The 4x4x4 example solve game

Next: U' F2 L2 B2 D2 L2 U L2 U' B2 U R' B' D' F' U B' U2 B2 F' Uw2 B' R Uw2 U2 R2 F2 Rw2 L B2 L' Uw' F2 U2 Fw2 L2 F2 L Fw' Rw B2 F' Uw' Rw2 R2
The crappy method I use which has no name but I guess it's in between OBLBL, Yau and Yau5, 103 moves.
y
D l U l' U' l 3d r U2 r' // first two centres
z' R2 U x' U2 r F2 U // red-green square
x2 R U' r U2 F' // red-yellow square
x' r' U r2 U r' D R' D' F // red-blue square
r' U' r2 U r U r U r' U2 r // finish centres; one free pair
U' l' D R2 D' l // +2
U' 3r' U 3r // cross
U R' U' F' R' F // first slot
r2 R' U' R U r2 // +3
R' u' R' U R 2U // +3
R2 U' B R' U B' // second slot
L R2 U R U' 3r' // third slot
R2 U' R U R' U' x' U' R U // last slot (VHLS)
y' 3r' U2 L U L' U2 R2 U' L U R' U2 // ZBLL


(I initially intended to do this linearly but got some bad cycles in edge pairing so I backtracked once there. Didn't do any intentional parity avoidance.)

Next: F2 D2 U2 F L2 F' U2 L2 F' D2 B D2 L U R' D2 U2 B D' U F' Fw2 Uw2 F Rw2 R' B D2 L U2 F' L R2 Uw R2 Uw R' L Fw U' Rw' Uw R2 Fw' R B
 
This looks like a lot of fun! I’m not at home right now, but I might do an example solve with this method later.
Well, there are a few mistakes in my example solve. EO should have been done before pairing last two edges and the FB is just highly inefficient.

Also, extending the 2x3x4 into a 3x3x4 and last two edges should have been algorithmic but algs haven't been genned yet lol.
 
Well, there are a few mistakes in my example solve. EO should have been done before pairing last two edges and the FB is just highly inefficient.

Also, extending the 2x3x4 into a 3x3x4 and last two edges should have been algorithmic but algs haven't been genned yet lol.
This might be a dumb question, but how do you do EO before pairing the last 2 edges? And what is the purpose? Parity avoidance?
 
Next: U D2 F U2 R F' R U F2 R2 B U2 R2 B D2 F' U2 R2 F R' Rw2 Uw2 D2 R U2 Fw2 U' R B2 D Fw2 F2 R' B' Uw2 Fw U L' Uw2 Rw' Uw U' F2 U2 Fw'
U B r B' U' r2 D r u2 y D' r' D2 r // F2C

B' u' L' // white-green edge
u R' // white-orange edge
F2 u2 R' // white-red edge

z' B L U2 2L2 L2 D' l // green center
L U' L F L' r U2 r' // blue center
3r' U r2 U r2 2L2 U2 2L2 // L2C

I somehow built a lot of edges during centers, so yeah, that's cool.

z' L2 2U' F' U' F u L2 u' R U R' F R' F' R u // edges

L U L' F' U2 F D // F2L 1
3f R' 3f' // F2L 2
F U' F' U' L U2 L' // F2L 3
U2 L' U' L U2 L' U L // F2L 4

U r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 // OLL parity

U2 R U R' U R U2 R' // OLL
R2 U' s R2 s' R2 U R2 U2 // PLL

alg.cubing.net

U B r B' U' r2 D r u2 y D' r' D2 r // F2C
z2 B' u' B' L D U' R' u2 D F' L' F U R u D' F L' U L // FB
R2 2U2 B U' B' u' // 3x3x4 minus a few centers
R' U R2 u' U' R' U R u R U R U R2 u R U2 R' u' // edges
r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 // OLL parity
U' R' U2 s' U s R' U' R' // EO Belt
U' R2 U' R2 // TDR
U' R2 D R' U2 R D' R' U2 R' // OLL
2R2 U2 2R2 u2 2R2 u2 // PLL parity
U' R U R' U' D R2 U' R U' R' U R' U R2 U D' // PLL
z' U 2R U 2L' U' 2R' U 2L U' 2R' U' 2L U 2R U' 2L' z2 2L U 2R' U' 2L' U 2R U' 2R U' 2L' U 2R' U' 2L U // centers
alg.cubing.net

