The 4x4x4 cube puzzle!
On the same day I was shopping for silicone spray (Saturday August the 16th) I popped into the juggling shop "Jugglers" in Hockley, Nottingham and there I was delighted to find a 4x4x4 cube, also known as a "Rubik's Revenge" (http://en.wikipedia.org/wiki/Rubik%27s_Revenge).
There was one on display for testing and it felt like a good mechanism (although I haven't touched a genuine Rubik's Revenge) so I quickly snapped one up for the sticker price of £9.85. Out in the street I opened up the plastic presentation dome and started shuffling it around a few moves and restring it to its original solved position - such a delight! How does it work?
I didn't want to scramble it until I was on the bus home as I wanted to see some solutions online! It seems that I was now uncomfortable with the puzzle when I didn't know or have access to a solution! Well this cube kept me occupied for many hours in the following days and I started to suspect that it might be an Eastsheen cube: a good quality cube often recommended for speedcubing. I studied the Eastsheen website (http://www.e-sheen.com/) and the cube's packaging: labelled as made in Taiwan, in a plastic presentation dome as seen here (http://www.e-sheen.com/products_magic%20cube_M4.htm) and distributed in the UK by Funtime Gifts Ltd, Unit 2 Old Post Office Lane, Kidbrooke, LONDON, SE3 9BY. I searched for Funtime Gifts on Google and found http://www.funtimegifts.co.uk/. I phoned Funtime (on 20/08/08) and they confirmed that it is indeed an Eastsheen cube).
"Help! The centres can move!"
This was news to me! I discovered that all "even" cubes (above 2x2x2), the 4x4x4, the 6x6x6, the 8x8x8 etc., have moveable centres so that any 3x3x3 techniques that rely on the centres not moving cannot be used! This adds a new dimension of "scrambled-ness"!
I started with the guide for the 4x4x4 at Dan's Cube Station (the website of a UK speedcubing champion Dan Harris - http://www.cubestation.co.uk/cs2/index.php?page=4x4x4/4x4x4) but found that simultaneously solving multiple dedges made my mind hurt (in my own defence this was day one with the 4x4x4!) so I started looking for solutions based on a simple logic and I found that I could use some of Dan's techniques along with some from http://www.speedcubing.com/chris/4-solution.html to (mostly) solve it.
Since I already know how to solve a 3x3x3 (albeit slowly) I use the "3x3x3 reduction method" where the 4x4x4 is initially partially solved so it can be treated and solved as a 3x3x3. First the centres need to be formed: any cubie with only one colour sticker - there are 4 on each of the 6 faces = 24 centre cubies! I've worked out how to do this by pattern recognition; i.e. trial and error! I then need to move the centres around into their correct positions. Later I started forming the centres in the right places as I learn the correct relative positions of the colours of my cube.
The second stage of the 4x4x4 solve is to form the "dedges": "Double Edges", pairs of edge cubies that make up a logical edge cubie of a 3x3x3. there are 2 in each pair (naturally!) of the 12 edges of a cube, each with 2 stickers of the same combination, so we have 24 edge cubies in total. The technique I used here was similar to Dan Harris' solution but I hadn't learned any algorithms (I'm not good at memorising them) so I used logic, deduction, name it what you will! There is only one algorithm I needed to get the 4x4x4 into a pseudo unsolved 3x3x3 - the rest was by slow but sure deduction! That is for the solving a the last pair of dedges (when on left and right of front face and the unsolved cubies colours match directly opposite each other- diagram needed!)...
Dw R F' U R' F Dw'
...the "Dw" and "Dw'" used here are a notation indicating a "Wide" slice, so the Dw is a turn of both of the Down layers. After some time I was able to work out exactly how this performs its magic! (TODO: outline the deduction for centre solving, centre swapping, dedge forming, etc.)
Another bit of news to me was the ability of Parity Errors to occur on the 4x4x4 that are impossible on the 3x3x3. It took me months to learn the solutions for these situations off by heart (I told you I'm not good with algorithms!) but I got there in the end. There are some good descriptions of parity fixes at http://www.bigcubes.com/4x4x4/finalsolve.html - the ones that I finally chose are as follows: -
This can be spotted at the OLL stage where a single dedge remains unoriented. The algorithm I learned for this situation is to hold the flipped dedge at upper-front and perform...
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
...the lowercase notation being a move of an inner slice.
This one crops up at the very end for me - everything is solved apart from a pair of dedges are in each others' positions! The algorithm I learned to fix this is...
r2 U2 r2 U2 u2 r2 u2
...again, the lowercase notation being an independent move of an inner slice.
If they are adjacent, do r U2 r' l' U2 l to swap the U and F centers.
If they are opposite, do r2 U2 D2 l2 to swap the L and R centers.
Now I have conquered the Revenge it's time to move on to bigger things!
The EastSheen 4x4x4 is great but there's absolutely no play in the mechanism for cutting corners. For speedsolving, some people swear by Meffert's or Rubik's brand revenge cubes each of which have different mechanisms. I came across an old Rubik's 4x4x4 on ebay and won the bidding for a fair price. It was disappointing to find it was not at all smooth and downright difficult to use! Upon dismantling it I found that one of the orange centres was almost broken off. I made the best repair I could with superglue, lubed it, and rebuilt it, but it still wasn't anything to write home about!
I now have a tiled white 4x4x4 from DX today for $10.79 and I must say it's pretty good out of the box.