Once and Only Once

Discrete Mathematics Level 1

Traveling along the edges of this figure, can you find a path that ends where it begins and that visits each of the 13 dots in the figure exactly once (with the exception of the one where it both starts and finishes)?

Details and Assumptions

You can start your path anywhere, but it must end in the same place
You can use the edges between the dots more than once

Bonus: If you believe it's impossible, prove why. If you believe it''s possible, how many different ways can it be done?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.