Inspired by Google...Am I the only one whose first thought was to take a Rubik's Cube apart?

Agreed, but I guess it’s the only way they could think of to insert their stylised logo into it.

I didn’t even catch that…
ETA: I also didn’t try clicking the cube until just now either. I expected to just go to some web page.

I never managed to solve it. I realized that what folks are calling ‘algorithms’ here were transforms, and various transforms preserved particular sets of squares. The closer to the solution, the longer the sequences of moves required to do a transform while preserving more of the solved puzzle. The closest I ever got was three pieces wrong, corners IIRC. At that point I got stumped. I don’t remember how many moves per sequence, but it was at least 7 and maybe 15. (My shortest sequence was 3, where the 1st turn something, the second changed something else, and the third undid the first move. The next sequence was two of these with another move in the center and then back out the first three. So, the next sequence after 3 moves would have 7 moves, and then 15, etc. Optimization? Screw that!)

I even tried writing down a spreadsheet of the transforms I knew that could move the three pieces around without mucking anything else up, and figured that I could somehow string them together into a new transform that would either get closer or solve the puzzle (that is, move the three into a new orientation, where either two or none were wrong – I assume that it’s impossible to have one square wrong, but I could be wrong.)

That was at least 15 or 20 years ago. I doubt I could be bothered now. I considered learning the steps from the booklet, but the booklet remained unopened, sitting on my dresser, for who knows how long. It’s long gone now. But I think I’d be dissatisfied without figuring it out myself.

Me too. I also did it to help see the consequences of moves, starting from a solved cube.

I don’t understand what you’re saying, because the center squares are fixed. They can’t be moved or rotated or anything. Furthermore, if you could rotate them, that would be a non-event, due to the symmetry of a square. Rotate a square any number of increments of 90 degrees, and it’s the same.

New cubes being sold now come with an instruction booklet telling you how to use the aforementioned “algorithms” to solve it. Or at least, they did as of 3-4 years ago.

They can’t be moved, but every time you rotate a side, the center square on that side also rotates (in place). I put small strips of tape along one edge of each center square, so I could tell how the center square was oriented. The tape is still there on my cube.

I thought of the white and yellow sides as top and bottom respectively, and arbitrarily picked blue as the front. In the fully solved state, the top and bottom center squares had to have the tape strips nearest the front, blue face. For the other four sides, the tape strips had to be on the bottom (nearest the yellow side).

ETA: So instead of the paltry 43 quintillion possible positions for your cube, mine has 86 sextillion positions. :slight_smile:

There were Rubik’s cube variations in which each side had a picture (there was one such that I saw for the Prince Charles/Lady Di wedding). In such a case, the center square DOES have to be in the correct orientation on each side, or the picture won’t be correct.

It’s true that a repeated sequence of fixed moves can’t solve the cube, but you can’t prove it just by counting numbers of positions. A repeated sequence of moves will, in general, reach many more positions than there are moves in the sequence. Rather, you can prove it from the fact that the cube group has many elements which are square roots of the identity.

That is to say, consider a cube which starts in the solved position. The identity is any set of moves (such as the empty set) which ends with the cube in the solved position. Any position can be regarded as the result of some sequence of moves (strictly speaking, an equivalence class of sequences of moves, since any position can be reached in many different ways). “Multiplying” two positions together means to make the sequence of moves which leads to the first position, and then, starting from that position, make the sequence of moves which would lead to the second position (except it won’t lead to the second position, because you’re starting from a different point-- It’ll lead to a new position that’s the product of the first two).

Saying that a position is a “square root of the identity” means that, if you make the sequence of moves that leads to that position, and then make that sequence of moves again, you’ll be back where you started from. For instance, turning one face 180 degrees is a square root of the identity, because if you do it again, you’re back where you started. The checkerboard pattern that most people learn when they’re new to the cube is another one. I don’t know how many square roots of the identity there are, but there are clearly quite a few: I can think of a couple of dozen just off the top of my head.

Now, here’s the kicker: Any repeated sequence of moves can only ever pass through at most one position that’s a square root of the identity (well, two, if you count the identity itself). And if you start off in a position that’s a square root of the identity, your sequence to solve it must also be that same square root of the identity. So if your repeated sequence solves the cube from one of those positions, it must not solve it from any of the others.

In another post, since that one was so long: Back to the OP, if you want to learn to solve the cube the “legit” way, you should start by learning to take it apart and put it back together, for two reasons. First, seeing it disassembled and seeing how it works can give you a greater appreciation for what you’re actually doing with it: You’re not re-arranging 54 flat facets (the stickers), as you might think at first, but rather you’re re-arranging 20 solid cubelets around a fixed central crosspiece.

Second, the way to solve the cube is to learn short sequences of moves which move some of those cubelets in particular ways, while leaving other cubelets (which you already have where you want them) undisturbed (or rather, disturb them but then put them back where they were). The way to learn such sequences is to just try various sequences and see where they get you. But this is much easier to recognize if you’re starting with a solved cube, and most of your experiments at first will leave you in a position where you’ll have a hard time backtracking to the solution. So in order to be able to do good experiments, you need to have some way of getting the cube back into a pristine state, before you know how to do it “legitimately”.

I’m not sure how this is true, but maybe I’m misunderstanding what you’re saying here. I’ll take my sequence of moves as “rotate left side 1/2 turn, rotate right side 1/4 turn”. After rotating the left side 1/2 turn, I’m in a position that’s a square root of the identity. Continuing, I rotate the right side 1/4 turn, rotate the left side 1/2 turn, then rotate the right side 1/4 turn again, and I’m in a different position which is a square-root of the identity.

After a week of trying to fix it like a “normal”, I decided that disassembling it and putting it back together was just as valid since it’s still a puzzle. Pulling the stickers off always seemed to end up with one either torn or no longer sticking properly. In my defence, I also took apart a Tonka dump truck when I was 2 1/2. To this day my Dad has no idea how a 40 lb child pulled an all metal truck apart with no tools. Niether do I.

Yeah, I took it apart. Not even difficult to do, really.

I’m not sure I understand how that’s possible - although it may be that we’re not always talking about the same thing when we say ‘moves’ and ‘sequence’.

Or are you talking about effect relative to the starting configuration?

Some of 'em came apart when you weren’t even trying to disassemble them. I have a cheap keychain cube (probably a knockoff) that I have be careful with or else a piece will pop off and the then the whole thing will fall apart.

Hm, good point. I was thinking in terms of the position at the end of the sequence, just before it’s repeated… But that still allows for hitting other square roots somewhere in the middle of a sequence. My proof has the complementary problem to the one the other proofs have.

Add me to the disassembling group. To me it was easier than rearranging the stickers.

I never took one apart. However, I did wait until we reached modern times, and then had a teenager in a YouTube video teach me how to solve it. I was quite happy with that outcome, although I guess it’s just the modern version of peeling the stickers off and putting them back on, as it didn’t really involve any creative use of my brain, beyond memorizing the steps.

Still, I firmly believe that I look like a genius whenever I solve one around other people, and I remain convinced that one day it will get me laid.