Here are today's two feature puzzles, at front, from left: the 2x2x3 Cuboid, whose package upon delivery (excluding chinese characters) adorably dubbed it the "223," and the Square-0. At back, from left, are the Square-1, part of the same line of puzzles as the Square-0, and a couple other 2-by-2-by-somethng puzzles for comparison – the 2-Cube, a.k.a. 2x2x2 Mini Cube, and the 2x2x4 Rubik's Tower.
I bought the Square-0 because I thought it might help me reduce the problem of learning how to solve the Square-1. It turned out to be an almost entirely different puzzle, apart from the bandaging of the middle layer on the green and blue sides. I sought advice (as one does) from a YouTuber, who pointed out – and this blew my mind – that the Square Zero is actually the same puzzle as the 223, except for that bandaging. Which only minimally affects the solution, as it turns out.
Sorry about the focus here. It's meant to show how Square-1 is pretty much a 3-cube but with skinnier edge pieces on the top and bottom (and no centers), and the middle pieces bandaged to form two edges with only one "slash" between them to allow turns from top to bottom. Meanwhile, Square-0 has the same bandaging, but no edges whatsoever; it's all corners at top and bottom, like a 2-cube with an added, but bandaged, middle layer, or – a more apt comparison – like a 2x2x3 Cuboid that allows R2 moves (and, technically, L2) but not F2 or B2 because, cough, bandaging.
Meanwhile, here are those 2-by-2-by-somethings, lined up to show you another thing about the world of cubing that makes my OCD itch. The color schemes are all mixed up. When you solve the 2-Cube, yellow goes on top, and if blue is to the left, red will be at front. Try this orientation on the 223, and you'll find it lying sideways, with the "bottom" color (blue) at the left and yellow, on the side that should be blue, on top. Meanwhile, on the 224, if I may address it on familiar terms, yellow-up and red-front will also mean laying the tower on its side, with white (the "bottom" color) at left. Clearly, white and yellow aren't opposite each other at top and bottom on either of these cuboids.
Flipped the other way around, my OCD breaks out in hives. Where the 2-Cube, like other standard Rubik's Cube variants, has green opposite blue, orange opposite red and white opposite yellow, we do find the same color scheme on the 223 – but only if you lay it sideways. So, green and blue are at opposite ends, and white and yellow are on the sides. Meanwhile, putting orange on top of the 224 (opposite red) means you get blue at the end, opposite white, and green at the front, opposite yellow, which is absolutely daft. And this is actually a Rubik's product! I don't know if this is meant to help colorblind people distinguish between opposite colors or what. But it throws all our certainties out the window. What next? Lions lying down with lambs? The sun rising in the west and setting in the east? Aaaargh!
But apart from "look out, folks, the color schemes are out of whack," the reason for this comparison is to show you that while the 224 (at right) can shape change – because a 90-degree turn does line up pieces for a turn, despite the risk of turning your nice cuboid into a piece of modern art – neither the 2-Cube nor the 223 has any shape-changing proclivities. The cube is all 90-degree turns, every which way, and always ends up being a cube again. The 223, meanwhile, can only do 90s at U and D; all other moves (F, R, B and L) are 180s (technically F2, R2, B2 and L2). So if I slip up and say R in this tutorial (as in, make an R move), I mean R2.
So, cheering section dismissed. Here are our two puzzles, in start-of-scramble position. Because of the bandaging, Square-0 needs to start with yellow up and the shorter end of the red side at front left. Keep that red square there and just do U, U', U2, D, D', D2 and R2 moves around it. Seriously. If you let that red square wander from that spot, you could break the universe. Or end up being unable to make a move, whatever. As for 223, you're good with green at top and white at front, I guess. It's not like there's an official scrambler for either of them. So, I used a 2-Cube scrambler – the same exact scramble, even, on both of them:
You have to get creative to use this scrambler, or any scrambler really, on the Square-0. Basically, I pretended there was a "slash" (meaning and R2 move) after each step in the pattern. Then I kind of randomly assigned the Ls, Fs and Rs to either the top or bottom layer, instead of attempting actual L, R and F moves. For the 223, I
did follow the notation letter for letter, except all L, R and F moves (and B, if there had been any) became L2, R2, F2 (and B2) moves by default. It's not scientific, but I reckon it's seat-of-the-pants enough to be fair and random. Results:
SOLVING SQUARE-0 – STEP 1: SOLVE WHITE – which is to say, the bottom of the cube. This will also pretty much restore the squareness of the puzzle. So, find a white corner on top and position it at front right, above the spot where it belongs at the bottom – like this white-orange-green corner, which belongs next to the green (-blue-white) corner at bottom. And of course, keep that red square on the middle layer at front left. The universe is depending on you.
