Mehtad

The Mehtad is a 4x4 speedsolving method proposed by Yash Mehta. It is one of the first feasible methods to solve a 4x4 using the ZZ method (along with 4Z4), because the edges are oriented and the line (in fact 3 of 4 cross pieces) are already solved. It builds upon the ideas of the Yau Method and the first three steps of the solve are in fact identical to Yau.
Some commonly used techniques compatible with the Mehtad method include:
 Solving 3 half centers out of the 4 last centers before fully solving them in order to increase fingertrickability for the remainder of the last 4 centers step. With the half centers technique, the solver can finish off the centers without destroying the partial cross by using only Rw and U moves rather than 3Rw, Rw, 2L, and U moves, essentially making the remainder of this step 2gen.
 Pairing edges using EO 62 edge pairing, also called the Pairing Mehtad. Basically, right after the last 4 centers are solved, solve one more edge piece using no specific technique and put it in the bottom, then pair up 3 edge pairs at once by slicing one way, followed by 3 edge pairs while restoring the slice. In Mehtad, however, there will be some extra moves while inserting the second set of 3 edges. The last 2 edge pairs are solved using an algorithm, while orienting the final few unoriented edges.
Overview
 Solve 2 opposite centers .
 Solve 3 of the cross dedges, called the sesquiline.
 Solve the remaining 4 centers, maintaining the partial cross or the sesquiline by keeping it on the left side and using only Rw, 3Rw, 2L, and U moves.
 Pair up the one dedge without messing up the sesquiline and insert it in the correct orientation on the bottom of the cube
 Solve 6 edges at once using an advanced version of 62 pairing, or any other method that orients at least 3 of the 6 edges thus formed.
 Solve the final two edges with one algorithm, and orient the few remaining edges.
 Solve F2L + LL (3x3) and PLL Parity.
The Steps
This subpart is fairly complicated. If you are here to learn, skim through all steps once, and solve along with the walkthrough solve(s). Then, have a look at the algorithms.
 First 2 Centres: Two opposite centres are made on the 4x4. These centres must be the ones preferred to be the top and the bottom colours during the 3x3 stage.
 SesquiLine: Three of the bottom colour edges are to be formed using the freedom of 4 unmade centres. The pair of opposite edges will form the line. It is not mandatory that the third edge is a bottom colour edge, but doing the bottom colour edge has its own benefits in the 3x3 stage, and also doesn’t hamper recognition.
 Last 4 Centres: The final 4 centers are solved, maintaining the partial cross or the sesquiline by keeping it on the left side and using only Rw, 3Rw, 2L, and U moves. Techniques like half centres may be used to aid this step. All the steps thus far are identical to Yau.
 Edge 4: One random edge is solved with no specific method, and placed in the bottom in the orientation (i.e. is the edge is solved in FR and the ‘empty’ piece on the bottom is in DF, the edge may be inserted using F’ if it is unoriented, and D R’ if it is oriented).
 Pairing Mehtad: Now 6 edges are paired at once using the ‘Pairing Mehtad’. With the desirable orientation (the orientation you solve ZZ in), the pair of the FLu dedge is put in FRd, and this is followed by a Uw3. Again, the pair of the FLu dedge is put in FRd, and this is followed by a Uw3. For the third time, the pair of the FLu dedge is put in FRd. This is followed by a Uw’ slice pairing 3 edges. Note that you are a y2 away from your desired orientation, and the edge orientation recognition should be just as easy since we have the same rules. For the restoration of the slice, the three new edges will be replaced by the relevant edges to be formed, and the edges removed will be oriented correctly. For an unpaired dedge in UF to be inserted in FR, depending on the orientation of the FR edge and the way the UF edge has to be inserted, one of (R U R’), (U’ F’ U F), (F R’ F’ R)* or (U’ R’ F R F’)* will be used. [The starred algorithms also affect the UR or UL edges’ orientation respectively, hence ensure there is no paired edge in this position.] This should be done while inserting the FR edge, the FL edge (using mirrored algs), followed by a (Uw3)x2, and the nowFR slot. When followed by a Uw, this restores the edges, ensures 3 oriented paired edges on the top layer, and 3 paired edges on the E slice.
