A Rubik’s Cube Weekend
I spent Thanksgiving weekend on my Mom’s Ranchito in Southern California. (I’m not quite sure what else to call it — it’s not that big, but it’s got more dogs, cats, horses, chickens and turtles than you can shake a cactus branch at.) A few hours before getting on the plane, I was at a friend’s house and saw a 2×2x2 mini Rubik’s cube sitting on their living room table. Knowing all the residents of the house would be away, I asked if I could borrow the cube for the weekend. My bookshelf had run dry of easy-reading novels, so I was happy to have some easy entertainment.
When I was in grade school, I could solve the classic 3×3x3 cube in about 3 minutes. I had memorized the moves from the book, so I don’t think of it as demonstrating much beyond the fact that back then I related better to colored plastic cubes than to people.
On this trip I thought it would be fun to try to rederive the algorithms needed to solve the cube. A little linear-algebra refresher. First come up with a vector representation of the cube’s state. Find a few moves that apply a transformation on the correct subset of the cube that’s currently being worked on, and then demonstrate that they form a basis set for an arbitrary transformation. Sounded like a good way to spend a plane flight – exercise my spatial reasoning brain. Since learning to ball-juggle, I’ve noticed my reflexes have definitely gotten faster and improved my ping pong game. So who knows what else would come of this adventure.
In the first Rubik’s coincidence of the weekend, the mother of the family sitting next to me on the plane to Ontario was playing with a 3×3x3 Rubik’s cube. We chatted for a while, but I lost interest when she insisted on trying to convince me that the 2×2x2 cube is actually harder than the 3×3x3. I think she was trying to make me feel better about the fact that I was taking notes on the 2×2x2 and she could just “figure out” the 3×3x3. That’s what the Ultimate Ears and Eminem are for.
On the plane, separated from google, I couldn’t figure out how to use math to solve the problem. Rotating an individual cube 3 times gets you back to where you started, which implied to me I needed to do something with either e2*pi*i/3 or epi*i/3 – couldn’t exactly remember which. And I wasn’t sure about the commutativity or transitivity of cube rotations, drawing into question the whole idea of trying to apply linear algebra. So I invented my own notation and brute-forced my way through the thing. By the end of the flight I could solve the 2×2x2 cube in under 5 minutes without notes.
Feeling like I hadn’t really gotten the challenge I wanted, I sought out a full-sized cube at a toy store in Santa Monica. They had standard 2×2x2, 4×4x4 cubes and 5×5x5 cubes, but the only 3×3x3 cube they had was a miniature keychain variety. Fine. It took me 12 hours to solve it the first time, and about an hour the second time, and by the end of the weekend could do it in under 10 minutes. I was surprised how much came back to me from when I was 8 years old – many basic moves, but basically no memory of when they were appropriate.
While packing and getting ready to leave, I noticed a shelf in my mom’s office that had a bunch of old puzzle games on it – my grandfather loved puzzles, and Mom had kept a bunch of them. Sitting there was a box labeled “Wonderful puzzler” and contained a Rubik’s cube from before they even called it that. The second Rubik’s coincidence of the weekend! Of course it was solved – actually left in a configuration more aesthetically pleasing than the standard solution. Again, not surprising. My grandfather would have reproduced Van Gogh in that cube if it was possible, and if he thought Van Gogh was more beautiful than concentric circles, which is about as likely. It brought back my only concrete memory of my grandfather speaking to me — showing me a different one of these toys and asking me if I liked puzzles. I wish I’d gotten to know him better, but considering how famously quiet he was, I feel honored that I remember anything he said to me.
I started trolling online to find any history behind the “wonderful puzzler” since there was no date on its package. I quickly found a site on speed cubing and learned that the world’s fastest cubists can reliably solve a 3×3x3 cube in under 20 seconds. Don’t believe it? I didn’t either – it just doesn’t seem possible. But watch the videos for yourself, and prepare to be humbled. Look around a while, and you’ll see that the world record for solving the cube blind-folded is under 2 minutes! I’m definitely not worthy. I think my hands would fall off before I could ever do that. But I expect if I ever did dedicate enough time and brain-space to that, that I’d be able to solve all sorts of other interesting problems without even trying.
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I’m a “cuber” and enjoyed your article. I was 9 or 10 when the Cube was released in the 80s and spent hours playing with it. I still do. Trial and error, trial and error, over and over, I figured it out over the summer and “amazed” my friends when I showed them. I guess some of the appeal has been lost now that anyone can go online and find a solution. Still, it is good to see the Cube has endured. I remember when just completing the puzzle was an accomplishment onto itself. Nowadays you need sub 30 second times to get noticed…
BTW, I too find the title of your blog quite interesting and catchy..