Rubik's Cubes? Lets upgrade to Cube21 sided solvers
I couldn't solve the easy version of the Rubik's cube, maybe with a hammer I'll be able to solve the Cube21 sided version. Pavel Šavara however solved the Cube21 programmatically with C++, CLI, WPF, SQL, WCF, and ASP + Ajax. Pavel goes into some detail on his methods and math on his blog post.
He also gives out the source code for his program.
Source code under LGPL on SourceForge subversion.
GUI client + database creation engine binaries, .NET 3.0 required. Analysis report
Database of shapes in XML
Update: After talking with Pavel, he said the Rubik's cube is a far harder problem to solve. Here is a wikipedia entry on it.
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