R3T
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R3T, which stands for "Reduction-3-Terence," is a method based on reducing the cube into a state solvable using mainly RUD moves. R3T's core is to leverage pseudo-blocks for the first two layers. The method was made to address ZZ's weakness of the need to use alternating L and R moves.
R3T-CT and R3T-CLS are alternate ways to finish solving the last layer. R3T-CT is based on ZZ-CT.
Important to Note
Solvers can choose to use triplet building with or without pseudo-blocks. Using R3T without pseudo-blocks trades the ability to option select for significantly easier lookahead. Using R3T with pseudo-blocks trades TPS for flexibility.
R3T-CLS attempts to address the lookahead issues in the F2L-1 and last pair steps of R3T. This variation removes the possibility of having to "adjust D face" before solving the last pair by solving both E-slice edges before CLS. Solvers may still have to "adjust D face" to perform CLS, but it is less awkward as the unsolved corner slot always has to be in the DFR position.
Steps (R3T)
1) EOEdge
Solve edge orientation and the LB and LF edges.
2) Triplet Building + Stripe
Triplet building: form a triplet (a 1x1x3 block) with one D-layer edge and two D-layer corners. Position the triplet in the D-layer to create a 1x2x3 block on the left face. This block is similar to a Roux block and may be a pseudo-block.
Stripe: solve the corresponding DF and DB edges to create a 2x2x3 block or pseudo-block.
Note. The triplet and the stripe can be solved in any order; prioritise the easier one.
3) Pseudo F2L-1
Form a pair using the last D-layer edge and a D-layer corner. Position an E-slice edge an R2 away from being solved. Insert the pair with the E-slide edge with an R2.
Note: It is important to (1) learn to solve the pair and E-slice edge as three pieces and (2) learn to "adjust D face" immediately to transition to the last pair. An alg set for (1) and a recognition system for (2) is needed for this. Incomplete
4) Last Pair
Form a pseudoslot with a D move if needed. Solve the last pair to complete the remainder of F2L.
- Knowing some/all Winter Variation and/or Summer Variation case may be useful here
5) OCLL
Orient the corners (7 cases).
6) PLL
Permute the pieces of the last layer (21 cases).
Steps (R3T-CT)
1) EOEdge
Solve edge orientation and the LB and LF edges
2) Triplet Building + Stripe
3) Pseudo F2L-1
Form a pair with the corresponding DR edge with a D-layer corner. Solve the pair with the RB edge by positioning the RB edge at the FR position and inserting them together with an R2. Form a FR pseudo-slot using a D move if needed.
4) TSLE
Insert the final E-slice edge while orienting all remaining corners using Tran Style Last Edge (104 cases). Beginner version: pair the last edge with any corner and do Winter Variation (WV).
5) TTLL
Solve the cube from this state using Tran-Thompson Last Layer (72 cases + 21 PLLs; 33% 2-gen).
Steps (R3T-CLS)
1) EOEdge
Solve edge orientation and the LB and LF edges
2) Triplet Building + Stripe
3) Pseudo F2L-1C
Form a pair with the corresponding DR edge with a D-layer corner. Solve the pair with both E-slice edges, leaving one D-layer corner unsolved. If needed, position the unsolved corner at the DFR position (using a D move).
4) CLS
Insert the final corner while orienting the U-layer corners using (104 cases).
5) PLL
Permute the pieces of the last layer (21 cases).
Example Solves
Note: I created these solutions without finding the most optimal moves, just went with what I'd do in a normal solve.
R3T
1) L D2 F' R D' R2 D2 F' U B2 R B2 L D2 R' F2 R D2 L2 D2
EOEdge: x2 D L' U L B' D2 L F2 L2
Triplet building: R U R' U2 R r2' D
Stripe: R U' r U2 r
F2L-1: U' R2 U R' D
Last pair: U' R' U' R U R' U' R D2
OCLL: U R U R' U R U2' R'
PLL: U R2' U' R U' R U R' U R2 U D' R U' R' D (59 HTM)
2) F' R2 U2 L2 U2 B D2 B R2 D2 F' U' R2 F R' U' R2 F' U B' D
EOEdge: x2 D' F D R U B U' L
Triplet building: R U' R2' U' R' D R' D2
Stripe: U r U2 r'
F2L-1: U' R U R' U' R2 U R
Last pair: U2 R U R' U R U' R' D2
OCLL: U2 R U2 R2' U' R2 U' R2 U2 R
PLL: R U R' U' R' F R2 U' R' U' R U R' F' U2 (62 HTM)
R3T-CT
1) B2 L' F U' B2 U' L2 U L2 B2 L2 U L2 U B' D' B2 L D' B' L2
EOEdge: x2 U' F L2' D' B' L U' L' U L
Triplet building: R' U' R M2 U2 M2 U R2 D2
Stripe: D R U R U' R' D'
F2L-1: R' U2 R' U2' R2
TSLE: U' R U R' (skip)
TTLL: U R U' R U' R' D R U' D' R2 D R D' R2 U2 R' U R' (54 STM)
R3T-CLS
1) U2 R2 D2 L' U2 B2 U2 R2 B2 R' U2 B' D F U B' L' D' B F
EOEdge: x2 U B R2' U D F L U2 L'
Triplet building: M2 U' R2 D2
Stripe: R U' r U2 r
F2L-1C: R' U R U' R' U R U2 R2 D'
CLS: U2 R U2 R' U R2 U2 R' U' R U' R2 D2
PLL: R U' R U R U R U' R' U' R2 U2 (53 STM)
Other Variants
1) R3T-Square-1: EOEdge, Pseudo First Block + E-slice, Corner Orientation (CO), Spam F2L, PLL
//About Spam F2L Complete F2L using R2, r2, M, U moves (e.g., R2 U R2, r2 U r2 U'r2, M2 U M2). Suggested steps: pair the last 2 corners with the last cross edge to make the 1x1x3 that goes in the first layer and solve the DF edges DB before, while, or after completing the second block. (You can solve the DF and DB at any time, even before solving the pseudo 1x2x3.) Another way is to insert the 2 corners into the first layer without the DR edge, PBL with Square-1 algs(a few modified to fix "parity"), then insert the DR edge.
2) R3T-Square-1-LSE: Don't finish F2L, instead, solve the second block with R2, U, and M, then permute the corners while influencing the UL and Ur edges and end with the rest of LSE.
3) R3T-old: First Block + E-slice, EO+CO, Spam F2L, PLL
