Snark Ball

Alice is stupid. There's no Obfuscating Stupidity either: her inability to grasp basic logic is one of the main driving forces behind the main plot. Except, outside the main plot she regularly plays Deadpan Snarker or Only Sane Man to smarter characters.

That means she just caught a Snark Ball: an imaginary device that makes a character consistently show more wit than he actually has.

May lead to fan theories that it's secretly Obfuscating Stupidity. Prevalent in cartoons of "wacky" variety, where absurdity of actions becomes funnier if the characters themselves comment on that.

Compare Smart Ball, where a stupid character does a smart thing because the plot says so, and Dumbass Has a Point, where a stupid character says something stupid that still makes sense.

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Film

 * In Blazing Saddles, Mongo (having just been used to give Rock Ridge one heck of a load of exposition) looks right at the screen and intones solemnly,

Live-Action Television

 * Depending on your point of view, Crichton from Farscape could be considered this. On the one hand, he is an Astronaut and a Scientist. On the other, the rest of the cast consistently views him as a complete moron. In either case, some of the stuff he comes up with is just fantastic.
 * Kelly Bundy from Married... with Children. She's barely literate, speaks almost entirely in malapropisms and nearly always misses the point of what's going on around her. She's one of the best examples of both a Brainless Beauty and a Dumb Blonde... yet she also very frequently delivered witty and inventive combacks and snark, especially when it came to fighting with her brother.
 * Brittany from Glee.

Web Comics

 * Monette and Kharisma from Something Positive. Both of them started as extremely stupid characters, and eventually developed into the same Deadpan Snarkers that the rest of the cast are. Some of this is character development, but they nonetheless behave with a level of intellect far higher than their original characterizations.

Western Animation

 * Homer Simpson.
 * Almost all the Simpsons do this at some point
 * Fry from Futurama. While much of the show's comedy rests on his stupidity and it even becomes a plot point, he has shown familiarity with the role of the Vice President in the US Constitution and a character from Moby Dick, indicating he's better read than one would expect. He's also capable of coming up with some pretty creative plans.
 * Johnny Bravo. Never lets go of the Idiot Ball when it comes to plot. However, he's perfectly capable of delivering very clever puns and commenting on other characters' actions in a snarky fashion.