https://www.speedsolving.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=Adrian+Currier 2026-10-22T21:17:55Z User contributions MediaWiki 1.43.8 https://www.speedsolving.com/wiki/index.php?title=OL4C&diff=25220 2015-01-08T01:29:24Z

<p>Adrian Currier: specified section of page redirection</p> <hr /> <div>#REDIRECT [[Corner Orientation#OLC Algorithms]]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=25026 2014-12-05T21:57:22Z

<p>Adrian Currier: </p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> You can use ZZ-r as a transition from beginner to full [[CFOP]]. Full CFOP might be faster than ZZ-r once you memorize all 78 algs.<br /> <br /> == The Steps ==<br /> <br /> <br /> === EOLine ===<br /> <br /> ''See [[EOLine|EOLine]]<br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other.<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=25025 2014-12-05T21:56:45Z

<p>Adrian Currier: </p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> You can use ZZ-r as a transition from beginner to full [[CFOP]]. Full CFOP is probably faster than ZZ-r once you memorize all 78 algs.<br /> <br /> == The Steps ==<br /> <br /> <br /> === EOLine ===<br /> <br /> ''See [[EOLine|EOLine]]<br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other.<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=25024 2014-12-05T21:56:13Z

<p>Adrian Currier: </p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> You can use ZZ-r as a transition from beginner to full [[CFOP]]. Full CFOP is probably faster than ZZ-r once you memorize all 78 algs (57 OLLs and 21 PLLs).<br /> <br /> == The Steps ==<br /> <br /> <br /> === EOLine ===<br /> <br /> ''See [[EOLine|EOLine]]<br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other.<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=25023 2014-12-05T21:55:31Z

<p>Adrian Currier: added info on ZZ-r as a transition method</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> You can use ZZ-r as a transition from beginner to full CFOP. Full CFOP is probably faster than ZZ-r once you memorize all 78 algs (57 OLLs and 21 PLLs).<br /> <br /> == The Steps ==<br /> <br /> <br /> === EOLine ===<br /> <br /> ''See [[EOLine|EOLine]]<br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other.<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24999 2014-11-10T00:21:36Z

<p>Adrian Currier: /* OLC */ trimmed info in this section</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> == The Steps ==<br /> <br /> <br /> === EOLine ===<br /> <br /> ''See [[EOLine|EOLine]]<br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other.<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24998 2014-11-10T00:20:01Z

<p>Adrian Currier: /* Phasing */ simplified explanation</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> == The Steps ==<br /> <br /> <br /> === EOLine ===<br /> <br /> ''See [[EOLine|EOLine]]<br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other.<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24836 2014-10-08T21:06:16Z

<p>Adrian Currier: /* The Steps */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> == The Steps ==<br /> <br /> <br /> === EOLine ===<br /> <br /> ''See [[EOLine|EOLine]]<br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24835 2014-10-08T21:02:41Z

<p>Adrian Currier: /* External links */ example solve YT link</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]<br /> * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=Template:A-PLL(b)&diff=24239 2014-07-16T03:33:24Z

<p>Adrian Currier: /* A Permutation : b */ added an alg</p> <hr /> <div>===A Permutation : b===<br /> {{case<br /> |image=a.gif<br /> |name=A-PLL b<br /> |methods=[[CPLL]], [[PLL]], [[L3C]], [[L4C]], [[ZBLL]], [[BLD]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R B' R F2 R' B R F2 R2|PLL}}<br /> {{Alg|(x) R D' R U2 R' D R U2 R2 (x')|PLL}}<br /> {{Alg|(y2) r U' L B2 L' U L B2 L2 (y2)|PLL}}<br /> {{Alg|(x') R U' R D2 R' U R D2 R2 (x)|PLL}}<br /> {{Alg|(y' x) R2 D2 R U R' D2 R U' R (x')|PLL}}<br /> {{Alg|(y2 x) L U' L D2 L' U L D2 L2 (x')|PLL}}<br /> {{Alg|(y z) U2 L' U2 L F2 U2 R U2 R' F2 (z')|PLL}}<br /> {{Alg|(z') F2 L' U2 L U2 F2 R U2 R' U2 (z)|PLL}}<br /> {{Alg|(y') R' U2 R U' L' U R U' L U R2 U2 R|PLL}}<br /> {{Alg|(z) (U R' D r2 U') (R U r2' U') (D') (z')|PLL}}<br /> {{Alg|(z' y2) (U' r x) (l2' U L U') (R' U) (L' U' L') (R' U) (z')|PLL}}<br /> {{Alg|(R' F l') D2 (R U' R') D2 (R l)|PLL}}<br /> {{Alg|(y2) r U' L z' l2 U' L U l2 z' R2|PLL}}<br /> {{Alg|(y') R2 B2 R F R' B2 R F' R|PLL}}<br /> {{Alg|(y' x') R2 U2 R D R' U2 R D' R|PLL}}<br /> {{Alg|(y2) L F' L B2 L' F L B2 L2|PLL}}<br /> {{Alg|(y') R' L' D2 (R U R') D2 R U' L|PLL}}<br /> {{Alg|(y2 x) L2 U2 L' D' L U2 L' D L'|PLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=Template:A-PLL(a)&diff=24238 2014-07-16T03:29:59Z

