In my previous post I mentioned Joyner's paper Mathematics of the Rubik's Cube.
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.
by : Created on March 27, 2008 : Last modified March 27, 2008 : (permalink)
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.
by : Created on March 27, 2008 : Last modified March 28, 2008 : (permalink)