My method for 4x4 edge pairing

coldsun0630

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- EDIT: I'll call this method as This method will be named as "Last 4 Edge Pairing" or "L4EP". I will cut out the >5 edge blocks cases.

/

This is a method for 4x4 edge pairing (which I had thought few years ago), basically a substep for Yau method. The concept of this method is just to reduce move count at the edge pairing step: do the common 2-edge pairing until 4 and use the algs, or pair at once if possible. It requires to be at most 7 unpaired edge blocks left after solving the cross (which means one of them should be paired while pairing the last cross edges). I'm not sure if this could be used in actual speedsolving, because of the recognition and efficiency by ETM. (Maybe good for 4x4 FMC though.) Please tell me if I missed something or if there's better alg/idea. (+You don't need to memorize all of the algs below unless you want to save little time more. Instead, I recommend to see the examples and learn the patterns of the solutions.)


- Terms and others
• same kind of edges: the edge pieces which have same kind of colors.
• aU, bE (cU, dE) = the position of the unpaired edge blocks (the bracket is for 2-cycle-included cases)
• Case Order: [FR]→[FL]→[BL]→[BR]→[UF]→[UL]→[UB]→[UR], [aligned]→[disaligned] (2-cycle), [upper piece]→[lower piece] (3~4-cycle), [CCW]→[CW] (3~4-cycle), [adjacent]→[opposite] (2-cycle)


- Algorithms (*Bracket = needs appropriate AUF)
- Example Solves
[Example 1] / [Example 2]
[Example 3] / [Example 4] / [Example 5]


[1-1] 2U
1-1Aa. r' U2 r' D' r U2 r' D r2 [UR-UB]
1-1Ab. r' F U' R F' U 2-2r [UF-UB] / r' F R F' R U' R' U 2-2r [UF-UB]
1-1Ba. r2 D' r U2 r' D r U2 r [UR-UB]
1-1Bb. B2 r2 F U' R F' U r2 B2 [UF-UB] / B2 r2 F R F' R U' R' U R' r2 B2 [UF-UB]

[1-2] 1U, 1E
1-2A. L u' R U R' F R' F' R u L' [UL] / L u L' U' L F' L F L' u' L' [UL]
1-2B. L' u' L R' U2 R L' u L [UL] / y R u R' L U2 L' R u' R' [UB] / F' l U' F R' U F' l' F R [UB] / y R' u' R U R' F R' F' R u R [UB] / L' u R U' R2 U R2 U' R' u' L [UL] / L' u R' U' R2 U R2 U' R u' L [UL]

[1-3] 2E
1-3A. u' R U R' F R' F' R u / y2 u R' U R' F R F' R u'
1-3B. L2 u2 U' R U R' F R' F' R u2 L2
1-3C. u2 R U R' F R' F' R u2 / u' R L' U2 L R' u / y' u R L' U2 L R' u' / u R' U' R2 U R2 U' R u' / y u' R' U' R2 U R2 U' R u
1-3D. L2 u L F' L' F L' U L U' u' L2
- Example Solves
[Example 1] / [Example 2] / [Example 3]
[Example 4] / [Example 5] / [Example 6]


[2-1] 3U {Fixed edge: uFL}
2-1Aa. l' R' U R U' l
2-1Ab. r U R' U' 2-2r'
2-1Ba. r' U' R U 2-2r
2-1Bb. l R U' R' U l' / y f R U R' U' f' / y' f U R U' R' f'
2-1Ca. B2 r2 F R F' r2 B2 R'
2-1Cb. x U2 r2 U' R U R' r2 U2 x'
2-1Da. F2 r2 U R2 U' r2 F2 / F' R' u' R U2 R' u R F / y' r U r' U r' U' r2 U' r' U r' U r
2-1Db. y r' U' r R U' R' U r' U r