<p>Adrian Currier: /* A Permutation : a */ added an alg</p> <hr /> <div>===A Permutation : a===<br /> {{case<br /> |image=a1.gif<br /> |name=A-PLL a<br /> |methods=[[CPLL]], [[PLL]], [[L3C]], [[L4C]], [[ZBLL]], [[BLD]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg| R' F R' B2 R F' R' B2 R2 |PLL}}<br /> {{Alg|(x') R' D R' U2 R D' R' U2 R2 (x)|PLL}}<br /> {{Alg|(x) R' U R' D2 R U' R' D2 R2 (x')|PLL}}<br /> {{Alg|l' U R' D2 R U' R' D2 R2 (x')|PLL}}<br /> {{Alg|l' U R' (z) r2 U R' U' r2 (z) L2' (x')|PLL}}<br /> {{Alg|(y x') R2 u2 r' F' r u2 R' U l'|PLL}}<br /> {{Alg|(y x') R2 D2 R' U' R D2 R' U R'|PLL}}<br /> {{Alg|(y' x) L2 D2 L' U' L D2 L' U L' (x')|PLL}}<br /> {{Alg|(y2 z) F2 R U2 R' U2 F2 L' U2 L U2 (z')|PLL}}<br /> {{Alg|(y z') U2 R U2 R' F2 U2 L' U2 L F2 (z)|PLL}}<br /> {{Alg|R' U2 R2 U' L' U R' U' L U R' U2 R|PLL}}<br /> {{Alg|R U' L' U' L2 U' R2 U L2 U' R2 U2 L U R'|PLL}}<br /> {{Alg|(y') R U R' F' r U R' U' r' F R2 U' R'|PLL}}<br /> {{Alg|(y') r U r' U' r' F r2 U' r' U' r U r' F'|PLL}}<br /> {{Alg|(y) R L D2 R' U' R D2 R' U L' |PLL}}<br /> {{Alg|(y2) L' B L' F2 L B' L' F2 L2 |PLL}}<br /> {{Alg|x R2 U2 R D R' U2 R D' R|PLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=Corner_Orientation&diff=24169 2014-07-01T05:27:11Z

