Here is a classic river crossing maths puzzle that tests logic, planning and simple addition. Four friends and a bag of supplies must cross a river in a small canoe that can carry only 100 kg. Can you work out how to get everyone across in the minimum number of trips?
The Puzzle
You (John) and three friends, Tom, Garry and David, need to cross a river in a small canoe. The canoe can carry at most 100 kg at a time. You also have 20 kg of supplies that must reach the other side.
- John: 90 kg
- Tom: 80 kg
- Garry: 60 kg
- David: 40 kg
- Supplies: 20 kg
How will you lead your friends across the river in the minimum number of trips? Remember, someone has to paddle the canoe back each time, and the supplies cannot paddle on their own.
Show hint
John is too heavy to share the canoe with anyone, and Tom can only share it with the supplies. Who is light enough to keep bringing the canoe back?
Answer
Show answer
The minimum is 9 trips (5 across and 4 back).
- Garry and David cross (100 kg).
- David paddles back.
- John crosses alone (90 kg).
- Garry paddles back.
- Garry and David cross (100 kg).
- David paddles back.
- Tom crosses with the supplies (100 kg).
- Garry paddles back.
- Garry and David cross (100 kg). Everyone is across!
Why 9 is the minimum: John must always cross alone, and Tom can only take the supplies with him. Only Garry and David are light enough to keep bringing the canoe back. With these limits, the canoe needs at least 5 trips across, which means 4 trips back, so 9 trips is the fewest possible.