Five Engineers Bridge Crossing Puzzle | MindYourLogic Bridge Crossing Puzzle

Five engineers need to cross a narrow bridge at night using a single lantern. Each engineer has a different crossing speed, and the lantern must be carried back and forth. The challenge is to find the minimum total time required for all five engineers to cross the bridge, which is 22 minutes. This puzzle involves strategic planning to minimize the total crossing time while managing the lantern and different crossing speeds of the engineers.

Conditions:

Engineer A: 1 minute
Engineer B: 2 minutes
Engineer C: 4 minutes
Engineer D: 7 minutes
Engineer E: 10 minutes
Steps:

First Crossing:

Engineer A (1 minute) and Engineer B (2 minutes) cross the bridge together.
Time taken: 2 minutes (the time of the slower engineer, Engineer B).
Lantern Return:

Engineer A (1 minute) returns with the lantern.
Time taken: 1 minute.
Total time elapsed: 3 minutes.

Second Crossing:

Engineer D (7 minutes) and Engineer E (10 minutes) cross the bridge together.
Time taken: 10 minutes (the time of the slower engineer, Engineer E).

Lantern Return:

Engineer B (2 minutes) returns with the lantern.
Time taken: 2 minutes.
Total time elapsed: 15 minutes.

Third Crossing:

Engineer A (1 minute) and Engineer C (4 minutes) cross the bridge together.
Time taken: 4 minutes (the time of the slower engineer, Engineer C).
Total time elapsed: 19 minutes.

Lantern Return:

Engineer A (1 minute) returns with the lantern.
Time taken: 1 minute.
Total time elapsed: 20 minutes.

Final Crossing:

Engineer A (1 minute) and Engineer B (2 minutes) cross the bridge together again.
Time taken: 2 minutes (the time of the slower engineer, Engineer B).
Total time elapsed: 22 minutes.

Conclusion:
By following this carefully planned sequence, all five engineers successfully cross the bridge in a total of 19 minutes. The strategy involves pairing the fastest engineers to handle the lantern efficiently and managing return trips to minimize the overall crossing time. This approach demonstrates the importance of optimizing each step to achieve the minimal total time, given the constraints of the different crossing speeds and the requirement to manage the lantern.