## Monthly Archives: March 2012

No explanation, just a new notation and the minimal alg list needed to learn square-1.

Notation:
R = Move the right half of the puzzle 180 degrees (clockwise)
u = move the U slice clockwise one “notch” Could be either (1,0) or (2,0) by old notation depending on what piece is to the right of the U notch.
u2 = move the U slice clockwise 2 “notches” Only used if there are 2 edges to he right of the U notch.
U = move the U slice clockwise 90 degrees. (3,0) in old notation
u4 = (4,0) in old notation
u5 = (5,0) in old notation
U2 = 180 degrees, (6,0)

Method:
Cubeshape: R u d’ R’ U’ d4′ R u2′ D R u’ d’ R U’ R
M2: u R u’ d’ R’
single EO: d’ R U’ R’ u4 d R u4′ d’ R’ U R
J/J: R U’ R’ U D R D’ R’
N/J: R U R’ U’ R U R’ U’ R
Opp/opp: u R u’ d’ R’ U2 R u d R’
Pure parity: R U’ R’ D R D’ R’ D R u R’ d R u’ R’ u4 R d2′ R’ d2 R u4′ d R U R’
Flip E Slice: R U2′ R U2′ R

I recognize PLL with a combination of “Blocks” and “Bars” A block is two or three connected pieces, like so:

A bar is a set of connected corners. I’ve put bars in red wherever possible. The term “bar” is taken from 2×2 PBL recognition, so a bar may or may not include the edge in between the corners. (If it does, it’s also a 1×3 block):

You can tell the permutation of a layer (and its parity) by comparing blocks and bars in most cases. I’ve included some lookahead information for square-1 permutation, but the recognition part applies equally to 4×4 PLL. Listed is which EP case each permutation goes to with a proper Vandenbergh solution, and then information on 1-look permutation if it applies.
The E/X/Q cases are difficult to recognize with this technique, so I’ve added some notes to the end of the page detailing how I recognize these cases.

 Permutation Recognition Corner Permutation Resulting EP 1-look Permutation No parity: U + J = U J 1 J Z + J = Z N/A H + J = H N 1 N A + J = U J 2 J T + J = U J 4 J Ga + J = U N J Gb + J = U J N J + J = Solved J or J J or J N or N J R + J = U N/A F + J = U N/A Y + N = U J 5 J V + N = U N/A N + N = Solved N or J 6 J E + N = Z N/A Parity: Opp Edges + Solved = Opp N/A Adj Edges + Solved = Adj N/A O + Solved = O N/A W + Solved = W N/A Opp Corners + N = Opp N/A Adj Corners + J = Adj N/A K + J = Adj N/A P + J = Opp or Adj N/A B + J = Adj N/A D + J = Opp N/A C + J = W or O N/A M + J = W N/A S + N = Adj N/A X + N = O N/A Q + N = O N/A

Notes on E/X/Q:
These are definitely the hardest to distinguish. The trick is to look at two edges, and the corner between them, and apply the 3-color rule. If there are 3 colors, that means EP is correct, so you have an E-perm. If there are 2 colors, you have an X, and if there are 4 colors, you have a Q.

 E X Q

So, this is how I do cubeshape. First off, do NOT go and learn all these algorithms. That’s not how it works. This page is missing a lot of mirrors that you would be unable to do. Look at how I orient the layers and what shape the first twist leads to. If you’re having trouble figuring out a mirror, let me know. I’ll be glad to help you out.

I know some of these algs are suboptimal. In every case this happens, it’s a better fingertrick than the optimal version. Most of my suboptimal algs go through paw-paw. I do an extra move that essentially takes two right fists and turns them into two left fists. It makes for a very fast 2gen alg. Try it.

