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That's not the only way to solve big cubes, but it's indeed the most common way (known as "reduction"), and what most people naturally come up with if they try
by Oreb 2y ago
That's not the only way to solve big cubes, but it's indeed the most common way (known as "reduction"), and what most people naturally come up with if they try to solve 4x4x4 or bigger on their own. In addition to what you said, there is also the issue of parity (basically, when you reduce a 4x4x4 to a 3x3x3 by solving centers and edges first, you will often end up with a 3x3x3 cube in an unsolvable state, and you need to figure out some tricks to convert it to a solvable state), but if you know how to solve parity problems on a 4x4x4, you can do it for a cube of any size.
- golf_mike 2y agoJust out of curiosity (no rubiks cube affinity at all), but how can there be an unsolvable state when there are 'tricks' get in a solvable state? Does that not imply that there are no unsolvable states at all? Or is that maybe related to a certain method of solving?
- glomph 2y agoThey mean that the outer 3x3 is unsolvable taken in isolaton. The tricks will involve unsolving the middle faces and solving them again.
- golf_mike 2y agothanks!
- Oreb 2y agoThe reduction method means reducing a big cube (NxNxN for N>3) to a 3x3x3 cube by first solving the centers (the central (N-2)x(N-2)x(N-2) square on each face) and the edges (the inner N-2 pieces along each edge of the cube). You are then essentially left with a 3x3x3 cube that you can try to solve by only turning the outer layers (which won't break the centers and edges you solved in the first stage). The problem with this is that you may end up with a 3x3x3 cube that is not solvable. For instance, you can get a state where the entire cube is solved, except for two edges that need to swap locations. This isn't possible. In group theoretical language, only even permutations are possible. You can swap two _pairs_ of edges, but not just two edges. When you end up in such an unsolvable 3x3x3 cube, you have to temporarily turn the inner layers of the cube and break apart the centers and edges you built in the first step, and then reassemble them again to a solvable 3x3x3 cube.
- golf_mike 2y agothanks!
- hinkley 2y agoThe moves to fix parity made the 4x4x4 less fun for me. The recommended solution is long. The hollow 3 has a similar problem. Because you can’t see the central piece there’s a way to rotate the core and a couple of edge pieces so they look like they violate parity.