Elkins Method (2x2x2)
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The Elkins Method is a 2x2 speedsolving method proposed and popularized by (however not commonly used by) Noah Elkins. His goal was to make an intermediate system of solving 2x2 cubes between the layerbylayer (LBL) method, and the Ortega method. It first orients the bottom layer in any way, so permutation is not required. Then, it requires OLL, of which there are just 8 algorithms, standard to both Layer by Layer and Ortega. both layers (PBL). This method is not very popular, but is incredibly easy to learn, a perfect method for easing into Ortega, the most accepted 2x2 method.
The Steps
 First, the bottom layer is oriented, and not permuted. This takes an average of 34 moves if the solver is colorneutral.
 Then, the OLL is executed.
 Finally, the solver must do only one of two PLL algorithms to permute the top layer, and then rotate the cube to the bottom and solve that face's PLL case and complete the cube. Most widely used for PLL in this method are the T Permutation for adjacentswaps and the Y Permutation for diagonalswaps.