The way to think about solving the cube is sequences of moves with helpful properties. For example, one sequence of moves might move a piece located in a top corner to a particular bottom corner while keeping all other faces unchanged. By memorizing these sequences of moves, you can move the pieces around the cube as directly as if you could simply pluck them off and place them where you like.
Of course, some of these sequences are very long and complicated. You can reliably solve the cube but may do so slowly. The fun in advanced solving is learning faster sequences that might change multiple faces at once. The most talented speed solvers can quickly recognize the utility of these sequences when inspecting the cube, then have the dexterity to execute them quickly and accurately.
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