Sunday, 6 February 2022

No Need to Fear It!

Progressive Exploration Helps a Solve
Master Clover Cube - looks ferociously tough
Halfway through last year I restarted purchasing twisty puzzles after a little hiatus (mostly induced by fear of how difficult the newer puzzles looked). This batch I worked through gradually over a few weeks and published about them here and here but the Master Clover cube caused me considerable an edge turner it is going to jumble and to shape-shift which is normally a fun challenge but with so many layers, this was potentially going to be painful. If you are not familiar with the concept then let me quickly explain. Normally with edge turning puzzles, the individual pieces are restricted in their positions to certain orbits and cannot leave them. However, a jumbling move occurs when a partial turn occurs of an edge which lines up the cuts enough to allow an adjacent edge to be rotated. This can cause shape-shifting if it isn't lined up with the opposite side or "just" take pieces out of their usual orbits. Part of the attraction to me with these edge turning puzzles is that there are two distinct solves to be done - a non-jumbled scramble can be mostly solved using an entirely intuitive approach without any fancy algorithms and just a bit/a lot of thought and planning - this is great fun usually. Then a jumbling scramble makes for a much tougher solve needing even more thought and often needs a more fancy algorithm or commutator to solve (and half the fun is working out these commutators). It also ends up with a hugely shape-shifted nightmare puzzle.

Inner edge turn and outer edge turn
A jumbling turn in process (outer edge)
I had put off the final one in that batch until just this week. It frightened me to death! I recalled that many years (2013) ago I had bought and eventually solved the big brother of the Master Clover Cube, Eitan's Master Curvy Copter and the process it had nearly killed me. It was a seriously difficult puzzle with a lot of shapeshifting and a hugely difficult set of commutators to find.
Are they subtly different? Both Master edge turners but a lot more pieces in the Curvy copter
Eventually after procrastinating a long time, I ended up discussing the puzzle with Derek who happened to be working on it at the same time. My fears seemed to fall on deaf ears and, as usual, he started to badger me to get on with it and eventually I succumbed when he practically screamed "DO IT" at me via FB messenger. This shamed me into at least trying a non jumbling scramble in the hope that it should be solvable by intuition:

"This should be fun", I thought/hoped and my initial approach was similar to how I solve the ordinary Curvy copter or Clover cube

I basically do it layer by layer working my way up from the white face. The petals in the Master clover cube are split up so it was just a matter of creating the white face (easy) and then assembling the 2 side faces of the corner pieces and then adding in the half petals. With delight I noticed that the centres and the corners are not separable so solving one solves the other. It can be a little arduous but I managed to get half of the puzzle solved really quite easily. I was on a roll and then I hit a problem - the half petals in the remaining half are much harder to pair up when there is very little room to play in. One of the most important things I realised was that doing the puzzle layer by layer always ends up with a scenario where there are single half petals that cannot be placed in the end game without doing jumbling moves to finish. I was ever so slightly disappointed in this but I should probably not have been surprised. It was always going to be unlikely that such a complex puzzle was going to end up with nice easy intuitive 3 cycles of pieces. Having solved the lower half, I was able to turn the puzzle back to that orientation and experiment with the jumbling moves to see what effect they have. In a normal Curvy copter, the double jumble swaps a the two opposite petals on adjacent faces as well as either side of the cube. This can occur here but it is possible to split the inner and outer edge jumbles as below:

A single jumble swap
Two jumble swaps
Four jumble swaps on both layers
As you can see that matching inner edges with the front outer edge swaps 4 petal pieces. Doing it twice swaps another 4 and then twice more leaves in a very nice scenario (pictured right). Could I use this? Oh yes, I was sure I had the puzzle beat...and then this happened:

Hell! Not enough pieces swapped!
I was stumped for ages. I tried every combination of jumbling that I could think of and was always left with 2 pairs of swapped petal pieces. Time to Think© - Ouch! that hurt. I eventually realised that I needed to swap 2 more pairs at the same time but not alter the faces. Think© you fool! Aha! A lovely moment happened when I realised that I could move petals from the bottom face onto each side and if they were swapped over in a double set of jumbling moves then there was no mixing up of something else that I didn't want mixed. YES! I had it solved layer by layer.

Reporting my success and struggle back to Derek, he replied that he had not had anywhere near so much trouble as me with a non-jumbled scramble. ???How is that possible? It transpired that he had reduced it to a standard Curvy copter first and this could be done without any jumbling moves at all. I had to have a try and yes this was also a LOT of fun. So many aspects to just one twisty puzzle. At this point we were both procrastinating...he said that he had not had time to do a full jumbled and shape-shifted scramble but practically shouted at me to get on with it! Gulp! I am, of course, too stupid to say no to an instruction like that so off I went. I note that Derek has still not fully scrambled his copy! 

First of all, I did a jumbled but not shape shifted scramble and at this point I was very pleased that I had done my earlier experiments and gained a lot of experience of what could be moved where - the solve took me a couple of hours of enjoyable fun. Then it was time to screw my courage to the sticking place and do it properly:

This might have been a very bad idea!
The shape-shifting does seem to get blocked at various points during the scramble. It is mostly internal and does feel like it could be pushed past. But my experience with the original Curvy copter plus warned me off forcing anything. Everything I had learned about the puzzle up to that point stood me in good stead. Returning to cube was no more than awkward and then it was just a fully jumbled solve. I love this puzzle! It is definitely less difficult than the Master curvy copter but in a way that is a good thing. The vast majority of this can be solved by intuition alone and then just a bit of experimentation using the already solved half will provide what you need to be able to complete it. There are several challenges (non-jumbled, reduction approach; non-jumbled, layer by layer, jumbled non-shape shifted and finally fully scrambled) - this is great value for money. I bought mine from the HKNowstore but for those of you in America/Canada then PuzzleMaster have it in stock as well. Go on, give it a try, you will love it!

There are a couple of other non-face-turning Master cubes that would be great if those wonderful cube producers would have a try at manufacturing: The Master Curvy Copter I have shown and the Master Rex Cube as well would be incredible:

3 Master cubes - hopefully the back two will be mass-produced

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