Agree with your good suggestion, and extend with rosalind.info for kinda the same experience but for bioinformatics instead of math.

Now what I'd be VERY interested in is an implementation of a list of "Like Project Euler, but for X" where X is all manner of things. WRT various values of X, I know there are periodic security challenges but nothing long term/permanently ongoing, I'd greatly enjoy being proven wrong. I'd be particularly personally and professionally interested in "Project Euler for HFT". How about "Project Euler for VLSI design"?

Yeah, yeah, If I want it, I should do it, and its true I probably could, other than the lack of infinite spare time.

I love Project Euler. Each time I pick up a new language I actually go to PE and solve some problems (often times ones that I have already solved) just to get a better feel for the syntax of the new language I am learning.

Afterwards I'd just go make some standard 'mock projects' that require a bit more of software architecture. Such as building Game of Life, a twitter clone, a HN clone,..

Depending a bit on if I actually liked the language :-)