Sunday, 22 July 2018

This Unicorn is Real and I'm Not Crazy!

The Crazy Unicorn Cube
After just one corner turn followed by a top face turn!
The lurgy has continued in both me and Mrs S (who is making some rather interesting gurgling/coughing noises) and has not helped my puzzle solving abilities much and has not helped her mood at all. She was seriously unimpressed at the abrupt expansion of my collection recently. Luckily she is too incapacitated to commit violence upon my person! Hopefully, our health will improve soon or I will be murdered in my bed and I hope that I will actually be in a position to solve something before I run out of puzzles to write about!

I have previously discussed the Unicorn cube - a fabulous cube that I initially found rather tough until I found my Aha! moment and understood that it could be solved by simple reduction techniques. It consists of a simple 3x3 Rubik cube with 4 deeply cut corners that can be twisted too which splits the edges in two and also cuts pieces off the centres. In the end, I found that it needed little more than intuition and simple 3x3 methods making it a rather wonderful puzzle for anyone who wants a challenge just one step up (OK maybe a BIG step) from a simple 3x3. At the same time, MF8 released a crazy version of the Unicorn puzzle which of course, I had to purchase (my arm was twisted) but I never expected to be able to solve it. In fact, when I took the top 2 photos, it scared me enough that I didn't pick the puzzle up for another 2 months after that! Eventually, an FB friend showed off his ability to solve the puzzle and encouraged me to give it a try. he said that I would be pleasantly surprised by it. GULP!

Luckily it is quite lovely scrambled - there is a high chance it would remain this way!
I threw caution to the wind and scrambled it using a similar process to the ordinary Unicorn cube. It ended up looking fairly horrific and I was fairly certain that it would stay that way forever. The first thing I realised was that this puzzle was going to have to be solved differently to the plain Unicorn cube. There would be similarities but much of it would be different. The circles are fixed and do not turn with the outer parts hence making this a full "circle cube" and not really one of the Crazy planet cubes that I extolled the virtues of many years ago. The Crazy planet cubes have various combinations where the centres do or don't turn with the outer parts making for a very challenging series (which I really should go back to). I am told that a circle cube, where all the centres are fixed, is actually a simple puzzle in its solution process. I was delighted to see that these were not going to be a crazy series although it would appear that there is a simple piece inside that can be flipped over to change the way each face functions and I guess that it will not be long before the twisty crackpots begin to turn this into a planet series too.

Generally, before I scramble a new twisty, I spend a while exploring to see how the pieces interact with each other and maybe if possible, to see whether I can work out any simple algorithms. I usually end up scrambling the damn thing before I manage to work very much out. This time, however, I did realise that some of the circle pieces are much more limited in their movements than I initially expected. Some were trapped in 1 of 3 positions and others followed a particular orbit. This would greatly simplify the process. If you have not yet solved this puzzle and do not want any help then do not read any further as I plane to describe my process...

My first step was very similar to the plain Unicorn cube. I needed to realign the faces to allow the corners to turn again. As you can see above, the use of 90º turns at the end of the scramble causes the corners to be blocked from further rotation. Unblocking the corners is mostly just intuition and judicial use of the 4 move edge piece series to ensure the edges are positioned and oriented correctly.

All the corners are now free to turn
Do you notice anything in the picture above? Look at the small triangles inside the circles - they are trapped in 1 of 3 positions. It is a trivial thing now to place them and produce a completed square in the centre:

Centre squares completed
After that, it may be that something else is obvious? I suspect that it's hard to say that from the photo but when playing with the cube it is fairly obvious that the circle edges that are not part of the turnable corner can only be on that face. There is actually no physical way to move them anywhere off the face and it is then fairly trivial to move them.

A few 180º rotations od the faces left me filled with confidence! So far the puzzle was being solved mostly by intuition and a bit of trial and error. I am not sure why I chose this order to approach the puzzle but it just seemed the right thing to do at the time. At this point, I had the squares complete and the circle edges on the non-turning corners in place with minimal effort. Now it was going to get a bit tougher!

So far, not too hard!
My next aim was for to try and complete the circles. This looks fairly impossible but I quickly noticed that there was a peculiarity of the remaining circle pieces...they are actually bound in pairs like a single edge piece. For example, in the picture above the small green circle piece below the MF8 logo is actually bound to the small white circle piece on the red face. They CANNOT be separated. This means that the G/W circle piece needs to be taken away from its current place and put back in that face but to the right where there is currently an O/Y circle piece (to the right of the MF8 logo). At least initially, it is a trivial thing to move these paired circle pieces into an unsolved position and then put them back into the correct place. Again, like the rest of the puzzle, it is mostly intuition and using a simple 4 move algorithm. As more and more of the pieces are placed there is much less room for play and the substitutions get tougher but during the movement, it quickly becomes apparent that each time you position one of these pieces, you are just carrying out a 3 cycle. Once this next Aha! moment has been passed it becomes a simple thing to arrange it such that the final 3 pieces to be placed can be done in a single 3 cycle. Once you have done the positioning sequence 4 or 5 times it becomes second nature. The process does not upset the pieces that have been solved already. One ends up with a circle cube with split edges:

All the circles are complete and now just the split edges to reduce
This is now looking rather like the plain Unicorn cube. Time now to reduce the outer edge pieces. Here it is just a simple matter of using the 4 move edge piece series to cycle the edges where you need them without upsetting the circles. Once a small edge segment is placed in an adjacent position to the corresponding large edge section, a simple turn of the corner pairs them up. Of course, that corner turn ruins the circles and hence care is required to use that same edge piece series to move the completed edge into a storage position and then turn the corner back again to re-complete the circle. Just as before (and in the plain Unicorn) it gets harder and harder to do this as there is less and less space to work in. In the end, they need to be positioned in such a way that the last 3 edges are solved simultaneously. It takes a bit of playing around to achieve this but really does not require anything fancier than an edge piece series and some planning. At this point I had a simple circle cube:

All circles are whole and the edge pieces are paired together
It still looks fairly fearsome to someone not familiar with Rubik type puzzles but this simply solves like a standard Rubik cube as long as you stick to algorithms that use paired movements. Taking advantage of Marshall's "Ultimate solution" which uses nothing more than the now infamous edge piece series and the corner piece series, it is a simple thing to solve this puzzle without ruining the centres. In fact, this puzzle is almost easier than the plain Unicorn cube! The pathway to completing the circles ensures that none of the parities that I saw in the plain version appear in the crazy version. I would again say that if you can solve a 3x3 and want a little extra challenge then the Unicorn cubes (both of them) are a really good path to take. They look great, they frighten your friends and family and solve with only a little extra from what you can do already.

Go buy them at HKNowstore or at PuzzleMaster whilst they are still in stock. You won't regret it!


3 comments:

  1. Great to see you solved it! Indeed a bit easier than it appears at first.

    Just realized because of your post that I once saw an advertisement of these two unicorn cubes which seemed to hint on the possibility of swapping centers, effectively giving a full planetary series of unicorns. Hmmm, need to try that... If possible, that may bring about a few unicorns from hell.

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    1. Just tried this... indeed a little piece inside for each of the crazy centers. Once flipped it makes a center rotate with its face. Little tricky to put the cube back together, but not terrible.

      So yeah, seems like we can create 8 crazy unicorn planets + the standard unicorn cube from this one crazy unicorn. Oh dear, there goes the holidays. Wife is not gonna like this... :}

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  2. It was interesting to see your thinking behind your solution.

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