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, many of them are 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
