I don't believe you can get that cross polination at Sun Microsystems (or other big name IT Company) though. Yes, they'll be working on problems that other companies need to have solved, but they'll be working on these problems. So if you are an enterpreneurially minded CS Student, then that means they got a headstart on these problems, along with a bigger budget and more coders to solve them.
I would approach the problem as follows. If I'd intern, I'd first find an internship in a totally unrelated field (like metalworking or gardening)and see whether I can help to implement systems to make work easier. And if it works, you have a first product which the company you intern at won't try to sell.
PS: Divide 1000 papers into stacks of 1000 and give to 10 people to subdivide into stacks of 100, which divide between themselves and 9 other people. Let all those people further subdivide the sheets till everyone has someones sheet. Put out an alphabetical list of those 1000 people where they can write some way to contact them. Or let them write their email adress/phone number on the paper next time you have a test. This way, everyone has to deliver 1 paper to one other person and receives 1 paper. There's most likely a better solution, but I can't think of one right now.