So, without further ado, I give you…a big table of algs.

 optimal depth 1 / optimal depth 2 /3,3/ /3,0/ optimal depth 3 /-2,0/3,3/ /1,0/-3,-3/ /1,2/-3,-3/ /1,0/-4,0/3,0/ /0,-1/-3,0/ /-2,0/-3,0/ /-3,0/-3,0/ /-2,-1/-3,0/ optimal depth 4 /0,-4/1,0/-3,-3/ /-2,0/1,0/-3,-3/ /-4,0/0,-1/3,3/ /-4,0/-2,-1/3,3/ /2,4/1,0/-4,0/3,0/ /2,4/-2,-1/3,3/ /2,2/0,-1/3,3/ /-2,0/-2,5/-3,0/ /-4,0/0,-1/-3,0/ /-4,0/1,0/-4,0/3,0/ /-2,0/-1,0/-3,0/ /-4,0/-2,-1/-3,0/ /-4,3/-2,-1/-3,0/ /-2,0/-2,-1/-3,0/ /3,2/0,3/0,3/ /-4,3/-2,-1/-3,0/ optimal depth 5 /2,0/-2,0/1,0/-3,-3/ /-2,0/-5,0/2,0/3,3/ /-2,-5/-4,0/0,-1/3,3/ /-2,1/-4,0/0,-1/3,3/ /0,-2/4,0/0,1/3,3/ /2,-5/-2,0/-5,2/0,3/ /3,0/2,4/-2,-1/3,3/ /-1,0/0,2/-2,5/-3,0/ /1,0/2,2/0,-1/3,3/ /2,0/-4,0/1,0/-4,0/3,0/ /-2,0/2,0/-1,0/-3,0/ /0,-3/-2,0/-2,-1/-3,0/ /2,0/0,1/-1,0/-3,0/ /-2,-3/-4,3/-2,-1/-3,0/ /-4,3/0,2/0,1/0,3/ /-3,0/0,4/1,0/-4,0/3,0/ /0,-3/-2,3/-2,-1/-3,0/ /-2,1/2,0/-1,0/-3,0/ /2,-3/-4,0/-2,-1/-3,0/ /1,0/3,-2/-1,-2/0,-3/ /2,0/-4,0/-2,-1/-3,0/ /-2,0/-2,3/-3,0/-3,0/ /3,0/3,2/1,2/0,3/ /-2,0/-4,3/-2,-1/-3,0/ optimal depth 6 /2,-3/2,0/-2,0/1,0/-3,-3/ /-2,3/2,1/-2,0/-2,5/-3,0/ /3,0/-1,0/0,2/-2,5/-3,0/ /2,2/0,-1/-2,-2/1,0/-3,-3/ /2,0/-2,0/2,0/-1,0/-3,0/ /-2,6/2,1/-2,0/-2,5/-3,0/ /-2,6/0,-3/-2,0/-2,-1/-3,0/ /-2,0/2,-3/-2,0/-2,-1/-3,0/ /2,-2/-3,-4/-2,3/-1,-2/-3,0/ /4,0/-5,-4/-2,3/-1,-2/-3,0/ /0,-3/-2,0/2,0/-1,0/-3,0/ /2,-3/-2,0/2,0/-1,0/-3,0/ optimal depth 7 /-1,0/2,0/-2,0/2,0/-1,0/-3,0/

Welcome to andrewknelson.com.  This site is going to focus mainly on speedsolving the Rubik’s Cube (and other similar puzzles).  There is a particular emphasis on Square-1 solving, method development, and teaching beginners to solve.  Most of what I plan to write has been developed by myself, but everything is ultimately building upon the work of those who came before me.  Some of this has already been posted to the Speedsolving.com message boards, but much of it is brand-new and never before seen.

A bit about my credentials: I was born and raised in Southern California, and am currently living in Fullerton.  I learned to solve a Rubik’s Cube in 2006 after seeing Leyan Lo’s world-record solve on TV.  I competed in my first World Cube Association tournament in 2007, and in 2010 I set a world record for Square-1 single solve (which stood all of 2 weeks), and secured the Square-1 national championship.  I currently hold the North American record for Square-1 single, and am still the defending national champion.  You can see all of my official results on my World Cube Association profile.