TecSpy.com Michael Erskine's Domain

Rubik's Revenge

The 4x4x4 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'm now uncomfortable with a puzzle when I don'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).

Learning the 4x4x4

"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. Actually I've recently started forming them in the right places as I learn the correct relative positions of the colours of my cube. The second stage 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 use here is similar to Dan Harris' solution but I haven't learned any algorithms (I'm not good at memorising them) so I use logic, deduction, name it what you will!

There is only one algorithm I need to get the 4x4x4 into a pseudo unsolved 3x3x3 - the rest is 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!)...

d R F ' U R ' F d '

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.)

"Party Errors?"

Another bit of news to me was the ability of Parity Errors to occur on the 4x4x4 that are impossible on the 3x3x3.

Single flipped dedge...
From http://www.cosine-systems.com/cubestation/cs2/index.php?page=4x4x4/3x3x3

From http://www.speedcubing.com/chris/4-step3.html...

r ² B ² U ² l U ² r ' U ² r U ² F ² r F ² l ' B ² r ²

...I think this is using pairs of slices for the lowercase notation moves as another algorithm is posted which shows the lowercase moves expanded...

(R ² r ²) B ² U ² (L l) U ² (R' r ') U ² (R r) U ² F ² (R r) F ² (L ' l ') B ² (R ² r ²)

...yes, I can confirm that having tried the first algorithm here whilst moving both right slices for "r", etc.

In my preferred notation with breaks after slice moves...

There are some good descriptions of parity fixes at http://www.bigcubes.com/4x4x4/finalsolve.html

TODO: more parity errors!

I think I have some real problems with the many forms of notation out there for that extra dimension of slices beyond the basic 3x3x3. The notation that I find easiest to use at the moment uses 'r' to mean both right hand slices at once.