Collection of 4x4x4 Reduction and Parity algorithms. Digital cheat sheet tutorial on how to solve 4x4x4 Rubik’s cube. Solution for 4×4 magic cube and. You can find all the 4x4x4 parity algorithms here: wiki/ ยท share|improve this answer. Learn how to solve the 4x4x4 Rubik’s Revenge Cube easily. Full guide Why PLL parity occurs on 4×4 cubes while it’s impossible on a regular 3×3 cube?.

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All algorithms can be applied to the 6x6x6 if instead of turning the outer 2 layers, turn the outer 3 layers; instead of turning 1 inner layer slice, turn 2 inner layer slices.

Clearly this algorithm has much more of a variety of moves than “Lucas Parity”. Although symmetrical algorithms patity technically conjugates of non-symmetrical algorithms, non-symmetrical algorithms are algorithms which are solely the result of a composition of one or more separate algorithm pieces, which all together accomplish the desired task.

rubiks cube – Simple 4x4x4 OLL parity algs? – Puzzling Stack Exchange

pparity Besides the notes mentioned already about what types of algorithms are contained within this page, including some of the specific common characteristics they share, this section touches on how they “look” and “feel” when they are displayed in notation and executed on a cube, respectively.

However, unlike all of the 23 single slice quarter turn algorithms presented in this section which oarity be applied to all big cube sizesthese two algorithms only work on the 4x4x4.

Not logged in Create account Log in. Should one wish to induce an odd permutation in the wing edges of the 4x4x4 with a short algorithm without having to restore the cube as much as party an inner slice quarter turn requires, below are fairly short and simple algorithms one can use.

4x4x4 parity algorithms

Most of the algorithms on this page affect some centers of the 4x4x4 supercube: Tom Rokicki and Ed Trice. However, we can also just use the inner slice turns r and r’ as well. Besides containing case images and algorithms for reduction parity cases, this page also contains odd parity cases which can technically be used to pair dedges, since they permute wing edges in a manner which separates wing edges in the same dedge from each other. Many of the algorithms on this page need to be “adjusted” to work for the n x n x n Rubik’s cube.


Below are two single dedge flip 2-cycle algorithms illustrating the idea. The obvious example is PLL parity in 4x4x4: Naturally, these type of parity cases are called reduction parity.

This allows one to use fewer moves to solve any given case and gives one more options. Reduction parity occurs when you try to reduce the puzzle so it can be solved by a constrained set of moves, putting it into some subset of the positions. An equally well-known form of reduction parity this term will be defined formally soon besides the single dedge flip is switching two opposite dedges in the same face. Note that with many algorithms, it’s not “all or nothing”.

A clear example of a symmetrical algorithm is Stefan Pochmann’s n x n x n opposite PLL parity algorithm, Rw2 F2 U2 r2 U2 F2 Rw2where all moves in the algorithm are conjugate moves except for the one move in the middle. In MayMichael Gottlieb defined reduction parity in detail.

4x4x4 parity algorithms – Wiki

One can split up r2 as r r or as r’ r’ and insert 3x3x3 moves to obtain the pure form of PLL parity. On January 24,speedsolving. However, many who solve the 5x5x5 Rubik’s cube using some variant of the Reduction Method will come across this case; and thus several but not all of the algorithms listed on this page which solve this case directly can be used for completing the tredge-tripling stage of a 5x5x5 Reduction solve. More will be explained about what other pieces of information in the algorithm bar above mean later.

This page will keep strong focus on reduction parity OLL parity and PLL parity cases, but it will also include a limited number of other parity situations which parrity also common in other solving methods, as well as cases which share paritj characteristics with reduction parity algorithms. For this particular set, a search up through depth 18 was performed. For example, one of the most common single parity algorithms used by the speedcubing community is “Lucas Parity”.


Their inner slice turns may all be replaced with wide turns and still preserve the first three layers F3L of the 4x4x4 and flip one dedge.

This page not only contains commonly practiced speedsolving algorithms: It is also clearly 4s4x4 a speedsolving algorithm as “Lucas Parity” is. U2 r2 U2 r2 Uw2 r2 Uw2. The “w” is short for “wide”.

That is, besides just showing parity cases and algorithms for those cases, this page attempts to attribute credit to the original founder of an algorithm as well. There is actually a total of last layer 4-cycles, but since 4-cycles in two dedges are the only ones encountered using the most popular 4x4x4 solving methods, they are the only ones shown on this page. However, despite that all 25,15 single dedge flip solutions which begin and end with an l2 or r2 move can instead be Parihy and Rw2, respectively, all slices will be expressed as single slice lowercase turns for simplicity for all 25,15 solutions.

Since the double parity case above and the single dedge flip case both have a single dedge flipped, and since OLL algorithms do not necessarily aim to permute move the pieces that they correctly orient in any particular fashion, patity 4x4x4 algorithm which solves:. OLL parity falls under this definition too so the reduced 4x4x4 has four times as many positions as you would expect.