It’s easier than you think.

Good Will Hunting, the iconic film starring Matt Damon as a young janitor with an unbelievable talent for mathematics, turns twenty years old today, Dec. 5th, 2017.

Early in the film Will is shown solving a math problem without any numbers or symbols. His answer looks like an alien language.


What’s going on here? The answer is simpler than you think.

Let’s look at the question: “Draw all homeomorphically irreducible trees of size n = 10.” Sounds like a bunch of mumbo jumbo, right? Well, removing the graph theory lingo actually turns the problem into more of a riddle.

For example, a tree is simply a set of points and line segments that never wrap around in a cycle.


Homeomorphically irreducible means that no point has only two lines stemming from it.


Last, you need to be sure that no two trees are the same, a.k.a. isomorphic. Therefore, changing the length of or slanting the branches of a tree do not change it.


With all these rules in mind, homeomorphically irreducible trees of size n = 10 (meaning that there are 10 points) look something like this:

trees n = 10

There are 10 trees in total. Can you find the rest?

If all else fails, find the answers here.

Good luck!