Why Rubik?
Why Rubik1.m ?All this started a couple of days ago when I was tidying my workroom. On my bookshelf stood a scrambled size-4 Rubik's REVENGE (tm) 3-D mechanical puzzle. I had spent some time solving it years ago, and then a visiting child had moved its state sufficiently far from pretty...I have owned mechanical puzzles from the Rubik line  of various shapes and sizes (snakes, reduced
and fragile keychain versions, originals and clones) since the early 1980's . Speedcubing was never my thing, but I was
fascinated by the simple-beauty of the cube and the ingenuity of its creator . I don't like cubes scrambled as they immediately betray that one is NOT a speedcuber. Well, I already told you I wasn't one. So then what's the point of having cubes? My AI professor Dr Agop Hachikian used to say that '... what's extremely easy for humans is extremely hard for AI, and what's extremely easy for computers is extremely hard for humans ...'. I guess that the Rubik's puzzles stay somewhere midway with their NP complexity, so even humans can't do better , but reduce the explosion of possibilities (see next section) by solving first for just 2 layers (http://www.ws.binghamton.edu/fridrich/Mike/middle.html). I keep the cubes as they are great examples for some my principal lines of work: mathematics of optimality (e.g. dynamic programming), 3D graphics and 3D transforms. So I wanted to tidy up the Rubik's REVENGE ... For similar purposes over the years I have used anything ranging from spoken, hand-written or googled advice from more knowledgable cubers. This time I wanted to deal away with this promptly, but not quite in the same way as Alexander-the-Great did  (see the next section for the full story).
So I went to my usual source of info these days... But, unfortunately the info even at the best places can be difficult to interpret or even be misplaced altogether. For example, Jessica Fridrich has a wealth of resources for to-be-cubers like me, but the page http://www.ws.binghamton.edu/fridrich/Mike/orient.html is not 100% bullet-proof.
So the to-be-cuber would come up with a cube that's even more scrambled, and what's worst would not know whether the poor result wasn't due to facing the cube from the wrong reference, or whether he failed to execute the sequence verbatim. Hence I decided to dig up a piece of code that would do the monotonous and human-error-prone testing work for me. In case you wanted to know more about the Rubik Cube In Greek legend, the Gordian knot was the name given to an intricate knot used by Gordius to secure his oxcart. Gordius - a poor peasant, arrived in a public square of Phrygia. An oracle had foretold the future king would come riding in a wagon. Seeing Gordius, the people made him king. In gratitude, Gordius dedicated his oxcart to Zeus, tying it up with a peculiar knot. Another oracle then foretold that he who untied the knot would rule all of Asia. Many people tried to undo the knot but all to no avail. In 333 B.C. Alexander the Great had invaded Asia Minor and arrived in the town of Gordium; he was 23, undefeated, but without a decisive victory either, he was in need of an omen to prove to his troops and his enemies that the outcome of his mission - to conquer the known world - was possible. In Gordium, by the Temple of the Zeus Basilica, was the oxcart, which had been put there by the King of Phrygia over 100 years before. The staves of the cart were tied together in a complex knot with the ends tucked away inside. Having arrived at Gordium it was inconceivable that the young, impetuous King would not tackle the legendary "Gordian Knot". Alexander climbed the hill and approached the cart as a crowd of curious Macedonians and Phrygians gathered around. They watched intently as Alexander struggled with the knot and became frustrated. Alexander, stepping back, called out, "What does it matter how I loose it?"With that, he drew his sword, and in one powerful stroke severed the knot. 'Because It's There'Those famous words were spoken by British climber George Mallory in 1924 when he was asked why he wanted to climb Mount Everest. In case you wanted to know more about the Rubik Cube
http://en.wikipedia.org/wiki/Ern%C5%91_Rubik http://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik%27s_Cube http://en.wikipedia.org/wiki/Cayley_graph http://en.wikibooks.org/wiki/How_to_solve_the_Rubik%27s_Cube http://en.wikibooks.org/wiki/How_To_Solve_Any_NxNxN_Rubik%27s_Cube http://vanderblonk.com/wp-content/plugins/rubik/cubeapplet.php?stickers=F2L&alg=BU%27B%27UR%27URU%27 http://en.wikipedia.org/wiki/Gordian_Knot http://www.alexander-the-great.co.uk/gordian_knot.htm |
