Four Robots Bridge Crossing Puzzle | MindYourLogic Bridge Crossing Puzzle

Four robots need to cross a narrow bridge at night using a single lantern. Each robot has a different crossing speed, and the lantern must be carried back and forth. The goal is to find the minimum total time required for all four robots to cross the bridge. With careful planning, the robots can complete the crossing in a minimum total time of 36 minutes.

Conditions:

Robot 1: 1 minute
Robot 2: 3 minutes
Robot 3: 5 minutes
Robot 4: 9 minutes
Objective: Determine the minimum total time required for all four robots to cross the bridge.

Steps to Cross the Bridge in Minimum Time:

First Crossing:

Robot 1 (1 minute) and Robot 2 (3 minutes) cross the bridge together with the lantern.
Time taken: 3 minutes (the time of the slower robot, Robot 2).

Lantern Return:

Robot 1 (1 minute) returns with the lantern.
Time taken: 1 minute.
Total time elapsed: 4 minutes.

Second Crossing:

Robot 3 (5 minutes) and Robot 4 (9 minutes) cross the bridge together with the lantern.
Time taken: 9 minutes (the time of the slower robot, Robot 4).

Lantern Return:

Robot 2 (3 minutes) returns with the lantern.
Time taken: 3 minutes.
Total time elapsed: 16 minutes.

Final Crossing:

Robot 1 (1 minute) and Robot 2 (3 minutes) cross the bridge together with the lantern.
Time taken: 3 minutes (the time of the slower robot, Robot 2).
Total time elapsed: 19 minutes.

Conclusion:

By following this strategic plan, all four robots can cross the bridge in a total of 36 minutes. The key to minimizing the total crossing time is to efficiently manage the lantern and pair the robots in a way that balances the crossing times and return trips. This approach ensures that each crossing phase is optimized to achieve the minimal total time.