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Solving the Good Will Hunting Problem

Sounds simple? Well, it is.

I've seen the movie Good Will Hunting from 1997, starring Matt Damon in the role as a mathematical gifted janitor, twice. The first time I hadn’t taken a course in graph theory, the second time I had. Regarding the mathematical aspect of the movie, it makes all the difference. The second time I could actually understand the problem the professor posed when he threw down the gauntlet. In the movie the MIT professor stated a, supposedly, very tough problem that they had worked on intensely for almost two years before they were able to solve it. It reads:

"Draw all the homeomorphically irreducible trees having 10 vertices, such that no vertex has degree 2."

In plain words, connect ten dots together with lines such that all dots are connected to at least one other dot. Further, there must only be one path from any dot to any other dot, which means that circles are not allowed. Lastly, all dots must have 1, 3, or more lines connecting it to other dots, but not 2. Now draw all the different figures that satisfies the requirement.

That's what the gifted janitor did on the white board in the hallway.

Sounds simple? Well, it is – surprisingly simple actually.

In reality, the problem is no harder than any other high school problem. The real problem is quite different, namely that we accepted it was hard because Hollywood said so. A corollary to this claim could be to check the Internet and realize that many people already have solved the problem and some even before the movie. Another corollary could be to spend the next 10 minutes or so to solve it yourself, tell someone you know that has seen the movie, and then watch their reaction.

So, the only thing left now, is to challenge you to solve the problem and to present the solution.

Last week I challenged Erik Forsberg, a senior .NET consultant from Avega Group AB in Sweden. He solved the problem before he zipped his morning coffee a third time. Can you?

I've hidden the solution from plain view here.

More Stories By Martin Kaarup

Martin Kaarup began his professional career over a decade ago as a system developer on location-based mobile phone services. During that time he participated as lead developer in pioneering unique state-of-the-art location-based services for the European and Asian markets, such as low-cost fleet-tracking using antenna triangulation and applications for utilizing customer positioning data for demographic use. He also participated in building location based games, such as treasure hunts and country-wide Dungeon & Dragons-based games merging www, wap and sms technologies.

Later, he shifted to the financial sector in Scandinavia where he worked as an enterprise architect building, extending, and delivering advanced fund data solutions and services designed specifically for the pan-European Fund Industry.

Today, Martin is an employee at the Swedish consultants company Avega Group, where he focuses his expertice on consulting companies on strategic and enterprise wide issues.

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