"The Revenge of Mags the Meter Maid"

Mags has been working for the city for about 10 years driving her cart up and down the city streets searching out and ticketing parking offenders. She gets particularly irritated at college students, as they are known to run out to their cars between classes and erase the chalk marks from their tires. As a result, Mags wants to find a more efficient route to speed up the ticket writing process. Create a dialogue between you, the expert on Euler and his theorems and Mags, the district meter maid. In your conversation, explain to Mags how to take this real life routing problem and turn it into a mathematical object. Talk to her about Euler circuits, Euler paths, eulerization and how they can make her route coverage more efficient. You can assume Mags knows nothing about the subject and will have a lot of questions. (Include her questions in your dialogue.) Show graphs and diagrams that you might use in your explanation.