| This explanation may be incomplete or incorrect: I started it, someone else (preferably who's actually solved the puzzle) can finish|
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XKCD's Blue eyes puzzle is a logic puzzle posted around the same time as comic 169. Randall calls it "the hardest logic puzzle in the world" on it's page; whether or not it really is the hardest is up to speculation.
The solution is at xkcd.com/solution.html.