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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No, it’s not possible. An “Euler circuit” is possible only if every bank and island is served by an even number of bridgeheads. Otherwise you’ll eventually get stranded or find yourself unable to return home. You can prove this to yourself — draw a map as complex as you like and try it out.

December 1, 2005July 17, 2013 | Puzzles · Science & Math