

this shows the 4x4 and 3x3 in equivalent states after doing 4x4 reduction. the 4x4 dedges correspond to a single edge on the 3x3, and the 4 center pieces on the 4x4 correspond to the center of each face on the 3x3 
now for the final solve. as there is nearly an unlimited number of pages on solving the 3x3 we won't go into great detail about that, below are links to pages that have good methods, and we provide some tips regarding the physical aspects of solving the big cube like a 3x3, and below we will show some of the nastier things that can happen because of parity issues with the revenge, with around 5 more algorithms, these cases will be just as easy to tackle as regular pll cases. you can get by learning just 2 extra algs, but it is a good idea to eventually learn them all. Here we will give you the method most commonly used for eliminating the parities. parities are caused when a cycle is created that doesn't exist on 3x3. There are 2 different types of these that happen, the oll and pll parity. usually one will solve the cube through F2L, then look for the OLL parity. this is usually easy to spot since there will be an odd number of correctly oriented edges. the most common approach is to use the double parity fixer, since it doesn't decrease or increase the chances of the pll parity happening. (still at 50%) the single parity fix can also be used but most can't execute that alg as fast as the double parity. after that is the pll parity which can be recognized not quite as easily as oll, but close. if the pll is one that you are not familar with from 3x3 solving, then more than likely you have the pll parity. applying the straight across swap from any orientation will turn these cases into a 'normal' pll. with practice and pattern recognition you can learn to make choices for apply the parity solve that leaves you with an easy final pll.
oll parity
these are cases that can be solved straight out and are seemingly simple, cases that are more difficult, or made up of a combination of these cases are shown below. the first algs are the speedsolve algs, the second is the pure version which uses only innerslice turns, instead of both outside layers, which will preserve the orientation of the rest of the top layer. for some other oll parity ideas, check out chris hardwicks page here. there are lots of good tips and advice on how to completely orient the last layer using the parity fix. be sure to experiment with cube rotations to make the double parity fix easier.
single parity fix (oll)  double parity fix (oll & pll) 


r2 R2 B2 U2 l L' U2 r' R U2 r R' U2 F2 r R' F2 l' L B2 r2 R2  r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2 
pure single parity fix (oll)  pure double parity fix (oll & pll) 


r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2  r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2 
pll parity
these are the 2 basic pll parities that occur, either opposite or adjacent edges are swapped. note the second alg is the same as the first, just with some setup moves to get one of the edges into the straight across position.
pll parity fix  


r2 R2' U2 r2 R2' u2 r2 R2' u2 U2  y' R' U R U r2 R2' U2 r2 R2' u2 r2 R2' u2 U R' U' R 
these cases seem to give the most problems for new solvers, but they are just typical pll's with the pll parity mixed in. its usually easier and faster to use the opposite dedgeswap when possible, as its shorter/faster to fix than the adjacent dedge swap. the first 2 are applied that that the pll left over is a tpermute, the last one on the right ends up as an npermute. now there are many more odd pll cases with the parity built in, but they are easily transformed into a normal pll with almost no thought by immediatey applying pll parity fix.



y r2 R2' U2 r2 R2' u2 r2 R2' u2 (pll parity fix)
R U R' U' R' F R2 U' R' U' R U R' F' (tperm) 
r2 R2' U2 r2 R2' u2 r2 R2' u2 (pll parity fix)
R U R' U' R' F R2 U' R' U' R U R' F' 
r2 R2' U2 r2 R2' u2 r2 R2' u2 (pll parity fix)
L' U R' U2 L U' R L' U R' U2 L U' R U (nperm) 
great pages to learn 3x3 solving on:
Lars Petrus' pagethese pages are made by the best of the best, these represent almost all the well known solving methods as well as some lesser known ones. there are many, many pages for the 3x3 so be sure to find a method and algorithms that suit your style best. what is right for one solver might not be (and probably isn't) what's best for you.
©20052023 frank morris & clancy cochran