<p>Adrian Currier: /* OLC 3 */ added alg</p> <hr /> <div>{{Method Infobox<br /> |name=Corner Orientation<br /> |image=COinfo.png<br /> |anames=CO<br /> |variants=[[OCLL]]<br /> |purpose=&lt;sup&gt;&lt;/sup&gt;<br /> * [[Speedsolving]], [[BLD]], [[FMC]]<br /> }}<br /> '''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.<br /> <br /> For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).<br /> <br /> The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named &quot;corner orientation&quot;.<br /> <br /> '''Algorithms'''; at this page you can find algortihms for two diffrent variations of CO;<br /> * [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.<br /> * [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).<br /> <br /> == See also ==<br /> * [[Orientation]]<br /> * [[Orient]]<br /> * [[Permutation]]<br /> * [[Edge Orientation]]<br /> * [[Corner Permutation]]<br /> * [[OCLL]]<br /> * [[Winter Variation]]<br /> * [[CLS]]<br /> * [[Partial Corner Control]]<br /> = Pure CO =<br /> '''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];<br /> <br /> [[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.<br /> <br /> Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).<br /> <br /> For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some diffrent start of the last layer that gives a easier case in the end).<br /> <br /> ===Algorithms===<br /> All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solveable using only two sides (RU [[2-gen]]). There are diffrent sections for diffrent types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.<br /> <br /> {{Algnote}}<br /> <br /> ==Two corners unoriented==<br /> Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === U ===<br /> {{case |image=Pure twist U.jpg<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}<br /> {{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}<br /> {{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}<br /> <br /> |<br /> <br /> === T ===<br /> {{case |image=Pure twist T.jpg<br /> |name=T<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}<br /> {{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}<br /> {{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> <br /> === L ===<br /> {{case |image=Pure twist L.jpg<br /> |name=L, Bowtie<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}<br /> <br /> '''HTM optimal:''' &lt;small&gt;(12 move commutator)&lt;/small&gt;<br /> {{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}<br /> {{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}<br /> {{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}<br /> <br /> |<br /> |}<br /> <br /> ==Three corners unoriented==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === S ===<br /> {{case |image=Pure twist S.jpg<br /> |name=S, Sune<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}<br /> {{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}<br /> <br /> '''Any other:'''<br /> {{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}<br /> <br /> |<br /> <br /> === -S ===<br /> {{case |image=Pure twist aS.jpg<br /> |name=-S, Antisune<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}<br /> {{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}<br /> <br /> '''Any other:'''<br /> {{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}<br /> <br /> |}<br /> <br /> ==Four corners unoriented==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === H ===<br /> {{case |image=Pure twist H.jpg<br /> |name=H<br /> |methods=[[L4C]], [[BLD]]<br /> |optimal=16 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}<br /> {{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|!}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}<br /> {{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}<br /> {{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}<br /> {{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}<br /> {{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}<br /> <br /> |<br /> <br /> === pi ===<br /> {{case |image=Pure twist pi.jpg<br /> |name=pi, Bruno<br /> |methods=[[L4C]], [[BLD]]<br /> |optimal=15 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}<br /> {{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}<br /> {{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|!}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}<br /> {{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}<br /> {{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}<br /> {{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}<br /> <br /> |}<br /> <br /> = OCLL-EPP =<br /> '''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.<br /> <br /> '''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).<br /> <br /> Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.<br /> <br /> ===Algorithms===<br /> {{Algnote}}<br /> <br /> ==Two corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === U (EPP) ===<br /> {{case |image=OCLL-EPP U.jpg<br /> |name=U, Headlights, Superman<br /> |methods=2-look [[L4C]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R2 D' R U2 R' D R U2 R}}<br /> {{Alg|R2 F2 R' B2 R F2 R' B2 R'}}<br /> {{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}<br /> <br /> '''Any other:'''<br /> {{Alg|R U2 R2 U L U' R2 U L' U R'}}<br /> {{Alg|R' U2 R F' R' F U2 F' R F}}<br /> <br /> |<br /> <br /> <br /> === T (EPP) ===<br /> {{case |image=OCLL-EPP T.jpg<br /> |name=T<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R' F' R B' R' F R B}}<br /> {{Alg|(x) R' U' R D' R' U R D (x')}}<br /> {{Alg|(x') R' D' R U' R' D R U (x)}}<br /> {{Alg|(y') r U R' U' r' F R F'}}<br /> {{Alg|(y) l U L' U' R' U L U' (x)}}<br /> <br /> '''Any other:'''<br /> {{Alg|F U F' R' F U' F' U R U'}}<br /> {{Alg|(y') R U R' U' L' U R U' M' (x')}}<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> <br /> === L (EPP) ===<br /> {{case |image=OCLL-EPP L.jpg<br /> |name=L, Bowtie<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R B' R' F R B R' F'}}<br /> {{Alg|(y) F R' F' r U R U' r'}}<br /> {{Alg|(x') U' R U L' U' R' U r}}<br /> <br /> '''Any other:'''<br /> {{Alg|U' F U R' U' R F' R' U R}}<br /> {{Alg|R U R U' L' U R' U' M' (x')}}<br /> <br /> |<br /> |}<br /> <br /> ==Three corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === S (EPP) ===<br /> {{case |image=OCLL-EPP S.jpg<br /> |name=S, Sune<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R U' L' U R' U' L U}}<br /> <br /> '''Any other:'''<br /> {{Alg|!}}<br /> <br /> |<br /> <br /> === -S (EPP) ===<br /> {{case |image=OCLL-EPP aS.jpg<br /> |name=-S, Antisune<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U' L' U R U' L U R'}}<br /> <br /> '''Any other:'''<br /> {{Alg|!}}<br /> <br /> |}<br /> <br /> ==Four corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === H (EPP) ===<br /> {{case |image=OCLL-EPP H.jpg<br /> |name=H<br /> |methods=2-look [[L4C]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|F (R U R' U')3 F'}}<br /> <br /> |<br /> <br /> === pi (EPP) ===<br /> {{case |image=OCLL-EPP pi.jpg<br /> |name=pi, Bruno<br /> |methods=2-look [[L4C]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R F' D2 F R' U' R F' D2 F R' U}}<br /> <br /> '''Any other:'''<br /> {{Alg|R' U L U' R U L2 U R U' L U R' U2}}<br /> {{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}<br /> <br /> |}<br /> <br /> [[Category:Puzzle theory]]<br /> [[Category:3x3x3 other substeps]]<br /> <br /> __NOTOC__<br /> <br /> == OLC Algorithms ==<br /> <br /> '''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> {{Algnote}}<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L|OLL}}<br /> {{Alg|y2 R' U L U' R U L'|OLL}}<br /> {{Alg|U R U' L' U R' U' L|OLL}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'|OLL}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'|OLL}}<br /> {{Alg|R U2 R' F R' F' R F2 L F L' F|OLL}}<br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'|OLL}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}<br /> {{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=Corner_Orientation&diff=24164 2014-06-30T04:42:36Z

