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You will notice sometimes that you’re left with PLL parity at the end of some solves (two edges seem to have swapped places with no other affected pieces). If you know all of the PLL algorithms then noticing PLL parity will be easy for you – if the permutation of the pieces does not match a PLL algorithm that you already know, then you know you have parity. To solve this case, a Uw’ move would push the incorrectly placed orange-blue piece out of the way and match the correct orange-blue piece with the centre edge piece (shown in Figure 6).

Because you’ve had to build the centres yourself in the correct orientation (due to the lack of a single defined centre piece) and there is no way of telling if your centres are actually correct, there is a possibility of parity occurring in two different ways. Now just realign your centres so they’re solved again (if your centres can’t be solved with Uw moves after you’ve done the first eight edges, then you’ve done something wrong and need to go back and rebuild the centres). It’s fast and efficient, allowing you to solve multiple parts of edges at a time in its most advanced applications.The final step is arguably the simplest one if you know how to solve a normal 3x3 (which most people do, as these larger puzzles tend to be attempted by those who have already learnt how to solve the original Rubik’s Cube). Combinations: 11 594 693 610 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 (1. For more examples or to see this in action please set the scramble length to 1 for a 11x11x11 cube and do some scrambles.

Try finding one (if not, simply build it by doing at most 2 moves), and then find another to insert next to it. After you’ve completed all eight of the first edges (shown in Figure 4), you need to solve the last four edges. You will have noticed that, now each edge has been solved and the centres have been separated, the cube resembles a big 3x3. In Figure 1, an example is shown of how the different layers have to be manipulated to construct the edges in their entireties. Next, you can put your now solved centres on the left and right of the puzzle and solve two more adjacent centres.

To build your first centre, construct a bar by attaching two of the inner centres to the defined centre piece. Activating this checkbox the program will insert separators into the algorithm for a better readability. PLL Parity becomes noticeable at the PLL stage due to the permutation of the top four edges upon completion of the orientation of the last layer.

Once you have an edge finished, you can do the following moves to swap the edge you’ve made with an unsolved one on the top layer (in this case, the edge in the UB position) – R U R’. Next, construct another bar of the same colour, but make sure that this one has two corner centres and one inner centre. As shown in Figure 1, an edge has been made by slicing across to match up two pieces (to align two pieces, simply insert the matching piece like an F2L pair using R U’ R’ moves). You can connect pieces by putting them next to one another in the middle layer and doing a Uw’ move (this will disturb your centres, but this is fine).

There are no parities on odd layered cubes due to their defined centres (in the same way a 3x3 doesn’t have parities), so there is nothing different about the 3x3 stage on a 5x5 and a normal 3x3 Rubik’s Cube (other than of course the size). The 4 centres on each side can now be treated as one, and each pair of two edge pieces can be treated as one edge. Using only outer layer moves, the 4x4 can be solved just like a normal 3x3 cube – Building the cross, then pairing corners and edges to insert them (F2L), orienting the last layer pieces ( OLL) and permuting them to finish ( PLL).

Some permutations demonstrate this – The J and T permutations swap two edges, but they also swap two corners, without which the edge swap would be impossible. You should be able to apply your knowledge from the first two centres to build two adjacent centres without disturbing your original two. The original puzzle has been expanded outwards to create bigger and more challenging alternatives: the 4x4, 5x5, 6x6 and 7x7. Combinations: 157 152 858 401 024 063 281 013 959 519 483 771 508 510 790 313 968 742 344 694 684 829 502 629 887 168 573 442 107 637 760 000 000 000 000 000 000 000 000 (1.If you’ve built the green centre and you’re moving on to the centre adjacent to its left, just look at the defined centre and build that colour using bars. e. if the centre to the left of red with yellow on top must be blue), or the cube will not be solvable. The odd layered edge pairing system is very similar to that of the 4x4 edge pairing, but on a larger scale. Orient: On official WCA competitions cube puzzles and Megaminx are scrambled with the white face on top and the green face on the front.