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Parity is the name given to an unpredictable outcome as a result of unpredictable/uncontrollable variables. After you’ve completed all eight of the first edges (shown in Figure 4), you need to solve the last four edges.

Last two centres – Use commutators and puzzle knowledge to solve one of the last two centres, leaving the last centre solved. Since the release of the original Rubik’s Cube, people have been striving to create new and harder twisty puzzles. To put those last numbers into perspective, some scientists believe that there's "only" about 10 Some have changed the shape completely from a cube to a cuboid (and various other shapes), some have only seen simple sticker modifications.

In this case, the correct set of moves would be R U’ R’ which places the solved edge in the top layer and preserves the centre positions). 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. If, in Figure 5, the two orange-blue edges on the right were correctly oriented (they matched), then you’d be able to place the last edge piece by performing a Dw’ (bringing the “location” of the final piece underneath the actual edge piece), performing the flipping algorithm and undoing the slice with a Dw. Next, you can put your now solved centres on the left and right of the puzzle and solve two more adjacent centres. There is no way of knowing on a 4x4 (or any even layered cube) if you’ve solved the centres correctly in relation to the core mechanism.

Once you’ve solved four edges, flip the cube and solve another 4, placing them on the (now) top layer.

Note: The r2 notation refers to the Inner-R layer ONLY (an R move would be the outer R layer, and a Rw would be both the outer and inner layers). 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).