Jerry Loo's Dirty Dozen and an Opportunity For You

Dirty Dozen, an exceptional puzzle from Jerry Loo.

Hi guys, I have been terribly remiss...I have failed to solve anything in the last week or so! Not for want of trying! My arse has been thoroughly kicked by the Slammed car and even a couple of my twisty puzzle purchases have caused me thorough misery. I have to admit that I am absolutely rubbish at this puzzling stuff - maybe I should give it up? Luckily for me, my good friend and helpful foreign correspondent has chipped in with a brilliant post about a puzzle that I have solved but never gotten around to writing about. Jerry Loo's Dirty Dozen.

Of especial importance just now is that you have a chance to buy a specially made copy of this wonderful puzzle from the great guys at PuzzleMaster via a Kickstarter campaign which they have set up. Their copy of this lovely puzzle will be made in anodised aluminium rather than stainless steel but the three puzzles available look fabulous and are really great value. So without further ado, over to Mike for a wonderful guest post:


Aloha Kakou puzzlers,

The topic of today’s post is designer Jerry Loo’s Dirty Dozen puzzle. Kevin owns a copy and I fully hope and expect that he will chime in liberally on this post, if not add a complete epilogue. In my not-always-humble opinion, it is worthy of extended treatment from multiple perspectives.

For those not in the know, Jerry Loo is an accomplished puzzle collector/designer/blogger hailing from beautiful, tidy Singapore. Jerry began blogging about puzzles in 2011, amidst a veritable explosion of puzzle blogs (e.g. Puzzlemad 2011, Allard's PuzzlingTimes 2011, Gabriel's Puzzle Collection 2010, and Roxanne’s Frustrations 2010). Jerry’s site, recently migrated and relaunched, is what I consider to be one of the Big Four. Check the sidebar and see if you can guess which ones I mean. If Puzzlemad is not in your four, you are dishonourably discharged (Ed - I'm not sure I agree with that...why would anyone read my drivel? Except for the exciting guest posts). Read no further.
How does one get into the Big Four? Launching your blog in the early part of this decade would have helped. Page hits are also clearly an important criterion. You should be approaching a million by now (Ed - amazingly, I am up to 1.28m page views now). That’s not much in this medium, I know, but we are talking puzzles after all. I suppose the main quality that differentiates the Big Four from others is pure consistency over time. Many great puzzle blogs have come and gone over the years. Most start strong but burn out and fade away in short order. Believe me, it’s not easy to do this regularly (Ed - tell me about it!), let alone every single week for nine years like my cherished but possibly deranged editor (Ed - maniacal laughter ensues!). The average person, and even the above-average puzzler, simply can’t maintain the pace. Most of us have full-time jobs, families, and/or cats to attend to. But somehow, someway, Jerry and a few others have managed to maintain consistent output at a very high-quality level for many years. These, then, are the Big Four. I should also mention that some former greats have flirted with revival and some late starters (Alcohol and Alcoves) have achieved greatness in record time. It can be done but requires a demoniac level of enthusiasm and commitment (Ed - or incalculable madness in my case).

Jerry’s  L(8)tice-2. How hard could it be? Very hard indeed. (photo from JL Puzzles)

Beyond his blogging accomplishments, Jerry is also a skilled designer. In fact, that has been his main focus for a while now. I first interacted with Jerry years ago when I was trying to get my hands on Ball in Cylinder, one of his first design efforts. He now has a wide range of designs under his belt in multiple puzzle categories, many of which have gone into limited production. His early efforts with the machined-metal hidden maze type evolved into a focus on packing problems, benefiting no doubt from his association with fellow countryman and esteemed designer/collector Goh Pit Khiam. Presently Jerry is exploring interlocking, assembly, and packing type designs using BurrTools. You can check these out at puzzlewillbeplayed. L(8)tice-2 was, I believe, the first interlocking design to meet Jerry’s characteristically high puzzle quality standard and was eventually produced in stainless by Metallofactura. It is still available now for $43. As Jerry notes, L(8)tice-2 builds on Andrei Ivanov’s Lattice Xi-2, itself inspired by Yoshiyuki Kotani’s ξ-Lattice. Quite a genealogy and I am lucky enough to own the former two. L(8)tice-2 is very tough - my copy remains unassembled to this day (Ed - indeed, mine was sent disassembled and remains that way as well!). Jerry, the designer himself, still uses Burrtools instructions to reassemble...it's that tough. Lattice Xi-2, with fewer pieces and a different release mechanism, is definitely more approachable, but by no means simple to reassemble. It took me quite a while.

The basic piece.

These early design efforts led, in time, to the 12-piece Dirty Dozen. Despite a relatively large number of pieces, Dirty Dozen has an elegance and beauty not found in L(8)tice-2, or most other board-matrix designs for that matter. This is due in large part to the fact that it is composed of only one basic piece. That is correct, all 12 components are identical. This is not nearly as easy to accomplish as it seems. I maintain, based on no actual evidence (Ed - hahaha! We are all entitled to an opinion!), that there are many more ways to construct a self-locking board matrix using irregular pieces than identical pieces. The self-locking quality is critical, and in a way separates the board matrix from the true board burr, which is necessarily held in place via tension. The charm of the board matrix, at least the examples I have played with, lies in its capacity to deform in a rather alarming manner but never throw a board out of the lattice. Dirty Dozen, faithful to this design requirement, is extremely unlikely to come apart. I won’t say impossible, but nearly so. It will take on some interesting rectilinear shapes, threatening always to let lose a piece and shatter the whole edifice. But it never does. As far as I or anyone else has found, there is no way for it to come apart without a very specific sequence of actions (Ed - I have never found any other way to dismantle it).

