Permute Last Layer Edges
This is the last step of solving the cube. At this step, everything should be solved except the last layer edge pieces (one sticker yellow and the other sticker something else). There are only two algorithms needed to be able to finish this step. Fortunately, these are simple algorithms and they are easy to learn and recognize.
There are only three different cases (actually four but those two are similar). Look for a solved edge on the last layer. If you do not find one, skip to case three.
This is for cases one and two–which have one edge solved. Look at the cube with the front face having the solved edge like in the diagram below (where the gray is the unsolved color and the red is your front layer):
Now, look at the cubie that was grayed out on the picture above. If it is opposite of the colors right next to them, then use case 1, if not, then use case 2. Don’t worry if you don’t understand since there are diagrams to show.
Case 1
R’ U R’ U’ R’ U’ R’ U R U R2
Case 2
R2 U’ R’ U’ R U R U R U’ R
Case 3 and 4
If all four edges are not in the right position, then just perform your favorite of the two algorithms shown above. Then, it will be reduced to either case 1 or case 2 and you can continue to solve.
Conclusion
If finished with this step correctly, the whole cube should be solved. Congratulations! Not many people have been able to do this.
Footnotes
If you want to learn this step better by learning a faster solution to cases 3 and 4, go learn the algorithms for the H-Permutation and the Z-Permutation on the PLL page of the Speedsolving wiki
