Four people must cross a narrow bridge at night. At most two may be on the bridge at a time, and a torch must be carried across each time, so somebody always has to bring it back. Walking alone they need 1, 2, 5 and 10 minutes, and a pair walks at the slower person's pace. In the shortest possible time, how long does it take all four to get across?

The trick is to send the two slow walkers over together, so that the 10 is paid only once and the 5 disappears inside it. Send 1 and 2 across (2 minutes); 1 brings the torch back (1); send 5 and 10 across together (10); 2 brings the torch back (2); send 1 and 2 across (2). Total 2 + 1 + 10 + 2 + 2 = 17 minutes. The traps: 19 minutes is the obvious plan of always using the fastest walker as escort — 2, then 1 back, then 5, then 1 back, then 10 — which pays for the 5 and the 10 separately; 21 minutes comes from using the 2 as escort throughout; 18 minutes is just 1 + 2 + 5 + 10, the four walking times added with the return trips ignored.