The Masterball Puzzle
The Masterball is a permutation puzzle of colored tiles confined to the surface of a sphere. Like its better known relative, Rubik's Cube, the Masterball can be thought of as a group acting on a set of 32 points. A few principles of elementary group theory can be used to cook up solutions to the puzzle. This paper shows how that is done. It also generalizes the ball to a ball with arbitrarily many meridians and parallels, discusses the group structure of the general ball, and describes how to take advantage of the puzzle's symmetries in an algorithm to find the best solution.
This paper was my honors thesis at Berkeley. Laurent Bartholdi helped me write it over coffee (and orange juice) at Brewed Awakenings once a week. Laurent is a great guy. He plays the alpine horn, follows international boat racing competitions and likes to walk around Berkeley with no shoes on. His webpage is worth checking out too.
~Downloads~
The paper in pdf format
The paper in uncompiled tex
The source for the 3d model
Related Links:
- The Masterball homepage
- Another paper on the Masterball
- Another explanation of the solution