Crossing Every Bridge Exactly Once (aka Eulerian Paths)

Objective

Students will try to find a path across this city which crosses each bridge exactly once.

Steps

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!

Resources

• Worksheet Part 1 (PDF) (Half sheets)
• Worksheet Part 1 (Google Slides)
• Worksheet Part 2 (PDF) (Half sheets)
• Worksheet Part 2 (Google Slides)
• Worksheet Parts 3 and 4 (PDF)
• Worksheet Parts 3 and 4 (Google Slides)
• Worksheet Part 5 (PDF)
• Worksheet Part 5 (Google Slides)
• Worksheet Part 5 - Solutions (PDF) For teacher's eyes only!