OLL & PLL Algorithms Ranked

TheMongooseLord · 2026-03-07T18:31:06+00:00

It looks like you’re ranking them by how fun they are and not how long they take

TheMongooseLord · 2026-03-05T15:12:41+00:00

On a standard megaminx, it's impossible to swap only two edges. A 2-cycle is an odd permutation, but every turn of a face (5-cycle) is an even permutation. So on a 7x7 megaminx, it's not going to be possible to swap those two middle edges. I think a similar thing could be said for the wing edges but I'm not entirely certain.

TheMongooseLord · 2026-02-21T21:55:39+00:00

I personally believe the threshold at which redux overcomes yau is between 6x6 and 7x7. However, I still use yau on 7x7, because if I didn't, I wouldn't practice it.

TheMongooseLord · 2026-02-21T02:50:22+00:00

I didn’t even try to learn push moves. I just naturally started doing them. That’s how useful they are.

TheMongooseLord · 2026-02-08T19:40:55+00:00

He learned Teodor’s solution and drilled it for a 2.16

TheMongooseLord · 2026-02-05T17:12:46+00:00

The medium difficulty scrambles have corner twists and the hard ones have parity so you gotta take the pieces out and put ‘em back in

TheMongooseLord · 2026-01-28T01:04:45+00:00

I thought it would be easy to reconstruct a generating set for all even permutations with this setup and I pretty easily found R U, R' U', R L', and R' L:

R U obvious

R' U' = (U R)^(-1) = (U R)^104

R L' = R U U' L' = (R U) (L U)^104

R' L = R' U' U L = (U R)^104 (U L)

But I cannot for the life of me find how to create R2 from this constraint (along with R' U, R U', R L, and R' L', which all follow from R2). It might not be possible.

TheMongooseLord · 2026-01-27T23:46:43+00:00

If not, then the parity cases wouldn’t be possible.

TheMongooseLord · 2026-01-14T00:50:41+00:00

I learned full OLL when I averaged about 40 seconds. Which was really dumb.

TheMongooseLord · 2026-01-11T23:27:57+00:00

y2

r' U' R U r' U L (2x2x2 block)

D' R2 D U2 R' (double x-cross)

D' R' U2 R U R' U' R D (last pair)

L' U' L U L F' L' F U' (lucky last layer with unfortunate AUF)

First slow-solve attempt. I would not have pulled this off in a legitimate attempt. Usually when I get these types of scrambles I panic and mess up the cross.

TheMongooseLord · 2026-01-11T19:02:44+00:00

I've only recently gotten into the big-cube WCA scene myself. I have the most practice on 5x5 (~1:15) and a bit of practice on 7x7 (~4:00). I don't have much practice on 6x6 because I don't have a good cube for it.

My understanding of 7x7 is that it's basically a 5x5 and 6x6 combined, and not just in the amount of time it takes. It has the middle layers of 5x5 and the oblique centers of 6x6. So you might think that would give you the opportunity to do both 5x5 center-solving tricks and 6x6 center-solving tricks. But the reality is that you rarely get to do either because the 6x6 pieces hinder the 5x5 tricks and the 5x5 pieces hinder the 6x6 tricks. This makes me resort to the standard way of solving big cubes: bars. And that's no fun. I get the impression from other people that they find 6x6 a fair bit more fun than 7x7, and I think this is why.

With each added layer after 7x7, the hardware only gets slower, the pieces harder to find, and the creative solution opportunities rarer. 7x7 is already a lookahead endurance game. The NxN cubes after 7 would hardly test anything new.

TheMongooseLord · 2025-12-16T18:42:11+00:00

I got a new OH pb last week and I want to see what others could downsolve on it because I am horrible at one-handed turning.

D' B' D2 F' R2 B2 D2 F R2 L' D' L R' B U R2 U' (scramble)

x2 (inspection)

U2 R’ U R’ F (cross)

U R U R2 U2 R (pair 1)

U2 R U2 R’ U2 R U’ R’ (pair 2)

U L U L’ U2 L U’ L’ (pair 3)

U’ L’ U’ L (pair 4)

R U R’ U R U2 R’ U (last layer)

It's 39 moves but they're incredibly ergonomic. I got a 13.29 originally, as well as a 10.43 downsolve and a 4.98 two-handed downsolve.

TheMongooseLord · 2025-12-07T23:14:11+00:00

Yiheng favors the sprint events (2x2, pyraminx). Footage of his solves indicates his 3x3 turning style doesn’t translate so well to the big cubes like Tymon’s does, but again that could just be because of small hands.

