CFOP method
Jessica Fridrich, a Czech speedcuber and the namesake of the method, is generally credited for popularizing it by publishing it online in 1997.
On top of that, there are other algorithm sets like ZBLL and COLL (corners of the last layer) that can be learned in addition to CFOP to improve solving efficiency even further.
Basic layer-by-layer (LBL) methods were among the first to arise during the early 1980s craze, such as James Nourse's The Simple Solution to Rubik's Cube, which proposed the use of a cross, and worked its way down.
The first official publication of CFOP was done by Anneke Treep and Kurt Dockhorn in 1981 in the Netherlands, based on the F2L-pairing idea of the Dutch professor René Schoof.
Users include Mats Valk, Feliks Zemdegs, Tymon Kolasiński [fi], Yiheng Wang, and Max Park.
Most CFOP tutorials instead recommend solving the cross on the bottom side to avoid cube rotations and to get an overall better view of the important pieces needed for the next step (F2L).
All these algorithms are based on a simple sequence which brings the pieces to the top layer, aligns them with the color faces showing, and then inserting them into the pair's correct position between the matching centers (called a slot).
This sequence can be done intuitively, but knowing the different special cases, and making use of another slot being still unsolved or "open", can improve on the general-case solution.
There are 58 possible combinations of piece orientations, so once again ignoring the solved case, this stage involves learning a total of 57 algorithms.
This would be at the cost of more “looks” at the cube to determine which algorithm is needed to solve the current sub-step, slowing down the solver, but can be used as a stepping stone into two-look OLL.
This method above, while only requiring knowledge of two algorithms, would constitute a “6-look OLL”, since at worst the solver needs to identify a case 6 different times, which is highly impractical.
They are distinguished by letter names, often based on what they look like with arrows representing what pieces are swapped around (e.g., A-perm, F-perm, T-perm, etc.).
This same ability can allow the solver, in specific known scenarios, to "force" a stage skip with a particular sequence of moves to solve the remainder of the current stage; for instance, by recognizing a particular OLL permutation and performing a specific OLL algorithm, the solver can simultaneously solve PLL, effectively obtaining a PLL skip.
[9] There also exist many advanced extension algorithm sets to be used alongside CFOP, such as COLL,[10] Winter Variation,[11] VLS, ZBLL, and more.
CFOP is heavily used and relied upon by many speedcubers, including Max Park, Feliks Zemdegs, Yiheng Wang and Tymon Kolasiński.
The vast majority of top speedcubers on the WCA ranking list are CFOP solvers, including the current 3x3x3 single world record holder Max Park with a time of 3.13 seconds.
