An Edge Turner That Is Not Intuitive

Eitan's Edge Turning Octahedron

I am working again (4th weekend in a row) and have produced this post in a bit of a hurry in advance. If there are any errors then please let me know.

Eitan Cher has been responsible for a lot of fun in the PuzzleMad HQ and also a LOT of angst! He has designed quite a few of my very favourite as well as the most difficult of my puzzles. Despite all the angst, I absolutely adore what he creates. The Edge Turning Octahedron (ETO) was purchased quite some time ago in the expectation of fun and very quickly shelved when I discovered that it most likely would cause angst! In general the edge turning twisty puzzles can be mostly solved with a lot of intuition and only needing one or two fairly easy to find algorithms for the very end of the solution. Overall, they have been some of my most favourite of twisties for this reason:

Edge turning cubes

Why did I shelve it so quickly? One of the features of edge turners is the fact that they jumble: that is, it is possible to perform partial turns to line up intermediate cuts and then continue turning other edges which removes pieces from their normal "orbits" and also can make pieces shapeshift wildly. This is one of the reasons that I recommend them in my "advice for a beginner" post. However, with the ETO it scared the pants off me:

 

Just one jumble!!

It was quite clear that this was going to be bloody difficult - probably too tough for a relatively poor twisty puzzler like me. Eventually, I was convinced by a number of puzzlers to give it a go and I decided to try a non-jumbling scramble first. I really hoped that it would behave like other edge turners and mostly solve by intuition. Off we go:

Oh Lord! What have I done?

Corners all sorted to ensure no parity

Attempting a single face

So far, with almost all the edge turning puzzles, I have tried and succeeded in solving almost all of it by starting at one face and working my way up the puzzle almost layer by layer until I have reached the top. Occasionally I have had to intuitively build partial components and then move them up rather than single piece at a time and then find out how to complete the endgame. Straight away with the ETO, I struggled. It is almost impossible to build even a single face by intuition without destroying previously positioned pieces. Above, was about as far as I could get and I feared for the worst. 

I thought this was going to go back on my shelf scrambled but I was fortunate enough to have a massive explosion when I tried to make a turn without fully aligning edges properly. I then had a good reason to completely dismantle it and reassemble unscrambled and seek alternative methods. I really should have done my "due diligence" first - but then I am well known for not being terribly bright!

What most decent twisty puzzlers do when they have a new puzzle is explore it before they scramble it and try and learn what different known sequences will do. Since this was an edge turner, I felt confident that intuition would be useful and did not bother with that crucial early exploration phase. Having reassembled it, I could try again and do it properly.

The first thing I often do is sequences of turns around a face or corner and see what happens after 2,3,4,...x turns and if nothing seems to be useful then I can very easily backtrack.

I very quickly found this lovely sequence which certainly looked like it might be useful - turning the blue/white edge and the purple/white edge sequentially three times cause 2 adjacent centre flat triangle swaps with the adjacent edge wings. This might be useful.

Next, I try the "edge piece series" and the "corner piece series" which are so crucial if using the "Ultimate solution" to the Rubik cube which Rline has shown off so beautifully on his Twisty Puzzling channel. The Edge piece series wasn't terribly helpful for me but a corner piece series (modified for edge turning) proved very useful.

As you can see - the end result of the simple 8 move CPS is to 3 cycle the centres (plus muck up some edge wings, but with no effect on the corners and centre flat triangles. This tells me that if I can find a way to solve the corners and flat triangles first and edge wings last then I have an approach to the solution.

3 cycle these composite corners takes 4 moves

Do the same F to B then undo

Next thing I did was look for any easy commutators. This was not terribly difficult - it is easy to perform a 4 move sequence of R, L, R, L to swap composite corners as done above left. If I can isolate one of those edge wings in the top and then undo it all then I have a commutator. Luckily isolating that edge wing is very similar (I just perform a F, B, F sequence and then I can undo the original sequence. The end result is to create a 3 cycle of edge wings. I'm getting closer. I can place and orient corners by intuition, I can place the centres and the edge wings. I now only have to find a way to move the flat centre triangles (either alone or with other pieces) and then I have my whole approach sorted. This takes me quite a while.

