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?

Unless I'm completely confused by the flashlights, which is very possible, I came up with 25 minutes. How I see it is that 1 flashlight is able to illuminate the entire bridge, so as long as one person on the bridge has a flashlight, both people can see. Based on this, I have found 25 minutes.

If 10 & 7 start out with the flashlight, 7 will fininsh 3 minutes before the flashlight leaves the bridge. This allows for 1 & 2 to cross as well; this takes ten minutes. Leaving 5 with the remaining flashlight. 5 crosses while 10,7,2,1 repeat their crossing process. This brings us to twenty minutes. Then 5 crosses adding an extra five minutes.

Posted by MathManiac on 2005-06-25 18:11:42