How to Solve a Rubik's Cube Using Graph Theory, by Ric Donati

Since I was ten, I’ve been fascinated by the Rubik’s Cube. After solving it for the first time with the help of a tutorial, I worked to get as fast as I could — three years later I went to…

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People who know how to solve a Rubik's cube, are you good at math? - Quora

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The Problem from Good Will Hunting —

I found this image on a random article, claiming that this Rubik's cube representation makes it easier. However, I don't get it. Can you explain to me what am I looking at?