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

However, the term pure is more formally associated with an algorithm being supercube safe –algorithms which do not permute move any centers in the supercube version of a given order. Although symmetrical algorithms are 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.

On January 24,speedsolving. One can split up r2 as r r or as r’ r’ and insert 3x3x3 moves 4xx4 obtain the pure form of PLL parity.

See the PLL Parity section for details. In fact, the most popular speedcubing single parity algorithms perform additional swaps besides flipping a single dedge due to the use of wide turns. Websites such as bigcubes. Clearly this algorithm does not preserve the pairing of dedges, but it does preserve the colors of the centers; and it contains 7 inner slice quarter turns, an odd number.

In addition to the fact that all parity cases on this page are each represented by a case image, The number of moves an algorithm contains in these two big cube move metrics is written next to them in the form of the ordered pair, BQTM, BHTM. Here’s one video tutorial that illustrates the typical process. Perhaps if the 3x3x3 Classic Setup is used up to depth 21, some 21 slice quarter turn solutions may be found. 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, any 4x4x4 algorithm which solves:.

Although the third column in the majority of 4x44x4 algorithm bars on this page is blank, when it is not blank, it is either an algorithm name given by the algorithm author or an algorithm label for organizational or classification purposes. In practice, human creation 4x4xx4 symmetrical algorithms requires more trial and error of different paths in both creation of the base the base is defined as the move sequence B in A B A’ and final setup moves, whereas the creation of non-symmetrical paritj requires having knowledge of forming 4x44x pieces individually and knowing how to combine them.


Some algorithms may only be translatable to higher order even cubes 6x6x6, and larger. 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. This page attempts to list move optimal algorithms for every common form of parity encountered in popular 4x4x4 Rubik’s Revenge solving methods.

Larity are links to either forum posts or video URLs in the right-most column of many “algorithm bars”. However, the other 54 will only be encountered during a K4 Method solve.

4x4x4 parity algorithms

Since this algorithm contains move repetitionit can be written more compactly as f2 r E2 2 r f2. This allows one to use fewer moves to solve any given case and gives one more options. Recalling that the term paroty is interchangeable with the common term “swap”, these cases perform 2 2-cycles of wing edges. An equally well-known form of reduction parity this term will be defined formally soon besides the single dedge pzrity is switching two opposite dedges in the same face.

Algorithms with fewer BHTM are listed first in each category. Clearly this algorithm has much more of a variety of moves than “Lucas Parity”. Many of the algorithms on this page need to be “adjusted” to work for the n x n x n Rubik’s cube.

How to solve a 4×4 Rubik’s Cube

The shortest 4x4x4 cube odd parity fix which preserves the colors of the centers essentially independently found in parityy Tom Rokicki and Ed Trice is f2 r E2 r E2 r f2 11,7. It’s worthy to note that the majority of algorithms in this section, pariity the 25,15 solutions, were found by using the 3x3x3 Classic Setup in Cube Explorer.

This 2-cycle of wings is as common during a K4 Method solve as the single dedge flip is, but it should never patity during a solve using the Reduction Method because two dedges are not paired larity. 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.

Two algorithms of similar length the number of moves an algorithm contains can look and prity, when executing very different. Since all OLL parity algorithms contain an odd number of inner slice quarter turns, one can technically fix any 4x4x4 wing edge odd parity case by executing a single slice quarter turn and then resolve the cube using an even number of inner slice quarter turns.


However, despite that all 25,15 single dedge flip solutions which begin and end with an l2 or r2 move can instead be Lw2 and Rw2, respectively, all slices will be expressed as single slice lowercase turns for simplicity for all 25,15 solutions. Solutions listed under a case image which are not move optimal in the move metric in which algorithms are sorted by:.

This PDF includes all 58 cases and short algorithms to solve each one.

This is especially common if two algorithms are in a different move set consist only of certain types of turns. Not logged in Create account Log in.

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.

Most of the algorithms on this page affect some centers of the 4x4x4 supercube: A few of the slice turns can be wide to still just flip a single dedge, for example. 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.

4x4x4 parity algorithms – Wiki

Wiki tools Special pages. The “w” is short for “wide”.

Besides containing case images and algorithms for paeity parity cases, this page also contains odd parity cases which can technically be used to 4x44x4 dedges, since they permute wing edges in a manner which separates wing edges in the same dedge from each other.

It is common convention among the speedcubing community to use algorithms which contain wide double layer turns to solve OLL parity instead of single inner layer slices. Such an algorithm is called a parigy algorithm when compared to algorithms which just flip a single dedge, which are often called pure flips.

Note that with many algorithms, it’s not “all or nothing”. However, we can also just use the inner slice turns r and r’ 4xx4 well.

However, you can often reach a position which seems like it is in your subset, but which is actually not, and to solve the puzzle you have to briefly go outside your constrained set of moves to bring the puzzle back into the subset you want. They also happen to be supercube safe.

Symmetrical algorithms are conjugates.