There are 4 people, called A,B,C,D, who want to cross a bridge in the dark. They only have one torch between them. The bridge can only hold a maximum of two people at once. A can cross in 1 minute, B in 2 minutes, C in 5 and D in 10 minutes. The other rule is that if two people cross, they go at the pace of the slower person.

So for instance, A could cross over with B. This would take 2 minutes. Then B might return with the torch (which takes 2 minutes) to help C across. This crossing would take 5 minutes. Then B returns again (another 2 minutes) to help D across which takes 10 minutes. Total: 21 minutes.

How can they cross most quickly?

Btw, lets invent some notation to avoid confusion. AB|CD shows A and B are on the original side and C and D have crossed. So the above example reads:

ABCD|
CD|AB <2 mins>
BCD|A <2 mins>
D|ABC <5 mins>
BD|AC <2 mins>
|ABCD <10 mins>
(Total 21 mins)