Crossing the Bridge

Four friends need to cross a bridge.
They start on the same side of the bridge.
A maximum of two people can cross at any time.
It is night and they have just one lamp.
People that cross the bridge must carry the lamp to see the way.
A pair must walk together at the speed of the slower person:

• Rachel: - takes 1 minute to cross

• Ben: - takes 2 minutes to cross

• George: - takes 7 minutes to cross

• Yvonne: - takes 10 minutes to cross

The second fastest way of getting the friends across takes 21 minutes.
The fastest takes 17 minutes. Can you work out how it is done?

You can use the interactivity below to experiment with different strategies.

By clicking on the purple cog you can enter the settings menu and change how long it takes each person to cross.

There are two optimal strategies for solving this type of problem:

Strategy 1 solves the original problem in 17 minutes
Strategy 2 solves the original problem in 21 minutes

Experiment with different speeds and work out when to use Strategy 1 and when to use Strategy 2.

Is there a way of determining which strategy will be best?

Can you find sets of speeds for which both strategies give the same crossing time?

Printable NRICH Roadshow resource