Supercritical Method

Lord "you know who", you're very right, and the small number of cases for Fridrus/Supercritical last layer is a good thing.
No, he's not. His math looks like he never took a single math class at Hogwarts.

It's 2*3^2*6 = 108.
Mirrors don't even halve that. Still doable, but it's always surprising how many cases 2 edges+3 corners have (and about as surprising that everybody assumes it's much less).
 
Have you guys ever tried 'tripod'? You start with F2L minus a c/e pair (use Heise, Petrus, Fridrich, whatever) and then build a 2x2x1 block on the LL, so you have a sort of tripod of 4 corners and 3 edges left. Then you solve any of the three available c/e pairs, and finish with this LL. I think this might be one of the better ways to reach that nice LL.

Incidentally it is also possible to solve LL by just making a 2x2x1 block (algorithmically) and then doing this. It's an interesting way to do the last layer.

If you look at this on the correct angle its sort of an OLL. I might be wrong or might have not understood you correctly.
I tried doing this (as from what I understand) and ended up with either sunes, U cases or T cases.

I might be doing something wrong. Can you explain this further?
 
You're doing it wrong. You're supposed to do the LL in one step, not go "oh yay easy OLL". The point is that there's a 2x2x1 block solved in the last layer; doing OLL will usually break the block up. It is definitely doable to learn all of the one-step LL algorithms for the situations with a solved block.
 
Qqref,

The Tripod F2L is similar Fridrus, just in a slightly different order... 2 by 2 by 3 block, then 2 edges of the "cross", then 2 corner edge pairs, and you are left with a tripod, and after solving another corner edge pair you get the nice last layer.

And to Lucas, even if there are 108 cases and some number less algorithms to do a "nice" last layer, it's much better than the 1000+ algorithms needed to do a "normal" last layer. I've found conjugates to be a very useful way to cut down on learning algorithms. For instance, if there are two miss-oriented corners diagonally opposite from each other, and I only know how to solve them when they are next to each other, I just move one face to put them together, use the algorithm, then undo the face turn. In fact, I can do a 2 look "nice" last layer if I know 6 algorithms!!! Here's a list:

-Orient edges
-Swap edges and front corners (I use this to solve permutation of both corners/edges. Can also orient edges.)
-Orient edges + cycle corners (I plan to learn this one to solve last layer in 2 steps.)
-Corner cycle
-2 corner orient
-3 corner orient

This is why I use the Fridrus method. I like to learn a small number of algorithms and focus on intuitive solving. ;D

And yes, the point of the last layer is NOT to have a nice "OLL". If you focus on orienting the last layer, you screw up the permutation of the already solved pieces. That's why I solve edges first, then corners.
 
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Qqref,

The Tripod F2L is similar Fridrus, just in a slightly different order... 2 by 2 by 3 block, then 2 edges of the "cross", then 2 corner edge pairs, and you are left with a tripod, and after solving another corner edge pair you get the nice last layer.

And to Lucas, even if there are 108 cases and some number less algorithms to do a "nice" last layer, it's much better than the 1000+ algorithms needed to do a "normal" last layer. I've found conjugates to be a very useful way to cut down on learning algorithms. For instance, if there are two miss-oriented corners diagonally opposite from each other, and I only know how to solve them when they are next to each other, I just move one face to put them together, use the algorithm, then undo the face turn. In fact, I can do a 2 look "nice" last layer if I know 6 algorithms!!! Here's a list:

-Orient edges
-Swap edges and front corners (I use this to solve permutation of both corners/edges. Can also orient edges.)
-Orient edges + cycle corners (I plan to learn this one to solve last layer in 2 steps.)
-Corner cycle
-2 corner orient
-3 corner orient

This is why I use the Fridrus method. I like to learn a small number of algorithms and focus on intuitive solving. ;D

And yes, the point of the last layer is NOT to have a nice "OLL". If you focus on orienting the last layer, you screw up the permutation of the already solved pieces. That's why I solve edges first, then corners.

when you do your 2x2x3 block you only have 1 edge for the "cross" missing, right? where do you put your block btw after you solve it? lower-left part?
 
The Tripod F2L is similar Fridrus, just in a slightly different order... 2 by 2 by 3 block, then 2 edges of the "cross", then 2 corner edge pairs, and you are left with a tripod, and after solving another corner edge pair you get the nice last layer.

Maybe, but my biggest problem with the Fridrus method mentioned in this topic is the 2 edges of the "cross", which just seem to make it more difficult to move pieces around without making the method more efficient. So for that reason I prefer just pure blockbuilding.
 
