Beginner 2x2 Method (2-alg Guimond)

[Cride5]

I've just been teaching my mate (a cube virgin) to solve a 2x2. I've been using Guimond for the 2x2 for a while, so thought I'd teach a cut-down version of that. This is how it goes:

1. Use intuition to orient three cubies on both U and D faces. Mixing U/D colours at this stage is fine, as long as each U/D face has three oriented cubies (ie. with U or D colour on top).
   
   
2. Using a U face turn, place the misoriented U-face cubie in UFL. Flip the cube using x2 and do the same for the opposite layer.
   
   
3. Now check the orientation of the mosoriented UFL cubie. If the U/D colour is facing you, use x2 to flip the cube. Now the misorineted cubie should have the U/D colour facing to the left.
   
   
4. Apply the algorithm R U' B L to complete orientation of the U/D faces.
   
   
5. Using F2 R2 and U moves, swap U/D cubies until the U-face contains only U colour.
   
   
6. Now look at the U layer only:
   
   • If you see 1 bar, position the cube (using y turns) so that the bar is in the back face. Apply the algorithm R' F R' B2 R F' R' B2 R2 (A-perm).
   • If there are no bars apply A-perm to create a bar.
   
   
7. Do x2 and repeat step 6 for the D layer to complete the cube.

I'm a big fan of minimum alg solutions, so just thought I'd share this one for the 2x2

 

[soccerking813]

Maybe adding the intuitive sequence R2 F2 R2 would make some cases for step 6-7 faster.

 

[Zaxef]

I just do it as 3x3 corners..

Orient all corners correctly on D face..
Use Sune and U Perm for U face.. Done..
2 algs.. much easier than this, no?

 

[Cride5]

I just do it as 3x3 corners..

Orient all corners correctly on D face..
Use Sune and U Perm for U face.. Done..
2 algs.. much easier than this, no?

Have you actually tried this??

U perm on a 2x2 lol

 

[Kian]

I just do it as 3x3 corners..

Orient all corners correctly on D face..
Use Sune and U Perm for U face.. Done..
2 algs.. much easier than this, no?

A U perm? That will literally do nothing on a 2x2.

 

[miniGOINGS]

I just do it as 3x3 corners..

Orient all corners correctly on D face..
Use Sune and U Perm for U face.. Done..
2 algs.. much easier than this, no?

wow, there are no edges on a 2x2

 

[Zaxef]

A U F Q whatever, you knew which one I was talking about.. I don't remember them by Letter -_-
A Perm?
The corner cycle one.. Jesus.

 

[Cride5]

Following the LBL approach for a 2x2 isn't necessarily easier for a beginner because:

(1) Intuitive completion of the bottom layer is not straight forward. I would argue that the intuitive steps in reduced-alg Guimond are easier. This is of course subjective opinion, but it is based on experiences teaching the 2x2.

(2) There are more moves to learn in the two LBL algs than there are in the two Guimond algs. Remember, for a beginner the first algs you learn are the hardest. The less moves, the easier they are to remember.

(3) Using repeated application of Sune to solve OLL requires up to three repetitions of the alg if the solver is aware of the exact procedure. Teaching a beginner exactly how to apply sune for each OLL case adds an extra level of difficulty.



Finally, although this is not necessarily a major consideration in beginner methods, the cut down Guimond method has the added advantage of being more efficient than the beginner LBL. Here's the explanation:

Because intuitive methods are used for the first stage I couldn't easily compile exact move count statistics, so instead I took an average of 10 for the first layer in LBL, and steps 1 to 5 of beginner Guimond. The results are as follows:

LBL first layer: 8.1 moves (6, 7, 8, 12, 8, 8, 6, 8, 11, 7)
Guimond steps 1-5: 11.0 moves (14, 14, 14, 12, 8, 8, 8, 12, 14, 6)


For the LL the move count stats are as follows:


OLL using Sune
--------------
MOVES | PROB | MOVES x PROB | CASE
------------------------------------------------
| 3x8 | 4/27 | 96/27 = 3.56 |Headlights
| 3x8 | 4/27 | 96/27 = 33.56 |T
| 3x8 | 4/27 | 96/27 = 33.56 |Bowtie
| 1x8 | 4/27 | 32/27 = 1.19 |Sune
| 2x8 | 4/27 | 64/27 = 2.37 |Anti-Sune
| 2x8 | 2/27 | 32/27 = 1.19 |H
| 2x8 | 4/27 | 64/27 = 2.37 |pi
| 0x8 | 1/27 | 0/27 = 0.0 | Oriented
-----------------------
AVG MOVES = 17.78


PLL using A-perm
----------------
MOVES | PROB | MOVES x PROB | CASE
------------------------------------------------
| 1x9 | 4/6 | 36/6 = 6.0 | A-Perm
| 2x9 | 1/6 | 18/6 = 3.0 | E-Perm
| 0x9 | 1/6 | 0/6 = 0.0 | Solved
-----------------------------------------------
AVG MOVES = 9




Comparing the two we have:

LBL
First layer: 8.1
Sune OLL: 17.78
PLL: 9.0
AUF: 0.75
Total: 35.63 moves average

Guimond
Steps 1-5: 11.0
U-Layer PLL: 9.0
D-Layer PLL: 9.0
AUF: 0.75
Total: 29.75 moves average

 

[fanwuq]

Very nice!
Do you have a good plan to expand this into a corners first 3x3x3 beginner method?

