Three Friends Bridge Crossing Puzzle | MindYourLogic Bridge Crossing Puzzle

Three friends, A, B, and C, need to cross a narrow bridge at night. They have only one flashlight, which is crucial for crossing safely in the dark. The bridge is too narrow for more than two people to cross side by side at once. Each friend has a different crossing speed, and the flashlight must be carried with them. The challenge is to determine how all three friends can cross the bridge in the minimum total time, considering that the flashlight must be brought back and forth as needed.

Conditions:

Crossing Times:

Friend A takes 1 minute to cross the bridge.
Friend B takes 2 minutes to cross the bridge.
Friend C takes 5 minutes to cross the bridge.
Rules:

Only one or two people can cross the bridge at a time.
The flashlight must be carried by whoever is crossing.
The flashlight must be returned to the starting side if needed for another crossing.

Objective:

To find the minimum time required for all three friends to cross the bridge.

Steps:

First Crossing:

Friend A and Friend B cross the bridge together with the flashlight. Since Friend B is slower, they take 2 minutes to cross.
Total time elapsed: 2 minutes.

Flashlight Return:

Friend A takes the flashlight and returns to the starting side. This takes 1 minute.
Total time elapsed: 3 minutes.

Second Crossing:

Friend C and Friend A cross the bridge together with the flashlight. Friend C is the slowest, so they take 5 minutes.
Total time elapsed: 8 minutes.

Conclusion:
By following this strategic approach, all three friends can cross the bridge in a total of 12 minutes. This solution accounts for each friend's crossing times and ensures the flashlight is used effectively to minimize the total crossing time. The process involves careful planning to optimize the use of the flashlight and the crossing times of each friend.

Total Time to Complete the Task:

The entire crossing task is completed in 12 minutes, which is the minimum time required for all three friends to cross the bridge using the given constraints.
By organizing their crossings and managing the flashlight efficiently, the friends can achieve the shortest possible crossing time.