After a lot of fiddling around and desperately trying not to forget what I moves I have made so that I can always undo them, I discover a very similar sequence to the edge wing commutator. If I turn the front edge and then follow this with a R, L, R and then undo it all, I have another commutator. This time it is not pure - as you can see to the left, I have moved centres and flat centre triangles with an adjacent edge wing in a 3-cycle.

This gives me my whole puzzle solution:

1. Solve the corners
2. Solve the flat centre triangles (the sequence moves everything apart from corners)
3. Solve the centres (the sequence doesn't upset corners or flat triangles)
4. Solve the edge wings (the sequence doesn't upset anything else)

Is it quite as easy as that? Erm... not really! Placing the corners is very simple except that there are lots of positions that places them in positions that the flat triangles cannot reach - they are in orbits as one would expect of an edge turning puzzle. It is ESSENTIAL to get those corners right first and seems to take me quite a while to get it right. I found a parity where 2 pairs of centre flat triangles need to be flipped. This cannot be done with the 3-cycles but luckily I had found my simple technique as the first thing I had found. All that was needed was to 3 cycle the pairs so that the were either side of a single centre. The centre positioning is pretty simple and then the edge wings are just plain arduous - as you work your way through, you need more and more complex setup moves to ensure the pieces I wanted to move are in the correct positions. Eventually the setup moves are so complex that I have to write them down before I perform the algorithm otherwise I will forget what I have done and then be unable to undo it. 

In the end - I have my solved Edge turning octahedron and a huge sense of relief! I have to say that yet again Eitan has created a most fabulous puzzle and any serious twisty puzzler should buy a copy. It is not an easy puzzle (certainly no intuitive like most edge turners) but definitely solvable with a bit of experimentation. I really need to add another chapter to my advice to a beginner series to include a few of the puzzles produced since my original post. I may need some help with that if anyone wants to help me. Now I need to get the courage to try a jumbled scramble and solve. I suspect it will take me some time to get the courage together for that!!!

Getting Ziggy With It

Ziggurat

This has been written ahead of time and set to publish at my routine time. Having had some time off work, I have to pay the price by working two weekends in a row! Sob!

Whilst I am here, can I ask that you all think about the awful atrocities that are going on in Ukraine. One of our fellow puzzlers, Peter Grabarchuk, has asked that I highlight to you what is happening and request that you consider doing anything you can to help out. Either give to a charity that is helping in Ukraine or that is helping support refugees. Anything you can do will help out and ease a terrible situation. 

Back to the puzzling…

My friend Eitan has been rather busy with work and having a family over the last few years and seemed to have almost withdrawn from Puzzle design and manufacture. My other puzzles of his were the incredible Eitan's star (one of the most difficult and marvellous twisty puzzles ever mass produced) and the Master Curvy Copter which he designed and used Shapeways to 3D print for me. With some considerable surprise I saw him offer up a new design called Ziggurat, which he was 3D printing himself. The Ziggurat is a massive Mesopotamian pyramid-like structure usually with 2 to 7 stories. Eitan was going even more massive with EIGHT! How could I resist? I jumped on the offer and sent off some electronic money (not actually a lot) and got some feedback from him that the colours that I had chosen were great. I waited for the US and UK postal services to get their acts together and finally took delivery.

In the meantime, Michel van Ipenburg had written about it in his newsletter as well as pronounced on Facebook that it was a very nice fun design which was a great relief. Michel is the foremost connoiseur of the N-ary puzzle group and if he approves then it is definitely worth purchasing. 

Eitan had thoughtfully sent the puzzles out with 6 of the plates already assembled into a stack connected to a display stand and another 2 extra plates were loose in the box ready to be added to the stack. Initially, I did wonder why he had started the puzzle off for me and possibly gone halfway but then I realised that he had actually been very clever and thoughtful. The stack of 6 was definitely not ready to just start adding the other 2 to. The stack had to be completely dismantled before the reassembly with 8 was going to be possible. Having 6 ready assembled allows the puzzler to explore the sequences and understand the puzzle before embarking on the main odyssey. Once apart, the clever design of the plates and how they interact with each other across 3 layers is apparent and I was further impressed with Eitan's skills. The 2 colours have plates that are mirror images of each other.

