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Solving 2x2 Twisty Puzzles Using Two-Look OLL and PLL

cr0wst profile image Steve Crow Originally published at smcrow.net on ・4 min read

This was something I noticed while playing around with my two-by-two rubik’s cube. I’m not a speed cuber, and I’m not very good at memorizing algorithms, however, solving twisty-puzzles has been a hobby of mine for a few years.

Three-by-Three Two Look OLL and PLL

I primarily use the CFOP or Fridrich method for solving three-by-three twisty puzzles. However, because I can’t memorize a lot of algorithms I supplement the last layer with the Two-Look OLL and PLL. Typically the process is as follows:

  1. Solve the cross. This is your standard beginner’s method starter.
  2. Solve the corners and middle edge pieces. This is a combination of the second and third steps of the beginner’s method. This is done by finding F2L pairs and inserting them in the appropriate spaces.
  3. Solve the top center pieces (at least forming a cross).
  4. Orient the last layer so that the cross-opposite color (traditionally yellow) is facing straight up.
  5. Position the last layer so that the pieces are in the correct spots.

Two-By-Two Twisty Puzzle

The two-by-two twisty puzzle is solved similarly to the three-by-three. It is essentially a three-by-three twisty puzzle without any edge pieces or centers. It is identical to working with the corners of the three-by-three. Typically the process is as follows:

  1. Solve the bottom layer. This is done by positioning and orienting the pieces so that a single color is on the bottom and matching colors are on the sides of the first layer.
  2. Orient the top layer so that the cross-opposite color (traditionally yellow) is facing straight up.
  3. Position the last layer so that the pieces are in the correct spots.

The neat thing about working with the corners is that there is a direct one-to-one relationship between the two-by-two and the three-by-three corners especially when solving the last layer.

Last Layer Relationship

When solving the last layer of the three-by-three it’s important to solve the center pieces first. This forms seven various conditions. These same conditions can be found on the two-by-two, however, you can skip solving the top center pieces because they don’t exist.

Two-Look OLL

The first part of the two-look OLL is to orient the edges. Since the two-by-two doesn’t have edges, this becomes a single-step process.

Here are the corner algorithms I use for orienting the last layer for both a three-by-three, and their equivalencies in the two-by-two.

Name Three-by-Three Two-by-Two Algorithm Notes
Headlights Headlights Headlights Anti-Sune U Sune
Chameleon Headlights Headlights r U R' U' r' F R F'
Bowtie Headlights Headlights F' r U R' U' r' F R Chameleon with F' at beginning instead of at the end.
Sune Headlights Headlights R U R' U R U2 R' The important part is that there is a yellow edge in the “tail” of the fish. The other sides may vary.
Anti-Sune Headlights Headlights R U2 R' U' R U' R' The important part is that there is a yellow edge in the “tail” of the fish. The other sides may vary.
Asym. Cross Headlights Headlights f (R U R' U') f' F (R U R' U') F'
Sym. Cross Headlights Headlights F (R U R' U') (R U R' U') (R U R' U') F'

Two-Look PLL

When dealing with the three-by-three you can do a two-look PLL to orient the corners and then the edges. However, with the two-by-two there are no edges, so this becomes a single algorithm that can be used. I start by finding an edge that already matches. I rotate the top layer until that edge is opposite of the front face and perform the algorithm: l'UR'D2RU'R'D2l2.

If you don’t have an edge that matches, you can do the algorithm initially and it will align one of the edges. You then just need to orient the correct edge so it is facing away from you and repeat the algorithm.

The algorithms are exactly the same. However, when you see f, r, or l indicating the two front or two right layers are to move, you only have to move the single front, right, or left layer.

Conclusion

I think a big part of solving twisty puzzles comes from being able to make comparisons against the three-by-three twisty puzzles. Whether you’re working with mirror cubes, different shape mods, picture cubes, etc.. making those comparisons can be rewarding and exciting.

Have fun!

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Steve Crow

@cr0wst

Steve is a lover of Greyhounds, twisty puzzles, and European Board Games. When not talking math to non-math people, and Java to non-Java people, he can be found sipping coffee and hacking on code.

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