[2-2] 2U, 1E {Fixed edge: dFR}
2-2Aa. L' u2 (L U' L') u2 L [uFR→UfL] / L' u2 (R U' R') u2 L [UfL→uFR] / r' U r U' R U R' r' U' r [uFR→UFr→UfL] / r U r' R' U' R U r U' r' [uFR→UbR→UbL] / y r U' L' U 2-2l' x' [uFR→UbR→UbL]
2-2Ab. // = <2-2Aa>
2-2Ba. (L' U L) d (R U' R') u' / L d (R U' R') u' F' [uFR→UbL] / r' F R F' 2-2r [uFR→UFl→UBl]
2-2Bb. (L' U L) u' (U R U' R') u / L u' (U R U' R') u L' [UbL→uFR] / 2-2r U R U' r' [uFR→UBl→UFl]
2-2Ca. // = <2-2Bb>
2-2Cb. // = <2-2Ba>
2-2Da. (L' U L) u (U' L' U L) u' / L u (U' L' U L) u' L' [uFR→UbL] / r' U' r R' F R F' r' U r [uFR→UbL→UfL]
2-2Db. // = <2-2Db>

[2-3] 1U, 2E {Fixed edge: dFR}
2-3Aa. u' (R U' R') u
2-3Ab. d (R U' R') u' / u (F' L F L') u'
2-3Ba. d' (L' U L) u / u' (F R' F' R) u // ↔ <2-3Ab>
2-3Bb. u (L' U L) u' // ↔ <2-3Aa>
2-3Ca. R u2 R' U2 R u2 R' [UR]
2-3Cb. L' u2 U R U' R' u2 L [UL] / y' r U r' U' R' U R r U' r' [UB] / y' r' U' r U R U' R' r' U r [UB]
2-3Da. (R U' R') d' (L' U' L) u / R' F R F' u' R' F R F' u [UR]
2-3Db. (R U' R') u (L' U2 L) u'
2-3Ea. u2 (R U R') u2
2-3Eb. u2 (L U' L') u2 // = [y2] + <2-3Ea>
2-3Fa. u2 (F R' F' R) u2 / y u2 (L' U L) u2
2-3Fb. y' u2 (L' U L) u2 // = [y2] + <2-3Fa>
2-3Ga. R u R' U' R u' R' [UR] / y R' u' R U R' u R [UB] / y' L' u' L U L' u L [UB]
2-3Gb. y R' u F' L F L' u' R [UB]
2-3Ha. L u L' U' L u' L' [UL] / y' R' u' R U R' u R [UF] // = [y2] + <2-3Ga>
2-3Hb. L u' F R' F' R u L' [UL] / y' R' u F' L F L' u' R [UF] // = [y2] + <2-3Gb>

[2-4] 3E {Fixed edge: dBR; added [y'] for better viewpoint}
2-4Aa. L' u' R' U' R u L / R' f' R' F' R f R / y F l' U L2 U' l F' L2
2-4Ab. F r F R F' r' F / y R u L U L' u' R' / y L f L F L' f' L' / F' r U' R2 U r' F R2
2-4Ba. y F' l' U L2 U' l F' L2 F2 / F2 R' f R F R' f' R F2 / R U' F r' U' R' U r F' R'
2-4Bb. L' u R U R' u' L / R2 F' r U' R2 U r' F
2-4Ca. R U' R' u2 L' U L u2 / R' F' U r U' R U r' F / R U' F r U R U' r' F' R'
2-4Cb. R U' R' u2 R' U' R u2 / R' U' F r U R U' r' F'
2-4Da. F r U' R2 U r' F' R2
2-4Db. R' U' R u' R U2 R' u / R2 F r U' R2 U r' F' / F l' U' R' U r U' 3l
- Example Solves
[Example 1] / [Example 2]
[Example 3] / [Example 4]
[Example 5] / [Example 6]


[3-1] 4U
3-1A. R U' R' U R r2 F2 r2 U' r2 F2 r2 R' [UF=UL]
3-1B. r2 F2 r2 U' r2 F2 r2
3-1C. r U r' U R U' R' r U' r' [UL=UB] / r' U' r U' R' U R r' U r [UF=UL]
3-1D. r U r' R U R' U' r U' r' [UL=UR]
3-1E. R2 U' R' u' R' U' R u2 R U2 R' u' R2 [UF=UR] / x U R' U' 2-2r2 U2 r2 B r2 U2 r2 R' x' [UF=UL]
3-1F. R2 U2 r U R U' r2 R U' R' U r U2 R2 / R2 U2 r' U' R U r2 R' U R U' r' U2 R2

