Sunday 1 October 2023

An Edgy Puzzle - But Still Intuitive

Son-Mum 4x4 cube (v1)
The Son-mum 3x3 cube was released back in 2018 and I loved it for the challenging thought processes it required and the nice parity that I had to think through. It was even mentioned in my puzzles of the year as one of the best challenges.  Then a few years later, those evil twisted men and women at MF8 decided to create a new "harder bigger" version and the 4x4 version was released. I bought it at the end of 2021 and had a little fiddle and shied away from it as impossibly difficult and likely to end in tears for me and laughter for Mrs S. I kept looking at it lying on my desk where it taunted me for nearly 2 years and upset Mrs S because she couldn't stand the mess that my desk was in but I could not bring myself to pick it up. I spent a bit of time on holiday in Scotland 2 weeks ago and having limited space to pack puzzles for the journey, I brought a couple of twisties with me as likely to keep me busy for a while. When I finally got around to pick them up, I actually realised that I had not solved any twisties at all for a very long time and was a bit rusty. I needed to play with this as a 3x3 and a 4x4 a few times to remind myself of the very basic techniques (you really should all try to learn how to think about the basics - it really is NOT difficult to solve basic cubes once you have an understanding about the simple edge piece series and corner piece series and how they can be used - I have discussed them previously with multiple other puzzles and Rline has a wonderful set of video tutorials here.

So what is special about this puzzle? First off, you can quickly see that the centres are formed from 16 pieces instead of the usual 4 and it looks impossible to separate many of them. Here is where the fun starts - of course you can do a standard 4x4 scramble but then it is possible to do a 45º turn of the middle layers and then continue to turn the faces - this not only splits up the centre pieces but it also allows the edges to be swapped with centres and the outer edges to be tilted. Here is the puzzle after just 3 turns with a 45º turn done:

This is why I kept picking it up and putting it down
Interestingly, there appear to have been no English language solution videos posted on YouTube which may have given an indication of the extreme difficulty of the puzzle - at least that was my thought process. 

As usual with any new twisty puzzle, I experiment with the edge piece series and the corner piece series to see what they will do when you add in the fancy moves that each new puzzle allows. Interestingly, the corner piece series was absolutely no use to me whatsoever! It either did nothing and the puzzle just remained solved at the end of the simple sequence or there was no real pattern to what it did (in fact one attempt was blocked by the bandaging caused by the 45º turn). Then, as usual, sob, I lost track of what I had been doing and ended up with a partially scrambled puzzle that I could not back out of. Damn! Oh well, I had better get on with it...

OMG! That was probably not a good idea!
This thing would now barely move - so many of the turns were now blocked by either a twisted edge piece lying across a face (see the red/blue edge above) or by a pair of tilted centre pieces lying across a face (see the green centre piece at the top right). What the hell do I do now? There were no instructions anywhere so I guessed that I had better figure it out. First step, get it back to cube shape - so blocked up that no algorithms are possible so just use intuition. To my huge surprise, it was just intuition to achieve this up to a certain point. Once a few pieces had been aligned either properly in a centre or on an edge then more faces would turn and it was time to try and put the edges where they should be. Here we just have to use the edge piece series aka "up-up-down-down". Yes, it's just a 4 move sequence - it cycles 3 edges around. I realised that if you can do a 45º turn to put an errant edge pair back and then cycle a centre pair out then gaps start to be filled:

Errant edge pair in a centre
Edge pair turned 45º onto an edge
Edge pair now front left & centres in place
If the centre stripe is turned back that 45º then then one edge part and centre set are in place. This will need to be done repeatedly and where there are single edge pieces out of place they will need to be turned and moved until they can be lined up in a pair and then rotated into an edge using the edge piece series. It is surprisingly fun and apart from the frustration of the bandaging forcing a bunch of preparatory moves to clear the way, it doesn't take long to get a near cube:

Sort of cube shaped
Here is where I have really struggled. I have edges and centres where they are supposed to be but a bunch of the centres are tilted. I have not managed to find an algorithm to easily flatten them and had to make something up. If there are 8 or 16 of them tilted then that makes either 4 whole faces or 4 half faces on a layer out of kilter and all that is needed would be to turn the slice 45º, use the edge piece series to place an edge in it and then turn another 45º to place the centre that came out into the next position along. If you do this 8 times then you have broken and recreated every edge and centre in a slice. Sounds awful but is, again, entirely intuitive. What I have not worked out how to do with ease is what to do when there is not a multiple of 8 tilted edges. I can fiddle with my 45º turns and break up the flattened centres and with some thought I can make it so that a multiple of 8 are left tilted (I either add some or fix some). It works but I don't really know a definite sequence. Either way, it is, yet again, mostly done by intuition. Once the centres are flattened it looks less horrific:

Nice and flat
Now it's time to recreate the 2x2 centre pieces
To most puzzlers who don't do twisties, it still looks awful but from now on, it is actually really simple and fun. All that is needed is to pair up the single cubies. In the picture above, there is an orange pair top right of the centres and another pair bottom left but inset a little. Another 45º turn and a face turn will allow them to be linked together:

45º slice turn
After turning the front face and replacing the slice
Once each centre 2x2 is formed then it is moved out of harms way and another one worked on until they are almost all done. There is plenty of leeway here as there are only ever four centres that are affected by that simple sequence and when you are down to just a few then placing two identical colours in opposite faces is trivial and means that 2 centres can be worked on in isolation.

After just have a 4x4 cube to solve which, if you are working on one of these, shouldn't be any difficulty. I had been expecting some sort of parity like I saw with the 3x3 version but this does not seen to occur with this puzzle. The 4x4 parities are still a possibility but nothing new.

All in all, I was rather surprised at my ability to solve this monster. I had been frightened of it for nearly 2 years and the lack of anyone on YouTube showing it off made me think it was impossibly tough. However, it is surprisingly a lovely process and requires nothing more than intuition and the Edge piece series. Thank heavens to Rline for showing that sequence to me all those years ago and making me truly understand the power of those 4 little moves! If you can solve a 4x4, then you should buy this puzzle.

After this one, of course I couldn't rest and I went to work on another monster! the Master Mixup type 1:

30º mixup turns will lead to a monstrous challenge!

I have been a very lucky boy - Mrs S got very angry with me! Yes, that is lucky. She got so fed up with the state of my desk that she "forced me" to go online to Ikea and buy some more bookcases. Whilst on annual leave I have been arduously constructing and mounting them and am just about ready to start clearing my desk into them.

Puzzle room number 2 is ready
All nice and level no thanks to Barratt homes!
In the process, I discovered that my house was built by 14 year old apprentices with no skills! The floor is horrendously off level! It has taken a lot of effort to get these cabinets level. Lucky me has 3 double Billies on the opposite wall and now 2½ on this wall plus a closed one for less beautiful toys.

Thank you to Mrs S! 😇😇😇

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