You may recall the spider from Part 1. It is sitting in the middle of one of the smallest walls in my living room, and a fly is resting by the side of the window on the opposite wall, some way above the floor and \(\quantity{0.5}{m}\) from the adjacent wall.

The room is \(\quantity{8}{m}\) long, \(\quantity{4}{m}\) wide and \(\quantity{3}{m}\) high.

Diagram shows the spider opposite the fly in the positions described

This time, the fly is at a height \(h\,\text{m}\) above the floor.

  • What is the shortest distance the spider could crawl to reach the fly?

  • How does the spider’s best route depend on \(h\)?

What different possible routes are there?

Are there some possible routes that I can reject immediately?

How can I use symmetry to simplify the problem a little?