[3-2] 3U, 1E
3-2A. L' u2 (R U' R') (L U L') u2 L [FR-UL] / R r2 F2 r2 U' r2 F2 r2 R' [FR-UL, UF-UB] / F' r U r' U R U' R' r U' r' F [FR-UR, UL-UB]
3-2B. L' u2 (L U L') (U' F R' F' R) u2 L [FR-UL]
3-2C. L u (F' L F L') u2 (R U2 R') u L' [FR-UL] / y L' l2 F2 l2 U l2 F2 l2 L [FR-UB, UL-UR] / y F r U r' U R U' R' r U' r' F' [FR-UB, UF-UL]
3-2D. L u (L' U L) u2 (R U R') u L' [FR-UL]

[3-3-1] 2U, 2E (2U)
3-3-1A. R2 u2 (R' L' U L R) u2 R2 / u' r' F R F' R U' R' U 2-2r u [UL-UR] / y z U2 2-2r2 F2 r2 U' r2 F2 2-2r2 U2 z' [UL-UR] / y z U2 R r2 F2 r2 U' r2 F2 r2 R' U2 z' [UF-UR]
3-3-1B. l' U l U R U' R' l' U' l [UF-UB]
3-3-1C. u' (R U' R') u2 y' (R U R') u'
3-3-1D. u' (R U' R') u2 (L' U' L) u'
3-3-1E. u2 r' F R F' R U' R' U 2-2r u2 [UF-UB]
3-3-1F. x' l' U L U' r2 R' U R U' r' L' [UF-UB]
3-3-1G. u2 (R U' R') (L U L') u2
3-3-1H. u2 (R U' R') y (R' U' R) u2 / y l' U l U R' U' R l' U' l [UL-UR]

[3-3-2] 2U, 2E (1U, 1E)
3-3-2A. R u2 (R' U' R) (L' U L) u2 R' [FL-UR] / y' (R' U' R) u (R U' R') u2 (R' U2 R) u
3-3-2B. L' u2 (L U L') (F R' F' R) u2 L [FR-UL] / (R U' R') u (F' L F L') u2 (R U2 R') u / r U' r' L' U' L U r U r' [FR-UB, FL-UF]
3-3-2C. R u2 (R' U' R) (F' L F L') u2 R' [FL-UR] / (L' U L) u' (F R' F' R) u2 (L' U2 L) u' / l' U l R U R' U' l' U' l [FR-UF, FL-UB] // ↔ <3-2-2B>
3-3-2D. (R U' R') u' (R U R') u2 (L' U L) u'
3-3-2E. F' u' (L' U' L) u2 (L U L') u' F [BL-UF] / y' R' u (L' U L) u2 (R U R') u R [BL-UF]
3-3-2F. y R' u (F' L F L') u2 (R U2 R') u R [FR-UB] / (L U L') u2 (L U L') (F R' F' R) u2 / y l' U l R' U R U' l' U' l [FR-UL, BL-UR]
3-3-2G. L u' (F R' F' R) u2 (L' U2 L) u' L' [FR-UL] / y (R' U' R) u2 (R' U' R) (F' L F L') u2 / y' l' U l R' U R U' l' U' l [FR-UL, BL-UR] // [y2] + <3-2-2F>
3-3-2H. y F u (R U R') u2 (R' U' R) u F' [BL-UR] / L u' (R U' R') u2 (L' U' L) u' L' [FR-UL]

