The second blackboard problem in the 1997 film Good Will Hunting asks for all the series-reduced trees (referred to by the alternate term "homeomorphically irreducible trees" in the film) on 10 nodes. Here, "series-reduced" means there are no vertices of degree 2 so that a topologically equivalent structure can be obtained by merging two incident edges at a vertex (i.e., no node merely allows a single edge to "pass through"). There are exactly 10 such trees, illustrated above (though only eight of them are drawn by the character Will in the film).
Good Will Hunting Problems
See also
Series-Reduced Tree, TreeExplore with Wolfram|Alpha
References
Horváth, G.; Korándi, J.; and Szabò, C. "Mathematics in Good Will Hunting II: Problems from the Students Perspective." Teach. Math. Comput. Sci. 11, No. 1, 3-19, 2013.Koraándi, J. and Pluhàr, G. "Mathematics and Good Will Hunting I." Teach. Math. Comput. Sci. 10, No. 2, 375-388, 2012.StackExchange: Mathematica & Wolfram Language. "List All Homeomorphically Distinct Irreducible Connected Acyclic Graphs of Size 10 ('Good Will Hunting' Problem)." Mar. 25-26, 2022. https://mathematica.stackexchange.com/questions/265641/list-all-homeomorphically-distinct-irreducible-connected-acyclic-graphs-of-size.Veisdal, J. "The Math Problems from Good Will Hunting, w/ Solutions." Jul. 31, 2019. https://www.cantorsparadise.com/the-math-problems-from-good-will-hunting-w-solutions-b081895bf379.Cite this as:
Weisstein, Eric W. "Good Will Hunting Problems." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GoodWillHuntingProblems.html