Big Oaks From Little Acorns Grow

What makes mathematics a subtle, beautiful and exciting subject is the range of ideas that grow out of the most simple of situations. In what follows I hope to show how ideas you are probably familiar with and some that are perhaps new to you, grow in a natural way from a problem that at first glance seems very circumscribed!

A group of six high school students (who are mutual friends) want to set up study group pairs to work to improve their mathematical skills. The six students live at the locations A, B, ... , F shown on a schematic diagram of their neighborhood in Figure 1. The students plan meetings at the home of one of the two members in the pair alternately. What is the best pairing?