Deforms pleasingly, but it won’t disintegrate.

The third leg of the stool and the most important quality for any puzzle is, of course, the solution process. Dirty Dozen delivers on this count. The solution is right square in the difficulty sweet spot and, further, rewards one with a deep structural understanding of the puzzle, not simply relief at having gotten it back together. At least for me personally, memorizing a complex movement sequence doesn't really qualify as properly “understanding” a puzzle (Ed - sometimes it's the only way that I manage it!). By this measure, not all puzzles are truly understandable (Ed - aaargh! What about this?). The only downside to an understandable puzzle is that it may have dramatically reduced replay value. That’s the trade-off. But honestly, how many people actually replay (disassemble and reassemble without instructions) highly complex burrs? Not a lot and not very often would be my guess (Ed - don't tell Mrs S, but I rarely replay any of my puzzles once they are understood). Non-understandable puzzles also have replay limitations.

When I ordered Dirty Dozen from Jerry, I had no idea at all what kind of solution it had, nor a clear idea of its difficulty. I asked him (with some trepidation) to deliver it unassembled. I didn’t do this lightly. There is nothing worse than brashly requesting an unassembled puzzle and then having to slink back for the solution a month later. But knowing that the pieces were identical signalled to me that there might be some higher-order logic to this puzzle. I went for it, and am glad I did (Ed - braver than me - or maybe more stupid?).

In most cases, ordering an assembly puzzle unassembled is the clearly more difficult option. You don’t have the advantage of carefully taking it apart, studying the structure at various steps, and even taking photos (I’ve recently learned). However, disassembly can be a significant challenge for Dirty Dozen because of the way it locks. The initial (or in my case final) move to lock the puzzle into shape is certainly not self-apparent. Given the way the puzzle moves, one might be searching in a whole different conceptual area for a long time. Kevin did not have a tough time with disassembly, but he is, of course, a very experienced solver, despite his protestations (Ed - hahahahahaha! Maniacal laughter ensues!).

The pieces (plus eight more).

Assembly for me took about four hours of work over a couple sessions (Ed - OMG!). According to the literature, 23 “moves” are required to fully construct the matrix, in the order 4.2.2.1.3.1.3.2. These sequential solution move counts are largely an artefact of Burrtools design and analysis, serving mainly as a proxy for difficulty level. Useful though this information can be for some puzzles, it can also be classified as inconsequential trivia for others, such as Dirty Dozen for example. It could also be considered a major hint, in some cases.

Although this puzzle has only one possible final configuration, it does have some that are very nearly possible. One such involves the completion of 11 of the 12 pieces. So very close! I got hung up trying to make that work for a long time before I finally gave up and backtracked. Such tantalizing dead-ends contribute significantly to the enjoyment of this puzzle (Ed - you are a sucker for punishment!). The solving experience is generally optimized when there are just enough false assemblies to be challenging, but not so many as to be completely overwhelming. Dirty Dozen straddles this line nicely.

The overall structure of Dirty Dozen is especially notable. Twelve pieces is a pretty high count for a board matrix, with potential for dizzying complexity. It helps to temper this somehow. For Dirty Dozen, this is achieved through the use of identical component pieces exhibiting a very pleasing nested symmetry. The exterior four slots reflect, and the interior two rotate 180 degrees. That second part can be a real help during reassembly. But I think it is particularly interesting how the assembled structure, viewed in plan (90 degrees off the plane on which we observed the component slots), retains these symmetries. The centre has a 90-degree rotational symmetry, and the pair of sides are faithful reflections of one another.

A nice reflection.

An equally nice 180-degree rotation.

Isolating some recurrent symmetries.

Perhaps this was to be expected, and surely it could occur even if the slots were of differing sizes, but I still find it intriguing. I wonder how a designer might play with different configurations of identical pieces, and how far out these symmetries can be extended while still crafting a “good” puzzle. For a case study, check out Goh Pit Kiam’s Partitions, a puzzle I frustratingly missed out on during its initial, and possibly only, JL Puzzles production run.

Back to the solving. Four hours sounds like a long time, and for some puzzles that can seem like an eternity. What makes me so upbeat about Dirty Dozen is that it was legitimately a fun puzzle to work on all the way through. Exploring the way the pieces fit or refuse to fit, and gaining an understanding of the constraints and possibilities was very enjoyable. The false constructions provided a really good challenge and the necessary build-up to the final solution. Some puzzles have singular, ecstatic A-ha! moments, while others like Dirty Dozen offer quite a few small A-ha!'s along the way, and then more of a whoosh of satisfaction when the final piece is placed. What I am trying to say is that this is a really fun puzzle. It has an appeal well beyond the hard-core crowd, in my estimation. It would be a perfect addition to a commercial line (Ed - well that would be coming right up!). On the hard side of the line, but certainly within the ability of the average person with above-average motivation. And the manufacturer only needs to produce a single piece. How efficient is that? Precious few puzzles can translate well to a mass audience and be economical to produce. This might be one of them.

Impassive stainless steel beast.

