The Bridges of Konigsberg

In old Konigsberg there were seven bridges:

http://commons.wikimedia.org/wiki/Image:Konigsberg_bridges.png
Image: Wikimedia Commons

Villagers used to wonder: Is it possible to leave your door, walk through the town, and return home having crossed each bridge exactly once?

Swiss mathematician Leonhard Euler had to invent graph theory to answer the question rigorously, but there’s a fairly intuitive informal proof. Can you find it?

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