Problem Archive

Browse through our collection of past weekly challenges. Each problem comes with student solutions and detailed explanations.

hard 2025-06-15

The bridge crossing problem

Four people need to cross a narrow, rickety bridge at night. They have one torch, and the bridge is too dangerous to cross without it. At most, two people can cross at a time, and they must move at the slower person's pace when crossing together.

Each person takes a different amount of time to cross:

Person A: 1 minute
Person B: 2 minutes
Person C: 5 minutes
Person D: 10 minutes

What is the fastest time for all four people to get across the bridge?

Constraints:
The torch must be carried on each crossing.
No more than two people can be on the bridge at a time.
When two people cross together, they move at the pace of the slower person.
Get everyone across the bridge in the least amount of time possible.

Enabling Prompts

For students who need help getting started:

Try with just 2 people crossing the bridge first. How would you get them across?
Use counters or drawings to represent the 4 people. Move them to show each crossing.

Extending Prompts

For students ready to go deeper:

What if there were 5 people with different crossing times? What would be the fastest way?
Is there a pattern you can use to solve this for any number of people?