 EOL2E: With 4 oriented paired edges in the bottom and 3 in the top; we have 2 unpaired edges in FL and on top, and 3 paired edges with unknown orientation in the E slice. The 3 orientations are check while or right after restoring the slice, and it is determined whether the number is odd or even. The top layer unpaired edge is brought in UR and bottom layer ‘Empty’ edge is put in DL, and with L’ U, the two unpaired edges are brought to the top. Now, depending on the relative position of the two unpaired edges (opposite dedge exchange or adjacent dedge exchange) and the parity of number of unoriented edges (odd or even, 0/2 or 1/3), the final edges are solved using one of 4 algorithms, that both pairs the remaining dedges and misorients exactly one of the two newly formed paired edges in case of an odd parity, to have an even number of misoriented edges. Now, there can only be 0, 2 or 4 misoriented edges, and all of the must be in DL, FR, BR or UF. These edges are oriented in a few moves. An advanced solver can learn ~20 algorithms to simultaneously pair the dedges and orient all misoriented edges at once in one algorithm. In the case that all edges are paired before reaching this step, if we do not have a parity, we will still have less than or equal to 4 misoriented edges. However, in case of a parity, where we may have 1/3/5 unpaired edges, we will need an OLL parity algorithm to deal with this rare case. The OLL parity algorithm will be much shorter since F2L doesn’t have to be preserved. An advanced solver can learn ~8 algorithms to orient all edges at once. Due to small number of edges to orient, relatively low number of algorithms and enough time during the previous step to lookahead to this step, this step should have low to none recognition time, and good execution speed due to the algorithmic approach.
 ZZ3x3: With all edges oriented and a sesquiline already formed, the ZZ approach may be followed to make up for any lag caused in the edge pairing compared to the Yau method. After ZZF2L which is faster than the traditional F2L, one will obtain an LL with all edges oriented and no OLL parity. One other particular strength this offers is with the COLL/EPLL alg set to solve the last layer, the PLL parity can be incorporated in the EPLL step itself, only increasing the number of algorithms from 4 to 9, and in the new ones, the move set will still be <R, U, r, u> which is quite comfortable to do. This gives a 2 look LL, instead of the occasional 4look set in Yau.
Algorithms
Insertions:
 R U R' (if paired edge is correctly oriented, and relevant dedge piece is in UFl)
 F R' F' R (if paired edge is correctly oriented, and relevant dedge piece is in UFr)
 U' R' F R F' (if paired edge is incorrectly oriented, and relevant dedge piece is in UFl)
 U' F U F' (if paired edge is incorrectly oriented, and relevant dedge piece is in UFr)
L2E Algorithms:
 Simple straight swap  Rw D U2 Rw D' Rw' U2 Rw D Rw' D' Rw'
To be used when you get either (even parity of paired edges, same orientation of both UF dedges, and straight swap) or (odd parity of paired edges, different orientation of UF dedges, and straight swap)
 Simple cross swap  Lw' U2 Lw U2 Lw U2 Rw' U2 Lw U2 Lw' U2 x U2 Lw2 U2 Lw
To be used when you get either (even parity of paired edges, same orientation of both UF dedges, and cross swap) or (odd parity of paired edges, different orientation of UF dedges, and cross swap)
 Flipping straight swap  Lw' U2 Lw' U2 F2 Lw' F2 Rw U2 Rw' U2 Lw2
To be used when you get either (odd parity of paired edges, same orientation of both UF dedges, and straight swap) or (even parity of paired edges, different orientation of UF dedges, and straight swap)
 Flipping cross swap  Rw D Rw D' Rw' U2 Rw D Rw' U2 D' Rw'
To be used when you get either (odd parity of paired edges, same orientation of both UF dedges, and cross swap) or (even parity of paired edges, different orientation of UF dedges, and cross swap)
Pros
 EO and sesquiline is already done when you start the 3x3 step.
 Always get an OLL parity skip.
 Certain LL alg sets like COLL/EPLL work especially well with this method.
Cons
 It can be hard to find the first 3 cross edgesEO edges.
 Removing paired dedges in edge pairing involves preframed moves.
 Centers are a little bit harder.
