I created http://www.learneroo.com which lets people solve programming challenges (and other challenges) online. It's not currently open-source, though if there was interest I would consider open-sourcing it. (I would first need to clean up some code that I didn't think anyone would see!)

I think that would be an interesting problem itself. Does PE export its problems & solutions in some kind of easily consumable way?

It's not open source, but https://www.hackerrank.com/ sounds exactly like what you're describing, in case you've been looking for something like that.

There's a number of sites that are not open source that use coding tasks like this and tie them with leaderboards and tie-ins to recruiters. As well as hacckerrank, there is codeeval, and there are some others whose names escape me at the moment.

But that doesn't really address a question about putting together an open-source one.

There's also at least one similar-to-Euler one -- rosalind.info (like Euler, but bioinformatics focus) -- which might be closer to responsive, since even though its not open source, their FAQ says they intend to open-source it...

Right, actually I created one as well.