Sunday 24 June 2018

Never Look a Gift Unicorn in the Mouth

Unicorn Cube
Having spent a week or so with wire and sequential discovery puzzles (with cavities), I decided it was time to move to something different. Yep, time for a twisty puzzle! I have bought a bunch of new MF8 twisties recently from the HKnowstore (Martin seems to struggle to obtain a stock of MF8 puzzles even if he does have pretty much everything else). If you are in the US then PuzzleMaster have the Crazy version of this which I have shied away from so far because it looks so horrific!

I love twisty puzzles that are an extension of existing standard puzzles. This one, the Unicorn cube, consists of a standard 3x3 Rubik cube with additional cuts to allow the 4 diagonally opposite corners to rotate. The effect of this is to split all the edges in two and two mobilise small triangles from the centres:

One face turned and one corner turned
This could get tough!
It turns fairly well but catches a little as one might expect for a puzzle with so many moving pieces. The important thing to remember when scrambling it is that initially at least, the faces should only be turned through 180º. As you can see above after a 90º turn the splits in the edges don't line up and limit the corner turns. Only after a whole lot of 180º turns interspersed with corner turns, should the standard 3x3 scramble be made. After that, it is worthwhile creating lined up corners and doing further corner turns. After a few minutes one ends up with something moderately frightening:

Looks fun?
I was determined (as I usually am) to solve this one without assistance and watched on the Puzzle photography Facebook group as well as the Twisty puzzles forum as people reported their successes and difficulties but I was careful not to read any solution methods or algorithms. There did appear to be a number of different approaches.

For me, it seemed that the best thing to start with was to reassemble the edges just as I would do when solving a 4x4 cube. This proved only a little awkward and involved nothing more than the edge piece series - a very basic 4 move sequence. After storing all of the assembled edges in unused slots, I was left with just 3 to go and a problem...two of them were facing the wrong way around and blocked any attempt to rotate that corner. Stuck already! One feature of the edge piece series is that it cycles 3 edges and flips one over so, in my infinite dimness, I tried for half an hour to get them to flip into a position that would allow me to no avail. It eventually occurred to me to flip one of the stored assembled edges and then continue. Not too much trouble but a nice little challenge so far.

At this point, I had no idea how I was going to solve the little centre triangles but I was hoping for a brainwave later on. Next step for me was a 3x3 solve. No problem at all - I usually take about 45-60 seconds to solve a 3x3 (very very slow by speedcuber standards but I cannot be bothered practising or learning extra algorithms to get faster). I thought that I was on to a winning technique when I was hit with another problem. This was what the guys had been referring to as the Unicorn cube parity:

Single rotated corner
In the picture above I have recreated the Unicorn parity on a solved cube - when I did it the first time, the little triangles were also scrambled. A single rotated corner is an impossibility in a standard Rubik cube unless you have forcibly twisted a piece in place. This must be caused by an incorrect reassembly of the edges but I did not know of any way to fix it without scrambling the cube. Here I got stuck for a week! I started trying all sorts of corner movements and rotations using my standard 3x3 methods which of course did not work. I should have known they wouldn't work as standard 3x3 methods would never produce this issue. I watched Pete (the geek) report his success with jealousy and shortly afterwards, whilst just playing idly I discovered the solution! Fixing that issue was EASY - it did not require any algorithms at all! All that is needed is an intuitive sequence of moves to separate the matched edges, turn the corner and reassemble them. Yessss! I was down to my final challenge:

How hard can this be?
All that was left for me to do was move the small triangles around...preferably without scrambling what I had. Surely that couldn't be hard? I was assured by Pete that it was definitely possible and fairly easy but Pete is a twisty genius and I am not terribly bright! Stuck again!

I was stuck like that for a few days when another brainwave struck me (that makes two in a fortnight!) There is a nice little algorithm to rotate centres of cubes through 180º. This is often used when solving Supercubes (i.e. puzzles in which the centres have an orientation). A few setup moves and numerous uses of this algorithm and it was solved. Only 2 weeks of work! Not bad for a beginner!

At this point, I had a look at methods that other puzzlers had described. I think that my method is by far the simplest approach.

This cube is definitely worth a place in any puzzler's collection. It really doesn't need a lot more than standard 3x3 methods with a bit of intuition and thought. The only extra algorithm used was that required for the rotation of the centres which is only 4 move sequence done 5 times. I think that the crazy version is going to be much tougher and will need to screw my courage to the sticking place before I attempt it.

1 comment:

  1. Great puzzle indeed. Took me one afternoon, but this was mostly thanks to my experience with supercube solving. Apart from the 180 degrees rotation of a single center, I also use the combined 90 degrees rotation of two centers quite often. First thing I found, though, was a nice 3-cycle of those little center triangles without the need for the longer 180 degrees center rotation.

    The crazy unicorn version took me a bit longer, but still is quite well doable for intermediate twisty puzzlers, I guess. I will not give any spoilers here, but the trick for me was to analyze carefully which pieces move together - and when. In this way I actually came to a solution 'in my head' before actually doing it for real. Experience with some of the easier crazy 3x3 cubes (Jupiter, Mercury) may be of help as well.

    Great puzzles - both of them. Indeed highly recommended.