TSLE inserts the last edge whilst orienting all corners. The D corner is completely ignored, and is recognized purely from corner orientation and shape, just like an OLL.(104 cases, all trivial) This step is 100% 2-gen and all but 4 cases can be solved by a linear combination of at most three R U R', R U' R', or R U2 R' triggers, which permits simple memorization and executions. Many of the TSLE insertions are the same as the traditional F2L algorithm, and has a much lower move count than other last slot methods since it ignores permutation of the corners and edges except UF. Using RUD, LUR, and non-2gen algorithms improves upon ergonomics and move count and allows for even shorter inserts.
TTLL forces an LL Skip with only 72 cases (42 w/mirrors, 30 non-trivial). It is named after Chris Tran (creator) and Blake Thompson ( who generated a significant fraction of the algorithms). It is still necessary to know the 21 PLL algorithms in case the last slot corner is solved during TSLE (1 in 5 chance).
- TSLE: Insert last edge and orient corners. (Tran Style Last Edge - 104 cases) 100% 2-gen
- TTLL: Force an LL skip. (Tran-Thompson Last Layer - 72 cases + 21 PLLs) 33% 2-gen
ZZ-CT was created with the intention of fixing everything wrong with ZBLL, and to create the first feasible LL-Skip method under 200 algorithms. Several months of brainstorming and evolution led to ZZ-CT, as reported herein:
The core fundamental concept is the orientation of corners before reaching last layer.
By abusing rotational symmetry of oriented pieces, it was observed that LL Skip algorithm count could be reduced greatly. This pre-orientation also allowed for simple and obvious recognition of permutation.
The first incarnation of this method was one which oriented all corners during the completion of the third slot, and then forced LL skip (~800-1000 algorithms).
ZZ-HW was the next big improvement, which oriented all corners and inserted the corner in the fourth slot, followed by forced LL skip(~200 algorithms). However, this method was limited by algorithm ergonomics, since diagonal corner swap and edge insertion algorithms are too long and are not sufficiently ergonomic for competitive speedsolving purposes.
By maintaining the same concept and algorithms, but instead inserting an edge instead of a corner. This ergonomic barrier was not only overcome, but completely annihilated in comparison. The overall quality and movecount was dramatically enhanced due to the properties of corner permutation.
This property serendipitously yielded very surprisingly short, ergonomic algorithms such as x' (R' U R U')*3 and R2 U2 R2 U' R2 U' R2. Additionally, an entire 12 case RUD subset was observed to be completely regripless.
When compared with ZBLL, ZZ-CT solves the issues of large algorithm count, recognition, statistical hindrances, practise requirement, and steep learning curve by having a significantly lower algorithm count, obvious colour blocks (PLL-style recognition), and better statistics for the same amount of looks.
TSLE is easily recognised, only involving the orientation of corners and finding the last edge. This requires a similar mental load as OLL, and does not require knowing where the last LS corner is.
The concept intuitive edge control in CFOP, can also be tweaked to simplify TSLE.
For example, in CFOP, intuitive edge control is seeing that there are no oriented edges and doing R' F R F'(sledgehammer) instead of U R U' R'. This ensures no dot cases, reducing OLL by 7 cases.
In ZZ-CT, intuitive corner control is as simple as observing when there are no oriented corners, and doing R' U2 R instead of U R' U R during third slot to avoid all misoriented corners, which reduces TSLE by 16 cases. Intuitive corner control can even force superior TSLE cases with better execution, recognition, and move count, in the same way that intuitive edge control forces a better OLL.
Lookahead into TTLL is also similar to lookahead into PLL during OLL. Since oriented colour blocks are being put together, it is easier to predict the last algorithm. This is opposed to ZBLL, in which formation of LS brings together misoriented colour blocks, which are harder to discern for lookahead purposes.
Statistically, ZZ-CT leads to good single times due to the following attributes:
- PLL occurs 20% of the time (1 out of 5 solves). Leading to a well known algorithm that most cubers already know.
- True LL skip (fully solved cube after TSLE) occurs 1 out of 360 solves (0.27%), as compared with 0.0064% in CFOP(1 out of 15552 solves), and 0.051% in ZZ(1 out of 1944 solves). Which means that the probability is increased by multiple orders of magnitude.
- 2-Gen EVERYTHING after first block occurs 33% of the time, which is twice as much as ZBLL (15% chance), and sixteen times greater than CFOP (1.8% chance), by making use of a single y' rotation before TTLL.
- Individual TTLL probabilities are similar to OLL. In comparison, the statistics for ZBLL cases are profoundly lower. This means that some cases will only pop up every few days during solves, meaning that it requires much less practice to execute TTLL than ZBLL.
- TSLE is skipped approximately one out of every 405 solves (0.24%), which adds another level of reduced single times.
Additionally, several algorithms are simply cancelled or conjugated PLL algorithms.
For example, executing the first move in the G-Perm (R U R' y' R2 u' R U' R' U R' u R2) with an R' instead of an R, (which also cancels the last R2) or replacing the first move in the J-Perm (R' U L' U2 R U' R' U2 L R U') with an R instead of an R'. This means that most people who know PLL will already know several cases. Recognition of these cases is also obvious, since every case which has a 1x1x3 block is a cancelled or conjugated PLL.
Every case which has a 1x1x2 block is a conjugated ZBLL, which permits advanced ZBLL users to quickly use provisional algorithms as they transition to full ZZ-CT.
Another useful advantage in ZZ-CT is that it theoretically requires no rotations. By adjusting the D layer after TSLE, it is possible to ADF for TTLL to avoid all rotations during the solve.
Relatively high algorithm count ~200 algs. Additional TSLE algorithms for multiple angles might also need to be learned since TSLE is not slot neutral.
ZZ-CT has a movecount similar to ZZ-b  and higher than ZZ-a.
Most TTLLs still require optimization. Pretty much all of them can only be recognized from one angle (last D corner in UBL) as well, so AUFs become a requirement when only looking at the top layer, unlike in ZBLL or PLL where two sided recognition is possible.
"(ZZ-CT) sounds like a good method-- the only disadvantage is that you have to use ZZ."
-Andrew Ricci (2012 US National Champion)
- Chris Tran
- Andrew Nathenson
Scramble: R2 F2 R' U2 R2 B2 U2 R' B2 D2 U' L2 F L' R2 F' U2 R2 U F' alg.cubing.net
EOLine: X' D' L' F L U R2 D' (7/46)
F2L-1: R U' R' U R' U2 L U2 L U L R' U R D R U' R' D' U (20/46)
TSLE: R U2 R' U' R U2 R' (7/46)
TTLL: y' U R' U R U' R' U2 R U R' U' R (12/46)
Scramble: B L2 B' U2 B D2 L2 B R2 D2 F2 R D' F' L' D' U2 F' L' F L2
x2 B R U' F// Eoline
L' U2 R' U2 R' // First pair
L U' L' U' L' U2 L U L' // Second pair
R' U2 R // Third pair
(D U) R U' R' U' R U2 R' // TSLE
(D U2) R' U2 R U R U2 R2 U' R2 U' R' U D2
MORE ON THE WAY
- Speedsolving.com: ZZ-a vs ZZ-CT
- Daily ZZ-CT 
- Movecounts for ZZ variants with different LSLL, including ZZ-CT