There's probably a comedy film with an AGI attempting to take over the world with its advanced grasp of strategy, persuasion and SAT tests whilst a bunch of kids confuse it by asking it fiendish brainteasers about carwashes and the number of rs in blackberry.

(The final scene involves our plucky escapees swimming across a river to escape. The AIbot conjures up a speedboat through sheer powers of deduction, but then just when all seems lost it heads back to find a goat to pick up)

There is a Star Trek episode where a fiendish brainteaser was actually considered to genocide an entire (cybernetic, not AI) race. In the end, captain Picard choose not to deploy it.

This would work if it wasn’t for that lovely little human trait where we tend to find bumbling characters endearing. People would be sad when the AI lost.