The Bridge and Torch Riddle

The Bridge and Torch Riddle 🌉🔥

Four people need to cross a bridge at night. They have only one torch, and the bridge can only hold two people at a time. The four people all walk at different speeds:

Person A can cross the bridge in 1 minute.
Person B can cross the bridge in 2 minutes.
Person C can cross the bridge in 5 minutes.
Person D can cross the bridge in 10 minutes.

The torch must be carried when crossing the bridge, and it cannot be thrown across. The group needs to cross the bridge as quickly as possible, but only two people can cross at a time.

What is the minimum time required for all four people to cross the bridge?

Hint:

To minimize time, the goal is to have the slowest people cross together as few times as possible. The strategy is to pair the faster people to shuttle the torch back and forth, while letting the slowest ones cross together.

Think about how to use the fastest people to quickly bring the torch back after the others have crossed. You’ll need to make the best use of the time of the faster walkers to avoid long delays with the slower ones.

Answer:

The Strategy: Minimize the Time by Pairing Wisely

We want to minimize the total time, so we need to think carefully about which people cross together and who brings the torch back.

Step-by-Step Solution:

First Trip:
- Person A (1 minute) and Person B (2 minutes) cross the bridge together.
- Time taken: 2 minutes (since the crossing time is determined by the slower person, Person B).
Return Trip:
- Person A (1 minute) returns with the torch.
- Time taken: 1 minute.
Now, the time elapsed is 3 minutes.
Second Trip:
- Person C (5 minutes) and Person D (10 minutes) cross the bridge together.
- Time taken: 10 minutes (since Person D is the slowest).
Now, the time elapsed is 13 minutes.
Return Trip:
- Person B (2 minutes) returns with the torch.
- Time taken: 2 minutes.
Now, the time elapsed is 15 minutes.
Final Trip:
- Person A (1 minute) and Person B (2 minutes) cross the bridge together again.
- Time taken: 2 minutes.

Total Time:

The total time taken for everyone to cross the bridge is:
2 + 1 + 10 + 2 + 2 = 17 minutes.

Conclusion:

The minimum time required for all four people to cross the bridge is 17 minutes.

This solution minimizes the number of times the slowest people (C and D) are crossing, using the faster people to shuttle the torch back quickly.

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