I love the movie Good Will Hunting for lots of reasons: It’s about being different and finding yourself, dealing with demons, the struggles with the ladies, but (much more superficially) it was at my school and deals with math. The movie glosses over some of the actual math problems, and I assumed that they were all way out of my league. Let’s be honest, although I went to MIT, there were many students beyond my capabilities. Do you remember the part of the film where the professor puts up a problem with these figures made up of dots and lines & claimed it was a problem it took the professors years to solve? The problem just looked cool and one day I got curious enough to look it up.

Here it is: Draw all the irreducible, homeomorphic trees of degree n=10

It’s actually not that hard, you just have to understand what that means to solve it. Here are the rules:

• Make as many figures as you can
• with 10 dots and lines that connect them
• that are unique (homeomorphic)
• that don’t create any internal shapes (i.e. closed loops)
• that don’t have any dot with just 2 lines connected (1 or 3+ is ok)

Here’s my solution (don’t look if you want to try yourself)

Oops had to cross out a mistake, but still pretty happy how quick & fun it was to solve.