[3-4] 1U, 3E {Added [y'] for better viewpoint}
3-4A. (R U' R') u' (R' U2 R) y' (R' U' R) u
3-4B. y R u' L' U' L y R' U2 R u F [FL-UB] / F R' F' R u' R' U R F R' F' R u [FL-UF]
3-4C. u' (R' F R F') R' U' R u / y' u (R' F R F') R' U' R u' / u (R F) U' F' R' u' / y u' (R F) U' F' R' u / y' u2 L2 u L' U L2 U' L' u' L2 u2
3-4D. u (L F' L' F) R U' R' u' / y u' (L F' L' F) R U' R' u / u' (F' R') U' R F u / y u (F' R') U' R F u'
3-4E. y2 R2 u' (U) L' U' L F R' F' R u R2 / y u2 R2 u R U R2 U' R u' R2 u2
3-4F. y' L2 u (U') R U R' F' L F L' u' L2 / d2 R2 u' R' U' R2 U R' u R2 u2 [FR-UL]
3-4G. y (L' U L) u2 (L R U' R' L') u2
3-4H. (R U' R') u2 (R' L' U L R) u2

[3-5] 4E
3-5A. u2 R2 F2 R2 F2 u2 / u2 R U' R2 U R2 U' R' u2 / y u2 R L' U2 L R' u2 / y u R' U2 F U' F' R u'
3-5B. x R2 f R2 U2 R2 U2 f' R2 x' / y' x U2 f R2 U2 R2 U2 f' U2 x'
3-5C. x R2 f U2 R2 U2 R2 f' R2 x' / y x U2 f R2 U2 R2 U2 f' U2 x' // = [y2] + <3-5B>
3-5D. y' u2 F' R' U' R U2 F u2
3-5E. u2 R2 F' R U' R2 U R' F u2
3-5F. x f R2 U2 R2 U2 f' x'
3-5G. x f U2 R2 U2 R2 f' x' // = [y2] + <3-5F>
3-5H. u' R' L' U2 L R u
- Example Solves
• Basic Pattern 1
[Example 1] / [Example 2]
[Example 3] / [Example 4]

• Basic Pattern 2 (*didn't find easy way to recognize yet)
[Example 5] / [Example 6]
[Example 7] / [Example 8]

• Easy Patterns to Memorize
[Example 9] / [Example 10] / [Example 11]


[4-4-1] 1U, 3E (FR→FL→BL→UF) {Fixed edge: dBR; added [y'] for better viewpoint}
4-4-1Aa. R2 u' R U' R2 U R u R2
4-4-1Ab. L2 u R' U' R2 U R' u L2
4-4-1Ba. y R2 u' L U L2 U' L u R2
4-4-1Bb. y L2 u L' U L2 U' L u' L2
4-4-1Ca. y2 u' F' L2 F L' U L' u / y u' 3l' U2 3l F' U F' u / y u' L F' L' U' F L' U L u
4-4-1Cb. y u F' L2 F L' U L' u' / u 3l' U2 3l F' U F' u' / u L F' L' U' F L' U L u'
4-4-1Da. y2 u' L U' L F' L2 F u / y u' L' U' L F' U L F L' u / y u' U' L F' L' U F L' U L u
4-4-1Db. y u L U' L F' L2 F u' / u L' U' L F' U L F L' u' / u U' L F' L' U F L' U L u'
4-4-1Ea. y' F' U' u' L U' L F' L2 F d R / y2 R' u' L F' L' U2 F L' U L u R
4-4-1Eb. L' U2 u R U' R B' R2 B u' L / L' u y L F' L' U F L' U L d' R
4-4-1Fa. y' L u' R U' F R F' R U' R' U R2 u L' / y' L u' y R' F R U' F R U' R' d L'
4-4-1Fb. y' L u R' F R U2 F' R U' R' u' L'
4-4-1Ga. y' u F R2 F' R U' R u' / u 3r U2 3r' F U' F d' / u R' F R U F' R U' R' u'
4-4-1Gb. u' F R2 F' R U' R u / y u' 3r U2 3r' F U' F d / y u' R' F R U F' R U' R' u
4-4-1Ha. y' u R' U R' F R2 F' u' / u R U R' F U' R' F' R u' / u R' F R U' F' R U' R' u'
4-4-1Hb. u' R' U R' F R2 F' u / y u' R U R' F U' R' F' R u / y u' R' F R U' F' R U' R' u
(AUF omitted)

