Sunday, 3 October 2021

Twistytex' 3x5x7 Masterpiece Gives Me a Hell Of a Challenge

But Using Basic Techniques Got Me Through

Twistytex' 3x5x7
That was really silly!
I have been chatting to my friend Casey Weaver, a wonderful generous Texan, for a couple of years. He had seen that I had a copy of SuperAntonioVivaldi's amazing version of the 3x5x7 cuboid and wondered whether I would swap my original copy for one that he had made by 3D printing extensions and hand finishing to a very fine polished surface. SAV had classified this puzzle as an "ultimate shapeshifter" - you can see why from the picture above. It was a collaboration between SAV and the incredible Gregoire Pfennig to create something truly wonderful and ground-breaking. I had solved it way back in 2013 and had incorporated it as one of the ways that a new twisty puzzler could go if they wanted to expand their puzzling skills in a logical progression. I had really enjoyed the approach to the various types of cuboids but very seldom solved them because this one as a Shapeways puzzle still dropped black powder from inside every time I played with it. This completely drove Mrs S crackers and so I had put it aside for a rather long time and when the opportunity came from Casey to obtain a still very limited edition version which I could actually use without threats of violence, I jumped at the chance. I had managed to obtain a couple of others in the interim period:

Ultimate cuboid family (3x5x7 by SAV, 5x7x9 by Traiphum and 4x6x8 by Jeremy)  
and we even had a mass produced version made by Calvin's puzzles after a design by Hunter Palshook. I was lucky enough to get the hand-made prototype and after giving it back so that the puzzle could be mass produced I was one of the first to receive the actual puzzle:

Calvin's 2x4x6
It has been several years since I had played with any of these puzzles - in fact I have not done a twisty for several months! I thought to myself that I should still be able to manage it despite the time gone by - so I scrambled it and admired the chaotic beauty that I had. Then, having scrambled it, I realised that I had forgotten every single one of my cuboid algorithms! I also had not even solved a 3x3 or 4x4 for many months.

It was going to be back to the basics for this one. I have refreshed my abilities with basic cubes and decided that I would try and use a technique that did not require any special algorithms at all. Yes, it "should" be possible to do this using nothing more than techniques used for a 3x3 and 4x4 cube and a bit of block building to reduce the puzzle to a rather beautiful but misshapen 3x3x3. The technique is reminiscent of the 4x4x4 AI cube that took the twisty world by storm:
Original AI cube
GRcubed AI Megamorphinx mod
These very difficult puzzles are solved by organising the 2x2x2 blocks onto the top two layers and manipulating these layers to recreate the correct piece positions. It actually is mostly done by intuition apart from the last few pieces. If a similar thing is done for a standard 4x4x4 cube then the fancy algorithm can be skipped because there are so many pieces in the last layer with the same colour and if really struggling the centres can be easily placed alone using standard 4x4x4 methods.

Obviously the 3x5x7 was going to be slightly difficult - I was going to have to make it into a 3x3x3. First thing to do is to recreate the edges:

Here we have longer edges - you can see where the 2 central edge pieces need to be moved to align with the green and red true edge. All edges of the correct length need to be moved onto the top half - this is easy and then the corners placed to allow the 2nd and 3rd layers to turn:

A corner is placed alongside the edges and if not oriented correctly then using just beginners 3x3 method (Ri, Di, R, D repeated ad nauseum until correct). This needs to be done until all the to corners are oriented to allow movements and then the central edge pieces are moved into place. Easy peasy...sort of! It definitely works but takes a lot of thought and planning:

All edges done - placing them like this is just for the photo
Once all the edges have been recreated then the same thing needs to be done for the compound corners. First create the outer 3x1 column and then the inner one. Then line them up and stash them in the bottom half for safety whilst continuing to use the top half for work:
OYB outer column formed
Outer column combined with inner
All Yellow corners done - start on white
Getting the final corners recreated is quite a logic challenge - it requires multiple movements of corners to different places and then rotation using the standard 3x3 algorithm and then rinse and repeat...many many many times. After several days of swearing and huffing and puffing (Mrs S said it sounded like I was doing a very painful workout and it certainly hurt my bwain), I had a 3x3x3 to solve:
Layer 1 solved
Layer 2 solved - top to go
After 3 or 4 days of blood, sweat, tears and threats of violence (again!) I finally had solved the 3x5x7 using nothing more than 3x3 and 4x4 techniques and a lot of thought. It is definitely not the most efficient way to do it but requires minimal specialist algorithm knowledge and is very rewarding!

Solved in front of a Cactus
Probably a lot smaller than the ones that Casey has near his home.
I always recommend to newbie puzzlers that they should seriously consider incorporating twisty puzzles into their repertoire. They are fabulous fun, a huge challenge and very repeatable. They are also collectible and can be worth a lot of money if solved later (so not a bad investment in terms of time or money). There are loads of really challenging puzzles out there for us all to play with and learn from. It is not necessary to memorise lots of algorithms for the vast majority. If you wish to try an Ultimate Shapeshifter then a few of the 2x4x6 cuboids are still available and they can be solved in this way (although reducing to a 2x2 cube instead will be much less arduous) and maybe I will give that a go next.

Thank you so much Casey for making such a wonderful challenge for me and reminding me of the fabulous puzzling that can be had from twisty puzzles. Amazing quality!


I got my booster jab a few days ago and, apart from a sore arm for a day, I had absolutely no adverse effects at all. This will help the world get out of this pandemic so if you have the chance to get your vaccine then please do so - it may save your life, it has an even higher chance of saving someone else's life - do it, the science says so. Reading a few crackpots on Google, Facebook and YouTube is NOT "doing research" - if you want to do research properly then get a research degree and then start reading all the scientific literature before joining a PROPER research institution and doing it well and publish your data in a journal not on the web!


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