For the moment, you will need to get your copy direct from Jerry (Ed - this was written and sent to me just before PuzzleMaster decided to start a Kickstarter campaign). He has produced several colourful, affordable, acrylic versions, but I was very happy that he made the extra effort to produce Dirty Dozen in stainless steel (Ed - me too! I lurve my copy!).

It is especially impressive to stack the identical pieces like this

I highly recommend that all serious puzzlers and collectors get this version. It is delightfully hefty at 640grams and is completely indestructible. You could run this puzzle over with a tank and I’m sure it would survive intact. No exaggeration. Let's just hope Dirty Dozen gets back on the market in the not-too-distant future (Ed - no sooner said than done!). Partitions too, for that matter, because I really need that puzzle.

To conclude, Dirty Dozen is a great design and a winner on all levels. I have not played with all of Jerry’s many designs, but I will go out on a limb and claim that this is among his best. It exhibits a blend of qualities that all designers aim for, but so rarely achieve—meaningful structure, simplicity, elegance, and that elusive difficulty sweet spot.

Ok, Kevin, that’s all I have. Take us home...

Thank you so so so much, Mike, for bailing me out yet again! I am eternally grateful to you for taking the time to write this post - it is quite clear that you take a lot of time and effort writing it.

I am not sure why I have not written about this puzzle before - I agree fully with your analysis that this is an absolutely brilliant puzzle and essential for every puzzler's collection. I am truly impressed that you were able to solve this as an assembly puzzle - I could not have managed that but for others thinking of buying a copy, it is just as much fun, if slightly easier, solving this as a disassembly challenge. The stainless steel version is incredible but in the absence of a supplier for these, it is still worthwhile buying in acrylic or, as will be happening very soon, in anodised aluminium - there are just 7 days left on the Kickstarter campaign to get the Dirty Dozen and L(8)tice designs from Jerry and I would heartily recommend getting both (but expect the L(8)tice to be the tougher of the two). The Kickstarter campaign also includes one of Ray Stanton's wonderful coordinate motion designs, the Slideways burr - I have written about 3 of the shape transformations of these made by the New Pelikan Workshop:

Slideways Cube

Slideways ball

Quad Slideways ball

If any of you feel the urge to contribute a guest post to help me maintain my weekly streak of publishing, then please contact me and we can come to some arrangement. In the meantime, I had better solve something quickly for next week!

Enjoy the rest of your weekend - keep puzzling!

Diniar A-mazes me and Unlocks Just the Right Combination

Mazeburr-L

Every year around now (i.e. just before IPP) I have a little chat with the King of the sequential movement puzzles, Diniar Namdarian, about his latest releases. He shows me a bunch of pictures of stuff he has designed and made and I pick a few. After a minute or so (the chat is via FB messenger so often a little disjointed), he asks whether I really don't want to choose one or other and makes a comment like "that one is really good" or "it's the best of the bunch" and I hesitate for a moment and tell him that I will buy them all. This happened yet again this year and I received a bunch of new toys a while ago. The latest batch looks like this:

I cannot resist the colours!

After the wheeling and dealing have been done, I usually have to admit to him that I have failed to solve one or other of his previous creations and he very gently makes fun of me. The problem is threefold...

1. I cannot resist buying all of his creations (they are really reasonably priced),
2. They usually have multiple challenges and come with a wonderful ebook of delight,
3. I am simply rubbish as sequential movement puzzles!

The Mazeburr-L immediately sprung to my attention amongst the pictures he showed me. The name Mazeburr for me is synonymous with fun...I have all three of the other shaped Mazeburrs and have an extensive supply of challenges for them.

Three Mazeburrs so far now I have another to add to the series.

The existing Mazeburrs (including the Split Mazeburr which I reviewed in March this year) all consist of a bunch of maze plates on the surface of a shape with pins that protrude into the maze from plates underneath. The aim is to remove the plate with the opening on it by effectively navigating multiple mazes simultaneously. They vary in length of solution from a nice easy 20 moves up to an impossible (for me at least) 350 moves. They are a delight to look at and a delight to play with too. The Mazeburr-L consists of sticks with gaps "cut" into them and a frame to hold them in place but that is where any similarity ends - the aim of this Mazeburr is to manipulate the gaps in the sticks to allow you to advance the little blue ball from its' starting position to the square exit hole and then out (in the picture at the top the blue ball needs to move from the top right position to the bottom left where you can just about see a small gap in the covering acrylic.

Diniar provided a lovely 16-page ebook (which lives on my iPad) to go with the puzzle and I have been working my way through the challenges. The sticks are all numbered and each end is marked with an 'a' end and a 'b' end to ensure that the puzzle is set up in the correct orientation:

22 different burr sticks

Initially, when I started playing I felt I had to guess where the gaps were going to be (or remember where they had been from setting up the next challenge when I realised that Diniar's attention to detail was superb...It's impossible to see it in my photos but there is a groove printed into the top surface of each of the sticks marking the position of the underlying gaps. This means that guesswork is not required. Once the puzzle is set up as shown in the diagram (complete with start and end position) then play begins:

Just 6 of the 84 challenges
Notice I have been marking the ones I have solved off in my pdf viewer app

The sticks all lie within notched grooves forming a 3x3 grid and each of the sticks can be in any of 7 positions (they all start in the centre of position) and they need to be moved where the gaps will allow. This moves the gaps around and then the ball can hop through the gaps into adjacent spaces and then the sticks moved again to set up the next move of the ball. At certain points, there are several options for where the ball could be moved and as the decision tree widens the puzzle gets tougher. On many occasions, I found myself fairly close to the exit and blocked, needing to backtrack a fair way to an earlier part of the decision tree. This can get quite confusing at times but is very rewarding when the ball finds its' way out.

