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There are a ton of ways to get the cube from solved state to solved state. One way is (R B D)x ~60 which I find quite interesting. Since the cube is very symmetric, there are a lot of these cases.


It seems like you are trying to find One such example that satisfies this is In particular, As mentioned by armb in the comments, there is a good answer here discussing the maximum orders for an $n \times n \times n$ Rubiks cube.


Here are some notes on my own approach: 1. Prep work I did a lot of prep work ahead of time so that the combinatorial engine could run as efficiently as possible. For example, I took each word in my word list and shifted it in a circular fashion into all possible positions around the wheel. I stored these results in a lookup array for quick referencing ...

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