4 Person Bridge Crossing Puzzle | MindYourLogic Bridge Crossing Puzzle

The Bridge and Torch Problem is a classic puzzle involving four individuals who must cross a narrow bridge at night using a single torch. The bridge can hold a maximum of two people at a time, and the torch is essential for crossing as it’s dark. Each person walks at a different speed, which adds complexity to the problem. The objective is to find the optimal strategy to get all four individuals across the bridge in the least amount of time. For this scenario, the minimum time required to get everyone across is 17 minutes.

Conditions:

Crossing Times:

Alice: 1 minute
Bob: 2 minutes
Carol: 5 minutes
Dave: 10 minutes

Rules:

The bridge can hold a maximum of two people at a time.
The torch must be carried by those crossing the bridge.
The torch must be returned to the starting side if needed for the next crossing.
Objective:

To determine the minimum time required for all four people to cross the bridge.

Steps to Cross the Bridge in Minimum Time:

First Crossing:

Alice and Bob cross the bridge together with the torch. Since Bob is slower, the crossing takes 2 minutes.
Total time elapsed: 2 minutes.

Torch Return:

Alice returns with the torch to the starting side. This takes 1 minute.
Total time elapsed: 3 minutes.

Second Crossing:

Carol and Dave cross the bridge together with the torch. Since Dave is slower, the crossing takes 10 minutes.
Total time elapsed: 13 minutes.

Torch Return:

Bob returns with the torch to the starting side. This takes 2 minutes.
Total time elapsed: 15 minutes.

Final Crossing:

Alice and Bob cross the bridge together again with the torch. This takes 2 minutes.
Total time elapsed: 17 minutes.
Conclusion:
By following this strategy, all four individuals—Alice, Bob, Carol, and Dave—can successfully cross the bridge in a total of 17 minutes. The approach involves careful planning and strategic management of the torch to minimize the total crossing time. Efficient pairing of individuals, especially considering the slower individuals, is key to achieving the optimal solution.

Total Time to Complete the Task:

The task is completed in 17 minutes, which is the minimum time required given the constraints and the differing speeds of the individuals. This solution illustrates the importance of strategic planning in solving complex problems with multiple constraints.

Conclusion:
By following this strategy, all four individuals—Alice, Bob, Carol, and Dave—can successfully cross the bridge in a total of 17 minutes. The approach involves careful planning and strategic management of the torch to minimize the total crossing time. Efficient pairing of individuals, especially considering the slower individuals, is key to achieving the optimal solution.

Total Time to Complete the Task:

The task is completed in 17 minutes, which is the minimum time required given the constraints and the differing speeds of the individuals. This solution illustrates the importance of strategic planning in solving complex problems with multiple constraints.