Solved it - on to the next one.

The solving process for me is a mixture of logic and trial and error which, for me, is rather soothing. The challenges escalate in the number of moves required but I seldom manage to solve them using the minimum number of moves. The difficulty level, like the other Mazeburrs, is not really just a function of the length of the solution (the longest is 45 moves), it is much more related to the size of the decision tree and how much back and forth is required. I found most of these quite soothing to solve (I have solved just over half of them so far) although I have been forced to play with this one when Mrs S is not in the room - the ratcheting in the burr stick grooves means that every single move of the sticks makes a clacking noise and if they move several notches at a time (up to 6) then there is a very annoying (to Mrs S) THRRRRAP sound. I guess that if I need to make 30 or 40 of these noises for each challenge then Mrs S may well go beyond the Whack! Ouch! and may even melt the plastic puzzles and encase me inside the molten mess (especially if the pile of burning wooden puzzles is still alight).

Lots of pieces and spares too

Diniar provided a nice little bag with all the sticks inside as well as spare blue balls (because everyone needs more blue balls!) and also spare corner pieces which may snap after repeated flexing to open the puzzle up. I have to say that this has been a wonderful purchase and for the number of challenges has been fabulous value for money. Diniar always prints his designs so well and puts so much thought into the challenges - when he makes them available, don't hesitate, just say yes!

---

Combination Lock

The one puzzle in the bunch that I hesitated on was the Combination Lock - I hesitated because it is just a single challenge and looks like a free-form sliding piece puzzle. I am simply terrible at this sort of puzzle. So when I left it out of my selection, Diniar put me straight and I quickly gave in. Let's face it, these are 3D printed and are not terribly expensive. Straight up, let me say, Diniar was right! This puzzle is a lovely challenge and a beautiful little voyage of discovery.

The aim is to move the lettered buttons from the start position at the top into the end positions along the bottom right-hand side. They move via the slots in the centre rotational piece and obviously, will need to be moved back and forth via the extra "storage area" on the left-hand side. To you, this looks easy but, to me, it looks like an impossible task. I have had this next to me in my pile of puzzles to be played with for a few weeks and have not dared to pick it up until now. This week I had a little free time when I had to wait for Mrs S to attend the dentist. I gave her a lift and stopped off in a nice little cafe to drink, stuff my face with a cake and play with toys (much to the amusement of both other customers and the baristas). With trepidation, I took it out and quickly started to move pieces around.

It becomes obvious quite quickly that, whilst it looks like there is a lot of leeway to move pieces, there are actually considerable constraints to what you can and cannot do:


The deepest slot in the centre cannot be accessed from any of the start positions due to the length of the arms of the slot which causes a problem later on in the solve, the shallow slots in the centre don't allow full movement of the pieces to or from the storage area and the centre cannot rotate much when pieces are in any of the shallow storage slots.

The learning curve is quite steep, I discovered the above constraints very quickly and gradually found more problems as I moved pieces around and found the moves that I wanted to make in the order I wanted to make them very definitely hindered. I had a nice 45-minute wait for Mrs S to have her mouth "seen to" (unfortunately the lips were not sewn shut preventing the frequent furious talking to that occurs chez Moi - Whack! Ouch! Sorry dear! This amount of time was just about right for me to have my coffee and a sneaky cake (Whack! Ouch!) AND solve this wonderful challenge:

Done it! Fabulous!

Diniar was right - when you buy any of his latest releases then you MUST ensure that this is in the purchase. It is just the right difficulty level, with several Aha! moments and a satisfying end. The reverse process is also a challenge (I doubt that you will remember the sequence that you performed to get there). This is also perfect for kids and newbies to try their hand at.

Thank you, my friend, these were wonderful.

25 Years of Marriage Have Turned Me Into a LunaTIC!

LunaTIC pieces

Well, I survived! Friday was my 25th Wedding anniversary and despite everything, I have survived, more or less intact! She has threatened me with "serious words", significant violence aka a Whack! Ouch! and even mild murder (can you have a mild murder?) including an offer to burn my body on a pyre of flaming wooden puzzle pieces. She has form...do you remember this?

Luckily I have hidden the matches since this famous moment!

To appease the wifely Gods, I purchased her some significantly beautiful (and expensive) jewellery and she seemed rather pleased with the gift. I even earned a few Brownie points for the nice things I wrote in her anniversary card. Unfortunately, in this household at least, Brownie points expire after just 1 week - GULP! Her gift to me? I have been sitting in the living room for a few months looking longingly at her gift to me but definitely not allowed to touch...A Berrocal Goliath puzzle sculpture awaits. Now I just need to find some time to play!

80 Pieces of beautiful polished brass

Today, however, I need to write about yet another of Andrew Crowell's designs, beautifully made by Brian Menold, the LunaTIC. The most recent batch of Andrew's designs have caused me a huge problem...I couldn't solve them! It took me weeks to finally dismantle the GalacTIC cube and then the reassembly was also a massive issue for me. As soon as I had solved that one, I moved on to another in that batch, choosing the LunaTIC partly because it only had 5 pieces. I sort of figured that if I am really REALLY bad at assembly puzzles then I should probably start on one with only a few pieces.

