Square-1 Tutorial Part 1: The Scramble

At one point in an earlier tutorial, I called the Square-1 puzzle "that bastard." Yes, this innocent looking thing (backed up by, from left, Square-0, Rubik's Tower and Rubik's Pyramid).

Since then I have cobbled together a reasonably straightforward process for solving it, partly thanks to a YouTuber who partially departed from using the horrendous Square-1 notation, and partly due to my own fiddling which entirely (and with only a tiny bit of embarrassment) rejects it for solution purposes. There's no getting around using the notation for scrambling this cube, however. Darn it. And despite simplifying the Square-1 solve to the level of my own stupidity, the tutorial that follows features steps that I still need to practice a lot, and that I still pony from notes that (after being recopied and condensed multiple times) still run to three notebook pages – a page longer than any other puzzle solution I have studied so far. This is a long way of saying Square-1 is and remains the hardest puzzle I currently know how to solve. Perhaps someday, when my notes go astray, this tutorial will help me remember those steps and save me from utterly losing my mind.

The first couple times I solved Square-1, I was using a four-page step-by-step solution guide with color illustrations. And a mystifying YouTube tutorial designed to accompany that guide. And long, complex algorithms in that horrid notation you'll be seeing in a moment. Algorithms that I frequently messed up on, like, the penultimate move, sending me back to the beginning of the whole solve. Those first two solves took me about 48 hours each, with lots of swearing and not very much sleep. Square-1 then became an ornament on my tray-table full of puzzle cubes (and towers, pyramids, etc.) for quite some time. I called it "that bastard" but kept it around as a vague promise to myself that someday, I would take take another run at it. And thank God, I cracked the code with the help of a different YouTuber, one more accommodating to my mere mortal, non-savant level of intelligence.

OK, let's talk about how I chose Square-1's cheering section. Here, to its left, is Square-1's simpler, easier sibling, Square-0.

I've grown a bit OCD-ish about displaying my cube puzzles white-side up, green-side at front. That tray-table I mentioned holds rows of cubes in that orientation. It's usually the way you're supposed to hold the cube when you start scrambling it; and then white naturally becomes the first side that you solve, before putting it at the bottom and working your way up to the yellow side. But with Square-1 and -0, that isn't the case. Don't get used to seeing white up or green at front. This is the more natural orientation of these cubes:

The reason is a twisty-puzzle phenomenon I haven't had to cover until now: bandaging. Notice how, on both of these puzzles, the middle layer doesn't have the same cuts as the top and bottom layers. The U (up) and D (down) layers can turn freely, but to make any other turn, you have to have certain pieces at the front and back. This is because the middle layer comprises just two pieces. So, effectively, the only moves you can do besides variants of U and D are R2 moves. Like:

This means that, on the middle layer, you must always have either the orange or the red square (the shorter segment of those sides) at the left of front. And in the case of Square-1, you have top- and bottom-layer edge pieces that are shorter than the corner pieces, and varying numbers of edges can pile up together between two corners. Hence, the strange deviation from the cube shape in the photo above. That brings up another high-falutin' cubing concept that these tutorials haven't touched on before: shape changing. To solve a scrambled Square-1, you not only have to get the edges and corners to line up, layer for layer, color for color; you also have to restore the puzzle to a cube shape.

The shape-changing thing is what Square-1 has in common with Rubik's Tower and Rubik's Pyramid, a.k.a. the Pyramorphix:

There are moves and patterns you can do on these that begin and end with the puzzle in its original, prismatic form. But you can also scramble them in such a way that they stop looking like a cube, pyramid or a tower. And getting them back into shape becomes part of the challenge of solving them.

There is one thing you can do to ensure that your move begins and ends with the Square-1 still more-or-less cube-shaped – or at least, square on top and bottom: you can off-set either the top or the bottom layer by one edge.

Then, provided the cuts between pieces form a straight line at both top and bottom, parallel with the cut across the middle layer, you can do an R turn. But not just an R turn, which results in a configuration like this, locking all the layers so you can't turn them:

No, you have to go the whole 180 degrees around, an R2 move, which that @#$% Square-1 notation designates as a slash – / – and which Square-1 peeps call "slice" even though that term means something else in other cubing contexts.