<p>Adrian Currier: /* OLC Algorithms */ {{Algnote}}</p> <hr /> <div>{{Method Infobox<br /> |name=Corner Orientation<br /> |image=COinfo.png<br /> |anames=CO<br /> |variants=[[OCLL]]<br /> |purpose=&lt;sup&gt;&lt;/sup&gt;<br /> * [[Speedsolving]], [[BLD]], [[FMC]]<br /> }}<br /> '''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.<br /> <br /> For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).<br /> <br /> The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named &quot;corner orientation&quot;.<br /> <br /> '''Algorithms'''; at this page you can find algortihms for two diffrent variations of CO;<br /> * [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.<br /> * [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).<br /> <br /> == See also ==<br /> * [[Orientation]]<br /> * [[Orient]]<br /> * [[Permutation]]<br /> * [[Edge Orientation]]<br /> * [[Corner Permutation]]<br /> * [[OCLL]]<br /> * [[Winter Variation]]<br /> * [[CLS]]<br /> * [[Partial Corner Control]]<br /> = Pure CO =<br /> '''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];<br /> <br /> [[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.<br /> <br /> Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).<br /> <br /> For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some diffrent start of the last layer that gives a easier case in the end).<br /> <br /> ===Algorithms===<br /> All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solveable using only two sides (RU [[2-gen]]). There are diffrent sections for diffrent types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.<br /> <br /> {{Algnote}}<br /> <br /> ==Two corners unoriented==<br /> Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === U ===<br /> {{case |image=Pure twist U.jpg<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}<br /> {{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}<br /> {{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}<br /> <br /> |<br /> <br /> === T ===<br /> {{case |image=Pure twist T.jpg<br /> |name=T<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}<br /> {{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}<br /> {{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> <br /> === L ===<br /> {{case |image=Pure twist L.jpg<br /> |name=L, Bowtie<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}<br /> <br /> '''HTM optimal:''' &lt;small&gt;(12 move commutator)&lt;/small&gt;<br /> {{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}<br /> {{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}<br /> {{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}<br /> <br /> |<br /> |}<br /> <br /> ==Three corners unoriented==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === S ===<br /> {{case |image=Pure twist S.jpg<br /> |name=S, Sune<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}<br /> {{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}<br /> <br /> '''Any other:'''<br /> {{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}<br /> <br /> |<br /> <br /> === -S ===<br /> {{case |image=Pure twist aS.jpg<br /> |name=-S, Antisune<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}<br /> {{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}<br /> <br /> '''Any other:'''<br /> {{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}<br /> <br /> |}<br /> <br /> ==Four corners unoriented==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === H ===<br /> {{case |image=Pure twist H.jpg<br /> |name=H<br /> |methods=[[L4C]], [[BLD]]<br /> |optimal=16 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}<br /> {{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|!}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}<br /> {{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}<br /> {{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}<br /> {{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}<br /> {{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}<br /> <br /> |<br /> <br /> === pi ===<br /> {{case |image=Pure twist pi.jpg<br /> |name=pi, Bruno<br /> |methods=[[L4C]], [[BLD]]<br /> |optimal=15 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}<br /> {{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}<br /> {{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|!}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}<br /> {{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}<br /> {{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}<br /> {{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}<br /> <br /> |}<br /> <br /> = OCLL-EPP =<br /> '''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.<br /> <br /> '''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).<br /> <br /> Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.<br /> <br /> ===Algorithms===<br /> {{Algnote}}<br /> <br /> ==Two corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === U (EPP) ===<br /> {{case |image=OCLL-EPP U.jpg<br /> |name=U, Headlights, Superman<br /> |methods=2-look [[L4C]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R2 D' R U2 R' D R U2 R}}<br /> {{Alg|R2 F2 R' B2 R F2 R' B2 R'}}<br /> {{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}<br /> <br /> '''Any other:'''<br /> {{Alg|R U2 R2 U L U' R2 U L' U R'}}<br /> {{Alg|R' U2 R F' R' F U2 F' R F}}<br /> <br /> |<br /> <br /> <br /> === T (EPP) ===<br /> {{case |image=OCLL-EPP T.jpg<br /> |name=T<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R' F' R B' R' F R B}}<br /> {{Alg|(x) R' U' R D' R' U R D (x')}}<br /> {{Alg|(x') R' D' R U' R' D R U (x)}}<br /> {{Alg|(y') r U R' U' r' F R F'}}<br /> {{Alg|(y) l U L' U' R' U L U' (x)}}<br /> <br /> '''Any other:'''<br /> {{Alg|F U F' R' F U' F' U R U'}}<br /> {{Alg|(y') R U R' U' L' U R U' M' (x')}}<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> <br /> === L (EPP) ===<br /> {{case |image=OCLL-EPP L.jpg<br /> |name=L, Bowtie<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R B' R' F R B R' F'}}<br /> {{Alg|(y) F R' F' r U R U' r'}}<br /> {{Alg|(x') U' R U L' U' R' U r}}<br /> <br /> '''Any other:'''<br /> {{Alg|U' F U R' U' R F' R' U R}}<br /> {{Alg|R U R U' L' U R' U' M' (x')}}<br /> <br /> |<br /> |}<br /> <br /> ==Three corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === S (EPP) ===<br /> {{case |image=OCLL-EPP S.jpg<br /> |name=S, Sune<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R U' L' U R' U' L U}}<br /> <br /> '''Any other:'''<br /> {{Alg|!}}<br /> <br /> |<br /> <br /> === -S (EPP) ===<br /> {{case |image=OCLL-EPP aS.jpg<br /> |name=-S, Antisune<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U' L' U R U' L U R'}}<br /> <br /> '''Any other:'''<br /> {{Alg|!}}<br /> <br /> |}<br /> <br /> ==Four corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === H (EPP) ===<br /> {{case |image=OCLL-EPP H.jpg<br /> |name=H<br /> |methods=2-look [[L4C]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|F (R U R' U')3 F'}}<br /> <br /> |<br /> <br /> === pi (EPP) ===<br /> {{case |image=OCLL-EPP pi.jpg<br /> |name=pi, Bruno<br /> |methods=2-look [[L4C]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R F' D2 F R' U' R F' D2 F R' U}}<br /> <br /> '''Any other:'''<br /> {{Alg|R' U L U' R U L2 U R U' L U R' U2}}<br /> {{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}<br /> <br /> |}<br /> <br /> [[Category:Puzzle theory]]<br /> [[Category:3x3x3 other substeps]]<br /> <br /> __NOTOC__<br /> <br /> == OLC Algorithms ==<br /> <br /> '''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> {{Algnote}}<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L|OLL}}<br /> {{Alg|y2 R' U L U' R U L'|OLL}}<br /> {{Alg|U R U' L' U R' U' L|OLL}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'|OLL}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'|OLL}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'|OLL}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}<br /> {{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24163 2014-06-29T05:57:52Z

<p>Adrian Currier: redirect to corner orientation page merge</p> <hr /> <div>#REDIRECT [[Corner_Orientation#OLC_Algorithms]]<br /> <br /> '''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> {{merge|Corner_Orientation#OCLL-EPP|OCLL-EPP}}<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L|OLL}}<br /> {{Alg|y2 R' U L U' R U L'|OLL}}<br /> {{Alg|U R U' L' U R' U' L|OLL}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'|OLL}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'|OLL}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}<br /> {{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=Corner_Orientation&diff=24162 2014-06-29T05:51:46Z