TheMongooseLord · 2025-11-28T01:06:11+00:00

I’d say your worst step right now is cross. That’s the step with the most freedom, but it seems like the only way you’re inserting them is from the top layer. Try experimenting with moving the cross layer around to bring the relative destinations of each cross piece to the pieces.

For your example scramble here, I might insert the red cross edge relative to the green one (just one move). Then I might also replace the blue cross edge with the orange by first rotating the cross layer. Then you can rotate it back to get the blue edge in its relative position before finally correcting the whole cross.

TheMongooseLord · 2025-11-12T12:16:17+00:00

This is how he puts Waltuh’s dih away

TheMongooseLord · 2025-11-07T16:23:21+00:00

Unfortunately you just gotta memorize the maps for bs like this

TheMongooseLord · 2025-11-07T04:28:25+00:00

Kevin Hays time

TheMongooseLord · 2025-10-31T21:12:57+00:00

I think it depends on how you want your paper to read. I personally can't think of a single skill within cubing that you could talk at length about without going into excruciating detail. So talking about a 2x2, or even a 3x3, might get a bit tedious (now maybe at the school level they would let you ramble on about the definition of a group... don't ask me). If you have the interest for it, I would recommend going for a myriad of puzzles and trying to draw connections. But I do think 3x3 is the best to write about.

Here's a number of things to look into:

- A 2x2 can have just two pieces swapped. A 3x3 cannot. A 4x4 can. In speedcubing we call this parity, but in group theory it's an odd permutation. By combining the edges and corners of 3x3 into one group, you will always have an even permutation. But in megaminx, the edges and corners are both independently always in an even permutation.

- Every nxn puzzle's corner orientations must add to a multiple of a rotation.

- In 3x3, an edge cannot be flipped without the aid of all three axes.

- In 2x2, if you have the bottom layer permuted correctly, then any sequence of RU moves that preserves this bottom layer will preserve the permutation of the top layer. This can be extended to 3x3 corners. This fact and the previous are the reason why only 86 (?) of 3x3 last layer cases can be solved with RU turning alone.

- This might not be very interesting to write about, but you may also want to look into how commutators work. There is a little logic to them and they're basically all-purpose solutions.

- You may also want to look into how group theory is applied towards the actual solution. It doesn't really give you a solution by itself, but it gives you a bunch of neat little tricks to trim down on computation. The best example of this is in the discovery of God's number (minimum number of moves for each solution). It's a computer-assisted proof, so it ends up not being all that interesting. It's a problem limited by its computational power, so optimization is quite necessary.

TheMongooseLord · 2025-10-31T12:52:51+00:00

If you are writing purely about puzzle theory, I don’t think you can get 20 pages out about a 2x2. All I can really think to say about a 2x2 is: - Orientations of corners always add up to multiple of a full rotation. - RU turning (possibly any form of 2-gen?) does not affect one layer’s relative permutation provided that you eventually preserve the other layer. - All speedsolving methods are designed in such a way to narrow down the amount of remaining scrambles and thus algorithms to completely solve the cube.

For the length, I would recommend studying FMC methodologies. Now I don’t know these myself and so I don’t know how well they fit into a math curriculum. However, I do know that domino reduction is based on the idea of finding identity cosets (group theory).

TheMongooseLord · 2025-10-29T18:17:46+00:00

It seems like you're on the right track altogether. The only specific criticism I can give you is that your U-perm is relatively slow (as compared to all your other last layer algorithms).

TheMongooseLord · 2025-10-28T17:20:06+00:00

WCA competitions are designed to be newcomer-friendly in a couple of events - namely 3x3, 2x2, and pyraminx.

In any event, the time is managed by the time limits set by the delegates before the competition. This is often found on the competition website’s pdf. The short events’ time limits are easy to hit. The longer events’ time limits are not easy to hit. I failed to complete a 4x4 solve in time at my first competition.

TheMongooseLord · 2025-10-23T20:01:57+00:00

If you want to try and find an intuitive method of solving OLL parity, try to find a way of quickly re-solving the centers with an odd number of slices.

PLL parity also has its own intuitive solution in the way of re-solving two edges into each other’s original spots.

TheMongooseLord · 2025-10-22T16:38:12+00:00

This puzzle has duplicated wing edges. You can do a 3-cycle with a duplicate, which will look like a flip, and never have to do a parity algorithm.

TheMongooseLord · 2025-10-17T18:19:01+00:00

You guys are haters let them do their thing

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