I spent a couple of evenings on my chair watching TV working out how it worked and got ready for the full assembly - there were going to be a LOT of moves that had to be done in the right order and in the right direction.

A very interesting beginning

Hidden by the spoiler button is the initial stage for the first assembly - having to do that was completely unexpected and very nice to realise. Once I thought I had it begun, it was time to begin the arduous process of working my way through the many many moves to stack the plates tidily. Everything moves very freely and easily despite the 3D printing. I initially just worked my way through but on 3 occasions realised that at some point I had turned myself around and was heading the wrong way. In fact, the first time this happened, I only realised that I had done this when I returned to the start position...DOH! Having inadvertently back-tracked 3 times, I decided to take notes to prevent further errors and to also allow me to take a break and obey Mrs S' commands with work to do around the house. I hate to think how many extra moves that I actually ended up performing but I got there in the end:

All 8 plates locked together

Stacked! As Eitan intended

I love it! The sliding mechanism places no strain at all on the very delicate thin tongues of plastic and it is a fun puzzle to explore. It will not be something that you solve multiple times but the experimentation and assembly was a pleasant diversion and even getting lost in the path multiple times only added to the enjoyment. It is ready now to go on display in my N-ary section.

Thank you Eitan, I look forward to future designs from you now that you are back designing again.

Cast Cricket

Cast Cricket

I know! I know! I'm late and it's not good enough! Yes I've even had an email from an expectant friend. He'd come back from Sunday lunch and was settling down for a rest and a read of my latest post. He was most disappointed to see that I had failed to provide but I reassured him that it would be coming soon and here it is.

I'm late because of this!

So why am I a day late? Well last week, having freed my angel, I said that I'd need her help to solve Eitan's star, the 1st ever icosahedral and the hardest mass-produced twisty puzzle ever produced. Having scrambled it last Sunday, I'd been working at it all week and only just managed to complete it late on Sunday afternoon and much too late to write this post. Certainly it was too late if I didn't want to get in trouble with Mrs S! How do you go about such a horrific twisty? First I knew that the Eitan's star is the geometric dual of the Bauhinia dodecahedron (a vertex turning 12 sided puzzle) with the turning vertices coincident with the faces of the icosahedral puzzle. So starting at one corner, I was able to solve half of it using intuitive moves alone, then the thin internal triangles of the top half were solvable from the equator up using nothing more than the 4 move edge piece series.

Can you see the similarity?
Neither can I but it is there!

At this point it started to get challenging - with the vertices requiring a 3cycle but lots of setup moves to match the 5 colours up. The 2colour edges were next - there are 60 but I had 32 to solve and these require a much more complex series of moves just to cycle 3 of them and place just 1 at a time. My own algorithm was too difficult to translate so I borrowed a nice 20 move sequence from my friend Rline's video series. This section of the solve is really arduous and took hours and hours. There's no room for error and you have to pray that you remember all the setup moves! A small rest was required to calm my nerves and finally a simple set of corner piece series were required to place the large triangular centres! As of this moment, I am the 11th name in the list of solvers on the Twisty Puzzles hall of fame. If you want a cheaper but still pretty tough twisty puzzle then definitely try the Bauhinia dodecahedron - it is a tremendously fun puzzle and will set you up nicely for the Star's challenge.

So you see I do have a good excuse. I was therefore needing a fairly quick puzzle to solve and write about for you. In my last batch from Puzzle Master, I had ordered a couple of the easier Hanayama cast puzzles, so I fetched one to solve as quickly as possible for this blog post. This one is the level 2 out of 6 (or 6 - Tricky, on the Puzzle Master 5-10 point scale) which I think is a reasonable assessment. Opening the usual beautiful packaging reveals a really lovely metal puzzle in an antique brass finish. It is 6.7 x 6.7 x 2.5 cm in size and seems rather finely made. The name Cast Cricket obviously comes from the fact that it is formed from the major parts of the game of Cricket. It consists of 6 cricket bats joined at the handles in an odd star-shape and linked into a wicket structure complete with Bails preventing it lifting out the top. For the Americans amongst you, see this article for a description of cricket. The aim is to find a way to remove the 6 bats from the wicket. Preventing it are a number of knobbles on one side or other of each bat (one of the bats looks like a skateboard with wheels on it at both ends) but to help you there is a gap in the central wicket and a notch in the centre one. Like all the Hanayama puzzles, it does not come with a solution and if you want one then it can be downloaded from here.