Next: B' L2 R2 F L2 D2 U2 B F2 U2 L2 D F' D2 L2 B R B2 U' L' U' Rw2 U Rw2 Uw2 F' Rw2 B2 U B2 F2 Rw2 D B' Rw' F' Uw2 B Rw' D2 F2 Rw' Fw Uw R2 L' Uw
 
Mehta-MH, 124 STM

x2
U2 Rw' U' Rw2 // 1st face (4/4)
y' 2R U 2R' U Lw' U2 Lw // 2nd face (7/11)
R Uw' D L' Uw R' F R2 D2 L' D B2 // 1x3x4 (12/23)
Uw' R' 3Uw R 3Uw' U' R' U R2 U R' 3Uw' R Uw R' 3Uw' // pseudo 2x3x4 (16/39)
R Uw2 R U R Uw' R Uw' R' Uw R' Uw' R2 Uw // pseudo 3x3x4 (14/53)
R' U' R Uw' // 1 edge (4/57)
U x' U' R U R' x Uw // 2 edges (6/63)
U' R U2 R Uw // 3 edges + orient DR (5/68)
R' F R F' Uw' // 4 edges (5/73)
B U2 B' R' U R Uw // 5 edges (7/80)
R U2 R' Uw' // Set up to L2E alg (4/84)
R2 F2 Uw' F2 Uw2 F2 R2 Uw R2 Uw2 R2 F2 Uw' R2 // L2E + OLL parity (14/98)
U2 R U' R U' R' U2 R' // 6CO (8/106)
U' R2 U2 R2 // 6CP (4/110)
U2 R U R' U R' U' R' U R2 U2 R' U2 D' // L5EP (14/124)

View at alg.cubing.net

Next: U R F2 D2 F2 U L2 D2 L2 R2 D B2 L2 B D' F L B2 D2 B U' Rw2 Fw2 D B2 Uw2 Fw2 L2 F' U' B2 F2 D' R2 Rw' D2 Rw' F2 U Rw2 U Uw' Fw' Uw2 F' Rw'
 
Next: B2 L R U2 R2 D2 B2 L' U2 B' D U L' B' D2 L R' Uw2 F U2 Fw2 Uw2 R' L F B2 Rw2 L2 F' Uw' Fw2 R' Uw2 B Uw Fw2 Uw F' Fw Uw D F2
U2 D2 r' B' r' // yellow center
L' R2 u l' D2 l y' D' r D2 r' // white center

z U r' D' // white-green edge
F r2 U' // white-blue edge
B r' L' D // white-orange edge

L F r F' r' L' U 2L' U2 r // green center
L F' L' r U2 r' // orange center
3r 2L' U 2L r U2 r' // L2C

z' L R U' R' u2 R U' R' u2 U' D R' F R // white-red edge
u R U' R' y R2 F R2 F' R' U2 R u' // GR, YO, YR, YB
R U' R' L' U L u' R U R' F R' F' R u // GO, YG
R U R' L' U' L u' R U R' F R' F' R u // RB, OB

D' R U2 R' D // F2L 1
L' U' L U' R' U' R // F2L 2
y' D' L' U' L D // F2L 3
R U2 R' U' R U' R2 F R F' // F2L 4
U 3l' U' m U' L U 3l' U 3l // OLL
U F R U' R' U' R U R' F' U' 2R2 U2 2R2 u2 2R2 u2 U' R U R' U' R' F R F' // PLL+Parity

alg.cubing.net
U2 D2 r' B' r' // yellow center
L' R2 u l' D2 l y' D' r D2 r' // white center

L u' R' F u2 L' B u' D' R2 L2 U2 R' L2 U R' U' R D2 // FB
3u' R U' 3u' R 3u R2 U' R' 3u R e' R 2D R2 3u // 2x3x4
u R u' R' u' R U R2 U' R u R2 u2 R u' // almost 3x3x4

