Sunday, 9 April 2017

Yet Another Twisty Candidate for my Puzzle Top Ten!

The Lim-cube 3x3 Mixup Ultimate
I can hear the non twisty puzzlers out there groaning! I really ought to see someone about those voices I keep hearing! Another year locked up in the padded cell with the special comfortable jacket again! Yes! It's another twisty puzzle review and story! I make no real apology for this as I am always going to try and convince you general puzzlers out there to have a try! It isn't all about teenage boys with nothing better to do in their lives than to practice the same thing over and over and over again until it can be done in seconds. For me the beauty of the twisty puzzle is NOT learning lots of algorithms and practicing. I just use the few things that I know and have learned in creative ways. Very occasionally I have to design an algorithm but I'm not very good at that and so I often am forced to use Allard's copyrighted Think© technique and find ways around something new. The challenge is tremendous and the Aha! moments are worth the effort. I am very proud of the fact that I probably only know 8 or 10 algorithms and just use those. If you are interested in this puzzle then I got mine from Martin's Puzzlestore but PuzzleMaster stock it here.

Dreidel 3x3
So what is special about this cube? It looks like a sort of deformed 3x3 cube with some rather suspicious extra cuts but no way to move them. It is a new design from the incredibly creative Guan Yang and has been mass produced and marketed by the relative newcomer, Lim cubes who produced one of my favourite puzzles of last year, the Dreidel 3x3 which I loved so much that I rated it as number 4 in my 2015 top ten. If you don't have it then stop reading this blog and go and buy it immediately (Puzzlemaster has it if you are in North America). Lim cubes seems to specialise in puzzles with extreme complexity but despite that with very high quality. I am staggered at how well these puzzles turn. Just like the Dreidel 3x3, the Mixup Ultimate is mostly solved by intuition and of course being able to solve a basic 3x3. There is only one very simple algorithm that is required.

So what are those cuts that don't line up for? Prepare to be horrified and amazed. Oskar designed the original Mixup cube which allowed 45º turns of the centre slices and then to carry on with other turns of faces and slices.

Oskar's classic mixup
Allows centres and edges to be interchanged
In this new puzzle however, the 45º slice turns have been altered. It now requires a 30º turn of a slice and then the faces and other slices can still be turned:

30º turns of the equator/slices line up the cuts
OMG! What a mess!
I had originally very much enjoyed solving Oskar's cube and most of it was solved by intuition plus figuring out a very interesting parity. I fully expected that this new puzzle would be a similar experience but "more so". One of the best things about this particular puzzle is the utterly horified looks on the faces of my colleagues at work when I showed them the extra moves and the horrific mess when it is fully scrambled. They really don't believe me when I say that intuition is most of what you need.

The solution to this beast is obviously a staged process. I started by just pairing pieces up. This was a rather laborious process of moving pieces to diagonal opposite sides and performing the 30º turn and then aligning the preprepared pieces. I managed to get almost the whole thing paired up into their triplets and then hit a brick wall. I suddenly realised that the centres were nowhere near their correct positions (blue and green were adjacent to each other instead of opposite, as was grey and yellow). I couldn't for the life of me work out how to get out of that position without breaking it all and also I had 2 edges left which were not matched up and there was no room to manoeuvre them! It was going to be back to the drawing board and reluctantly I redid my scramble.

Next try, start with the centres. Put them back into the centre and make sure that the right ones are opposite each other. Check! Managed that after only a couple of hours of swearing under my breath. Again, NO algorithms required - just intuition. What next? I decided to use one of the (very simple 8 move) algorithms from the Mixup plus cubes which will cycle inner edge pieces and outer edge pieces. It took me quite a while to work out how to go about preparing the cube prior to performing the sequence but after a few hours I had all the thin edge pieces in correct place if not with matching colours. Next I needed to try and move the big edge pieces to flat on the cube. My usual opposite diagonals method gradually managed to get these pieces flat and then I used the same technique to move them around the cube to pair with the small edges. To my horror, I saw that the centres were out of place but I realised that it was a simple thing to flip them over and just swapped 2 edge pieces in the process. Phew! Once all the edges were paired up I happily went to work on the 3x3 aspect of the cube and.....

AAAARGH! What happened here?
I posted that photo on Facebook and got a bit of sympathy and some not very helpful suggestions. It looks like there should be just 2 pieces to swap over but the "law of the cube" says that this is impossible - it needs to be a 3 cycle. I worked on it for several days and everything I did seemed to end up in the same place. I was stuck! Nooooo! I contacted my friend Pete who is one of the best Twisty puzzlers in the world with a great YouTube channel and asked him if he had found this position and if he could help. He's a bit busy just now helping his class with their robot building but he said he would have a look for me. After 3 days of failure and frustration (Mrs S told me this was a 4 "Plugs" out of 5 puzzle (if you read last weeks blog post then you will understand the concept of the Plug) I went to bed with it on my brain and woke up with a solution entirely formed and ready to try. I delayed my breakfast to try it and it worked! I also saw that Pete had produced his own video and had used the same sequences. Yay - I must be getting better at these!

Of course, solving these once does not mean that you have truly understood it and maybe have not found all the other possible problems. I scrambled it again and got to thinking (yes twice in one puzzle!) Pete had said that he had never met that particular problem so there must be a way to go about the reduction without allowing this to occur. I changed things about and did the large edge pieces first. Now that was MUCH easier. I managed to get the shape back to cubic very quickly and all the pieces paired up in only about an hour. I was on to something. The final 3x3 solve looked like it was going to be trivial and suddenly I crashed down to earth:


2 opposite edges were swapped! This is another issue that is impossible on a 3x3. It is a common parity on a 4x4 cube but the technique used to deal with that was not available to me here. Luckily the solution to this is pretty simple and just requires the use of the thin edge algorithm a few times and then swapping over the fat edge pieces.

This sounded horrific BUT let me tell you that the vast majority of this solution process was done by intuition and no algorithms were required. Anyone who can solve a 3x3 should have a play with this puzzle as it is great fun and for the puzzling challenge it is really good value for money. It remains in my work bag for idle moments and I absolutely love it! Buy it! You WILL love it!


To finish up my blog I would like to show you a lovely technique for a particularly challenging group of puzzles. Any 4x4 can be converted into an AI puzzle and the bandaging makes them hugely challenging. I was able to solve the cube version with no problems but the Megamorphinx v2 had centre pieces that were all unique and proved to be impossible for me. SuperAntonioVivaldi found a very fancy commutator to do it but I couldn't follow his instructions. Eventually in desperation I sat down and spent an hour working out what he did and now have a great technique for approaching all AI puzzles. I thought nothing of it until I heard from my friend Paul who is struggling with this puzzle. So I made a video to show off the technique - it is not my own method but I have modified it to make it easier to perform. I hope that it's useful to a few of you:



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