Robbie's 2-Cube Tutorial

This second 3D cube puzzle tutorial will be much smaller than the Rubik's Cube one, partly because there's less to the 2x2x2 puzzle cube and partly because we've already got a lot of the introductions out of the way. But a few more intros are in order. The cute little toy pictured here is deceptively simple. Sure, there's less puzzle to solve than with the standard 3-cube. But as I've found out by experiment, you can pick it up confident that you can unscramble it in no time, and find yourself frustrated a quarter of an hour, or a half an hour, later. Every time you feel like you're making headway, your next move undoes all the progress you've made. And its solution, while really quite simple (only three steps!), actually has no analogy to how you solve the 3-cube. Even knowing the solution algorithms, it sometimes throws you and you find yourself having to back up a step or so and go at it again. It's an outlier, and no mistake.

Originally marketed as Rubik's Pocket Cube or Mini Cube, the 2x2x2 as we know it was also invented by Ernő Rubik, probably in the 1970s. A lot of these puzzles, including the 3-cube, seem to have been independently invented by multiple people but with differences that led to some designs dominating over others. So let's just say that assertion is historically accurate and move on.

Unlike the 3-cube, the 2-cube doesn't have center pieces. It's all corners: eight of them, rotating around each other every which way. Sure, it has six layers, so theoretically all the moves I described in the previous tutorial are still possible, like R, R' and R2, L, L' and L2, and so on. But when you think about it (and the designer of that puzzle scrambler obviously has) an R move is effectively the same as an L', U the same as D' and F the same as B', so there's almost no point in notating L, D and B moves, at least for scrambling purposes. The solution algorithms below do use some L/L' moves, though. I guess that makes the moves easier to follow and allows you to use both hands.

Despite its relative simplicity, the 2-cube can be scrambled into 3.67 million possible permutations. So, rumors that you can solve the 2-cube just by repeating the same couple of moves over and over are greatly exaggerated. That might actually work if you had, say, a million years at your disposal, but on the time scale you want to devote to this puzzle at any particular time—I'm thinking minutes, tops—you'd probably better learn a couple of algorithms. There are really only two algorithms to worry about, but one of them is applied two different ways. They're both quite simple. Perhaps this is why the current world record for a single solve is 0.43 seconds. Or maybe that kid with the fast hands just knows things, deep things about puzzles.

All right, so I went back to that puzzle scrambler, set the puzzle type to 2x2x2 Cube and ran not one, but two scramble algorithms on this puppy to get it into this state.

STEP ONE: Solve the first layer. You can pick any color you like to be the first layer, keeping in mind how the colors need to end up being arranged at the end. (In case the 3-cube lulled you into a sense of not needing to keep track of this, picture the white side at the left, yellow at the right, and the other colors going around the cube in ascending order as blue, orange, green and red—BOGR.) But let's assume we're starting with white as the first side to be solved. Put a side with one white piece facing down and that corner at front left. Position the white corner that (based on its other two colors) belongs in the next spot to the right, either in that spot (regardless of which way it's facing) or in the upper front right corner, above that spot. Like, in this picture, you know that red, white and green piece needs to end up white-side-down with both red pieces side by side.

Then repeat the move R U R' U' until that corner goes into its place with the white side down. Like so:

Then rotate the cube to put another unsolved, bottom corner at front right and its proper piece in or above that spot and do the same algorithm, and so on until all four white corners are white-side-down.

STEP TWO: Permute the last layer. Keeping white at the bottom, try to twist the top layer so that exactly one top corner is above the bottom corner with the same two colors, other than yellow. Put that corner at the front right, like the yellow-blue-orange corner in this picture.

If you can't find such an orientation, don't worry about it. Now try this algorithm (careful!): U R U' L' - U R' U' L. You might find the mnemonic "Twist, up, twist up, twist, down, twist, down" helpful, as long as you remember to switch every couple of moves between your right and left hand. At the end of this step, at very least, your bottom layer should be whole again and, hopefully, all your top corners will be in the place they belong (i.e. correctly permuted), even if they're not correctly oriented.

If they aren't, look again for a way to turn the top layer so exactly one top corner matches the colors of the corner below it and repeat this step.

STEP THREE: Orient the last layer. Turn the cube over, putting what will be the yellow side down with an unsolved corner at front right, like the red-green-yellow corner in this picture.

Recalling the algorithm from Step One, do R U R' U' until that corner is yellow-side-down. Don't forget to complete the whole algorithm. Then, holding the top layer in place, twist the bottom layer to put another unsolved yellow corner at front right and repeat. Unless you've made some mistake (and I still do, about 50 percent of the time), by the time you've oriented all four last-layer corners yellow-side-down, you should only have to twist the other layer a quarter-turn or two and you'll have the cube solved.

So, it's really not that difficult. And if you screw up, there aren't that many steps backward you have to go. Knowing which step you have to go back to, without needlessly going further back, is an important skill to develop at any level of cubing; but on the 2-cube, at least, any setback isn't much of a setback. So there's no reason to get mad, once you give up on trying to solve it intuitively because, friend, that way lies madness.

In summary:

1. Solve White: R U R' U'
2. Permute Yellow: U R U' L' U R' U' L
3. Orient Yellow: R U R' U'.

UPDATE: Since I wrote this, I've switched to doing Step 1 with the white side up, and step 3 with the yellow side up, using the algorithm R' D' R D. It's exactly the same move, actually, just viewed right-side-up; and of course, you twist the top layer to dial the next unsolved corner into place (at front right) during Step 3. Making the switch hasn't actually changed anything about how I solve this puzzle, but it has helped me with certain other puzzles that apply the same algorithm.