Good Will Hunting is a movie about a young genius, played by Matt Damon. In the movie, Damon’s character figures out the solution to a problem that has alluded mathematicians for many years. The problem is find all the homeomorphically irreducible trees such that n=10.

Now this problem really that difficult? Turns out, not really. The most challenging part to most people is figuring out what the problem wants. Well we know what trees are: connected graphs using all vertices but not creating circuits. So it this case, the number of vertices would be 10 as n=10. Now then, what are homeomorphically irreducible trees? Simply put, they’re trees that are actually different(2 tress are the same if one’s difference from the other is a slightly different angle between vertices or a different rotation between the trees), and must not have any vertices with any reducible vertices(those with only 2 lines/edges going through them). So now you can do this problem, it just takes a bit of thinking. The trees at the end should look like these:

http://stanford.edu/class/archive/cs/cs106x/cs106x.1142/lectures/GoodWillHunting.pdf