[4-4-2] 1U, 3E (FR→FL→UF→BL) {Fixed edge: dBR; added [y'] for better viewpoint}
4-4-2Aa. y L U L u' F2 L F2 L' u L2
4-4-2Ab. y2 F u2 R U R' d' L' U L u' L' / y F2 u L U' L F' L2 F u' F2 / R2 u L' U' L F' U' L F L' U2 u' R2 / y' L u l' U l R U R' U' l' U' l u' L'
4-4-2Ba. L' 2-2u' L' B2 L B2 u L
4-4-2Bb. L' u y R' F2 R F2 d' R
4-4-2Ca. y u' L F2 L' F2 u
4-4-2Cb. u L F2 L' F2 u'
4-4-2Da. u' R U' R2 U R u
4-4-2Db. y' u R U' R2 U R u'
4-4-2Ea. y' L d R' U2 R2 U2 R' u' F'
4-4-2Eb. u L F' L' F u R' U2 R u2
4-4-2Fa. R U' R' d' L U' L2 U L u / y2 F 2-2u R' U' R2 U R' u' F'
4-4-2Fb. y' L u' R' U' R2 U R' u L'
4-4-2Ga. u2 R' U R d L U L' u
4-4-2Gb. u' R' U' R d' R U R' u2 / F R' F' R u' R' U R2 U' R' u
4-4-2Ha. y u2 R U' R' d R' U R u / R U' R' d R' U R2 U' R' u'
4-4-2Hb. y u' R U' R' d' L' U' L u2 / R U' R' u' U' R' U' R2 U R' u
(AUF omitted)

[4-4-3] 1U, 3E (FR→UF→FL→BL) {Fixed edge: dBR; added [y'] for better viewpoint}
4-4-3Aa. L' U L u L' U2 L u F' L F L' u2 / y2 R' u' r U' r' L' U' L U r U r' u R
4-4-3Ab. L' U L u2 L' U L u' y' R U' R' u'
4-4-3Ba. y' R U' R' u R' F R F' u R U2 R' u2
4-4-3Bb. R' U' R' u F2 R' F2 R u' R2
4-4-3Ca. y' u2 R' F R F' 2-2u' R U' R' u' / R' F R F' 2-2u' R U' R2 U R u
4-4-3Cb. y u L U L' d L' U' L u2 / R U' R' u F2 R' F2 R u'
4-4-3Da. u2 L' U L d' L U' L' u' / y L' U L d' L U' L2 U L u
4-4-3Db. u L' U L d R U R' u2 / y L' U L u L U2 L2 U2 L u'
4-4-3Ea. L' u R U R2 U' R u' L
4-4-3Eb. L' d' R U2 R2 U2 R d L
4-4-3Fa. y L U L' u' F2 L F2 L' u / y u' R' F R F' u' L U2 L' u2
4-4-3Fb. y' R' F R F' u R' U2 R2 U2 R' u'
4-4-3Ga. u R' F2 R F2 u'
4-4-3Gb. y u' R' F2 R F2 u
4-4-3Ha. R2 u' R' U' R2 U R' u R2
4-4-3Hb. y' L F' L' F 2-2u L U L2 U' L u
(AUF omitted)


[Other Cases]
*Setup & go to <4-4>. (Too many; couldn't make them all.)

• Miscellaneous Algs
u2 r' R' F R F' r u2
R U' R' d L U' L2 U L u'

u r U' r' U R' U' R r U r' u'
u' r U r' R' U' R U r U' r' u
u' r U' r' U' L' U L r U r' u
F r U' r' R U2 R' U2 r U r' F '

r U' r' U' r U' r' U' r U' r'
z r U2 r U2 r U2 r U2 r U2 z'

r' F' r U r U' r' F r U2 r' U' r U' r'
r U2 r' U' r U' r' U' r U' r' U' r U r'
/
[5-1] 2+3-cycle of edges
[Example 1] / [Example 2]
[Example 3]

• Miscellaneous Algs
F' r U r' U' r' F r U r U' r' U2 r U r'


[5-2] 5-cycle of edges
[Example 4] / [Example 5]
[6-1] 2+2+2-cycle of edges
[Example 1] / [Example 2]
[Example 3] / [Example 4]

[6-2] 2+4-cycle of edges
[Example 5] / [Example 6]
[Example 7] / [Example 8]
[Example 9]

[6-3] 3+3-cycle of edges
*2-edge pairing will give you <Case 2>.

