POW – Quick Escape

This is the first of a new series of posts called the “Problem of the Week” (POW). As is evidenced by the title, these problems will be posted weekly. Every Sunday, I will post the answer to the previous week’s POW.

Problem

You are a member on a team of four people competing against five other teams. Each person gets a distinct number which represents how many minutes it will take that person to get across a bridge. Person A can go across in at least 1 minute, person B in 2 minutes, person C in 5 minutes, and person D in 10 minutes. Your team, just as the others, has one flashlight to share between one or two people as you cross the bridge. One of the people crossing must have the flashlight in hand. The goal is to get everyone from one side of the bridge, to the other in less time than the other teams did. The time to beat is 19 minutes. The reason it takes so long is because two people can only cross the bridge at the speed of the slowest individual. Also, the flashlight may not be thrown to someone to cut down on time. Is it possible for your team to get everyone across the bridge in less than 19 minutes? If so, how can you do it?

Example Run

1. Person A (1 minute) and person D (10 minutes) go across to the target side with the flashlight in 10 minutes.
2. Person A (1 minute) comes back across the bridge with the flashlight in one minute, bringing the total time to 11 minutes.
3. Person A (1 minute) and person C (5 minutes) go across to the target side with the flashlight in 5 minutes, bringing the total time to 16 minutes.
4. Person A (1 minute) comes back across the bridge with the flashlight in one minute, bringing the the total time to 17 minutes.
5. Person A (1 minute) and person B (2 minutes) go across to the target side with the flashlight in 2 minutes, bringing the final time to 19 minutes.