Crossing the Bridge

Crossing the Bridge

Four friends are walking together at night, and they come across a bridge. They all need to get to the other side so they can continue their walk.

The bridge looks very rickety - they decide that a maximum of two people can walk across it at a time.

The four friends only have one flashlight between them - whoever is crossing the bridge must be carrying the flashlight so they can see the way ahead. The flashlight can be passed between people who are standing on the same side of the bridge.

The four friends will all take different lengths of time to walk across the bridge:

Isabella takes one minute to cross

Feranmi takes two minutes to cross

Yvonne takes seven minutes to cross

Adam takes ten minutes to cross

If two people are walking across the bridge together, they must walk at the rate of the slower person.

Can you think of some different strategies to get all four friends across the bridge?

The second fastest way takes 21 minutes.

The fastest way takes only 17 minutes!
Can you find and describe the two strategies that result in Time A (17 minutes) and Time B (21 minutes)?
Is Strategy A always most efficient? Choose four new crossing times and try it again. What happens this time?
More questions to investigate:

If I give you a set of four crossing times, can you find a way to work out in advance which strategy will be optimal?

Can you find any sets of crossing times where both strategies get the friends across in the same time?

Suppose that after every time one of the friends crosses the bridge, they get tired and one minute is added on to their journey time. Does this change the optimal strategy?

The two fastest friends have an argument and refuse to walk across the bridge together. How much longer does it take everybody to cross the bridge?