Hey folks, just to follow up: as BrowserUK noted, to make a new briefcase, I simply right clicked on the desktop and selected New->Briefcase, and there it was. I moved the briefcase to the memory stick (D:), and then copied a directory from one of my network drives into the briefcase. It proceeded like a normal copy.

Then, I added files and a directory (in Linux--it's a Samba share) and right clicked on the briefcase and selected "Update All." A window of what had changed popped up and I clicked the "Update All" button. Then I tried deleting some of the stuff I just created and the same thing happened. When new files need to be copied, there's a green arrow, and when there are orphans in the briefcase, there are red arrows. All seems to work exactly as promised. One interesting thing to note is that if I only do a mkdir on the source and then update the briefcase, it's "smart" enough to know it's just an empty directory and states there are no updates.

Anyway, it turns out that the problem is indeed trivial in Windows and it just took the right information. Thanks again, and feel free to add comments. I hope that this solution is acceptable; it's not EXACTLY what I had in mind, as it's not just an icon that the people can double-click once, and it has to be set up separately for each person (as opposed to a script I could just email to people with some instructions), but I think it's the best solution.

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I like computer programming because it's like Legos for the mind.