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I think I tend to be entertained by things that work, but seem sorta ridiculous. For example, I remember being entertained by some of the proofs in the Mathcamp complexity theory classes, where you prove that, say, multiple tapes aren't very useful (which in complexity tends to mean something like "doesn't change whether something is polynomial or not"), because you can simulate them while "merely" squaring the running time of your algorithm. Sure, it's still polynomial, but... that seems like a big difference practically...
Anyway... Today's paper for my security class, which talks about the economics of CAPTCHA's, amused me for somewhat similar reasons --- I'm not used to papers for my security class focusing on cost, even if in practice human labor is cheap enough that "how much do CAPTCHA's make accounts cost" is much more important than the basic "can you make computers break them at all" (answer: maybe, but people don't really bother, because that costs more than using humans).