1LLL
1 Look Last Layer means completing the last layer using only one look. Currently ZBLL is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg may have potential.
Number of 1LLL Cases
Assuming the last layer is an outer layer, the number of cases is calculated as: corner orientations * edge orientations * corner permutations * edge permutations / 2
3^3 * 2^3 * 4! * 4! / 2 = 62208
Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
62208/4 = 15552
Although these cases may be regarded as unique, some of them can be solved with exactly the same algorithm, because rotational asymmetry means they are the same if viewed from a different angle. In addition, many are also mirrors and inverses of each other. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
1212
The number of algorithms a solver would require to solve the last layer in one look depends on the solver's ability to work out mirrors and/or inverses. If a solver can work out the mirror/inverse of any alg 'on the fly', then the number of algorithms they would need to learn would be:
1212 - 1 = 1211 algorithms
See Also
External Links
- Bernard Helmstetter's last layer algorithms
- All 1211 last layer algorithms(1MB zipped)
- Speedsolving.com: 3x3 last layer: number of positions
