Quick post to share a really interesting problem a student of mine (G.) posed the other day.

Here’s the context: Last week, our school held a Box Lunch Auction, which involved homerooms preparing lunches of various sizes (e.g., for 6 people, for 10 people, for 30 people) and groups of students bidding on said lunches. The money raised was donated to various local charities.

Reflecting on the experience, G. wondered if the sizes of the lunches might be determined in a way that better suited the needs of the student body, rather than more or less randomly (truthfully, based on how much work a homeroom was prepared to do). This is the question he posed:

Let’s imagine that any two people in the school have a 50% chance of being friends. With

npeople, what’s the most likely size friend group?

I was hooked immediately. Continue reading “A problem worthy of attack: Friend groups”