I'd prefer it if they just said "slash" instead, but I'm not the boss of anybody. Except you, if you find this tutorial helpful. And in any event, I don't see any reason not to stick with R2, since standard cubing notation actually works for solving this cube. With a big asterisk to be addressed later.

To have that smaller red (or orange) square at the left of front does mean that, at the start of your scramble and throughout your solve, the yellow side will always be up – even if white pieces sometimes find their way up there by accident. You'll know you've got the thing turned the wrong way if the longer red or orange bar is at left of front. And it seems Cubing.net's Square-1 scrambler assumes you'll start the scramble with red at the front. Here are just a couple pictures illustrating the drawbacks of having, say, a corner (top or bottom) running across the slash line (middle layer), or trying to make a turn with blue at front. A lot of turns you'd like to make just can be done, because bandaging, and the way different sequences of edge and corner pieces deny you a straight cut where you want to turn. Always a challenge, our Square-1.

OK, it's time to lay this scramble notation on you.

It's fair to say that I hate it, hate it, hate it. It's tricky to follow but if you mess it up, you'll find that the coded instructions it's giving you become impossible to execute. You have to get it right from beginning to end, unless you're OK with just doing random turns and taking your chances. It frankly drives me nuts. But enough about me. Let's talk notation.

Each of those slash marks is an R2 turn, which is only possible (without fudging around) if you've gotten all the moves correct up to that point. So be careful. Between slash marks are sets of parentheses containing two numbers separated by a comma. The number before the comma represents a move on the top layer: positive in the U direction or clockwise, negative in the U' direction or counterclockwise. The second number pertains to the bottom layer: again, positive in the D direction and negative in the D' direction. You never realize how hard it is to keep D and D' straight until your slash move locks up because you twisted the wrong way. Think! Be perfect! And what about the numbers themselves? Each is a sum of 1s, representing edge pieces, and 2s, representing corners. Zeroes mean no move on whichever layer. So, that first "(-2, 0) /" move comes after turning the top layer counterclockwise past one corner, leaving the bottom alone, and turning an R2:

Notice that the scrambler's usually helpful, step-by-step illustration is as confusing as the notation itself. If it helps (and if it didn't, I would never have been able to figure out how to execute this notation), the top square shows the top of the cube, looking down, with the front edge of the layer toward the bottom. The bottom square shows what you would see if you inverted the cube via an "x2" move (similar to R2 but moving the whole cube). It's particularly confusing because the edge at the top represents the front of the cube. The color bar running horizontally between them represents the middle layer of the cube, always with the smaller red piece to the left of the slash line. So here's that move, step-by-step from the starting state:

Now let's move on to the second slash:

That "(-3, -3)" bit means you set up the move with a counterclockwise, edge-plus-corner move on both top and bottom; understanding "counterclockwise" from the point of view of facing the side in question. So, from your perspective, you're moving top front to the right and bottom front to the left.

Here's the "(2, 5) /" move:

Then "(0, 3) /":

Then "(-3, 0) /":

Then "(-5, -2) /":

Then "(-4, 0) /":

Then "(-3, 3) /":

Then "(3, 0) /":

Then "(1, 2) /":

Then "(0, 2) /":

And finally, "(-6, 0) /":

Aaand now we have a scrambled Square-1, which is as far as today's tutorial goes. The solve will have to wait till Part 2. And though the solution has quite a number of steps (and lots of photographs to go with them), I seriously think the scramble is the most brutal part, thanks to that awful notation. I don't see a good alternative, though, because simply saying U or U' doesn't cut it when you're measuring turns by the width of an edge piece or a corner. For solution purposes, those traditional cube notations will do quite nicely, with one minor exception that you'll just have to absorb into your system. But from here on out, U / U' / U2, D / D' / D2, R2 and M2 will suffice. Oh, didn't we discuss M moves before? No? Well, there's the hook for next time. Be sure to tune in!