coldsun0630
Member
- 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.
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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)
/
- TODO (Maybe won't done forever...)
• Develop Case 5~7
• Graphics
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This is a method for 4x4 edge pairing (which I had thought few years ago), basically a substep for Yau method.
- 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 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 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 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'
• 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]
[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>.
[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.
[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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