This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
Four men are on one side of a rickety bridge on a dark night. The bridge
is only strong enough to support two men at a time. It is also necessary
for the men crossing the bridge to carry a lantern to guide their way, and
the four men have only one lantern between them. Andy can cross the
bridge in 1 minute, Ben in 2, Charlie in 5, and Dan in ten minutes. How
quickly can all four men be together at the other side?
The solution is surprising to some people because they initially suspect
that it is fastest if Andy escorts everyone across because he can return
the fastest. However, a faster method requires only 17 minutes. First,
Andy and Ben cross (2 min), then Andy returns (1 min). Then, Charlie and
Dan cross (10 min) and Ben returns (2 min). Finally, Andy and Ben recross
(2 min). In short, you save two minutes by having the two slowest people
cross the bridge in the same trip.