I once did a job for a European client who ended up being a manager in some government department. He had a use-it or lose-it budget and needed an app prototype turned around in 48 hours to avoid losing the money.

After the initial prototype we did a few more rounds. That ended up being IIRC $30-$40k for what amounted to 5 days of work.

Client was super-happy. I guess the prototype was enough to convince his bosses to fund the project for real.