<p>Adrian Currier: merged OLC</p> <hr /> <div>{{Method Infobox<br /> |name=Corner Orientation<br /> |image=COinfo.png<br /> |anames=CO<br /> |variants=[[OCLL]]<br /> |purpose=&lt;sup&gt;&lt;/sup&gt;<br /> * [[Speedsolving]], [[BLD]], [[FMC]]<br /> }}<br /> '''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.<br /> <br /> For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).<br /> <br /> The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named &quot;corner orientation&quot;.<br /> <br /> '''Algorithms'''; at this page you can find algortihms for two diffrent variations of CO;<br /> * [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.<br /> * [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).<br /> <br /> == See also ==<br /> * [[Orientation]]<br /> * [[Orient]]<br /> * [[Permutation]]<br /> * [[Edge Orientation]]<br /> * [[Corner Permutation]]<br /> * [[OCLL]]<br /> * [[Winter Variation]]<br /> * [[CLS]]<br /> * [[Partial Corner Control]]<br /> = Pure CO =<br /> '''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];<br /> <br /> [[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.<br /> <br /> Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).<br /> <br /> For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some diffrent start of the last layer that gives a easier case in the end).<br /> <br /> ===Algorithms===<br /> All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solveable using only two sides (RU [[2-gen]]). There are diffrent sections for diffrent types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.<br /> <br /> {{Algnote}}<br /> <br /> ==Two corners unoriented==<br /> Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === U ===<br /> {{case |image=Pure twist U.jpg<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}<br /> {{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}<br /> {{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}<br /> <br /> |<br /> <br /> === T ===<br /> {{case |image=Pure twist T.jpg<br /> |name=T<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}<br /> {{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}<br /> {{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> <br /> === L ===<br /> {{case |image=Pure twist L.jpg<br /> |name=L, Bowtie<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}<br /> <br /> '''HTM optimal:''' &lt;small&gt;(12 move commutator)&lt;/small&gt;<br /> {{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}<br /> {{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}<br /> {{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}<br /> <br /> |<br /> |}<br /> <br /> ==Three corners unoriented==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === S ===<br /> {{case |image=Pure twist S.jpg<br /> |name=S, Sune<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}<br /> {{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}<br /> <br /> '''Any other:'''<br /> {{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}<br /> <br /> |<br /> <br /> === -S ===<br /> {{case |image=Pure twist aS.jpg<br /> |name=-S, Antisune<br /> |methods=[[L3C]], [[L4C]], [[BLD]]<br /> |optimal=13 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}<br /> {{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}<br /> <br /> '''Any other:'''<br /> {{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}<br /> <br /> |}<br /> <br /> ==Four corners unoriented==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === H ===<br /> {{case |image=Pure twist H.jpg<br /> |name=H<br /> |methods=[[L4C]], [[BLD]]<br /> |optimal=16 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}<br /> {{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|!}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}<br /> {{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}<br /> {{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}<br /> {{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}<br /> {{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}<br /> <br /> |<br /> <br /> === pi ===<br /> {{case |image=Pure twist pi.jpg<br /> |name=pi, Bruno<br /> |methods=[[L4C]], [[BLD]]<br /> |optimal=15 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}<br /> {{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}<br /> <br /> '''Any other 2-gen:'''<br /> {{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}<br /> {{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}<br /> <br /> '''Sune combos:'''<br /> {{Alg|!}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}<br /> <br /> '''Any other:'''<br /> {{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}<br /> {{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}<br /> {{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}<br /> {{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}<br /> <br /> |}<br /> <br /> = OCLL-EPP =<br /> '''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.<br /> <br /> '''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).<br /> <br /> Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.<br /> <br /> ===Algorithms===<br /> {{Algnote}}<br /> <br /> ==Two corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === U (EPP) ===<br /> {{case |image=OCLL-EPP U.jpg<br /> |name=U, Headlights, Superman<br /> |methods=2-look [[L4C]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R2 D' R U2 R' D R U2 R}}<br /> {{Alg|R2 F2 R' B2 R F2 R' B2 R'}}<br /> {{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}<br /> <br /> '''Any other:'''<br /> {{Alg|R U2 R2 U L U' R2 U L' U R'}}<br /> {{Alg|R' U2 R F' R' F U2 F' R F}}<br /> <br /> |<br /> <br /> <br /> === T (EPP) ===<br /> {{case |image=OCLL-EPP T.jpg<br /> |name=T<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R' F' R B' R' F R B}}<br /> {{Alg|(x) R' U' R D' R' U R D (x')}}<br /> {{Alg|(x') R' D' R U' R' D R U (x)}}<br /> {{Alg|(y') r U R' U' r' F R F'}}<br /> {{Alg|(y) l U L' U' R' U L U' (x)}}<br /> <br /> '''Any other:'''<br /> {{Alg|F U F' R' F U' F' U R U'}}<br /> {{Alg|(y') R U R' U' L' U R U' M' (x')}}<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> <br /> === L (EPP) ===<br /> {{case |image=OCLL-EPP L.jpg<br /> |name=L, Bowtie<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R B' R' F R B R' F'}}<br /> {{Alg|(y) F R' F' r U R U' r'}}<br /> {{Alg|(x') U' R U L' U' R' U r}}<br /> <br /> '''Any other:'''<br /> {{Alg|U' F U R' U' R F' R' U R}}<br /> {{Alg|R U R U' L' U R' U' M' (x')}}<br /> <br /> |<br /> |}<br /> <br /> ==Three corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === S (EPP) ===<br /> {{case |image=OCLL-EPP S.jpg<br /> |name=S, Sune<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R U' L' U R' U' L U}}<br /> <br /> '''Any other:'''<br /> {{Alg|!}}<br /> <br /> |<br /> <br /> === -S (EPP) ===<br /> {{case |image=OCLL-EPP aS.jpg<br /> |name=-S, Antisune<br /> |methods=2-look [[L4C]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|U' L' U R U' L U R'}}<br /> <br /> '''Any other:'''<br /> {{Alg|!}}<br /> <br /> |}<br /> <br /> ==Four corners==<br /> {|border=&quot;0&quot; width=&quot;100%&quot; valign=&quot;top&quot; cellpadding=&quot;3&quot;<br /> <br /> |-valign=&quot;top&quot;<br /> |<br /> === H (EPP) ===<br /> {{case |image=OCLL-EPP H.jpg<br /> |name=H<br /> |methods=2-look [[L4C]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}<br /> <br /> '''Any other:'''<br /> {{Alg|F (R U R' U')3 F'}}<br /> <br /> |<br /> <br /> === pi (EPP) ===<br /> {{case |image=OCLL-EPP pi.jpg<br /> |name=pi, Bruno<br /> |methods=2-look [[L4C]]<br /> |optimal=12 [[HTM]]<br /> |text=<br /> }}<br /> '''Optimal 2-gen:'''<br /> {{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}<br /> <br /> '''HTM optimal:'''<br /> {{Alg|R F' D2 F R' U' R F' D2 F R' U}}<br /> <br /> '''Any other:'''<br /> {{Alg|R' U L U' R U L2 U R U' L U R' U2}}<br /> {{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}<br /> <br /> |}<br /> <br /> [[Category:Puzzle theory]]<br /> [[Category:3x3x3 other substeps]]<br /> <br /> __NOTOC__<br /> <br /> == OLC Algorithms ==<br /> <br /> '''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L|OLL}}<br /> {{Alg|y2 R' U L U' R U L'|OLL}}<br /> {{Alg|U R U' L' U R' U' L|OLL}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'|OLL}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'|OLL}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}<br /> {{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24161 2014-06-29T05:36:19Z