Walkthrough solves
Walkthrough solve 1: In depth, tutorial type solve  to be scrambled in ZZ orientation
Scramble: y' U2 Uw Fw B U' Uw Rw2 U2 Rw2 U2 F2 D' U2 Fw D L2 Rw2 Uw' Fw D2 Rw2 Fw2 Uw L2 B' D' R Fw' F2 Rw D2 R2 Rw F D B Fw Uw' Fw' D'
Inspection  y First two centres  U' Lw' U' F Lw' F2 Lw' Uw U2 y Rw' F2 Rw Sesquiline  z (U D' Rw' F) (U' Rw 3Rw' D') (U2 Rw2 L F) Last 4 centres  U 3Rw2 U 3Rw U Rw2 U Rw' U Rw U Rw U' Rw' z' Note that the solve so far is identical to Yau. If you have only one solving orientation, then ensure that the sesquiline contains both your line edges  DF and DB. Most ZZ solvers prefer to be comfortable with two adjacent front colours with the same top colour as their orientation; they have the freedom to choose any 3 edges, and the two opposite edges will form the line for them. At this point, the cube should be rotated to the solving orientation, as is done with the final z'. An orientation y2 away from the solving orientation is acceptable too (i.e. if you have white top green front as your orientation, you must have white centre on top and either blue or green centre in front at the current stage). For the fourth edge, one can choose any edge to fill the last cross slot. Usually, one edge is already paired up; just like the edge in BL in this solve. This can be used to fill the last cross slot, and then the three quarters cross can be aligned. If no readymade edge is found, one can choose any edge and pair it before inserting it. This step is fairly faster than the Yau counterpart due to the very frequent ready made edges, and the liberty of choice in case of no paired edges. Edge 4  D' B D' Note that the edge was inserted with D' B, and not simply L'. This was because the edge was misoriented, and had to be inserted in a correctly oriented way. The next three edges will be paired just like the first three edges of 62 pairing. Here, the edge in FLu is a 2 swap case, hence to simplify the tutorial solve, we shall insert another edge here before starting the pairing Mehtad. Extra  L' U2 L Pairing Mehtad (I)  (F R' F' R) 3Uw (R' U R F R' F' R) 3Uw (R U R') Uw' This pairs 3 edges. Now, while restoring the slice, we need to preserve these edges in the top layer by converting them into the correct orientation, and pair 3 more edges. Pairing Mehtad (II)  U' (F' U F) Pairing Mehtad (III)  U2 (L F' L' F) Pairing Mehtad (IV)  3Uw2 (R' F R F') Uw Note that in (IV), we couldn't pair any new edge. However, what is important is to place the previous edge in the top layer, correctly oriented. Hence, we replaced it with any random junk edge we found. Now, since the Pairing Mehtad asks us to pair at least 6 edges, we shall pair one more edge. however, its orientation does not matter, and will be taken care on in EOL2E. Pairing Mehtad (V)  Uw (F U' F') Uw' Hence, we have finally completed the Pairing Mehtad. This was not the best example, since we couldn't pair 6 edges at once, but the idea should have gone through. Now we can have a maximum of 3 misoriented edges and 2 unpaired edges, and their positions will always be 4 of them in the E slice, and one of them in the U face. In this particular case, we have 2 unpaired edges in FL and FR, and 2 misoriented edges in BR and BU. The BL edge is correctly oriented. This inspection can be done while the solve is going on, and shouldn't require any pause. Currently, the only information required for EOL2E is the parity of edge orientation. In this case, we have 2 edges misoriented, and 2 is an even number. Thus, we have an even parity. Now, we bring the unpaired edges in UF and UB position, and go ahead with EOL2E. EOL2E (I)  L' R U To identify the case, we need to ask ourselves 3 questions. (A) Is the number of misoriented edges even or odd? (B) Do both UFr and UFl dedge pieces have same orientation or different? (C) Does the UFr dedge piece need to be swapped with UBr or UBl (straight or cross)? Remember, we want to make the total number of misoriented edges even at the end of this substep. After 46 solves of getting used to, this step is effortless. It is just like how PLL recognition takes some getting used to. In our case, our answers are even, both same (correctly oriented) and cross swap. Since we have even number of misoriented edges and both UF dedges have same orientation, we will have a simple swap. Here is a listing if it is not obvious: even, same > simple swap odd, same > flip swap even, different > flip swap odd, different > simple swap Thus, in our case, we shall use the simple cross swap. EOL2E (II)  Lw' U2 Lw U2 Lw U2 Rw' U2 Lw U2 Lw' U2 x U2 Lw2 U2 Lw Now, we will usually have 2 misoriented edges, and rarely 0 or 4. These can be oriented while preserving the line. In our case, we shall do as follows: EOL2E (III)  R F' U' F Hence, we have the cube reduced with EO line solved. once can learn all ~25 algorithms to solve any EOL2E case in one look. Now, solving using ZZ  ZZF2L  U (L U L U L') U2 ((R U' R' U R U' R U2 R2 U2 R2)) (L' U L U' L' U' L) COLL  U R U R' U F' R U2 R' U2 R' F R EPLL  Operm  M2 U' M2 U' M U2 Lw2 L2 U2 Rw2 R2 Uw2 Rw2 R2 Uw2 U2 M Hence, we have solved the cube using the Mehtad.
More walkthroughs, coming soon.