Now do the same move you would use on a
3x3x2 Cuboid (not pictured): R2 U R2 U' R2. That swaps the top and bottom corners at front right. It works in so many different contexts!
That just leaves one white corner at top. So, again, match it up at front right above the spot where it belongs, and do R2-U-R2-U'-R2.
Result: a completely solved white/bottom side.
STEP 2: PERMUTE YELLOW CORNERS. That's the top layer, don'tchaknow. If you have a side with two solved corners, keep it to the left of the slash line, putting the two swapped corners at right.
Then do the algorithm R U R U' R U' – D – R U' R U R. Those dashes are just there to make the structure of this move a little more memorable. With apologies for my focus:
FINAL CASES. Step 2 could be all it takes to solve Square-0. But sometimes it isn't. For example, here we've ended up with the right half of the middle layer flipped around.
To fix this, use the same, rather simple algorithm that serves the same purpose on the Square-1: R2 U2 R2 U2 R2 U2.
The only thing left to do, to clinch your solve, is the E (equatorial) slice move we discussed
back here.
The only other case that may apply is if the whole middle layer is upside-down.
If you've kept that red square at front left, this actually means you've been a doofus, solving the cube with white on top and yellow on the bottom. The world is kind to fools and children, however: all you need to do to rectify this is offset both the bottom and the top layer to line up the cracks between corners – honestly, I don't know how you got this far without noticing what was happening! – and pull an R U2 D2 R move. In the following pictures, I combined U2-D2 in one shot:
BONUS TUTORIAL: SOLVING THE 223. I told you it's the same puzzle. You only have to add a couple steps because the middle layer isn't bandaged. For example, I started by making sure the middle layer is solved. In this case, that simply meant setting up, and doing, an R2.
I could have saved myself the trouble of doing this, as you'll see later.
Now, because the 224 Rubik's Tower solves (eventually) with white on top and blue on the bottom, I have decided, and so decree, that blue goes on the bottom for this solve; meaning green goes up. Then I go about solving the bottom layer, just like in Square-0 step 1. Find a blue corner at top and the corner where it belongs on bottom, and put them both at front right. Then, swap them using the R2-U-R2-U'-R2 pattern.
This process brought another unsolved blue corner to the top. So, move it to front right and put the bottom-layer corner where it belongs below it, then do the same algorithm.
Notice how this pattern brought the corner we previously sent to the bottom back up, paired it with the problem corner and returned them both to the bottom.
Now our issue is that two top corners (the orange side) are correct, but the other two are flipped around. Put the two unsolved corners at right.
Then do the Square-0 step 2 algorithm, which will swap the top-layer pieces at front-right and back-right. Remember: R U R U' R U' – D – R U' R U R. This is also similar, if you recall, to the "permute top corners" step of solving the 332.
We're now in the "Final Cases" phase of the solve. To sort out the now discombobulated middle layer, use the same move that flips the right edge of the the middle layer from back to front on both Square-0 and Square-1 – R2 U2 R2 U2 R2 U2. It may also be familiar from the 332 solve (though it serves a different purpose there). In the 223's case, it swaps the two middle layer pieces at the front and back of right.
Since I didn't have a solid bar of solved middle-layer pieces, that means I can put the two pieces I just solved at left and repeat the same algorithm on the other two middle-layer pieces. Before and after:
The other case, again, is when your middle layer seems to be turned upside down; but actually, you've gotten the top and bottom layers swapped. The case would look like this, and it totally doesn't mean you're a dufus; it's much easier to lose track when your middle layer sides aren't bandaged.
Again, the fix for that is R2 U2 D2 R2, shown here with the U2-D2 bit combined:
I actually purchased the 223 on purpose because I knew it was almost exactly the same as the Square-0. It's the same personality flaw that led me to buy the Rex Cube on purpose, knowing it's
exactly the same puzzle as the Super Ivy Cube. Scrambling them both, even using the same scramble, gave me more time to enjoy what is essentially the same, fun, little, not-too-difficult distraction from the existential horror of etc. etc. etc. And in this case, the same exact scramble actually turned out quite differently, because the Square-0 has limitations that the 223 doesn't. They're pretty simple puzzles – count 'em: two steps, plus "final cases" ‐ with no parity issues or titanic struggles to tame an uncooperative shape-changer into a square like on, say, Square-1. Put the bottom corners where they belong, and you have a Square. Square-0. And the rest of the solve is kind of like doing a 3x3x2 Cuboid, but with the edge pieces circling a different orbit. The interrelatedness of these puzzles starts to give you insights into how the geometry of moving puzzle pieces fits together, and maybe you'll be able to predict strategies that work on other puzzles that come your way. Little step by easy step, you'll feel like you ain't as dumb as you used to be. Just the kind of positive reinforcement you need once in a while.
