I’ll put my notes here for learning 3-style over the month of February, so if you’re interested in solving the Rubik’s cube blindfolded, you might find this thread interesting. Also, if you already use 3-style or tried to learn it before but never completed the task, I’d appreciate any comments from you too.
For those of you who don’t know, you can in fact solve the Rubik’s cube blindfolded!
The beginner’s method here is called Old Pochmann (after its inventor). The idea is that you repeatedly swap two corners on the cube until all are in the right position. You then repeat the process with edges until they are all in place as well and voila, the cube is solved.
There are 8 corner pieces and 12 edge pieces on a cube. Since the centers can’t move that’s 20 pieces of information you need to memorize for each solve. Similar to #card-memorization where you’d memorize 52 cards and then put an un-shuffled deck into the order you’ve memorize, in #blindfolded-speed-cubing, here you put the “shuffled” deck (the scrambled cube) into the order of an un-shuffled deck (solved cube).
In order to put the pieces back into place, you have to perform a swap algorithm on the cube. For this you have to perform either the Y-permutation for corners or the T-permutation for edges. You can find both of them here: http://badmephisto.com/pll.html
So what is 3-style and why would you want to learn it?
Sticking with the above comparison, it’s a double card system with one image for each card pair (52x51=2,652) rather than 52 single card images. On a cube you can have each of the 8 corners in three different orientations (8x3=24) or either of the 12 edges in two different orientations (2x12=24). You can easily assign the letters A-X to these 24 possibilities.
In Old Pochmann, you’d now keep the A-position on the cube as your buffer and swap the J piece that might be in there into where J belongs. The piece that was in J before the swap is now in A, so you swap that to where it belongs and then the new piece you get from that position, etc. until solved. So you have a total of 23 possible swap from A into anywhere from B to X.
In fact, R and E share the corner piece with A, because White, Blue, Orange is the same as OWB is the same as BOW just in different orientations. So you really only have 21 positions you can shoot to, because A to E or A to R is not swapping anything on the cube.
In 3-style on the other hand, you cycle three pieces at a time instead of just swapping two. So instead of shooting to one position from the buffer and then to the next, you swap the buffer into the first position, the first into the second position, and second into the buffer position. That’s on average half as many swaps to complete the corners when compared to Old Pochmanm.
Of course, just like with 2,652 double card images instead of 52 single card images, you are now looking at 378 possible cycles instead of 21 positions you can shoot to with Old Pochmann. An example of this would be using the A-permutation in the link above (instead of the Y-permutation) or the U-permutation (instead of the T-permuation) for corners and edges, respectively.
What’s the plan for February
Basically one letter per day. My buffer is the corner that is Up Front Right aka C and from there you can cycle CAB, CAD, CAF, CAG, etc. On day 2 all the CBx algorithms, then CDx on day 3, etc. for a total of the aforementioned 378 algorithms.
We’ll see how all that goes… there is after all another set of 440 edge 3-cycles that could be learned afterwards.