Brian had felt confident enough to send it out in pieces and both he and Andrew felt that it was doable as an assembly challenge - the descriptive blurb said:

"LunaTIC is another TIC with relatively few pieces, only 5. And with only 2 rotations, it would seem to be a good challenge for a new puzzler. But I think it will also challenge the rest of you too. I like the look of these woods with the darker, richer look to them. Made from Moabi, Padauk, Cambodian Ormosia, Wenge, Monterillo Rosewood or Lacewood."

He said it is a good challenge for a new puzzler! That would describe my skills very well so I packed it into my work bag and off I went. My workload has recently seemed to focus more on big high-risk operations with no breaks during the day giving me little opportunity to play but every time I had a few moments of downtime, I set too. I assume that I am not much different to most of you better puzzlers in that I start out by trying to work out how these pieces will all eventually fit together once complete. Usually, this approach quite quickly produces an awareness of what goes where but with this one, quite a few of the pieces will fit together in a number of orientations. Not very helpful...especially when I have something promising which looks great but then none of the other pieces can possibly fit in that group. Two days go by before I have worked out how the puzzle can form a cube shape! Damn! I am not very bright!

Having found the positions, it is obviously time to work out how they can reach that final resting place. I have previously taken a pair of pieces and put them together and then try to introduce a third and then a fourth and then... This time it fails rather spectacularly! I spend a week (which would be a LOT of hours) trying to find a sequence to introduce all the pieces in order. After trying every order I can think of, even being mathematically rigorous, I decide this ain't going to help me. Either I am being more than usually dim (which Mrs S would not argue with) or Andrew has been a sneaky Bastard! I developed the sneaky suspicion that this one would go together as 2 separate sub-assemblies - but which ones? Was it two 2s and a single or a 2 and a 3? If so, which pairings were the correct ones? Aaargh! Logic and thought do not come naturally to me! I worked on it for even longer than the GalacTIC and after 2 weeks I still had not managed to solve the damned thing. I had a sneaking suspicion that I was on the right track but was getting a little frustrated. I asked Mike, who has begun his own puzzle blog and who had posted about this very puzzle for a little hint. All I wanted to know was the pieces that are used in each sub-assembly. I didn't want to know (at least at first) what the sub-assemblies looked like. He replied very fast with a picture of 2 groups of pieces. I would love to say that this was a fantastic Aha! moment but all it did was confirm that I had been right all along. It also confirmed that I was being particularly thick - I had the pieces correct, the order correct and still could not manage it.

At least I knew that I did not need to go right back to the drawing board. The puzzling continued for another few evenings and suddenly, on Thursday evening, I had a huge Aha! moment...it slid together smoothly into a lovely little (5.7cm) cube.

At last! Nearly 3 weeks of toil in one puzzle!

The final sequence was absolutely beautiful! The fact that there are "only" 2 rotations in this puzzle and that the rotations are not the main challenge does not detract from it in any way - if anything, the new approach was a very nice refreshing change. The voyage of discovery and thought was a wonderful experience. Reading back over Mike's assessment of the same puzzle, we seemed to have gone through exactly the same torture and process - he just seems to be better at it than me.

The cube looks gorgeous in all those wonderful woods and I am torn now, as to whether I should store this in my shelves as a made-up cube or as pieces for future challenges. It won't take long for me to forget the sequence and then I will have a nice fun puzzle to solve as if it is new. DON'T tell Mrs S or she will stop me buying anything else!

MF8 Takes it to the Max...or is it Plus?

Skewby Copter Plus

At the back an edge turn, diagonally a corner turn

Here I am again, fresh from a day of DIY yesterday replacing light switches, sockets and fused connection switches and actually managed to NOT electrocute myself for once! I usually do a batch at a time and test them as I replace them. Sometimes I forget to switch off the mains before moving on to the next and, bloody hell, it hurts when the shock spreads across your chest! Here in the UK, we use 240V which really is quite powerful and, as we say in Yorkshire, it "smarts" a bit! I have set a record of completing a whole day without any pain (apart from the quadricep agony of doing 300-400 squats) - who knows, with this kind of luck, I might even manage to solve a puzzle soon!

Just a month ago, I discussed how I was going to extend my advice to progressing twisty puzzlers to include a special group of new puzzles that consist of two different twisty puzzles combined into one. So far in this group, the amazing Chinese producers have made the Grilles II cube and the 4 Leaf Clover Plus cube. Now the ultimate in this group (at least so far) is the Skewby Copter Plus cube has been released and after an initial period when it was in very short supply, it is now generally available. This puzzle, as the name suggests, is a mixture of the Skewb, a simple deep cut corner turning cube and the favourite of mine, the Curvy Copter. Not just the plain old Curvy copter but the Curvy Copter PLUS which allows a whole lot more movements than the original. The Curvy Copter plus was mentioned in my article on the extreme forms of edge-turning puzzles but has never been properly reviewed by me because of some major flaws in its' design.

Curvy Copter Plus cuts across the centres

Allows swapping centres and corners

The extra cuts in the plus version allow the centres and corners to be swapped which really adds to the fun but the design leaves the protruding pieces sticking so far out that they interfere with further turns and it quickly becomes completely locked up after inadvertently pushing past blockages.

