Sunday 24 December 2023

I Can See Why Elon Wants To Go To Mars...

Jupiter is MUCH too hard!

Crazy 2x2x2 Plus cubes
Thank you for your well wishes after last weeks' "too spaced out" post. I had completely forgotten how painful a hernia repair is and how long the pain lasts. I am recovering well and have stopped the stronger pain killers to allow me to think a little straighter (let's face it - my thoughts are never what one would really refer to as......ordered at the best of times). I had bought these Sengso Crazy 2x2 cubes a while ago and thought they could not be too hard and I was kinda wrong.

I reviewed the 0,0,0 variant at the end of October after spending quite a long time working out how to understand the odd way it moved. It should have been fairly easy as all the circles on the cube were zero faces (that means the inside is fixed and the outsides move around them - this means it is what is called a "circle cube" and should require just turning the outer faces and solving them having fixed the inner parts. The complicating feature was that there are ONLY outer faces and the inner circles are a sort of bandaged 3x3x3. Yes, my head hurts just typing about it!

I then scrambled the 0,1,1 version thinking that with only a single fixed centre then it should effectively solve like the Jupiter Crazy cube and Jupiter Crazy Megaminx which looked absolutely horrific but were surprisingly easy to solve as they needed only a tiny bit more than a standard cube and standard megaminx (which solves like a cube).

Crazy cube Jupiter
Crazy Megaminx Neptune reconfigured as Jupiter
The whole point of the Jupiter cube and Megaminx is that there is just one single face that will allow the inner and outer circles to be split apart. This means it takes a while to scramble the puzzle properly because all the pieces need to be moved to that 0 face and turned at least once before being moved elsewhere. But then it has the extreme solving advantage that "all" that is required to do to solve the puzzle is move all the pieces onto that 0 face and align the inner and outer parts before moving them off for storage elsewhere until all of them have been aligned with their partner pieces. After that solve the zero face before turning it to the bottom and solving the rest of the cube without moving the bottom face. If you know the beginner's approach or the "Ultimate solution" then it's pretty simple to solve the puzzle without having to move that bottom face again.

I set to the crazy 2x2x2 (0,1,1) thinking that this was effectively just a Jupiter version of the 2x2x2 crazy cubes and would involve the same sort of approach as described above. In my particular version all the faces were effectively turning as 1 faces with inner and outer parts turning together and the white face alone had the outer part turn leaving the inner circle unmoved. With my theory loudly bailing in my empty head, this meant that I scrambled it straight away without any preparatory exploration and stared trying to pair up the inner and outer pieces using just the white face. 
Oh dear, what had I done?

I suddenly realised that this was definitely not a Jupiter 2x2! It was MUCH more complex than that. The reality of this puzzle is that the zero face can change. 😱😱😱
The zero face is actually which ever face holds the white inner piece that is opposite the blue/red/yellow cube (which itself cannot ever be scrambled). OMG what do I do now? 

I have learned over many years from Allard that I mustn't just stop and give up, I must Think© - that's a pretty impressive thing to learn considering that he doesn't do twisty puzzles. Luckily, I was working on this before I had my little operation and started the mind-altering medication so think©ing was still possible. I quickly realised that, with a bit of "fannying around" (that's a twisty technical term!) I was still able to use my Jupiter face to pair everything up as I should and leave myself with what looks like a 2x2x2 cube to solve. 

This looks promising! Or is it?
Having done this, I tried the "simple 2x2x2 solve and quickly realised that it was NOT the same as the 3x3x3 Jupiter puzzle - I did not have the ability to move all faces apart from that 0 face. Any movement of a face that included the bandaged corner (blue/orange/yellow) would move the crucial white corner and move the zero face about. In reality, I had to solve the 2x2x2 using ONLY two faces - on the photo above, I could only move the front right and front left faces to solve the cube. This is a HUGE restriction and proved a massive problem. Almost every single approach that I know requires at least 3 faces to be movable. I was stuck! 

After a week or so of playing about and remembering the large corner bandaged 3x3x3 cube with one huge 2x2x2 fused corner and three movable faces, I did manage to solve the puzzle just once after multiple scrambles and failures and realised that this would be possible about 1 in 12 scrambles by just sheer chance arriving in the right solvable state. I needed more think©ing time and to work out a restricted way to solve the 2x2x2 this way. It is quite simple to solve the back 4 corners leaving just the front 4 using just intuition. At this point I realised that there was a very neat feature of this puzzle. I could not always solve that from 4 corners every time because they had been recreated incorrectly mismatching the centres and outsides. All I needed to do was use my two faces to rotate the faces correctly on that top white face and rotate out the incorrect pairing and put them back in again correctly. This then leaves you with a solvable 2x2x2 cube:

All corners placed but not oriented
Orienting the corners is a trivial thing to do when you know the SUNE algorithm - it only needs to move 2 sides. It's not quite trivial because some setup moves need to be done and undone but it is a fun thing to do (I need a notebook by my side to keep track of the moves). Using this technique, I was able to solve the puzzle multiple times - it was quite mind bending but did not require a lot more than standard cube techniques and the ability to warp my mind a lot. I was soooo pleased with myself until I did this:

All solved with 2 pieces to be swapped - impossible!
Anyone who solves cubes knows that a single 2 way swap is an impossible situation. What had I done here? In the end I had swapped out 2 pairs of pieces but one was not easily seen being the centres that move but not easily visible. 

With a little thought© and planning, I was able to move bits around (fiddly little bugger) and finally could say that I properly understood this puzzle.

These Crazy 2x2s were bought with the initial thought that they might be a little easy entry into the crazy cube series being only 2x2 cubes - I initially felt that this might a nice Jupiter solve. But in reality, having now solved 2 of them, they are definitely not a gentle introduction at all. The hidden internal bandaging makes these incredibly challenging and properly interferes with the ability to move pieces where you want them to be and use basic algorithms. If you are into Twisty puzzles then these are in the "MUST BUY" category.

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