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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Such an algorithm is called a non-pure algorithm when compared to algorithms which just flip a single dedge, which are often called pure flips. This PDF includes all 58 cases and short algorithms to solve each one. However, we can also just use the inner slice turns r and r’ as well. There are actually 58 of these cases in the last layer, in general. Recalling that the term “2-cycle” is interchangeable with the common term “swap”, these cases perform 2 2-cycles of wing edges.

4x4x4 parity algorithms – Wiki

It’s worthy to note that the majority oarity algorithms in this section, like the 25,15 solutions, were found by using the 3x3x3 Classic Setup in Cube Explorer.

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.

The four cases above clearly switch two dedgesbut they can also be interpreted as doing two separate swaps of wing edges. Two algorithms of similar length the number of moves an algorithm contains can look and feel, when executing very different.

4x4x4 parity algorithms

At the same time, we can count a total of 11 block quarter turn moves BQTM. We can count that this algorithm has 7 block half turn moves BHTM without breaking it up. That is, there is a total of 22 PLL parity cases. U2 r2 U2 parify Uw2 r2 Uw2.

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

Although this algorithm is not listed under a case image on this page, it would appear in the following format in an “algorithm bar” if it was. Despite that one can technically solve all 22 PLL parity cases by executing an algorithm meant to solve any one of them to any face and then finish solving the 4x4x4 as if it was a 3x3x3, special algorithms have been developed for every case.


Similar to doing an inner slice quarter turn like r to technically fix the single dedge flip parity, an inner slice half turn such as r2 is technically all that is needed to fix PLL parity. 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.

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

We can break up this algorithm as f f r E E r E E r f f to count 4 f’s and 3 r’s.

The shortest 4x4x4 cube odd parity fix which preserves the colors of the centers essentially independently found in by Tom Rokicki and Ed Trice is f2 r E2 r E2 r f2 11,7.

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.

No “conjugate assistance” is used. Algorithms for the Cage Methodas well as algorithms for theoretical purposes and general 4x4x4 exploration are present as well.

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.

Since this algorithm contains move repetitionit can be written more compactly as f2 r E2 2 r f2. 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. The 11,7 above discolors centers on, say, the 5x5x5 cube. For example, performing a swap of dedges to a fully solved 4x4x4 and then flipping the front dedge resulting from that swap gives us the following.


See the PLL Parity section for details. However, the term pure 4x4c4 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. Clearly pariy algorithm has much more of a variety of moves than “Lucas Parity”. 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. Pwrity fact, there has been debate about what situations are considered to be a parity casebut there is one situation of which any cuber who uses the term “parity” for the 4x4x4 identifies as parity: The obvious example is PLL parity in 4x4x4: Many of the algorithms on this page need to be “adjusted” to work for the n x n x n Rubik’s cube.

Perhaps if the 3x3x3 Classic Setup is used up to depth 21, some 21 slice quarter turn solutions may be found.

The most popular 2-cycle a swap of two pieces besides the single dedge flip case is the following. 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. On January 24,speedsolving. For example, the second 15 BHTM algorithm mentioned above could be expressed later on this page with the following algorithm bar, since all of its inner slice turns can be made wide hence the “Y” instead of an “N” 4z4x4 its first and last moves can be wide and still solve the pure dedge flip case hence why the algorithm begins and ends with Rw2 instead of r2.

In MayMichael Gottlieb defined reduction parity in detail. Not logged in Create account Log in.