R U R' u R U2 R' u' // WR, YO
R' U R u F' U F u' // GR, RB
B U' B' R2 U' R2 u F' U F u' // YG, YR, YB

U' R F' U2 F R' U' R' // EO Belt
R2 U' R2 U' R2 U' R U2 R2 U' R2 U' R2 U2 R // 6CO
U' R2 U R2 U2 R2 U R2 U2 R2 // APDR
2R2 U2 2R2 u2 2R2 u2 // PLL parity
U R U R' F' R U2 R' U2 R' F R U R U2 R' U' // PLL

x' y 2L' B' 2R B 2L B' 2R' B // orange center
2L' U' 2R U 2L U' 2R' U' 2L' U 2R U' 2L U 2R' U // L2C

alg.cubing.net

Next: U R L2 U2 R2 D' L2 R2 F2 U R2 B2 U B F R' D' R2 U L U2 Fw2 Uw2 U R' Uw2 L U2 F2 Uw2 L' D2 L2 Fw' R D2 Fw' D B2 R2 Rw U' Fw' Uw' U L2
 
Next: D2 R2 D2 R2 B D2 F2 U2 B' D2 U2 R' D2 U' L B2 L' F2 R Uw2 Fw2 F L2 U B' Rw2 L2 D' Fw2 D B' Rw B D R L2 B2 Uw' Rw' F2 Uw2 B' F2 Uw
x y2 // Inspection

L' D u' r' // white center
B r' U2 r u2 U f' U2 f // yellow center

z U F' r' U // white-orange edge
L2 B R' F' r L' B // white-red edge
U2 r2 L F // white-green edge

L' l' F' l // red center & white-blue edge
r D r' D L2 U' r2 U2 2L2 // blue center
r U' r' 2L' U' 2L // L2C

z' U' L2 u' L' U L R' U R L U L' R' U2 R u // GO, YR, YB
L' U2 L u F U' F' u' // OB, YO
R U2 R' u' F' U' F u // GR, RB, YG

y' D2 R U2 R2 U' R // F2L 1
F' U' F U2 L' U' L // F2L 2
U L U L' // F2L 3
U' F' U' F U F' U' F // F2L 4
U s' U' F R' F' R U R U' R' s // OLL
U R2 F R U R U' R' F' R U2 R' U2 R U2 // PLL

alg.cubing.net
x y2 // Inspection

L' D u' r' // white center
B r' U2 r u2 U f' U2 f // yellow center

2U2 R U L U' L' u2 F R L' B' u U B2 U' B' // FB
L2 2D' L' F U' F' 3u' L2 u L 2D L2 B' U B 3u // 2x3x4
L u2 L F' L F L' u' L' u2 s U2 s' u L' u L2 u' // 3x3x4

y' F' U' F' U2 F2 u' R U2 R' u // WO, YR
F U F' u' F' U' F u // GR, RB
L' U2 L u' R U R' F R' F' R u // YG, YO

y' R' 3u U R U' R' // EO Belt
U R U R' U R U2 R U2 R2 3r U R' U' 3r' F R F' // 6CO
R2 U2 R2 U R2 U R2 // APDR
2R2 U2 2R2 u2 2R2 u2 // PLL Parity
R' U' R U D' R2 U R' U R U' R U' R2 e2 // PLL

alg.cubing.net

Next: B' L2 U' R2 D' B2 D F2 R2 F2 D U' F2 L' B' L2 B' D B2 R2 Uw2 B' Uw2 Fw2 U' L2 B2 U' F' Rw2 B D' F Rw B2 R Fw2 Uw F2 Rw' U2 Fw U' R B'
 
