I've been getting a lot of requests for 4x4x4 cubes, and we're looking into
getting them. However, I have a couple questions.
1) Why are 4x4x4 cubes so interesting? Do the additional symmetries make for
interesting questions, are they more fun, or easier to solve?
2) It appears to me that if you know how to solve the 3x3x3 Rubik's cube,
then you can easily solve the 5x5x5 rubiks (i.e., the solution is
derivative). For example, you can treat the inner 3x3 faces of the 5x5x5
as a single 3x3x3 cube. Alternately, you can treat the edges/faces along
with the the middle three slices combined into a single slice as its own
3x3x3 cube, and this would not really disturb the "inner face" 3x3x3 cube.
Is this really so, or am I missing something? Is the 5x5x5 cube simply
the group product of two 3x3x3 cubes and one or two sub-groups of a 3x3x3,
or is it more complex than that? How does this relate to the 4x4x4?
I do have a Bachelor's degree in mathematics and am familiar with abstract
algebra. I appreciate any light you can shed on these questions. I would
like to be able to converse intelligently about the cubes; that is why I
subscribed to this list.
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