<p>Adrian Currier: /* The Steps */ phasing see external links</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> ''See [[ZZ-r#External_links|External links]]<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24160 2014-06-29T05:28:54Z

<p>Adrian Currier: </p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method at 16 total.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24159 2014-06-29T05:22:58Z

<p>Adrian Currier: /* OLL 23 */ fixed an alg</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> {{merge|Corner_Orientation#OCLL-EPP|OCLL-EPP}}<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L|OLL}}<br /> {{Alg|y2 R' U L U' R U L'|OLL}}<br /> {{Alg|U R U' L' U R' U' L|OLL}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'|OLL}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'|OLL}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}<br /> {{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24158 2014-06-29T05:20:03Z

<p>Adrian Currier: /* PLL probabilities */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method, with a total algorithm count of 16.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24157 2014-06-29T05:15:38Z

<p>Adrian Currier: /* OLL 23 */ fixed a bad alg</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> {{merge|Corner_Orientation#OCLL-EPP|OCLL-EPP}}<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L|OLL}}<br /> {{Alg|y2 R' U L U' R U L'|OLL}}<br /> {{Alg|U R U' L' U R' U' L|OLL}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'|OLL}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'|OLL}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24109 2014-06-25T22:55:45Z

<p>Adrian Currier: /* OLC Algorithms */ added missing |OLL to certain algs</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L|OLL}}<br /> {{Alg|y2 R' U L U' R U L'|OLL}}<br /> {{Alg|U R U' L' U R' U' L|OLL}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'|OLL}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'|OLL}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24108 2014-06-25T22:54:08Z

<p>Adrian Currier: /* OLL 23 */ added algs</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> {{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24107 2014-06-25T22:42:51Z

<p>Adrian Currier: /* OLL 23 */ added algs</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2}}<br /> {{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24106 2014-06-25T22:38:12Z

<p>Adrian Currier: /* OLL 23 */ added algs</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|y' F L' D2 L U2 L' D2 L U2 F'}}<br /> {{Alg|y' B L2 B R2 B F2 R2 B L2 F2}}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24105 2014-06-25T20:26:09Z

<p>Adrian Currier: /* OLL 24 */ removed algs that don&#039;t preserve edge permutation</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D'|OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24104 2014-06-25T20:23:04Z

<p>Adrian Currier: /* OLL 23 */ removed algs that don&#039;t preserve opposite edges</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D' |OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'}}<br /> {{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24073 2014-06-22T00:55:27Z

<p>Adrian Currier: oll subset</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R' U2 R F U' R' U' R U F'}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|R' U L' U R U' L U2 R' U R}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|R d' R' U R d R' (y) R' U2 R}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D' |OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'}}<br /> {{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24072 2014-06-22T00:53:50Z

<p>Adrian Currier: </p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a last layer step in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R' U2 R F U' R' U' R U F'}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|R' U L' U R U' L U2 R' U R}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|R d' R' U R d R' (y) R' U2 R}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D' |OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'}}<br /> {{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24071 2014-06-22T00:51:14Z

<p>Adrian Currier: /* OLC Algorithms */</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a last layer step in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step in are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R' U2 R F U' R' U' R U F'}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|R' U L' U R U' L U2 R' U R}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|R d' R' U R d R' (y) R' U2 R}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D' |OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'}}<br /> {{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24070 2014-06-22T00:47:12Z

<p>Adrian Currier: oll subset</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the limited PLL set in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24069 2014-06-22T00:28:06Z

<p>Adrian Currier: /* Cons */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the limited PLL set in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24068 2014-06-22T00:07:49Z

<p>Adrian Currier: /* PLL probabilities */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the limited PLL set in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the the PLL increased skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24066 2014-06-20T21:24:56Z

<p>Adrian Currier: pll case odds</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> ==PLL probabilities==<br /> <br /> The probabilities for the limited PLL set in ZZ-r are different than full PLL. They are updated as follows:<br /> <br /> * H 1/24<br /> <br /> * Z 1/12<br /> <br /> * A 1/3<br /> <br /> * E 1/12<br /> <br /> * F 1/6<br /> <br /> * N 1/12<br /> <br /> * T 1/6<br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the the PLL increased skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24065 2014-06-20T21:21:04Z

<p>Adrian Currier: /* Cons */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the the PLL increased skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24064 2014-06-20T21:19:34Z

<p>Adrian Currier: /* OLC Algorithms */</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a last layer step in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of skipping this step in ZZ-r are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R' U2 R F U' R' U' R U F'}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|R' U L' U R U' L U2 R' U R}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|R d' R' U R d R' (y) R' U2 R}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D' |OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'}}<br /> {{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24063 2014-06-20T21:19:18Z

<p>Adrian Currier: /* OLC Algorithms */</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a last layer step in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of a skipping the orientation step in ZZ-r are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R' U2 R F U' R' U' R U F'}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|R' U L' U R U' L U2 R' U R}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|R d' R' U R d R' (y) R' U2 R}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D' |OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'}}<br /> {{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=OLC&diff=24062 2014-06-20T21:18:37Z

<p>Adrian Currier: /* OLC Algorithms */</p> <hr /> <div>'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a last layer step in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.<br /> <br /> == OLC Algorithms ==<br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> Odds of a OLC skip are 1/27.<br /> <br /> === OLC 1 ===<br /> Probability 4/27<br /> {{case<br /> |image=o27.gif<br /> |name=S, Sune, Swimming Left<br /> |methods=[[ZZ-reduction]]<br /> |text=<br /> }}<br /> {{Alg|R U' L' U R' U' L}}<br /> {{Alg|y2 R' U L U' R U L'}}<br /> {{Alg|U R U' L' U R' U' L}}<br /> <br /> <br /> === OLC 2 ===<br /> Probability 4/27<br /> {{case<br /> |image=o26.gif<br /> |name=-S, Antisune, Swimming Right<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L' U R U' L U R'}}<br /> <br /> <br /> === OLC 3 ===<br /> Probability 2/27<br /> {{case<br /> |image=o21.gif<br /> |name=H, Double Sune, Flip, Cross<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]], ? [[STM]]<br /> |text=<br /> }}<br /> {{Alg|y F (R U R' U')3 F'}}<br /> <br /> <br /> === OLC 4 ===<br /> Probability 4/27<br /> {{case<br /> |image=o22.gif<br /> |name=pi, Bruno, wheel, T-shirt<br /> |methods=[[ZZ-reduction]]<br /> |optimal=? [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|f (R U R' U') F f' (R U R' U') F'}}<br /> {{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2}}<br /> <br /> === OLL 23 ===<br /> Probability 4/27<br /> {{case<br /> |image=o23.gif<br /> |name=U, [[Headlights]], Superman<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=9 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}<br /> {{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}<br /> {{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}<br /> {{Alg|R2' D' R U2 R' D R U2 R|OLL}}<br /> {{Alg|R' U2 R F U' R' U' R U F'}}<br /> {{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}<br /> {{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}<br /> {{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'}}<br /> {{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}<br /> {{Alg|R' U L' U R U' L U2 R' U R}}<br /> {{Alg|l2 U' R D2 R' U R D2 R|OLL}}<br /> {{Alg|l2' U' z' U R2 U' L U R2 z' R|OLL}}<br /> {{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}<br /> {{Alg|R d' R' U R d R' (y) R' U2 R}}<br /> {{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}<br /> <br /> === OLL 24 ===<br /> Probability 4/27<br /> {{case<br /> |image=o24.gif<br /> |name=T, chameleon, shark, Hammerhead, Little Horse, stingray<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|r U R' U' L' U R U' x'|OLL}}<br /> {{Alg|r U R' U' r' F R F'|OLL}}<br /> {{Alg|(y' x') R U R' D R U' R' D' |OLL}}<br /> {{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}<br /> {{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'}}<br /> {{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')}}<br /> {{Alg|(y x) D' R' U R D R' U' R x'|OLL}}<br /> {{Alg|(y x) D L U' L' D' L U L' x' |OLL}}<br /> {{Alg|(y x') U' R' D R U R' D' R x|OLL}}<br /> {{Alg|(y2) R' F' L F R F' L' F|OLL}}<br /> {{Alg|(y2) R' F' r U R U' r' F|OLL}}<br /> {{Alg|(y2) l' U' L U R U' r' F|OLL}}<br /> {{Alg|(y') l U l' F R B' R' F'|OLL}}<br /> <br /> === OLL 25 ===<br /> Probability 4/27<br /> {{case<br /> |image=o25.gif<br /> |name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship<br /> |methods=[[OCLL]], [[OLL]]<br /> |optimal=8 [[HTM]]<br /> |text=<br /> }}<br /> {{Alg|y' F' r U R' U' r' F R}}<br /> {{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}<br /> {{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}<br /> {{Alg|y2 R' F R B' R' F' R B|OLL}}<br /> {{Alg|y2 F R' F' L F R F' L'|OLL}}<br /> {{Alg|y F' L F R' F' L' F R|OLL}}<br /> {{Alg|y' F' r U R' U' r' F R|OLL}}<br /> {{Alg|y' x U R' U' L U R U' r'|OLL}}<br /> {{Alg|R' F' L' F R F' L F|OLL}}<br /> {{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}<br /> {{Alg|y2 F R' F' r U R U' r'|OLL}}<br /> {{Alg|y2 l' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x' L' U' R' U L U' R U|OLL}}<br /> {{Alg|x' D R U R' D' R U' l'|OLL}}<br /> {{Alg|x' U L' U' R U L U' l'|OLL}}<br /> {{Alg|x' R' D R U' R' D' R U x|OLL}}<br /> {{Alg|x R' U R D' R' U' R D x'|OLL}}<br /> {{Alg|y2 x L U' L' D L U L' D' x'|OLL}}<br /> {{Alg|l' U' L' U R U' L U x'|OLL}}<br /> {{Alg|U r U R U' L' U R' U' x'|OLL}}<br /> {{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}<br /> {{Alg|y2 L' R U R' U' L U R U' R'|OLL}}<br /> {{Alg|F R B R' F' l U' l'|OLL}}<br /> {{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}<br /> {{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24061 2014-06-20T21:18:10Z

