Can You Traverse It?

Why I like this problem: Although I chose it as a stand alone activity, it is a great introduction to graph theory for those who teach it. I liked the brain teaser feel of this task and that it is accessible to any level, even those who have no previous knowledge of  graph theory. 

Observations from class: This task really feels like a game, and ALL of my students were excited about it. Many of them had a similar game on their phones and were familiar with the concept. I had students insert the pages into page protectors and use dry erase markers to try out graphs to keep them clean in case it took several tries to traverse them. Some students got wrapped up in solving the graphs and forgot to keep track of where they started and ended, so they had to go back at the end to make those observations, which was time consuming. 

Follow-up questions I asked: 

1. How did certain characteristics affect the outcome for each graph?
2. For graphs with a center vertex, how would the graph be affected if that vertex was placed on the outside?
3. Have you counted the number of vertices / edges / edges coming out of each vertex?

Required skills / content: Following paths.

Links: PDF / Google Doc

Source: https://nrich.maths.org/