Any Cubers?

Worlds Smallest Cube

 

@TryingMyBest121 So what's the color scheme?

 

This spring I set out to beat the 3x3 cube during the covid lockdowns. I didn't look up any solution, I just figured out my own algorithms from scratch.
It took some time but I got it! Once I beat it a few times I looked up the notation, and wrote out my solution. I'll paste it below, sorry its kinda a LOT of text:

--------------------------------------------------------------------------------------------

Alex’s rubric’s cube solution

Layer 1 is just easy, I could normally just look at it and figure it out. Not efficiently though.
Now I have more efficient methods, but they just sorta utilize parts of my later algorithms, so I’ll start with second layer:

Layer 2:
Get the piece you want to put in L2 into FU:




To move it to the left (ie the position in the photo):
R’ D’ F’ D R F’ U F

To move it to the right:
L D F D’ L’ F U’. F’

Layer three: First, get the cross on top:

Whichever colour L3 edge piece isn’t oriented correctly, put that colour in F position, and then put that piece in the LU or RU spot.

If LU:
F’ L F L’ U’ L’ U L

If RU:
F R’ F’ R U R’ U’ R ‘

You may have to repeat this a couple times, try not to spin U/U’ in between repeats of the algorithm if you can avoid it. That seems like it helps (?).

Layer 3: swap edges:

I discovered two different algorithms for this, one of which is the algorithm used in the beginner method:

With LU and BU in the ridge spots:

L’ U’ L U’ L’ U2 L U’

But I actually discovered that algorithm while trying to move layer three corners around. The first algorithm I found to move edge pieces is:

With LU and FU in the right spot:
L F’ U’ F L’ F’ U F U L U’ L’ U’

Its a little longer/sloppier, but it works.

Layer 3: change corner positions

This is when I discovered the simpler of the L3 edge swapping algos above, but I didn’t realize thats what it could be used for until later.

Eventually, I discovered that my algorithm for getting the cross on top could be run thrice, and it would swap 3 of the corners, but leave the last one in place. So with this you can cycle them into place, within at most 2 iterations of this algorithm I think:

put correctly positioned piece in BRU:
L F’ L’ F U F U’ F’
F’ L F L’ U’ L’ U L
R B’ R’ B U B U’ B’

I split this algorithm into three lines, so you can see the symmetry in the moves. It is just the algorithm for getting the L3 cross from above, but performed thrice, from different perspectives/mirrored.

Layer three: Change corner orientation

My solution involves a 78 move algorithm to finish the cube, it is a 26 move sequence, repeated thrice.

Sometimes when the pieces are in the position, they will still be in the wrong orientation in a way that this algorithm cannot solve. So you have to cycle the above algorithms further, until you get to the correct relative orientation of corners.

This algorithm swaps each corner to the opposite corner.
FLU <-> BRU and BLU <-> FRU

Two of them swap and stay in the same orientation. Two of them swap and change orientation.

I reorient the cube in my hand, a Z rotation I think. The third (unfinished) layer is now on the right instead of the top.

Now, in this new orientation, the pieces in FRD and BRU will swap, but stay in the same orientation. The pieces in FRU and BRD will swap, but change orientation. You want the U face of the FRU piece to be the colour of the R face, because that’s where it will end up once the algorithm is done.

So to complete the cube after running this algorithm, you want FRD and BRU to be in the right orientation, but opposite spots. You want FRU and BRD to be in opposite spots as well, but they will start in the wrong orientation. This is where you need to have the U face of the FRU piece to be the colour of the R face, to reach the complete cube end.

Sometimes even if you get the carner pieces in the right positions, the relative orientations can be off. You will need to cycle through the earlier algorithms to get to a different relative orientation. This is where some inefficiency really starts to come in…


So anyways, once you have all that, here is the algorithm:

U’ R U R’ U’ R U R’ U’ R U R’ U’ R U R’ U’ R U R’2 U’ R2 U R’
U’ R U R’ U’ R U R’ U’ R U R’ U’ R U R’ U’ R U R’2 U’ R2 U R’
U’ R U R’ U’ R U R’ U’ R U R’ U’ R U R’ U’ R U R’2 U’ R2 U R’

Each line is the same, it is the same moves repeated three time. Hopefully your cube is done now! But sometimes you have to cycle this algorithm a couple times to get to the finish, plan ahead!

 

Thanks! Agreed, I like math-y puzzles, so it was a fun challenge to explore.

That was really the foundation of my approach for solving the last layer: find patterns that, when repeated, would eventually return the cube to the position it started in. Then, try adding a move at some point in that pattern, to add some 'asymmetry', that hopefully results in a few pieces being in different positions at the end of the cycle. Lots of interesting symmetries to be found, most of them in 3's, or multiples thereof. (as example, iirc, my long-ass last algo returns the cube to the starting position, if you run it three times)

After I finished, my fiance showed me the beginner method (she learned it a few months prior), and I realized I was SO close to figuring out the last algo, but never quite got to it. She was losing her mind watching me dance around the well-known algos without quite hitting them, but I insisted she give no hints hahaha.

I have a mirror cube that I've beaten (same thing really, but the different piece heights/sizes is an interesting new way to think through it), but I'm thinking about getting some larger sizes to work through. @KendamaGoat (Danny Rankin) is a cube nerd, he was pushing me to get deeper into it during one of our poker games

Have you played with larger sizes much @TryingMyBest121 ?

 

A local friend has also ranted to me about parity errors, he said its why he just avoids even numbered cubes.
It seems like a common sentiment among cubers. Might make for a painful grind to figure out... but I guess those sorts of grinds are the ones that are most rewarding when (if) they work out lol

Appreciate the recommendations!