SECOND HEAD: He's lying. You get three questions.
THIRD HEAD: Oh no, it's definitely one question.

NARRATOR: Not willing to risk counting on three questions, I asked [the dragon] ... what the second head would say if I were to ask it if the third head had been lying when it agreed with the first head that I could only ask one question.
FIRST HEAD: (*non-answer*) Oh ... okay, hold on a minute. ...
SECOND HEAD: He'd say, "Yes, the third head was lying."
THIRD HEAD: ... [The second head is] lying [in the statement he just gave].

To my delight, I discovered that the information given was sufficient to triumph over the Paradox Dragon! Anyone else out there care to reproduce my work and solve Rob Balder's riddle?

(n.b.: Comments for river crossing riddles now unscreened. Comments here, as with my other riddle posts, are screened to give everyone time to play along at home.)


Edit, 1-11-2005: Going back through old entries to tag everything up, realized that I never unscreened anyone's solution. Oops! Fixing that now -- keep in mind all answers below were the product of independent work.
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