This new Skewby Copter plus can be used as a Curvy Copter plus with the advantage that the puzzle has been fully redesigned such that the overhang bandaging has been completely eliminated. This is the puzzle that should have been released in the first instance - as just a Curvy puzzle it is FANTASTIC! What-is-more the additional Skewb cuts are possible even after all the Curvy Copter moves have been made and, on top of that, it is possible to perform half Skewb turns and then STILL make edge turns! This can lead to an amazing scrambled mess which looks impossible to solve. To show how amazing this puzzle is, I created a video showing how it moves and how to perform a full scramble - it takes a good 15 minutes to scramble it but you don't have to watch the whole thing to get an idea of how it moves.

Having learned how it moves and worked out the approach to get the best scramble - yes, it is always fun to have a twisty puzzle that is so complex that you need to plan the way to scramble it, you end up with an almighty mess that looks almost impossible to solve:

Dear Lord, what have I done?

Despite this horrific appearance, if you are brave enough to buy this puzzle, you really MUST perform a full scramble! It is actually very solvable! In fact, I would go as far as to say that this puzzle requires no more knowledge or fancy algorithms than are required to solve the base puzzles that it is based upon. Yes, if you can solve a Skewb and a Curvy Copter then, with a bit (maybe a LOT) of thought, you can solve this monster.

The first challenge is to get it back to a vague cube shape which means reconstituting the edges into the correct diamond shape like the one above. Then put the corners back into corner places and centres back into centre positions. Just thought alone and logical movements are required. At this point, some of the centres will appear to be sitting not quite flush with the cube surface and they will need to be temporarily taken out of position to a corner and rotated around the cube before placing them back into position and this time sitting flush. Finally, you will have a cube shape - this took me a few hours the first time but now I can do it in about 15 minutes.

Zachary and I worked for ages to get this far

I took advice from my Burmese boy and we had a fun time pairing up the triangular centres with the rectangular centres and the outer rectangular centres (each needed a different technique but no fancy algorithms) to produce complete petal-shaped pieces. At this point, it looks like I was well on the way to solving it but...take note of the diamond-shaped edges...they consist of 4 pieces and none of them matches up. Despite discussing it for a few hours Zachary could not come up with a way to fix the edges so it was back to the drawing board. Ignore the centres/petals, and make the edges first.

Recreating the edges was a huge challenge! Again, there are no fancy algorithms, just a combination of skewb setup moves then Skewb pairing of pieces and Curvy Copter moves to store the pieces - this left me with all of the small dual cloured pieces paired up and in the correct position. FABULOUS! Next to place the single colour diamonds within the edges. I was stuck for a while. A long while! Then I remembered what happens to the centres when making corner moves on a Skewb. A fantastic Aha! moment occurred and I was suddenly able to move them about at will. The hardest part was remembering my setup moves. It took me a couple of days but Zachary and I finally recreated all the edges:

That is one talented cat!

As you can see, the forming of the edges did break up the outer centre pieces from the inner two parts but putting them back together is almost trivial for anyone who understands the jumbling moves and orbits of a Curvy Copter. Another day and my puzzle had been reduced to a simple Curvy Copter solve and away I went...except this happened:

All solved except 2 corners out of place

In the normal Curvy Copter this is impossible - In fact, the "law of the cube" states that it is impossible to have a requirement to swap or move just 2 pieces - there MUST be a third piece that needs to turn or swap position. I will not give it away here but if you think about it, it is quite obvious where the third swappable piece might be and luckily that fix is quite simple without disrupting everything that has been done before. Zachary was very smug when we finally managed this:

Simply brilliant! Both cat and puzzle!

Of course, one has to solve a puzzle several times to prove that it was not simply luck as well as to ensure that other nuances have been found and understood. I scrambled it at least a half dozen times and convinced most of the nursing staff at work that I am crazy when I showed them how it moved and how mixed up it got. On my third attempt, I was rather shocked to find this at the very end:

Just one turned corner

The solution to this is definitely NOT straightforward - it requires a massive disruption of the puzzle and then resolving it with the corner placed correctly. I have subsequently worked out that this can be checked for earlier on during the solve (just after the edges have been created) and fixed before doing much more that needs to be undone.

In conclusion, both Zachary and I think that this particular twisty puzzle is one of the very best puzzles ever to have been created! I would go as far as to say that everyone should own one. It is the Curvy Copter plus that should have been released from the beginning (and if you wish can just be scrambled as one) as well as providing a massive challenge for any twisty puzzler when they introduce the Skewb turns. It is probably not suitable for beginners but I would hope that you would grow your skills into it with time. Just BUY it! It will be appearing in my top ten(ish) of 2019.

Phew - Now I need to solve something else quickly for next week!

Enjoy the rest of your weekend guys and gals.

Cast Trinity - Redux from our Foreign Correspondent

Cast Trinity (again) a new point of view

I have abandoned hope!!!!! I have just spent nearly an hour trying to provide remote computer support to the Mother-in-law which, at one point, included her managing to pull the power cable out of the computer and shutting down everything with a bang and even crashing my remote support software in the process! All is finally working but now I need a gin! A VERY large one!

