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 Post subject: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 9:49 am 
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Has anyone tried scrambling and solving a 3x3x3 with only QUARTER TURNS on ADJACENT FACES?

No slice moves, cube rotations don't count as moves (So D, X, U is not okay! :P) and using algorithms to leave the cube unaffected ( such as (R, U, R', U')x6 ) is against the rules (since you're not using that advance the solve, only cheat the system.)

So if you started with U', you couldn't do D or D' unless you did a turn on F, R, B, or L? And then solving it the same way?

I was trying this waiting for the bus but didn't get very far.

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Last edited by theVDude on Fri Sep 10, 2010 11:47 am, edited 1 time in total.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 10:08 am 
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If I started with U', can I do R'?

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 10:17 am 
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Chilen wrote:
If I started with U', can I do R'?

Yeah. If you start with U or U', you can only do R or R', B or B', L or L', or F or F'.

Basically If you do U or U', you can't do D or D'. If you do R or R', you can't do L or L'. And if you do F or F', you can't do B or B'. (and in reverse for all of them, as well.)

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 10:28 am 
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I use the edge first method and follow you law. It's OK.
The only trouble is that I have to read the color while turning.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 11:13 am 
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Fridrich does that, so long as you're careful with how you move the sides.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 11:24 am 
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SEBUVER wrote:
Fridrich does that, so long as you're careful with how you move the sides.

I'm curious about how you set the positions of last 3 corners.
U'RU'L2UR'U'L2U2 is illegal here.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 11:47 am 
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SEBUVER wrote:
Fridrich does that, so long as you're careful with how you move the sides.

I find myself using halfturns during cross and the first two layers, that's the more puzzling part to me. IDK, maybe it's just me.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 3:22 pm 
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I just wrote down an entire outline on how to achieve this and then realized that you could only do quarter turns :lol: My method got shattered when taking that into account. I'm working on an alternative, but it's a lot harder than I originally thought. I have no trouble getting to the last layer. For this kind of solving I would go for permutation and orientation of edges and corners separately, which I know how to do by using some easy commutators. But the restrictions complicated this just enough for me to have to work out some new ones for it to work using this approach.

EDIT: So, I did it. I went back to plane Friedrich. The key is to work with three adjacent faces at a time, for instants use moves that only require you to use the F, R and U face. Which will allow you to get the job done without using any opposite faces. Also, you of course have to limit it to using sequences without R2, U2, F2 etc. For cross and F2L that wasn't too hard. When I got to the OLL part, I just had to try and fail until I got a pattern I knew wouldn't break any of these rules. In this case I got this one: r U R' U' r' F R F', which didn't break any restrictions in the move itself or taking previous moves into account. For PLL my favorite algorithm doesn't break any of the two rules: F R U' R' U' R U R' F' R U R' U' R' F R F', as this is RUF moves only. BUT - in this case it did according to previous moves, as that ended with an F' move and this algorithm starts with an F move. But this has a simple fix: I just did a U turn and then canceled this and was able to perform it which (with a lot of luck) resulted in a solved cube.

I guess you could say that I got lucky with this one, but hey the end result is the same: a cube solved just by using quarter turns and without be able to do U turns followed by D turns and R turns followed by L turns etc.


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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Thu Sep 09, 2010 10:35 pm 
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There is a universal way to change an arbitrary sequence of moves into another sequence of moves satisfying your rule.

If the original sequence has F2, which is forbidden, then you insert (R,U,R',U')x6 between the two F turns.

If the original sequence has (F,B), which is forbidden, then you insert (R,U,R',U')x6 between F and B.

For other forbidden move, just reorient the cube so that it becomes F2 or (F,B).

Of course, this method takes the fun out of the challenge... :(

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Fri Sep 10, 2010 1:20 am 
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I use edge first method and solve it several times except one time.
The situation is the last step is U2.
What can I do? So, I think schuma's method is helpful.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Fri Sep 10, 2010 1:30 am 
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schuma wrote:
There is a universal way to change an arbitrary sequence of moves into another sequence of moves satisfying your rule.

If the original sequence has F2, which is forbidden, then you insert (R,U,R',U')x6 between the two F turns.

If the original sequence has (F,B), which is forbidden, then you insert (R,U,R',U')x6 between F and B.

For other forbidden move, just reorient the cube so that it becomes F2 or (F,B).

Of course, this method takes the fun out of the challenge... :(
On the topic of cheating the rules :wink: , Jaap showed in his "Useful Mathematics" article a nice sequence to cause a turn on the D face using only turns on the other 5:
[R2,L2,U2,R2,B2,R2,L2,F2,L2,U2],U,[U2,L2,F2,L2,R2,B2,R2,U2,L2,R2]
Obviously via reorientation this can be used to cause a quarter turn in any face without turning that face. By using schuma's short-order sequence to insert useless moves between the half turns and non-adjacent face turns, you can apply this strategy quite mechanically to solve under these rules.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Fri Sep 10, 2010 3:36 am 
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schuma wrote:
Of course, this method takes the fun out of the challenge...
Yeah, I did similar things my first try, but then realized it wasn't fun anymore. Also when I needed to do a U turn after a D turn, I did a cube rotation so that it wouldn't be a U turn anymore :lol: Though I managed to complete a solve with these rules, I had way too much luck with the last layer.


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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Fri Sep 10, 2010 11:45 am 
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Mmkay, I'll edit the first post to change the rules a bit.

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 Post subject: Re: Puzzling 3x3x3 scramble and solve
PostPosted: Wed Sep 15, 2010 4:43 pm 
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Here's an interesting way to do U2 or U D without inserting useless turns (well, not in an obvious way ;)). What I mean is that every sub-sequence of this sequence has some effect on the cube. So it's slightly more legit than schuma's.

U2 = U F R' F' R U F' U L' U' L F
U D = D F R' F' R U F' U L' U' L F
U D' = D' F R' F' R U F' U L' U' L F
These sequences end with an F turn, sure, but you can make it end with any of F, R, B, L using a variant of this sequence, so you can make sure that this sequence ends with a move adjacent to whatever your next move will be.

Example, J perm:
R U2 R' U' R U2 L' U R' U' L =
R U F R' F' R U F' U L' U' L F R' U' R U F R' F' R U F' U L' U' L F L' U R' U' L

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