Learners explore paths, cycles and trails before meeting Euler trails: special routes that use every edge exactly once. Carefully chosen examples help distinguish ideas that can initially look very similar.

This lesson includes:

• clear definitions of paths, cycles and trails;
• examples showing the difference between repeating vertices and repeating edges;
• practice tracing and recording routes;
• an introduction to Euler trails and Euler circuits;
• puzzles requiring both experimentation and explanation;
• answers and discussion;
• supplementary examples with worked solutions.

Suitable for learners aged 10 and over. It works best after Lessons 1 and 2 but can also be used independently with some adult guidance.

This is Lesson 3 of the six-part Beyond Curriculum: Graphs course.

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