Answer to old chestnut: crossing a bridge
The first answer most people think of requires 19 minutes. In this solution, the 1 minute person crosses together with the 2 minute person, runs back alone, then crosses with the 5 minute person, runs back alone, and finally crosses with the 10 minute person.
It turns out that there is a faster method that requires only 17 minutes. In this method, the two fastest people cross first (2 minutes), the 1 minute person goes back (total 3 minutes), then the two slowest people cross (+ 10 = 13 minutes), then the 2 minute person takes the flashlight back across (+ 2 = 15 minutes), and then the two fastest people cross together again (+2 = 17 minutes).