Crossing Every Bridge Exactly Once (aka Eulerian Paths)

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Related

Math Curiosities →Math Puzzles and Challenges →

Summary

How can you cross each bridge in this city exactly once?

  1. First, students will cross five bridges exactly once.
  2. Next, they'll try to cross seven bridges one time each. ⚠️ Note: This is impossible.
  3. They come up with three more layouts using seven bridges. At least one should work.
  4. Students count how many bridges come out of the cities. They're looking for patterns to determine whether a map will work.
  5. Finally, they try four other maps and learn about Euler and the [Seven Bridges of Königsberg](https://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg)!

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