Back in 2007, I wrote:
Like many people (I'd guess most people reading this blog), I had a Rubik's Cube in the 80s.
The only way I could solve it was looking up moves in the book You Can Do The Cube by Patrick Bossert. (Patrick was only 12 when he wrote the book—he's now an entrepreneur and management consultant; see his home page).
In high school I had Rubik's Magic which I took detailed notes on and came up with a solution on my own. Later I came across a book with a much shorter solution that I seem to recall memorizing in the bookstore without buying the book.
Also in high school, I had Rubik's Clock which was also easy enough to solve on my own.
Then last year, when I was in Walt Disney World surprising my sister for her 21st, I bought a Rubik's Cube again with the goal of learning how to solve it.
Wikibooks has a nice page on How to solve the Rubik's Cube that has a straightforward algorithm as well as a discussion of various other approaches favoured by speedcubers.
Wikipedia also has a very interesting article on Optimal solutions for Rubik's Cube. It was only August this year that Kunkle and Cooperman proved Twenty-Six Moves Suffice for Rubik’s Cube (pdf of paper).
In March 2008, I blogged:
I've talked about the Rubik's Cube before and linked to last year's paper by Kunkle and Cooperman proving Twenty-Six Moves Suffice for Rubik’s Cube.
Now Tomas Rokicki has proved that Twenty-Five Moves Suffice for Rubik's Cube. Actually, what he proved is that no configuration takes 26. If x <= 26 and x != 26 then x <= 25 QED.
It is known that some configurations need 20 moves and that no configuration needs 21. So the possible optimal move maxima are 20, 22, 23, 24 and 25.
Via Dave Long, I also found out about Joyner's Mathematics of the Rubik's Cube (pdf) which became the book Adventures in Group Theory.
UPDATE: Actually, I don't think it's been proven that no configuration needs 21, just no configuration has been found that needs 21.
UPDATE 2: David Joyner informs me a 2nd edition of his book is coming out soon.
A blog post that followed shortly after the March 2008 one above:
The phrase "The Rubik's Cube" sounds odd because you can't normally use an article with a pre-nominal genitive if the pre-nominal itself wouldn't normally take an article.
You can say "the paper", "the professor" and "the professor's paper". You can say "David's paper" but not "*the David's paper". (Although note that if talking about the sculpture "the David", you can say things like "the David's left hand". And, because of Donald Trump, you could say "the Donald's hair".)
You can't say "the Rubik" and so "the Rubik's cube" seems ungrammatical if you think about its component parts.
What's happening is, of course, that "Rubik's" isn't acting as a genitive anymore but rather "Rubik's Cube" has been reanalyzed as an opaque compound noun. It's just still written in terms of its components.
The above explains why many people, when hearing rather than reading it, analyze "The Rubik's Cube" as "The Rubix Cube".
"Every position of Rubik's Cube™ can be solved in twenty moves or less" http://cube20.org
— Jeff Atwood (@codinghorror) October 19, 2013
I love that the "20 moves suffice" code is not only available but is in a literate programming style: http://cube20.org/src/
— James Tauber (@jtauber) October 19, 2013