Luckily for me (and you) my wonderful "missing in action" foreign correspondent, Mike Desilets, has recently been found (he's had a lot going on in his life) and has sent me/us a nice little reprise of a puzzle that many of us have struggled with this year. It is definitely interesting to compare his experiences with mine. This has really taken the pressure off me - work and home life have been overwhelming and I actually don't have a puzzle to review for you this week. If anyone would like to write a guest post then please contact me and we can get something organised. I always edit so don't worry about your writing skills.

Now on to Mike...

Aloha Kākou Puzzlers,

Thanks to a generous research sabbatical granted by Puzzlemad’s senior editor and CEO (Ed - snort!), I’ve gone completely offline for these past many months, ostensibly to work on various important metagrobological projects. Following the advice of a certain academically-accomplished friend, I’ve spent most of this time in a hammock sipping fine scotch (Ed - sigh, I wish I could drink Scotch...I ruined it for myself by drinking a whole bottle as a Med student!). I was assured this approach would lead to great productivity in the long term. As it turns out, I’ve completely squandered my sabbatical and achieved precisely nothing. I did manage to purchase a few puzzles and then solve even fewer. But that hardly needs to be said.

At any rate, I REALLY need to get back on track. This little review signals my intention to do just that. Hopefully, it will give Kevin a slight breather as well (Ed - thank you!!!). These long absences show why I do not deserve my own blog. As always, a heartfelt Mahalo goes out to Kevin for providing me with electronic space, and also for his unrelenting puzzle coverage. (Ed - it is always my pleasure to help and entertain all puzzlers.)

Today we will be looking (again) at a relatively new and widely available puzzle known simply as Trinity. Everyone is surely aware of this puzzle by now, and many readers have doubtless already locked horns with it. You may have even read about it right here at PuzzleMad. I have been away so long, I did not even know Kevin had reviewed it when I drafted this (Ed - I am surprised that anyone reads any of my drivel!). His original post forced me to go back and clarify a couple points, but the review is basically intact. If you are reading this, then the good doctor has determined this second opinion is worthy and of at least marginal value (It certainly is!). Sorry in advance for any redundancy. You’ll find our takes on the puzzle to be pretty similar overall, with perhaps some interesting differences in the final analysis.

As you’ll recall, Trinity is produced by the incomparable Hanayama Company and is the invention of veteran Hong Kong puzzle designer Kyoo Wong. You may know Mr Wong from his previous Hanayama designs, Cast Delta (reviewed here) and Cast U&U (reviewed here). These are a couple of my favourite Hanayama puzzles. Delta is one of only a very few of its class in the Hanayama catalogue. I can’t say the class because that information could definitely be a spoiler. U&U is in a class of its own, unique in all ways, as well as being great fun and challenging to solve. Both offer high replay value and I particularly enjoy repeating the clever movement of Delta. Cast Trinity is a move in yet another direction by Mr Wong and confirms his great versatility as a designer. The puzzle has received critical acclaim of the highest order, having been awarded a Jury 1st Prize in the design competition at the 2018 IPP in San Diego.

A very attractive version of Mr Wong's Trinity
Image from John Rausch's 2018 IPP Design Competition Page

Hanayama’s version of Trinity is cast in a zinc alloy, unsurprisingly, and finished with a bronze-coloured plating. This is not a bad choice of finish and seems to work aesthetically. Behold, however, the trichromatic, ultra-smooth finish of the IPP version. Very beautiful, but perhaps unrealistic to mass produce.

Trinity consists of three pieces which, at first glance, all appear identical. Closer inspection reveals that they are, in fact, quite unique. I can’t be sure, but I suspect that Mr Wong’s original concept called for identical pieces. Identical elements are usually a designer’s first preference because it contributes significantly to design elegance. As it happens, however, creating a non-trivial puzzle with identical elements is a formidable challenge. Cast Quartet is an example of success (review here). So is the venerable bent nail and its countless variants. But regardless of original intent, the final Trinity design comprises three significantly different pieces. Most noticeably, the orientation of one of the “heads” is rotated 90 degrees relative to the heads of the other two pieces. Less apparent are the subtle differences in the little projections running down the “arms.” There are six arms in all, two per element. If you look closely, you will discover that no two are exactly alike. Inspecting the cross-section of each arm all the way to the base of the “U”, you can see how dissimilar each of the pieces really are. These flowy blips and blops are what designers, and more often marketers, mean when they speak of “organic” design. Contrast Trinity’s curvy irregularity with the highly angular, geometric, and vaguely crystalline design of Quartet (for example). But although we generally speak in terms of irregularity, asymmetry, and fluidity of form for “organic” puzzles, I think the term is also an apt descriptor for the design process that creates them (fittingly). For Trinity, one can imagine the designer utilizing, perhaps unwittingly, some kind of natural selection process to get all those little knobules (Ed - interesting word choice!) and gaps just exactly right; trying and discarding different variations, retaining things that work until they don’t anymore, backtracking to earlier versions and trying again. The ultimate objective being to minimize tolerances along a unique, narrow pathway and sequence belied by the apparent similarity of the pieces. It seems to me that a LOT of manual trial-and-error tweaking must have gone into this design. And probably also a small fortune in 3D printing. The end result is an idiosyncratic puzzle whose final design probably could not be predicted from the initial state. The chances of the Trinity design being independently invented again in the span of human existence is negligible. A puzzle like Quartet seems like it could come forth again, either on our planet or some other. Hmmm . . . interesting thought. Kevin, we may need to initiate a separate exo-metagrobology blog. (Ed - erm...I think I might leave that one to you mate!)

