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Math Puzzles of the Month: May 2002
The Seven Bridges of Königsberg

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In May we invited you to visit the bridges of Königsberg: can you cross each bridge just once without missing any of them?

Bridges over the Pregel River

The Pregel River had two branches and flowed around an island through the center of the city of Königsberg. There were seven bridges connecting the various landmasses, as shown in this diagram.

The townspeople, who liked to stroll over the bridges, tried to figure out a path that would cross each of the seven bridges just once. You couldn’t miss any of the bridges, and you couldn’t cross any bridge more than once.


Misses the goalMisses the goal again

The path on the left doesn’t do it because it misses one bridge:

The failed attempt, on the right crosses one of the bridges twice:

Do you think it was possible to find a path that would cross each of the seven bridges just once? If so, draw a path that fits the requirements. If you think it’s not possible explain why it isn’t.

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