It’s the beginning of a new year, and you’re feeling optimistic: “This year, I’m going to manage my time well and do all of the extracurricular activities that I want to, in addition to the coursework for my Math/Stat, Comparative Literature, and Japanese triple major!” In your moment of naivety, you and a fellow cross country teammate dash over to the Purple Key Fair, but you only have 15 minutes before practice starts. Being a typical omnivorous Williams student, you want to find out about every Club Sport and every Art/Performance, Academic, Religious/Spiritual, and Special Interest group, and exactly 64 of these student organizations have tables at the fair. The groups are compactly organized into 8 rows and 8 columns of 8 tables each, and your older (and hence wiser and more cynical) friend tells you she’ll just wait for you in the corner there by the first table in the first row, and hurry up! To make practice on time, you have no choice but to run. However, you’re recovering from an ankle injury, and making turns kills your foot. Your job is therefore to run in straight lines past each of the 64 tables, making as few turns as possible. You have 15 minutes to get all 64 flyers and return back to your friend. What is the path that minimizes the number of turns you’ll have to make?
You can hit all 64 tables at the fair making as few as 13 turns: