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 Post subject: shortest sequences for the 2x2x2
PostPosted: Mon Mar 04, 2013 3:52 pm 
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Joined: Sun Mar 15, 2009 12:00 am
For a very beginner's algorithm, I am looking for the shortest sequences with the following effect on a 2x2x2:

1. swap the corners FUR and FUL (orientation does not matter)
2. twist the corners FUR and FUL


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 Post subject: Re: shortest sequences for the 2x2x2
PostPosted: Mon Mar 04, 2013 4:44 pm 
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Location: Bay Area, California
Cube Explorer is the tool for this.


Christoph Lohe wrote:
1. swap the corners FUR and FUL (orientation does not matter)


It's easy to show this requires at least 8 moves and it turns out, if the two are adjacent it requires 10. If they're diagonal it requires 9.

Here are all the ones that begin with U:

U R2 F2 R U R' F2 R F' R (10f*)
U R2 F2 R U L' U2 R U' L (10f*)
U R2 F2 R U L' U2 L F' R (10f*)
U R2 F2 R D F' U2 B D' L (10f*)
U R2 F2 L F L' F2 R F' R (10f*)
U R2 F2 L B D' F2 U B' R (10f*)
U R2 B2 R F R' B2 R F' R (10f*)
U R2 B2 R F L' D2 R U' L (10f*)
U R2 B2 R F L' D2 L F' R (10f*)
U R2 B2 R B U' B2 U B' R (10f*)
U R2 B2 R B D' R2 D B' R (10f*)
U R2 B2 L U B' L2 F D' L (10f*)
U R2 B2 L D L' B2 R F' R (10f*)
U F U' F R2 F' R F R2 F2 (10f*)
U F U' F R2 B' D B R2 F2 (10f*)
U F U' F L2 F' U F L2 F2 (10f*)
U F U' F L2 B' R B L2 F2 (10f*)
U F U' B U2 F' U B L2 B2 (10f*)
U F U' B U2 B' R F R2 F2 (10f*)
U F U' B D2 F' L B R2 B2 (10f*)
U F U' B D2 B' U F L2 F2 (10f*)
U F D' R U2 L' D B L2 B2 (10f*)
U F D' R D2 R' D F L2 F2 (10f*)
U F D' L F2 R' U F R2 B2 (10f*)
U F D' L B2 L' D F L2 F2 (10f*)
U L2 F2 R F U' L2 D B' R (10f*)
U L2 F2 R B R' F2 L U' L (10f*)
U L2 F2 L U R' D2 R U' L (10f*)
U L2 F2 L U R' D2 L F' R (10f*)
U L2 F2 L U L' F2 L U' L (10f*)
U L2 F2 L D F' R2 F D' L (10f*)
U L2 F2 L D B' D2 B D' L (10f*)
U L2 B2 R D R' B2 L U' L (10f*)
U L2 B2 L B R' U2 R U' L (10f*)
U L2 B2 L B R' U2 L F' R (10f*)
U L2 B2 L B L' B2 L U' L (10f*)
U B R' U R2 U' R B R2 B2 (10f*)
U B R' U L2 D' R F L2 B2 (10f*)
U B R' D F2 U' L B L2 F2 (10f*)
U B R' D B2 D' R B R2 B2 (10f*)
U B L' F U2 F' U B L2 B2 (10f*)
U B L' F U2 B' R F R2 F2 (10f*)
U B L' F D2 F' L B R2 B2 (10f*)
U B L' F D2 B' U F L2 F2 (10f*)
U B L' B R2 F' D F R2 B2 (10f*)
U B L' B R2 B' L B R2 B2 (10f*)
U B L' B L2 F' L F L2 B2 (10f*)
U B L' B L2 B' U B L2 B2 (10f*)

Christoph Lohe wrote:
2. twist the corners FUR and FUL


Here are all the 10-move sequences that start with U:

U R F2 U2 R' U' F R' F R' (10f*)
U R F2 U2 L' F' R F' U L' (10f*)
U R F' U F' U R' U' F2 R2 (10f*)
U R F' U F' D B' D' F2 R2 (10f*)
U R F' U B' L F' D' F2 R2 (10f*)
U R F' D R' U B' D' F2 R2 (10f*)
U R F' D R' D L' U' F2 L2 (10f*)
U R F' D L' F R' U' F2 L2 (10f*)
U R B2 U2 R' U' R U' B R' (10f*)
U R B2 U2 R' U' L F' U L' (10f*)
U R B2 U2 R' D' B L' D L' (10f*)
U R B2 U2 L' F' D R' D L' (10f*)
U R B2 U2 L' F' D L' F R' (10f*)
U R B2 U2 L' B' L U' B R' (10f*)
U R B2 D2 R' B' U B' U L' (10f*)
U R B2 D2 L' D' B D' B R' (10f*)
U R B' R F' L F' D' F2 R2 (10f*)
U R B' R B' U B' U' B2 R2 (10f*)
U R B' R B' D L' D' B2 R2 (10f*)
U R B' L U' B R' U' F2 L2 (10f*)
U R B' L D' R F' D' F2 R2 (10f*)
U L U2 F2 R' F' R F' U L' (10f*)
U L U2 F2 L' U' R U' B R' (10f*)
U L U2 F2 L' U' L F' U L' (10f*)
U L U2 F2 L' D' B L' D L' (10f*)
U L U2 B2 L' B' U B' U L' (10f*)
U L U' R U' B R' U' F2 L2 (10f*)
U L U' R D' R F' D' F2 R2 (10f*)
U L U' L F' U L' U' F2 L2 (10f*)
U L U' L F' D F' D' F2 L2 (10f*)
U L U' L B' L B' U' B2 L2 (10f*)
U L D2 F2 R' F' D R' D L' (10f*)
U L D2 F2 R' F' D L' F R' (10f*)
U L D2 F2 R' B' L U' B R' (10f*)
U L D2 F2 L' U' F R' F R' (10f*)
U L D2 B2 R' D' B D' B R' (10f*)
U L D' F U' R F' D' F2 R2 (10f*)
U L D' F D' F L' U' F2 R2 (10f*)
U L D' B R' B R' D' B2 R2 (10f*)
U L D' B L' U B' D' F2 R2 (10f*)
U L D' B L' D L' U' F2 L2 (10f*)

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