This puzzle only has an average rating on puzzle master of 2 out of 5 stars but I think this is due to one particularly scathing (and unfair) review of 0 stars from one person who felt it was too easy and fragile. The other reviews were much more favourable. This is an easy puzzle but not everyone wants something that takes months and if you don't want an easyish puzzle then why are you looking at a Hanayama level 2? Gabriel reviewed it back in 2012 and really enjoyed it whilst acknowledging the difficulty level.

I'm a puzzler on the edge!

The Master Curvy Copter
"HELP! I need someone!!"

Introduction

It has been quite a while since I have posted anything about twisty puzzles and I have recently managed something REALLY special so I thought I would discuss it and also try to give enough information about the process to hopefully entice a few more of you into the wonderful world of twisties! My aim is to talk about edge turning puzzles, a bit about jumbling and then give away "the secret" to twisty success!! Read on!

I started it!

The fearsome looking puzzle pictured at the top is the Master Curvy Copter - it was designed by one of the great twisty puzzle designers, Eitan Cher. It was first announced in June 2010 when Eitan posted about it on the Twisty puzzles - "New puzzles" forum and even though it did not turn very well in version 1, there was a lot of interest in it and then it all quietened down. Subsequently he produced a version 2 which solved all the initial problems and put it up for sale on his Shapeways store where it is now available for a very reasonable €180 in Black. Now mine cost a bit more because I got mine ready made from Eitan (I'm not allowed to dye plastic in my new kitchen on pain of torture!) I chose it because I had absolutely adored (and still do) the original Curvy Copter (pictured left) which I wrote about almost at the beginning of my Twisty puzzling career. I still maintain that it is a fantastic puzzle even for people who are not into twisties. Obviously when you have finished the 3x3 cube then the next step is a 4x4 - so I figured that the step up from the Curvy Copter would be the master version.

This gorgeous puzzle arrived in May this year and I fiddled with it a little and marvelled at how complex it was and yet how well it moved - even the jumbling moves were really easy! I then put it on the shelf next to me where it stayed for a month or so. Yes! it's the "puzzles to be done" shelf and it has quite a few on it! It screamed obscenities at me for weeks but I was far too frightened of it to scramble it and try a solve - partly because I seriously doubted that I had the necessary skills to solve it and also because it is so rare in the wild that no-one has posted anything on-line at all about how to go about solving it - meaning that I would not even be able to look at a tutorial if I got stuck! I believed I was on my own!

Yeah! I can hear you all screaming at me that I'm a puzzle wimp and I freely admit it! Strange that I keep hearing these voices! But..... Just look at it! It's horrendous!

It looks so innocent like this!

So nearly 4 months ago, I finally succumbed and decided to do what I had done with it's daddy (the Curvy Copter) and did a scramble without any jumbling or shapeshifting and did not take any pieces out of their orbits. I recalled when I did the same thing to the Curvy Copter and that I actually managed to solve all but the last corners by intuition alone and then, using some very simple series of moves, I managed to solve them too. I remember how great it felt and what a phenomenal puzzle it was - it ended up as my second ever twisty blog post. If you don't have the Curvy Copter yet, then BUY it.... NOW!

Having done the most basic of scrambles on my new monster,  I set to work and........
I couldn't do it! I spent a week trying everything I could but nope, I didn't have the skills. I couldn't, to my shame, even do the first face. I tried reducing it to a standard curvy copter and failed at that too. So I put it back on the shelf where it looked quite pretty in the scrambled form but every time I looked up it made me feel guilty. I would take it off the shelf and try again every week or two and fail again!