These are the possible cases that can happen during the solution of a 4x4 cube:
[ r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' ]
[ 2R2 U2 2R2 u2 2R2 2U2 ]
What is OLL parity?
OLL parity is when only one edge block is not oriented. This is an impossible case in a regular 3x3 cube. This case is solved using the algorithm above. It's important to execute the OLL parity algorithm, if needed, before solving the last layer, because it does not preserve the last layer pieces positions. The probability to encounter an OLL parity during a 4x4 solve is 50%
What is PLL parity?
PLL parity is when only 2 edge pieces are remained unsolved while the rest of the cube is fully solved. This case also cannot happen on a 3x3 cube (reasons below), and is being fixed by the PLL parity algorithm. The PLL parity algorithm does preserve all pieces but the switched edge pieces, and therefore can be used at the end of the solving (after solving all other last layer pieces). The probability to encounter a PLL parity during a 4x4 solve is 50%
Note! You might encounter a weird PLL case, where all pieces are solved but 2 corners for example. That’s because of the PLL parity. After applying the PLL parity algorithm it'll become a solvable PLL case.
Notations explanation: The PLL parity uses an internal layer movement. The number "2" shown before the specified face letter, means moving the internal layer of its face. Example: [2R] = [r R']. The move "2R" can be done by moving both layers by doing r, and then returning the R face back by doing R'. The move "2R2" means moving this internal layer twice. You can see image examples in the intro section above.
Why PLL parity occurs on 4x4 cubes while it's impossible on a regular 3x3 cube?
The reason is because of the mechanics and math of the Rubik's cube. As you know, moving only 2 edge pieces while preserving all other pieces is impossible* (U-perm algorithm affects 3 edge pieces, which is the lowest possible). Moving only one piece is clearly impossible (where will it go without switching with another piece?).
Therefore, a case where only 2 edge pieces needed to be switched is an impossible case on a 3x3 cube. However, on a 4x4 cube it's not really 2 pieces, but 4 pieces, and 4 pieces needed to be switched between is a possible case.
(* At least not by legal moves, the only possible way to do that is by disassembling the 2 pieces by breaking the cube and assembling it wrongly (the cube will become non-solvable)
The same rules apply for all cubes (3x3, 4x4, 5x5, etc..)
What about OLL parities?
OLL parity happens in the 4x4 cube for the same reasons as well. The minimum number of pieces orientation while preserving all other pieces is 2 (applies for all sizes of cubes). Therefore it's impossible that only 1 edge piece will be un-oriented in a 3x3 cube. While in a 4x4 cube it is actually 2 different edge pieces (even though we treat them as "one edge block") which is a possible case.
After understanding the parities, let's continue and finish solving the 4x4 cube:
If after completing step 3 (solving the cube until the last layer) you noticed that an OLL parity occur- then apply the algorithm and continue in solving the last layer using the 3x3 solving technique. Apply a PLL algorithm as well if needed.
That’s it! You had just solved the 4x4 Rubik's Revenge! Just keep and practice on solving the 4x4 cube till you'll be able to do it without using this guide. You will be happy to know that you have to memorize only 4 algorithms for that (2 parities + 2 algorithms from step 2)! Congratulations!
OLL parity:
[ r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' ]
PLL parity:(Top view)
[ 2R2 U2 2R2 u2 2R2 2U2 ]
What is OLL parity?
OLL parity is when only one edge block is not oriented. This is an impossible case in a regular 3x3 cube. This case is solved using the algorithm above. It's important to execute the OLL parity algorithm, if needed, before solving the last layer, because it does not preserve the last layer pieces positions. The probability to encounter an OLL parity during a 4x4 solve is 50%
What is PLL parity?
PLL parity is when only 2 edge pieces are remained unsolved while the rest of the cube is fully solved. This case also cannot happen on a 3x3 cube (reasons below), and is being fixed by the PLL parity algorithm. The PLL parity algorithm does preserve all pieces but the switched edge pieces, and therefore can be used at the end of the solving (after solving all other last layer pieces). The probability to encounter a PLL parity during a 4x4 solve is 50%
Note! You might encounter a weird PLL case, where all pieces are solved but 2 corners for example. That’s because of the PLL parity. After applying the PLL parity algorithm it'll become a solvable PLL case.
Notations explanation: The PLL parity uses an internal layer movement. The number "2" shown before the specified face letter, means moving the internal layer of its face. Example: [2R] = [r R']. The move "2R" can be done by moving both layers by doing r, and then returning the R face back by doing R'. The move "2R2" means moving this internal layer twice. You can see image examples in the intro section above.
Why PLL parity occurs on 4x4 cubes while it's impossible on a regular 3x3 cube?
The reason is because of the mechanics and math of the Rubik's cube. As you know, moving only 2 edge pieces while preserving all other pieces is impossible* (U-perm algorithm affects 3 edge pieces, which is the lowest possible). Moving only one piece is clearly impossible (where will it go without switching with another piece?).
Therefore, a case where only 2 edge pieces needed to be switched is an impossible case on a 3x3 cube. However, on a 4x4 cube it's not really 2 pieces, but 4 pieces, and 4 pieces needed to be switched between is a possible case.
(* At least not by legal moves, the only possible way to do that is by disassembling the 2 pieces by breaking the cube and assembling it wrongly (the cube will become non-solvable)
The same rules apply for all cubes (3x3, 4x4, 5x5, etc..)
What about OLL parities?
OLL parity happens in the 4x4 cube for the same reasons as well. The minimum number of pieces orientation while preserving all other pieces is 2 (applies for all sizes of cubes). Therefore it's impossible that only 1 edge piece will be un-oriented in a 3x3 cube. While in a 4x4 cube it is actually 2 different edge pieces (even though we treat them as "one edge block") which is a possible case.
After understanding the parities, let's continue and finish solving the 4x4 cube:
If after completing step 3 (solving the cube until the last layer) you noticed that an OLL parity occur- then apply the algorithm and continue in solving the last layer using the 3x3 solving technique. Apply a PLL algorithm as well if needed.
That’s it! You had just solved the 4x4 Rubik's Revenge! Just keep and practice on solving the 4x4 cube till you'll be able to do it without using this guide. You will be happy to know that you have to memorize only 4 algorithms for that (2 parities + 2 algorithms from step 2)! Congratulations!
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