A Spider-Fly Problem with a Surprising Solution

A spider and a fly are on opposite walls of a 30 × 12 × 12 meter room. The spider is 1 meter above the floor, the fly is 1 meter below the ceiling. They are both 6 meters from adjacent walls, as shown in the diagram below.

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If the fly does not move, what is the shortest distance the spider can crawl to reach it? (along the surface only — no web-shooting!)

A sensible first attempt would be to travel straight up (or down) and across. For example, straight up the spider’s wall (11 meters), along the roof (30 meters) and down to the fly (1 meter).

This gives a total distance of 42 meters.

But if that were the optimal solution, it wouldn’t be “surprising” and I wouldn’t be writing an article about it! 🧐

So what would you try next?

How about diagonally up and across via the front (or back) wall?

The shortest path between two points is a straight line. But given that the spider must…