DuckDuckGo is mostly closed source. However, a rapidly growing portion is open source. For an overview of that piece, check out our open source wiki. A great place to get started is at DuckDuckHack, our platform for instant answers.
DuckDuckGo is also largely built with Free and Open Source Software (FOSS). That's why we're committed to giving back to FOSS -- check out 2010 donations and our 2011 request for nominations.