User:Brayzn/Speedcubing

Solving methods for cubes larger than standard Rubik's
The methods to solve a standard 3x3 Rubik's Cube are insufficient to complete. Although, those methods are almost always the final step in solving bigger cubes. The competitive methods follow the basic reduction style outline of solving the centers, pairing up all of the edges, and then solving the resulting 3x3x3. What makes this tricky is the possibility of parity after reduction, which has three main types: OLL parity, PLL parity, and edge parity. OLL parity describes the situation where it appears that one edge is flipped and is thus an impossible 3x3 to solve. PLL parity describes the situation where two edges or corners are swapped resulting in an impossible 3x3. Lastly, edge parity describes the situation where everything but one edge is not built properly. This results in a long but necessary algorithm that can greatly slow down times.

Reduction Method
The reduction method (also known as the beginner method or redux method) is the most prevalent method for cubes of order 5x5x5 or greater. It boils down to the idea that after solving the center and combining the edge pieces all that is left is a 3x3x3 Rubik’s cube. The first step is to create the centers, generally starting with the colors of opposing sides and then filling out the rest. For even-sided cubes, the center colors are not set so extra consideration is needed to make sure they match a standard Rubik’s cube. This consideration is not needed for odd-sized cubes. The second step is to craft the edges by using slice moves, moves that break up the centers, to combine edge pieces and then recombine the centers so as to not mess them up. Lastly, is to solve the resulting 3x3x3 using any method. An optional step before or during the 3x3x3 is solving for any parity that may have occurred.

The reduction method leaves a lot to be optimized (see Yau Method and Free Slice Method). What the reduction method gives is flexibility, the solver can decide during the solve what they want to optimize or combine parts from other methods given the scramble.

Yau Method
The Yau Method is a variation of the Reduction Method created by Robert Yau with uses seen in 4x4x4 and 5x5x5 speedcubing. This method makes use of the fact that the edges do not need to be solved in any specific order before the 3x3x3 stage so it creates the cross during the pairing phase to skip a stage in CFOP. The general outline still remains almost identical to the reduction method.

The first step in the Yau method is to solve two opposite centers. Next, solve three cross edges for one of the two solved opposite centers. The last one is open to allow for the turning of an unsolved center without breaking up a created edge and wasting time. Once the three cross edges are solved, solve the remaining centers while using the open edge to not break up the solved cross edges. Then solve and place the remaining cross edge in its correct position. One optimization used in the Yau5 method specifically for 5x5x5 is solving two adjacent F2L pairs and then placing them in the back before solving the rest of the edges to skip that step later on. Lastly, the remaining steps are identical to reduction with the solving of the remaining edges and then solving the resulting 3x3x3. This still includes the possibility of parity.

Freeslice Method
The Freeslice method is the most common variant of Reduction and is seen in cubes of size 4x4x4 and up. The singular distinction is how edges are paired up, besides that all steps are identical. Although it is not generally considered its own method, it is used to create the distinction between the general reduction method without Freeslice edge pairing and with Freeslice edge pairing. Freeslice edge pairing can be combined with any reduction variant that requires freeform edge pairing.

Freeslice edge pairing utilizes the fact that after all centers are solved the middle centers do not need to be realigned until all edges are created. However, it is generally stopped at the last four edges as solving the last edge and recombining all four of the broken centers is unreasonable. Once there are four edges remaining, the solved edges are moved to the layers with the solved opposite centers, and then the sliced-up centers are recombined leaving a maximum of four edges remaining. The remaining solve is identical to reduction.