Salt shaker problem
Here's a math problem that kept me occupied for a little while at work. I've been asking my smarty-pants friends about it, and they've gotten a solution using computers, but no slick closed-form equation yet. Have fun!
The other day my boss suggested we clean the salt and pepper shakers (there is a pair at every table). I noticed there were still a lot of table occupied, so they couldn't all be done at once. Besides, doing them all at once was an incredibly tedious proposition. So I thought, what if I cleaned some set number n every day out of the total N pairs. Each day I picked n pairs at random and didn't keep track of which ones I'd cleaned the day before. How long before I was 99% sure I'd cleaned them all?
I'll ask some of my friendly nerds to post their solution so I can link to it.