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.



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.