Experimental Methods

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Pseudoprogrammer

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I've recently gotten back into cubing. You may remember me as the (Advanced) Human Thistlethwaite guy. Before I left, and currently, I've always been obsessed with the creation of new ways to solve the cube (When I first got into cubing I was saddened that nearly everyone used basically the same method (Fridrich)). I'm often found throwing out ideas in the chat room (Much to Dan's dislike ;D). I think it'd be neat to have a specific thread for this (Sorry if it's already been done). I'd like to hear all of you guys' crazy new ideas!

One I was working on before I left was basically a speedcubing version of Ryan Heise's "Heise" method. It made the penultimate step into 57 algorithms and averaged in the low 40s for movecount on speedcubing, and in the 30s if you sat down and tried to get a low movecount for a few minutes. I still think it's a rather neat idea, although recognition is tricky.

Most of you know me (if you do know me) from my Human Thistlethwaite tutorials on youtube. I developed an Advanced method which used around 100 algorithms total to achieve an average of 43ish move solves that required no thinking, just recitation of algorithms. However since it is so contrary to human thought (building with blocks, chunks, etc) recognition was difficult for some steps.

My most recent idea was an attempt to create a method that was predominately 2-gen. Basically it works like this: Solve a 2x2x3 F2L block. Orient all edges while permuting (but not orienting) LL corners with 1 of 30ish algs. This makes the entire cube solvable by 2-gen from here on. Finish F2L with 2-gen. Use 1 of 30ish algs to orient the LL corners(they are already permuted, because they remain permuted due to the 2-gen nature of solving the F2L after you permute them once) and solve the LL edges (which are already oriented). Averages sub 50 move count. Half of the solve is 2-gen. I think it's pretty sexy.
 
Do you know how to orient the edges and permute the 6 remaining corners after building the 2x2x3 block? The corners only need to be permuted relatively, that is to say the cube just needs to be put into the <R,U> subgroup so that it can be solved with RU 2-gen from that point on. However, I don't know of a nice way to do this. If you do, I'd love to hear it.

Of course, if you can get that to work, you can finish the solve with 2GLL. This orients the LL corners and permutes the LL edges. There are 50 algorithms, I believe, and they are pretty fast and relatively easy to recognize. This would ould make for a great speedcubing method, similar to zz-d but with a Petrus start instead of EO-line, but I'm a bit doubtful about that one step. Please tell us your thoughts.
 
It's cool, I want to learn this method. Where can I get algorithms for this method?
 
Oh wow, didn't know there would be such interest in that one method ;D I'd like to hear you guys' ideas too!

But to answer your questions, I didn't actually go into much detail on that method because I didn't think it'd garner so much interest.

Let me go into the method in detail:

Solve 2x2x3. Similar to Petrus. Not much to see here.

Now this next step seems to be the most controversial. I left out some details in my description. Before doing the algorithm certain goals must be met: Put the first layer corners in their places (they do not need to be oriented, just in their places) while assuring that you do not have 4 bad edges. By meeting these two goals you lower the alg count from the hundreds down to about 31 (not counting mirrors). Usually this pre-step only uses 3-5 moves and is really easy to recognize after a while. Then do the algorithm to permute LL corners and orient all edges.

Then you do one of 30+x (I can't remember the exact number, it's in the 30s) of algorithms that permute LL edges and orient LL corners. (I think you guys call this 2GLL? I'm not familiar with a lot of cubing terminology, I often think of ideas before knowing they've been tried and done before (Before I entered the online cubing community I thought I'd invented the tripod method)). Maybe I miscalculated, you guys said there were about 50 algs. I don't know if you were counting mirrors or not. Not counting mirror cases, I counted 30ish algs.

I'll post an example solve in a second, after I take this spanish test ;D

EDIT: Here is that example solve. The various steps are split up line by line.
http://tinyurl.com/algL-D2L2FR2LF

Pretty sexy 35-move (37 if you count the R R' I did at the end of 1 alg and the beginning of the next) solve. Average solves are low 40s, so this was a nice solve. It could have been lower (around 32 or 33) moves had I not used 2-gen algs, but that would defeat the point!
 
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Close to 7x sounds like double the amount that I calculated, so it probably counts mirrors as separate algs.

EDIT:

Here is another example solve. 43 moves, this solve is right in the middle of the bell-curve. I got the unfortunate 4-bad-edges case that you need to get rid of, so like I said before, it took about 5 moves to permute the F2L corners and make it so I had 6 bad edges instead. A pretty average solve. Average length alg, slightly below average luck. Upon putting the scramble into cube explorer I see that my 2x2x3 is not optimal, so I dunno how it would have turned out (I used 9 moves, optimal is 7).

http://tinyurl.com/algB-L-F-L2D2R

But lets hear some of you guy's experimental ideas too (Not that I don't like all of the attention, muahaha), I love new ideas...
 
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Pseudoprogrammer said:
But lets hear some of you guy's experimental ideas too (Not that I don't like all of the attention, muahaha), I love new ideas...
Click to expand...

Lots of new concepts/ideas discussed here:
http://www.speedsolving.com/forum/showthread.php?t=14323

There's also a section on the wiki dedicated to experimental methods here:
http://www.speedsolving.com/wiki/index.php/Experimental_Methods

As Joseph mentioned, this idea is similar to ZZ-d (reducing the cube to 2G after the 2x2x3), but I like how it combines EO and CP after the 2x2x3 - as far as I'm aware this is a novel concept. I'm interested to know more about the EO+CP step, do you have methodology for recognition? Is there an alg-list, and would you be willing to publish it online?
 
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I came up with an Orient First method which:

1. orient corners (guimond algs)
2. Orient and place E-slice edges (M U action)
3. Orient remaining edges (M U action after a z-rotation)
4. Build 1x2x3 block using 3 centers and the DF DB edges (and preparing E-slice edges for step 5
5. solve f2l using only U-moves and R2 L2 moves.
6. PLL

I love step 1-3 which can be done fairly fast and move optimized with practise. But step 4 and especially 5 are not nice. It would be great if someone had a better idea on how to solve the cube after it has been reduced to being solvable using only <L2, R2, F2, B2, U, D>.
 
Cride5: The step works like so:
2x2x3 block is on DL (So R and U are the only unsolved sides). Insert F2L corners into their slots (but not oriented necessarily). To permute the corners you will need to swap two corners, they will be diagonal or adjacent. If adjacent, place the two corners on the R face (On U R? I believe you'd call it. Like I said before, my cube terminology is lacking. I mean to say your two corners to be swapped are UFR and UBR). If you have a diagonal swap, it doesn't matter the alignment, you can swap any diagonal corners. Look at your EO case. Execute alg. Recognition really isn't as bad as it sounds, it just takes some getting used to looking at permutation before orientation, because most solvers are accustomed to that.

EDIT:

And as for the 2GLL. I went back through and calculated every case. I got 75 (plus or minus a few, I can't remember exactly) cases with mirrors, and 39 cases without. So this method would have roughly 70 algs total.
 
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B2 D R F L B2 R' F R L U2 B U' B R2 F' D' L' U' L' R F B2 U' L2

F' D' L' F' D' R U R' (8)
z2 y U R2 U R (4)
F R2 F' U' R' U R U' F R F'(11)
U' R2 U' R U2 R U' R U' R2 U' R' (12)
U R U R' U R U2 R' (7)
 
I generated all the algs for that method I described. The CP+EO step and 2GLL. If anyone wants them, shoot me a message with your email address. I'm currently looking into making algorithms to solve all of F2L in one alg, but it looks like there will be a lot of cases so I probably won't.
 
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