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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Pariity if the 3x3x3 Classic Setup is used up to depth 21, some 21 slice quarter turn solutions may be found. 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. In MayMichael Gottlieb defined reduction parity in x44x4. However, this PDF includes all cases and relatively short algorithms to solve each one directly.

4x4x4 parity algorithms

Wiki tools Special pages. 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.

44×4 example, performing a swap of dedges to a fully 4x4x44 4x4x4 and then flipping the front dedge resulting from that swap gives us the following. 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.

Symmetrical algorithms are conjugates. 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.

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

This is especially common if two algorithms are in a parihy move set consist only of certain types of turns. 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.

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. There are actually 58 of these prity in the last layer, in general.

The obvious example is PLL parity in 4x4x4: One can split up r2 as r r or as r’ r’ and insert 3x3x3 moves to obtain the pure form of PLL parity.


Such an algorithm is called a 44x4x4 algorithm when compared to algorithms which just flip a single dedge, which are often called pure flips. More will be explained about what other pieces of information in the algorithm bar 4xx4x4 mean later. 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. This page attempts to list move optimal algorithms for every common form of parity encountered in popular 4x4x4 Rubik’s Revenge parith methods.

However, the other 54 will only be encountered during a K4 Method solve.

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 pqrity it was a 3x3x3, special algorithms have been developed for every case.

The most popular 2-cycle a swap of two pieces besides the single pafity flip case is the following. Besides containing case images and algorithms for reduction parity cases, this page pariry contains odd parity cases which can technically be used to pair dedges, since they permute wing edges oarity a manner which separates wing edges in the same dedge from each other. 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:.

Parjty, we can also just use the inner slice turns r and r’ as well. Algorithms for one such parity case already mentioned are included on this page. 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 applying an inner slice quarter turn requires, below are fairly short and simple algorithms one can use.

Algorithms for the Cage Methodas well as algorithms for theoretical purposes and general 4x4x4 exploration are present as well. Two of the most popular 15 BHTM move algorithms which flip a single dedge on the 4x4x4 are the following. The following 21 slice quarter turn algorithm was the only 21 slice quarter turn 3x3x3 algorithm which was closest to being a single dedge flip algorithm.

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.

This was deduced from the same idea that Floyd Newberry came up with for using a short repeated sequence to directly solve a 2-cycle. 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” and 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.


For convenience, an algorithm is written with the maximum number of wide turns, should that version of it still preserve as much as the version of it without any wide turns.

4x4x4 parity algorithms – Wiki

It’s worthy to note that the majority of algorithms in this section, like the 25,15 solutions, were found by using the 3x3x3 Classic Setup in Cube Explorer. We can clearly see this in the above algorithm bar.

For illustration of how algorithm bars are going to be labelled, let us temporarily name it “Old Standard Alg” and called the author “anonymous”. 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. Two algorithms of similar length the number of moves an algorithm contains can look and feel, when executing very different.

Finally, one of the simplest OLL parity more specifically, 4x4s4 double parity algorithms found in December of to remember also consists of a short repeated sequence:. Tom Rokicki and Ed Trice. That is, there is a total of 22 PLL parity cases. The creation of a symmetrical algorithm requires one to confront the question “how can I change what I have into what I want it to be?

How to solve a 4×4 Rubik’s Cube

This page not only contains commonly practiced speedsolving algorithms: 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, 44×4 slices will be expressed as single slice lowercase turns for simplicity for all 25,15 solutions.

There are links to either forum posts or video URLs in the right-most column of many “algorithm bars”. See the PLL Parity section for details. The remaining PLL parity cases which paritg the fewest number of pieces besides the most popular case above are the following.

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. Clearly this algorithm has much more of a variety of moves than “Lucas Parity”.

Below are two single dedge flip 2-cycle algorithms illustrating the idea.