In the puzzle Four people on a Bridge we met four people who needed to cross a bridge at night. In this puzzle, there are five people who must cross two sequential bridges at night. As in the original puzzle, there are some hindrances:

The bridges can only support two people crossing at a time.

Each person has a different speed in which they can cross: 10 minutes, 7 minutes, 5 minutes, 2 minutes, and 1 minute.

They have only two flashlights to share among them.

What is the shortest amount of time it will take for all five people to cross both bridges?

(In reply to re(2): Fastest solution yet? correct? by jduval)

As Tristan and Hugo pointed out, the second leg of the 1, 2, 5 minute people's journey cannot start until the 7, 10 minute people have crossed the second bridge, and this doesn't happen until the end of minute 20.  Therefore the second leg, which takes 8 minutes, starts at the end of minute 20 giving a total of 28  minutes.

Just so you know, as I was coming up with this puzzle, the 28 minute solution was the first one I came up with too.  I discovered a shorter one while driving home from work, then forgot how I did it when I got home and wanted to write it down.  I did figure it out again without too much difficulty.

Tristan's final answer is the shortest I could find, and I found two ways of getting that number, although the difference between the two methods is rather trivial.

Posted by Erik O. on 2005-06-27 20:37:59