Z4

Z4 is a reductionbased method for solving the 4x4x4 using ZZ principals: minimal rotations and F/B moves.
Contents
Steps
A full description is available here.
 Solve Centres
 EOpair DF/DB and place
 EOpair 10 remaining edges
 Flip final bad dedges (including orientation parity)
 ZZF2L
 COLL
 EPLL including PLL parity (1 step)
Necessary Principles
EO Pairing
The basic idea is to orient edges while pairing them. This is achieved by using a variant of Robert Yau's edge pairing method, and solving edges using only the subset <Lw,L,Rw,R,U>.
Most pairing can be done with algorithms such as Lw U' R U Lw' or Rw' U' R2 U Rw, but when pairing two unoriented dedges, you can place them in UBl and FRd and perform Lw U' R U Lw2 U R' U' Lw instead.
Algorithms
Note: Some of the algs on this page are in SiGN, some are in WCA notation.
EOPairing
To pair two edges in general, one of the following algorithms (or their mirrored versions) can be used:
l U' R U l'
r' U' R2 U r
The algorithm l U' R U l' pairs up the pieces BUl and FUr, UBr and FRd, and UFl and RFu.
The algorithm r' U' R2 U r pairs up the pieces UBr and UFl, BUl and RFu, and FUr and Frd.
To pair two unoriented edges, place the unoriented edges in the UBl and FRd positions and do
l U' R U l2 U R' U' l
The algorithm pairs up the pieces UBl and FRd, RFu and FUr, and UFl and UBr.
For the last three pairs where all orientations match, do
F {pairing alg} F'
For the last two pairs, if the edges are both oriented, place them in UF and UB, along with a bad edge in UL if available, and do one of the following algs:
r' F R2 U' R' F' U r
r' F U' R' F' R2 U r
For the last two pairs, if the edges are both unoriented, place them in UF and UB, along with a bad edge in UL if available, and do one of the following algs:
r' U' F R' U F' r F U2 R' F'
r' F U' R F' U r R' B L' U2 B'
For OLL parity, place the bad edge in UR and do
y' r U2 r' U2 r' D2 r D2 r' B2 r B2 r' y
EPLL + Parity
See 4x4x4 EPLL + parity algorithms.
Guide
Step 1a: First 2 centres
For this step you need to create 2 opposite centres, which will be your R/L face centres. This can be done using any types of moves, but wide turns are faster than inner layer slices.
Step 1b: Remaining 4 Centres
First of all, rotate your cube so that your R/L face centres are on the correct sides, then using any moves except for F, B, or S to form the other 4 centres in the 2 central layers. You need to ensure that your chosen U colour is on top, D face on bottem etc. This step can be very fast becuase it only uses 3 types of moves
Step 2: EOPair and Place DF and DB
This is when we start to use the EOPair concept explained above. You want to EOPair DF and DB, the 2 EOLine edges and then move them to the correct places to give a EOLine.
Step 3: EOPair remaining 10 dedges
Using the EOPair concept above, the remaining edges need to be EOPaired. To make lookahead easier, After pairing edges, move them into the RD,RB,LB or LD positions, so that you can see the other edges that need to be paired.
Step 4: Finish EO (Including OLL Parity)
Similar to fixing EO at the End of the 2x2x3 block in petrus, You need to finish Orienting all of the edges using F/B moves. If an odd number of edges is flipped, you can use the Flip Single Edge (in UR) algorithm above.
Steps 5–7: ZZF2LCOLLEPLL
This is the final step and involves solving the 3x3 stage as in the ZZ method, without the EOLine becuase it has already been formed. COLLEPLL is recommended becuase then it is easier to deal with PLL parity becuase it can be dealt with in a single step. For the 4 cases that arise with PLL parity, see the algorithms section above.
Walkthrough Solve
The following uses SiGN notation, so lower case = double layer turn.
Scramble: D' r2 D u' r2 u2 d' f' D' B F' r2 D' f2 R2 D' U' B2 D2 l2 b2 u2 F' r2 U' B2 f2 U2 F' l2 b U' F u' d r D2 d' F2 L
L+R Centres: u2 r' R' L2 f U l U' l' z' (9) Finish Centres: r' U r U l' U l2 U2 l' x U2 r2 U2 r2 (13/22) First line dedge (+dedge): L U D' L' U r' U L' U' r (10/32) Second line dedge: R U' R r' U' R2 U r (8/40) Place line: R' L' D' (3/43) 1x dedge: U2 R' l U' R U l' (7/50) 2x dedges: U2 r' U' R2 U r (6/56) 3x dedges: L U L' r' U L' U' r (8/64) Final 3 dedges: L' U' l U' R U l' U R' U' l U' R U l' (15/79) Finish EO: B L' B' (3/82) ZZF2L: R2 L' U2 L2 R2 U2 R U' R' U R' U' R U' R' U R U2 L' U L U L' (23/105) OCLL: y2 R U2 R' U' R U' R' (7/112) PLL: y x R D' R U2 R' D R U2 R2 x' U' (10/122)
See also
External links
 Speedsolving.com: Simultaneous EO and edge pairing for ZZ on 4x4