<p>Adrian Currier: /* PLL */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24060 2014-06-20T21:17:43Z

<p>Adrian Currier: /* OLC */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL#PLL_algorithms|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24059 2014-06-20T21:16:42Z

<p>Adrian Currier: /* PLL */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OCL_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> ''See [[PLL#PLL_algorithms|PLL Algorithms]]''<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24058 2014-06-20T21:16:32Z

<p>Adrian Currier: /* OLC */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> ''See [[OL4C#OCL_Algorithms|OLC Algorithms]]''<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> See [[PLL#PLL_algorithms|PLL Algorithms]]<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=Zz-reduction&diff=24057 2014-06-20T21:15:10Z

<p>Adrian Currier: Redirected page to ZZ-reduction</p> <hr /> <div>#REDIRECT [[ZZ-reduction]]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=Zz-r&diff=24056 2014-06-20T21:14:42Z

<p>Adrian Currier: Redirected page to ZZ-reduction</p> <hr /> <div>#REDIRECT [[ZZ-reduction]]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24055 2014-06-20T21:12:52Z

<p>Adrian Currier: /* PLL */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> See [[OL4C#OCL_Algorithms|OLC Algorithms]]<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> See [[PLL#PLL_algorithms|PLL Algorithms]]<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24054 2014-06-20T21:11:02Z

<p>Adrian Currier: /* OLC */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> See [[OL4C#OCL_Algorithms|OLC Algorithms]]<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24053 2014-06-20T21:09:58Z

<p>Adrian Currier: /* OLC */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> See [[OL4C|OLC#OLC_Algorithms]]<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24052 2014-06-20T21:08:29Z

<p>Adrian Currier: /* OLC */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> See [[OL4C|OLC]]<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24051 2014-06-20T21:07:48Z

<p>Adrian Currier: /* OLC */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> See [[OL4C|OLC]]<br /> <br /> OLC (Orient Last Corners) is a last layer step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 OLLs in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24050 2014-06-20T21:07:32Z

<p>Adrian Currier: /* Pros */</p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> See [[OL4C|OLC]]<br /> <br /> OLC (Orient Last Corners) is a [[LL]] step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 OLLs in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few last layer cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier https://www.speedsolving.com/wiki/index.php?title=ZZ-reduction&diff=24049 2014-06-20T21:06:46Z

<p>Adrian Currier: </p> <hr /> <div>ZZ-reduction, also called ZZ-r, is a variant of the [[ZZ method]] for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of [[PLL]] cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any [[2LLL]] method.<br /> <br /> == The Steps ==<br /> <br /> <br /> === Phasing ===<br /> <br /> After [[EOLine]] is completed, [[Phasing]] is employed during the insertion of the final block pair in [[F2L]], with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. (An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.)<br /> <br /> === OLC ===<br /> <br /> See [[OL4C|OLC]]<br /> <br /> OLC (Orient Last Corners) is a [[LL]] step that orients corners only and also preserves two opposite or all four edge permutations.<br /> <br /> Of the 7 OLLs in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).<br /> <br /> === PLL ===<br /> <br /> Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.<br /> <br /> Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.<br /> <br /> == Pros ==<br /> <br /> * '''Reduced algorithm count''': Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method.<br /> * '''Faster recognition''': Because there are so few LL cases, recognition is very quick.<br /> * '''Frequent skips''': The low number of LL cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648.<br /> <br /> ==Cons==<br /> <br /> * '''Phasing''' - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increased PLL skip probability and faster recognition.<br /> <br /> == External links ==<br /> <br /> * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained]</div>

Adrian Currier