How should you arrange 7 water fountains in a mall to minimize the longest possible walk?

The video tutorial explores the optimal arrangement of water fountains in a circular mall to minimize the maximum walking distance. Initially, the problem is simplified using three fountains, leading to a mathematical approach involving radius and arc calculations. The solution is extended to seven fountains, where a central fountain and six perimeter fountains are used. The tutorial concludes with a discussion on the complexity of the problem and references to further exploration.

What is the significance of the perimeter in determining the radius of the water fountains?

How does the arrangement of water fountains change when increasing the number from three to seven?

What is the optimal placement of the water fountains in relation to the mall's shape?