y z2
u2 U' l U l' U2 r'//yellow centre
3d F' l' U2 l//white
L u z' F R2 x' U2 x D' 2L' D//cross edges
U 3r' U' r U' 2L U 3r' r U r U' r U' r U2 r' U r' U2 r//centres
R U2 R U' l U' R' U 2L' z' F2 D//cross edge
u L U L' 3d R U' R2' U' R u' L' U L U' L U L' R U' R' 3r' U' R U 3r R' u L' U' L u' R U2 R' u L' U' L u'//edges +f2l 12
U' L' U2 L U L' U' L//f2l 3
U' R' F R F' U2 R U R'//f2l 4
U' R U R' U R U' R' U R U' R' U R U2 R' y 2R2 U2 2R2 Uw2 2R2 Uw2//LL
137 HTM

next:
U2 F2 L2 U2 F2 U' R2 B2 L2 F2 U' L B F L D' F D2 U B2 Fw2 Uw2 B R2 D Fw2 B Rw2 B2 D L2 F' B' Rw' Uw2 F R Fw2 U2 Fw' Uw' Fw2 Uw' Rw' D' L'

y' x2
//centers HGKE TQUJ FBVR NWLC
//edges EQNB JWIT GDMA OPLR FLCK XS
//corners AOSC BUWV

[L: [2L U 2L', 2U]]
[2U, 2L' U2 2L]
[2L': [2L' U 2L, 2D2]]
[z' 2U: [2U2, 2R U 2R']]
[U': [U2, 2R' 2U' 2R]]
[U: [2R U' 2R', 2D']]
[R' y: [2D2, 2R U' 2R']]
[y': [U, 2R' 2U 2R]]

[3Rw' : [U' 2R U, L2]]
[2R', U' R' U]
[2R, U L' U']
[L, D 2R' D']
[Lw' Rw' U : [R, U 2R U']]
[2R' U : [U R' U', 2R2]]
[Dw 3Lw R : [U 2R U', R2]]
[2R' : [U' L U, 2R2]]
[L' : [U2, 2L' D' 2L]]
[z D : [2R', U R U']]
[D : [2R2, U' R2 U]]
R2' D' Rw2 3Rw' U2 2R' U2 2L U2 2L' U2 m' U2 2L' U2 Rw' D R2 //wing parity

[U' : [R D' R', U']]
[R B R', F2]
[R D' R' : [R' D R, U2]]
[R': [R U R' U' R U R', D']]

Recon: https://alg.cubing.net/?setup=U2_F2...2]] [R-:_[R_U_R-_U-_R_U_R-,_D-]]&puzzle=4x4x4


Next: F' R D F2 D L2 B2 L2 B2 D2 B2 U' R2 F2 R B2 R2 F U' L U2 Uw2 Fw2 F Uw2 F2 U' Rw2 U B' Rw2 D B L2 Rw' U B2 L2 Uw Fw U' R' Uw' Fw R' D'
 
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Next: F' R D F2 D L2 B2 L2 B2 D2 B2 U' R2 F2 R B2 R2 F U' L U2 Uw2 Fw2 F Uw2 F2 U' Rw2 U B' Rw2 D B L2 Rw' U B2 L2 Uw Fw U' R' Uw' Fw R' D'
z // Inspection

l' D' l D2 l D' l' R u' R L u r' U2 r U y F' r U2 r' // F2C

z' 3r' U r2 D' // WB
F U2 r2 F U' B // WO & WR

3r' U r U' r' 3r' U 2L' // green center
3r U r2 U' r2 U 2L2 U 2L2 // orange center
3r r U r' 2L' U2 2L // L2C

z' u R U' R2 U2 R u' // RB, YG, YR
y' D R u' F' U F u // GR, YO
U' L' U L u' F' U2 F u // WG, OB, YB

R2 L' U L D // F2L 1
U2 L U2 L' U' L U L' // F2L 2
L' U2 L y' L U' L' // F2L 3
R U2 R' U' s' R U R' s // F2L 4
R' U' F U R U' R' F' R // OLL
U x R2 F R F' R U2 3r' U 3r U2 B // PLL

alg.cubing.net

Next: D' F2 U' D2 F U2 L' U' F R2 B R2 D2 B2 D2 B2 R2 F' D2 Rw2 U R2 Fw2 Rw2 F' Rw2 B' D2 R2 B2 L2 Rw Uw2 R' F2 D B Rw' Uw F Uw' Fw' U L2
 
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