[mickeyg13]

I love this problem, and the answer is awesome, although I'd never seen it stated quite that way; I had seen it generally as the secretary problem.

I'm not sure if any of you are familiar with it, but there used to be (maybe still is) a dating show on MTV called "Next." There would be a van containing 5 potential dates for the contestant. The contestant's goal was to choose the best date, but he had to do so with incomplete information. There was some random order (maybe not actually random, don't know) assigned to them, and the show would start with the first one leaving the van to go on a date with the contestant. The contestant would have to decide if he wanted to choose this date, or "Next" the date and proceed to the next one, with no chance to revisit a date once he or she is "Nexted." One of my friends is a fan of the show, and he used to talk about the strategy he would use if on the show. It turns out to be essentially the same problem DS posed, and my friend's strategy coincidentally turned out to be the mathematically correct strategy when you consider rounding. I thought it was funny how that worked out.