3x3x2 Cuboid Tutorial

As threatened, here's the first of several tutorials about Rubik's Cube variants that aren't quite cubes. Below, front and center, is the 3x3x2 Cuboid, which according to Ruwix was invented in the 1980s by Tony Fisher, one of 12 cuboids that he put out. His first cuboid was the 3x3x4, shown in the background, cheering its little sibling on.

Ruwix also informs us that the 3x3x2 was originally called the Domino Cube, because in its first iteration it had dots instead of colored stickers. My model is stickerless, of course. And while it turns nicely, it bears noting that only the "Up" and "Down" layers are capable of quarter (90-degree) turns; F, B, L and R can only make half (180-degree) turns, otherwise locking the puzzle. So, yellow and white are the only colors it can have on the top and bottom. Also U and D are the only layers for which prime moves (U' and D') and double turns (U2 and D2) can be meaningfully distinguished from vanilla U and D. Meanwhile, moves like F and F' (etc.) are all essentially F2 moves (etc.). In my solution algorithms below, I'm going to use the letters F, B, L and R with the understanding that they're really F2, B2, L2 and R2, because typing all those 2s would be tedious, and I think we're all smart enough (I was about to say "grown up enough," ha ha) to follow.

All right, how do you scramble this thing? Myself, I coopt this 3x3x3 scrambler from scramble.cubing.net.

And I ignore the prime signs and the 2s wherever they don't apply to a U or a D move. Here, to illustrate how those moves look, is that scramble step-by-step:

STEP 1: BUILD A WHITE CROSS. That is to say, arrange the white edges around the white center, in the order B-O-G-R (blue, orange, green, red) turning counterclockwise. (Don't ask me why the mnemonic runs counterclockwise. If you don't like "booger" as a mnemonic, you can always go clockwise and use "goober" instead.) So anyway, here I find the blue-white edge already in place, so checking where the other white edges around the yellow center, I dial red-white into position and flip it into place next to blue-white.

Then, with apologies for the fuzzy focus, I locate orange-white, dial it into its slot, and flip it around to the white side.

And finally, green-white completes the white cross.

STEP 2: SOLVE WHITE CORNERS. From here on out, we're working with the white side facing down and the yellow side up. So, here's the orange-green-white corner above its proper place; to dial it in, put that corner at front-right and use the algorithm R-U-R-U'-R. I'll show it step-by-step just this once; but it's an important algorithm for these cuboids, so commit it to memory.

Here's the green-red-white corner, dialed into position above the space where it belongs, then slotted into place using the same algorithm.

The other two corners present a problem; they're already on the white side but their positions are swapped. So, use the R-U-R-U'-R algorithm to put the blue-red-white corner on top, then put it above the corner where it belongs and use the same algorith to swap it for the orange-blue-white corner; then put that above its slot and dial it down in the same way.

STEP 3. SOLVE YELLOW CORNERS. Check whether there are any sides on the top layer that have "headlights," i.e. matching corners. Here, for example, I had blue headlights.

Put the headlights, if any, to the left; if you have none, don't worry which side is which. Then do this long, symmetrical algorithm – R-U-R-U'-R - y' - R-U'-R-U-R – remembering that y' (why-prime) means rotating the entire cuboid in the U' direction. I didn't shoot step-by-step pictures of this whole pattern. So, the next two photos illustrate the y' move in the midst of this algorithm, followed by the final result.

STEP 4. SOLVE YELLOW EDGES. There are two possible cases you may have to deal with – and there's no reason why you won't face both cases within the same solve. The first case, illustrated below, is where you have two adjacent sides whose top edges need to swap places, like blue-yellow and orange-yellow below. Put them at front and right, and do another rather long algorithm: R-U-R-U - R-U2-R-U2 - R-U-R-U'-R. I think you can manage that without a step-by-step illustration, so here's just the before-and-after:

The other case is where you want to swap the edges on two opposite sides of the top layer. Like this red-yellow center at front and the (take my word for it) orange-yellow at back. Between this before-and-after goes the easy-to-remember algorithm R-U2-R-U2-R-U2.

At this point, I could say, "That's all there is to it." But in reality, you may have to do the F-R swap to set up an F-B swap, or vice versa, in order to move all the unsolved edges to where you want them. It happens pretty often. So, despite this puzzle being almost entirely a matter of executing rote algorithms, there is that little bit of strategy (and the intuitive part at the beginning, building the white cross) to keep it interesting. Overall, it's a pretty easy puzzle to solve, once you're aware of the order of battle and a handful of patterns. If you commit these few algorithms to muscle memory, you could get pretty fast at solving this – almost, perhaps, to the point where it isn't worth the trouble of scrambling it. But a light challenge is sometimes just what you want; also, it's good practice for the 3x3x4, which has a few extra wrinkles – including a parity case you don't get on the 3x3x2. So, there's that to look forward to in a future tutorial.

I'm not big on keeping track of the specific brands of the puzzles I've picked up. A search of my email history leads me to an invoice from Speed Cube Shop that reminds me this 3x3x2 cuboid is a QiYi product. I'd recommend it. It's stickerless, smooth turning, with an easy-to-grip texture that feels good in the hands. Personally, I prefer stickerless puzzles, after having some stickers start to peel off – a total pain – and I also prefer the deeper color scheme to the, um, "bright" format of my 3x3x4, where red means pink and, in low light, yellow and green are hard to tell apart. Not an issue on the cuboid, really, but I have a 7x7x7 cube with the same bright color scheme and I need strong light to play with it. So, those are my thoughts. What are yours?