## 1000.12 – Looping Paths

Prince Carlisle is designing looping pathways for his new, multi-level, royal garden. Here are two preliminary plans he’s come up with. What kinds of shapes of pathways are in each garden plan? Go for a walk on each pathway and describe what happens when you do.

## Solution

The figure on the left is composed of four distinct interlocking loops, so you cannot traverse the whole figure in one continuous walk. The figure on the right is a single elaborate path, so indeed you can traverse the entire figure in one continuous walk.

It may be that some of your students think that this problem is very easy--particularly that the drawing on the left is quite obvious. If that's the case, maybe some of them would like to make a version that won't work but that is not so obvious. If they do, send us the results and we'll upgrade the problem.