To Patrick:

There are 2 edges to solve in the cross, not one; the block stays in the back laying vertically. As I solve corner edge pairs, I break the block up (a lot!).

And to Qqwref:

You do have a good point. I may consider using block building instead of placing 2 edges, but then I won't be able to say I use the FRIDRus method. XP That's OK though.

BTW, where did you find out about the Tripod method, and is there a site where I can get more info? It seems like the method I've been searching for.
 
BTW, where did you find out about the Tripod method, and is there a site where I can get more info? It seems like the method I've been searching for.

I didn't learn it from anywhere, just made it up. It was the end result of my attempts to try to solve as much of the cube as possible with just blockbuilding and no algorithms of any kind.

I tried to find a way to consistently solve the last 7 pieces (the tripod) in two algorithms, but I could never find one. Even with the corner/edge pair approach, there are still many times when it's not at all obvious what to do... but it's closer than ever to being speedsolve-worthy :)
 
Qqwref, because I've been messing around with supercritical so much, I am very good at the last corner/edge pair in this method. I can consistently form a pair in a maximum of 8 moves. You can see my site for all the cases. I just need to practice block building before the tripod... I'll probably do some analysis to find the most efficient ways to do so. With any luck, I might be able to get good solve times! X3

Thanks a lot again for all the help.
 
How many algorithms would one need to solve the cube after a "tripod" with all edges oriented? If you do a ZZ start and then solve the 3 slots and top part, that's what you end up with.
 
Yurivich, I don't think that orienting edges before the tripod would be very helpful, because by solving a corner edge pair in the tripod, you would ruin the edge orientation. It would help, however, if there were specialized algorithms for such a situation.

I've actually been on vacation in Florida for a few days, writing from my iPhone. When I return to my computer, I'll be able to do more work on this method and search for more algorithms. Perhaps I'll make a new site for the tripod method...
 
Stuck in lots of traffic... Only have iPhone + rubik's cube... So time for a forum post!

I think that the tripod method is one of the most versatile methods, giving the solver the most options. Let's see how many ways each step can be solved:

1. 8 (2 by 2 by 2 block on any corner)
2. 3 (extend any side to 2 by 2 by 3)
3. 8 (2 by 2 by 1 can be solved anywhere on either unsolved face)
4. 2 or 4 (next 2 by 2 by 1 block cannot intersect with previous one)
5. 3 (any corner edge pair in a slot)
6. 1? (it's the nice last layer :P)

This method is even more flexible than petrus (I'm fairly certain, someone correct me if I'm wrong). Steps 3 and 4 remind me of heise's first couple steps, where blocks are made then put into place.
 
1. 8 (2 by 2 by 2 block on any corner)
2. 3 (extend any side to 2 by 2 by 3)
3. 8 (2 by 2 by 1 can be solved anywhere on either unsolved face)
4. 2 or 4 (next 2 by 2 by 1 block cannot intersect with previous one)
5. 3 (any corner edge pair in a slot)
6. 1? (it's the nice last layer :P)

The way I do it the numbers are actually 8 3 4 3 3 1. For step 3 it is because I want the block to line up so I don't have to do a pseudo-F2L or pseudo-LL, and for step 4 I don't want to have the block cover the 'slot' in the F2L. I guess in theory there are a few other choices but they are a bit unweildy. Remember that it's really important that after step 4 all of the 7 unsolved pieces are touching each other.
 
You could solve the first 2 layers so that the tripod and last layer are always in place, but I find it to be quicker to take advantage of already formed pairs and make easier blocks. Doing so requires a simple conjugate later on, but it might make recognition for algorithms more difficult. I don't get confused by conjugates for the last step... I guess it's a matter of preference. I am returning home tomorrow. :)
 
to ostracod

wow, thank you for that tutorial at least i can study your method.. I just want to have another method but as i can see this cannot be used for speedsolving so i guess i'm just gonna practice it to increase the number of methods i can use in solving the rubik's cube.. Well, pretty cool... Thank You...​

to qqwref

Uhm. Can you make a tutorial video or a sample solve of that "tripod F2L method"?.. Well, guess I'm just good at learning when i watch videos... I can't fully understand what you meant... Well.. Thank you...​
 
Bluephoenix, I know you're probably upset that the supercritical method isn't so fast... I am too! But this method helped me a lot to learn how to intuitively solve. It's especially helpful when learning the tripod method, because most skills can be carried over. If Qqwref won't make a video, then I will do so.
 
uhmmm... thank you ostracod... well.. I really liked your method... It was so cool for me because of blockbuilding... Well, somehow, I'm currently learning your method... Uhm... For the tripod F2L video... I guess qqwref won't make one... So I guess can you make one? Please.. Thanks
 
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