[6-4] 6-cycle of edges
*2-edge pairing will give you <Case 3>.
[7-1] 2+2+3-cycle of edges
[Example 1] / [Example 2]

[7-2] 2+5-cycle of edges
*2-edge pairing will give you <Case 5>.

[7-3] 3+4-cycle of edges
*2-edge pairing will give you <Case 3> or <5-1>.

[7-4] 7-cycle of edges
*2-edge pairing will give you <5-2>.
**4-edge pairing will pair the edges at once, but not compatible with <7-3>, and it's still slower than 2-edge pairing because of the setups.


- TODO (Maybe won't done forever...)
• Develop Case 5~7
• Graphics
 
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Zeroing means cancellation.(*) This method doesn't contains whole new system but more closer to zeroing process.

If you meant Feliks' 19.36 WR solve, this method doesn't have any relation with the solution. I'm sorry if I confused you.


- EDIT: According to its reconstruction, he did similar method with <Case 6> - [Example 6]. He did 2~3 recognitions, 4 u-turns, 3 insertion. I did here 3 recognitions, 3 u-turns, 3 insertion. If he did recognition when saving RG, my method is better since it does one less u-turn. If he didn't do recognition there, it doesn't work when he inserted OB at uFR (doing U R U' R' instead R U' R' to save RG).

- EDIT 2: For the reconstruction: [Link]

- EDIT 3: *I thought zeroing meant cancellation.
 
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Oh, really? I didn't know that. XD
What the meme stands for?


Just replaced <1-1Aa> and <1-1Ba>. Thanks!

Just for clarification, these guys are really big trolls. You're right that zeroing is cancellation. If we're talking about Felik's zeroing, then that is a totally different method.
 
Oh, really? I didn't know that. XD
What the meme stands for

It's a joke about Feliks's old name on YouTube, fazrulz1 (I think he changed it to Feliks zemdegs). The joke is that FAZ is a method he uses, F2L After Zeroing. What is zeroing? We don't know its a secret

Just for clarification, these guys are really big trolls. You're right that zeroing is cancellation. If we're talking about Felik's zeroing, then that is a totally different method.

Nope they aren't trolls zeroing is just a meme. Cancellation is cancellation
 
It's a joke about Feliks's old name on YouTube, fazrulz1 (I think he changed it to Feliks zemdegs). The joke is that FAZ is a method he uses, F2L After Zeroing. What is zeroing? We don't know its a secret



Nope they aren't trolls zeroing is just a meme. Cancellation is cancellation

yah I know. But isn't it F2L AND Zeroing? And doesn't his name mean Feliks A. Zemdegs? @feliks zemdegs @David Zemdegs
 
Just for clarification, these guys are really big trolls. You're right that zeroing is cancellation. If we're talking about Felik's zeroing, then that is a totally different method.
https://www.speedsolving.com/forum/threads/zeroing-tutorial-discussion-text-video.25576/
http://www.speedsolving.com/forum/t...el-9-feliks-zemdegss-solve.25488/#post-484856
http://www.speedsolving.com/forum/showthread.php?25517-Predict-Faz-s-secret
https://www.speedsolving.com/wiki/index.php/List_of_cubing_memes#Zeroing_.28November_2010.29
So no. We might troll sometimes but this is definitely not one of those times.
Zeroing never has and should never mean cancelling. The only time that it might have meant that was other people trolling which you clearly fell for.
Also you spelled Feliks' wrong
 
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Alright, thanks for the correction. Changed the title to prevent any other confusion.
 
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