Sounds like a marvelous challenge. Anyone have other similar "technological frontier then, high-school science fair project now" type challenges? OPer notes BioCurious as one. A major factor in education is walking kids thru a subject from basic principles to state-of-the-art, recreating historical milestones along the way.
Content publishing: Weekend project. Rails, memcached and CloudFront and you're done.
IM and Buddy Lists: 1.5 million simultaneous users doing n^2 pub/sub-type distributed transactions.
Mail: 4,000 emails per second with live unsend and recipient read/unread status. I think PostgreSQL tops out in the millions of rows per second nowadays.
Web caching/acceleration: pick your favorite proxy solution and configure it.
Single sign-on: Form strategic partn-- Hey, you said technical challenge, not political.
opening a web shop.
Building robots(at today's kid's levels).
Designing really complex and fast digital circuits(using FPGA, and IP blocks).
Building a global, scalable and complex database application(using something like MS lightswitch).