Rubik's Cube
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).
UPDATE (2008-03-27): Now see Twenty-Five Moves Suffice
Comments (3)
Dave on Jan. 13, 2008:
I should follow the links first -- it was Thistlethwaite's algorithm (as described in the Optimal solutions article) that I was barely recalling.
For those who are into this sort of thing, David Joyner has written "Mathematics of the Rubik's Cube", a set of course notes: "biased towards group theory not 'the cube'. To paraphrase the German mathematician David Hilbert, the art of doing group theory is to pick a good example to learn from. The Rubik's cube will be our example. ... We regard a solution strategy merely as a not-too-inefficient algorithm for producing all the elements in the associated group of moves."
James Tauber on Jan. 13, 2008:
I'll check out Joyner's notes. It did occur to me it would be a great way to teach group theory.
Last Modified: March 27, 2008
Author: James Tauber
Dave on Dec. 7, 2007:
Having always solved in the classical practical layer-by-layer manner, I dimly remember the description of an algorithm (Singmaster's?) from Gardner's column which worked by progressively projecting onto smaller and smaller groups -- after each subgroup was attained, one no longer needed a certain class of manipulations and ceased to use them. The general idea was that, very close to the end, the cube would still appear fairly scrambled, but a few half-turns later, and it would be solved. By judicious application of adjunctions, one pulls the rabbit from the hat. (not so appropriate for a proof, but for a "magic" cube, why not?)