This is a tutorial on how to solve a Square-1.  When finished, it will consist of several stages, to be learned in order, and built on each other. The first step is a beginner’s Square-1 tutorial intended for someone who has never solved the puzzle before, and the culmination is the method I used to set the former world record for fastest single solve (10.90 seconds) and North American record for best average (15.95 seconds) and (used to) average 14 seconds with in practice.  Various parts of my method are also in use by Dan Cohen, the current World Champion, and several other top-level solvers. I am confident that this is the most advanced method currently in use for Square-1 speedsolving. This tutorial is still under construction, but please direct any questions to me on Speedsolving.com or email me at blade740-AT-gmail.

Thanks for this guide include, but are not limited to:

First and foremost, Lars Vandenbergh. Lars’ guide (cubezone.be) was my number one source of knowledge, and this method is largely built off of his.

The square-1 solvers of #. Namely, Dan, Tomas, Woner, and Dene.

Team # in general

Takao for always beating me and pushing me to get better

Jaap Scherphuis, for his brilliant sq1optim program.

Notation and Terminology

First of all, this is the diagram I’ll be using to show square-1 positions.  I have the standard western (BOY) color scheme with white on top and red on front, and I hold the small side of the middle layer on the left hand side.  The left image is the top layer, viewed from above.  The right image is the bottom layer, also viewed from above.  Note that this is different than the images used on Lars Vandenbergh’s site, http://www.cubezone.be.  I find that this way is more like the way I see the puzzle, and helps with recognizing parallel patterns.

Speaking of which, let me get a little bit of terminology out of the way so I don’t have to explain it later:

Cubeshape – The cubeshape can refer to either the current shape of the puzzle, the algorithm used to solve that shape, or the state in which the top and bottom layers are both square.

E Slice – The E slice is the middle slice of the square-1.  I refer to the E slice as “flipped” if it is not in a square shape.

Corners – The corners are the kite-shaped pieces that form the corners of the solved square-1.  Each one has 3 stickers.  Each occupies 60 degrees of the full arc of a layer, and is 2 wide in move notation (below).  In this method the corners are generally oriented and permuted before edges (or at the same time, if at all possible).

Edges – By process of elimination, edges are the smaller triangular pieces  that make up the edges of the top and bottom layers of a solved square-1.  Each has 2 stickers, and fills 30 degrees, or 1 unit wide in standard notation.

Parity – The parity of the puzzle is the odd/even overall permutation of the pieces.  For the purpose of this tutorial, parity only exists within the puzzle in cube shape.  Parity can only be changed by leaving cube shape, and is difficult to determine before the orientation steps are completed.  In this method, parity is solved immediately after orientation.

Bar – When discussing permutation (and specifically corner permutation) a bar is a set of two matching adjacent corners.  There is one bar on a J perm and no bar on an N perm.

Block – A block refers to any two or more connected pieces of the same color, or when discussing orientation, connected pieces with the same U/D color.

Square-1 shapes are named as such: square/square means square shape  on top, square shape on bottom.  In other words, this is solved cube shape.  Other shapes are similarly named.  There are names for most other shapes, although some are just referred to by letters indicating the arrangement of corners and edges represented by the letters c and e.

Note that many shapes have mirrors, and so there are multiple different shapes for some names.  Sometimes I’ll refer to these as “good” and “bad”, and sometimes “parallel” or “opposite”, indicating whether the shapes are congruent or mirrored from each other when both viewed from above.

Parallel Fist/Fist:

Opposite Paw/Paw:

I also refer to permutations with similar notation, usually referring to a PLL letter, or combinations of  “adjacent” (or “adj”) and “opposite” (“opp”), meaning swaps of adjacent or opposite corners/edges, and orientation of pairs of opposite or adjacent edges.

N/J:

Anyway, now to actual notation.  There are 2 kinds of moves: moves of the U and D layers and turns of the entire right half of the puzzle.

U/D Turns – U and D turns are done independently of each other.  They’re notated together like so: (3,-4)

The two numbers specify how far to turn the U and D layers, respectively, in multiples of 30 degrees clockwise.  A negative number means to turn counterclockwise.

-> (3,-4) ->

Slice Moves – Slice moves are 180 degree rotations of the entire right half of the puzzle.  Slice moves can be done in either direction.  I normally alternate clockwise and counterclockwise for fingertrick purposes.  I suggest you do the same, but any way works.  They’re represented by a slash (“/”) in move notation.

Move sequences alternate between U/D turns and slice moves.  An example algorithm is (0,-1)/(-3,0)/(1,1)/(2,-1)/(0,1).  Try it.  you should end up with this:

I usually leave the final layer adjustment up to you, and so I would leave the final (0,1) off of that algorithm in my solution pages. Also, sometimes I omit the parentheses because I’m lazy. The alg reads the same way.

Mirroring Algorithms

When I speak about mirroring algorithms, I mean mirroring them across the E plane.  This easy to do with a written algorithm: Switch all positive numbers to negative, and vice versa, and reverse the order of each integer pair.  For example, let’s take a U-permutation. The normal algorithm for clockwise U-perm on top is /(3,0)/(1,0)/(0,-3)/(-1,0)/(-3,0)/(1,0)/(0,3)/

If you want to perform a U-perm on D instead, you would do something like /(0,-3)/(0,-1)/(3,0)/(0,1)/(0,3)/(0,-1)/(-3,0)/, which would give you this:

It’s a bit easier, in my opinion, to learn an alg in muscle memory before trying  to learn its mirror.  All moves stay the same when viewed from above, and sometimes I find it easy to think of moving a layer “left” or “right” rather than clockwise/counterclockwise.

When you’re ready, continue to the first step to start learning.  Even if you already know how to solve a square-1, I’d suggest reading through every step before skipping to the advanced stuff.  I often reference previous steps and throughout the tutorial I assume that you’re following the exact method up to that point.