Challenge.gov crowdsources some government projects to the public, with paid prizes for winning solutions. Projects range from 'develop an email newsletter HTML template' and 'design a graphic for NASA' to 'engineer a sensor technology for septic systems' and 'detect a fungus that is killing frogs'

https://www.challenge.gov/

DARPA is offering $5 million in prizes for solutions that allow warfighters to rapidly map, navigate, and search underground environments during combat operations

https://www.subtchallenge.com/