1 The diagram shows the layout of a Mediterranean garden. Thick lines represent paths.
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1. Draw a graph to represent this information using the vertices listed below, and with arcs representing the 18 paths. Vertices: patio (pa); pool (po); top steps (ts); orange tree (or); fig tree (fi); pool door (pd); back door (bd); front door (fd); front steps (fs); gate (gat); olive tree (ol); garage (gar). [2] Joanna, the householder, wants to walk along all of the paths.
2. Explain why she cannot do this without repeating at least one path.
3. Write down a route for Joanna to walk along all of the paths, repeating exactly one path. Write down the path which must be repeated. Joanna has a new path constructed which links the pool directly to the top steps.
4. Describe how this affects Joanna's walk, and where she can start and finish. (You are not required to give a new route.)