Schoolyard Adventure:

Imagine a schoolyard with several connected play areas: swings, slides, a sandbox, and a climbing frame. You want to plan a fun route for your younger sibling that allows them to visit each play area once without retracing their steps.

a$)$ Draw a simple graph where each vertex represents a play area $($swings$,$ slides, etc.$)$ and edges connect areas you can walk between.

b$)$ Can you create a path that visits each edge $($walkway$)$ only once and allows your sibling to return to the starting point $($like the swings$)?$ If yes, what kind of path would this be $($Euler circuit$)?$ Explain why.?