Your move count stats are wrong. OLL always take 2 or less sunes. A perm is 9 moves. Also add 0.75 for AUF.

 

[Cride5]

Very nice!
Do you have a good plan to expand this into a corners first 3x3x3 beginner method?

Your move count stats are wrong. OLL always take 2 or less sunes. A perm is 9 moves. Also add 0.75 for AUF.

Oops, silly mistake with the A-perm! Cheers for pointing out the probs tho

Are you sure about the sune. I'm not including anti-sune here. How do you solve the headlights case with two sunes :confused:

Interesting you should mention a beginner CF method. The dude who learned this last night is now trying to intuitively place edges to complete the cube, so I guess its not such a difficult progression to the 3x3. U and D layer edges can be placed using intuition, and the final E-slice edges can be solved with a further two algs.

 

[fanwuq]

Very nice!
Do you have a good plan to expand this into a corners first 3x3x3 beginner method?

Your move count stats are wrong. OLL always take 2 or less sunes. A perm is 9 moves. Also add 0.75 for AUF.

Oops, silly mistake with the A-perm! Cheers for pointing out the probs tho

Are you sure about the sune. I'm not including anti-sune here. How do you solve the headlights case with two sunes :confused:

Interesting you should mention a beginner CF method. The dude who learned this last night is now trying to intuitively place edges to complete the cube, so I guess its not such a difficult progression to the 3x3. U and D layer edges can be placed using intuition, and the final E-slice edges can be solved with a further two algs.

Sorry, I always consider Sune and antiSune the same case. I did not know that you are only using one. When I was fast learning and when I teach other people, mirroring the Sune is no problem.
I don't know how to explain to some people how to place both of the last edges on U and D at the same time. Should orientation be explained, or should a pure commutator edge flip be used for last few M slice edges?

 

[MistArts]

I would use R' F R' F2 R U' R' F2 R2 for A-perm on a 2x2. Also, R U' B R for the orientation to keep the U/D colors on U/D.

Guimond is still inferior to Ortega...

 

[Cride5]

Sorry, I always consider Sune and antiSune the same case. I did not know that you are only using one. When I was fast learning and when I teach other people, mirroring the Sune is no problem.

Yea I guess mirroring the Sune would be an easy shortcut to the OLL, but then it's at risk of becoming a 3-alg solution

I don't know how to explain to some people how to place both of the last edges on U and D at the same time. Should orientation be explained, or should a pure commutator edge flip be used for last few M slice edges?

The way I was thinking about explaining the final two U/D layer edges is to try placing them into the E-slice so that they are adjacent and both U/D face colours face away from each other. The adjacent pair are then moved to the back face of the E-slice. A F/F' quarter turn is then made on the front face and E2 followed by F'/F places the last two edges.

For the final edges I was just planning on showing:
For permutation: M' U2 M U2 - edges to permute in UB, UF & DF
For orientation: M' U M' U M' U2 M U M U M U2 - two edges to orient in UF & UB

The orientation alg is horrible tho

 

[TMOY]

For orientation, B2 U M U' B2 U M' U (edges to orient in DF and DB) is IMHO better.
Note that it also permutes the edges, so you have to do orientation before permutation if you want to use it.

 

[rahulkadukar]

A good shortcut is to use A perm instead of T perm

 

[DAE_JA_VOO]

A U F Q whatever, you knew which one I was talking about.. I don't remember them by Letter -_-
A Perm?
The corner cycle one.. Jesus.

Please have some respect. There are some members on this forum that are Christians, and that sort of uncalled for vulgarity is offensive. Thank you.

 

[moogra]

Easier method would be
get to the last layer, find corners that aren't oriented
use R' U L U' R U L' or something like that.
Then use R U R' U R U2 R'
first layer is intuitive.

 

[fanwuq]

Bump.
I'll be making some modifications to make the method even easier in the next few days.
I'll make a comprehensive tutorial that extends into a CF 3x3x3 method.
Then I will teach it to beginners in my school cubing club. I get so tired of explaining how to make a cross. I hope CF works better.

 

[miniGOINGS]

Awesome, I'm looking forward to it.

 

[riffz]

A U F Q whatever, you knew which one I was talking about.. I don't remember them by Letter -_-
A Perm?
The corner cycle one.. Jesus.

Please have some respect. There are some members on this forum that are Christians, and that sort of uncalled for vulgarity is offensive. Thank you.

Lol... I'm a christian and that doesn't offend me in the slightest. But I guess I don't speak for everyone.