Re: I wonder how many people have actually solved the cube?
Until I read this I assumed everyone who'd solved it did so without help - how naive I was!
An IBM colleague in Nottingham, who'd discovered the Rubik's cube some time before they were on general sale in the UK, was selling them to interested colleagues including me. It also took me about three months to solve it the first time but I didn't dismantle it or move stickers. The second time took a few days, and after that I could do it in around 15 minutes. Then I got bored and haven't touched for the last 35 years or so, although I still have it somewhere.
For a time I was fascinated by the mathematics and realised there was a connection with group theory, although I wasn't clever enough to gain any interesting insights from this. I also wrote some code (on my 1kB Nascom 1 computer) to attempt to find useful sequences of moves - the tools described in the article.
Maybe it's time to get the cube out again and see if I can still do it.