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.
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?
Upper Primary
2025-06-01
Food Truck Festival Challenge
Two food trucks are catering at a local festival.
Truck A can serve a full lunch to 160 people in 4 hours.
Truck B can serve the same number of people in 2.5 hours.
If they work together (at full speed), how long will it take them to serve 160 people?
Stretch my thinking...
What if there were 200 people? What about 500?
Truck A can serve a full lunch to 160 people in 4 hours.
Truck B can serve the same number of people in 2.5 hours.
If they work together (at full speed), how long will it take them to serve 160 people?
Stretch my thinking...
What if there were 200 people? What about 500?
Enabling Prompts
For students who need help getting started:
- How many people can Truck A serve in 1 hour? What about Truck B?
- If both trucks work for 1 hour together, how many people would they serve in total?
Extending Prompts
For students ready to go deeper:
- Is the combined time exactly half of Truck A's time? Why or why not?
- If you added a third truck that could serve 160 people in 8 hours, would it make a big difference to the total time? Explain your reasoning.
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