Rubik had a cube long before the Borg did. Oh, sure, the Borg Collective might be an ancient race, or perhaps just an extremely old one, but we didn't sight any of their cube until sometime in the 90s, and that was glancing three or four centuries into the future even with that. Rubik had a cube while I was in high school. According to what I've read today, Rubik's Cube is 40 years old. This is a little surprising, because that puts its invention in the early 70s (1974, obviously ... I know, I'm a math teacher!), but the cube as a phenomenon didn't occur until the early 80s, at least seven years later. I remember. I had them in high school. My brother even set me up in business once at a block party, solving them for a quarter a pop. Actually, I only made fifty cents because two of the cubes were unsolvable. And I had to prove it to them.
Unsolvable cube Number One was completely finished except for two corners which were rotated out of place. They couldn't be rotated back into place. Rotating them involved a minimum of three corners. That's just the math. To move one thing, something else had to be moved. There was no way that those could be moved. Why? "This cube has been taken apart and put back together." I didn't say that they had done it or that it had been done on purpose. In fact, knockoff cubes fell apart fairly easily because they didn't spin well. If you didn't completely twist, say, the front face and then tried to turn the top face, a corner or two might fly off. Should this happen, someone would scoop up the loose piece and snap it back in. The problem is that you had a two of of three chance of snapping it in incorrectly. At this point, it would almost have been better just to have taken the entire cube apart and resemble it in the original state of six solid faces. But that was a daunting task. Snapping in one or two loose pieces didn't pose a big problem. Reassembling the entire cube could be problematic. I don't know anyone who ever tried it.
It took a while to explain, but they finally accepted my explanation of Unsolvability. In retrospect, I should've charged her the quarter anyway. I did solve it as far as it could be solved.
Unsolvable cube Number Two: another knockoff. It didn't have the "Rubik's" logo and it had the wrong color scheme. On a real cube, white was opposite blue, yellow opposite green, red opposite orange. (I wrote that from memory without checking ... hope I'm right!) Knockoff could have colors anywhere. This one did. To make matters worse, a couple of the center pieces had fallen off. The center of a face didn't really go anywhere. Yes, you could move them around, but they were essentially the plus and minus ends of the x-, y-, and z-axes. They determined what the other eight square around them should be.
Now this didn't pose a problem for me because I was a high school teenager and, therefore, a Super Genius. She had one side completely done, all yellow. However, they weren't in the correct places. You see, it's not enough that all the yellows are on one face, but the corners have to be in the correct positions as well as the edges so that they line up with the center pieces on the adjacent sides. I looked to see which colors yellow was touching so I could figure out which color was on the opposite side from yellow, by process of elimination. The opposite side wouldn't touch yellow. Except that they all did. He had peeled off the stickers and put the yellows on one side. Going around the top ring, yellow touched all five other colors, which is impossible. Thankfully, that didn't take much time or effort to figure out, so I didn't feel like I was cheated out of a quarter (not that he was going to pay me in advance -- he didn't believe I could do it even after I'd done two.)
My method wasn't one of the quick ones, and I never solved a cube in under two minutes. Forget about the 25-second methods. They weren't going to happen. I'd have to relearn. At that point, it was all about color recognition and fast reflexes. That wasn't going to happen. I was happy enough to know how to solve one. (And thanks to Bro. Steve for handing out the instructions in our Number Theory class.
One final note: I like to play a game called Fluxx produced by Looney Labs, founded by Andrew and Kristin Looney (no, really). I discovered online from one of her friends, that Kristin (not yet Looney) was a Regional Rubik's Cube champion on TV's That's Incredible years ago. Here's the link. Enjoy.