What were we talking about? Oh yes! Mr Wong’s Holy Trinity. The objective of Trinity is to disassemble the three pieces and then, of course, return them to the initial state. What could be simpler? Hanayama rates the puzzle at a 6 on their 1 to 6 scale, making it theoretically among the toughest of the line. It is notoriously difficult to evaluate puzzle difficulty and one should, therefore, treat ratings as only a rough guide. They are fun to haggle over and are required ground in a proper review, but they tell you precious little about the intellectual or emotional value of a puzzle. In relation to disassembly, I believe Trinity should probably be a 5 on the Hanayama scale (Ed - I agree). Reassembly is another matter altogether and will receive closer attention later on (spoiler – it's not a 6 either).

Trinity in hand.

Although I have brazenly downgraded Trinity’s difficulty rating, I think every normal person will have a tough time with disassembly. It is not easy at all. There are many different configurations and it is very hard to keep the pieces straight. You will tend to try the same movements over and over if you are not careful. My trick with Trinity and many other Hanayama puzzles is to pay close attention to the stamped words. Puzzle and company name can almost always be found somewhere on Hanayama puzzles; in this case, Trinity is on one element and Hanayama is on another. Using this to keeping track of the pieces may help you to work a little more systematically. It worked for Kevin and me, at least.

The disassembly process includes one major transformation that is particularly difficult to find, and of course, there are many seemingly similar moves that lead only to dead ends. Persistence is the key. You might be lucky (or smart) enough to get it apart in one session, but I would plan for a couple at least. This is a great pocket puzzle to be worked on in spare moments. Although all Hanayama puzzles are technically pocketable, I wouldn’t want to endanger myself with, say, Cast O’Gear (review here). Trinity is smooth, round, and surprisingly collapsible. No poking or chaffing whatsoever.

Despite its recent IPP fame, I was not initially excited about Trinity. This based solely on its appearance. I know that doesn’t sound very enlightened, but that’s the way it is sometimes. Being a Hanayama product, I knew I was going to buy it eventually anyway, so I was in no particular hurry. My first impressions upon playing with it were mainly frustration and confusion, trying to figure out some pattern to the movement. To be honest, it was not a lot of fun at first. The “organic” quality seemed to make the whole thing appear arbitrary, especially when I fully grasped the fine-tuned dissimilarity of the three pieces. The more I played, however, the more enjoyable this puzzle became. This was partly due, no doubt, to increasing manipulation skill over time, but I think that the movement of the pieces also became smoother with play. Trinity seems to wear-in exceptionally well.

They look similar but don’t be fooled.

After much struggle, I finally managed to release the pieces. Once two of them are unlinked, the rest is very simple. Having plenty of experience with vexing reassembly, I paid very close attention to the disassembly process. This represents an uncharacteristically high level of forethought on my part. I subsequently found reassembly to be fairly straightforward, but I, unfortunately, can’t credit my puzzling skills for this. The reassembly process highlights a certain limitation of the design, at least in my estimation. Although I had properly interlinking all three elements, I am almost certain that they are not in the original configuration. I first suspected this because reassembly seemed so much easier than disassembly. Furthermore, I could now quite easily disassemble and reassemble from my particular “solved” configuration. It seems that the tricky transformation largely responsible for the puzzle’s level 6 rating can be bypassed to achieve an alternative interlinkage. This means that according to established PuzzleMad doctrine (I had to sign papers (Ed - I have them stored safely!)), I have not fully solved the puzzle. I have not actually returned it to its correct interlinked configuration, the one it started at, out of the box. Ed - Get to it, man - you have an unsolved puzzle!

Not being able to properly solve a puzzle is nothing new to me. I have a certain shelf in my house that groans under a seething mass of unsolved objects. But I am not so certain I should add Trinity to this shelf. According to the Hanayama packaging, I only need to take Trinity apart and put it back together. But does that mean back to the exact initial configuration (YES it does!), or to any fully interlinked configuration? Three objects, each with a binary set of states (positions), results in eight possible combinations. That should be the math for Trinity. It is unclear to me how many of the eight possible interlinked combinations are actually solvable. I think I have done three. I doubt that I have the patience to test all eight. Ed - Aaaaargh!

The problem for the puzzler is that, with three pieces designed to appear very similar, it quickly becomes unclear what exactly the original position was. I paid attention to the disassembly, but not THAT much attention. And like Kevin, I immediately discarded the box, so I couldn't study the pictures (yes, of course, I could have googled it and looked at the package online, but I didn't, and now I refuse to). Ed - surely you take photos of the puzzle before you play with it? It is tough to try to get back to a state you cannot visualize, and it seems somehow unfair to expect the puzzler to study and memorize the starting state. The solved state of any puzzle should be intuitively self-apparent. In fact, one could argue this as a cardinal design rule. Maybe this quirk is simply a feature of the puzzle, the component that drives it to a level 6 difficulty. I’m not convinced, however. I think this aspect of the puzzle was unintentional. It is highly significant that the original package includes a small note stating, in part:

“A puzzle that interlocks each piece with the two other pieces via an elusive, organic design. There are numerous possible combinations other than the ones shown here, giving you plenty of room to enjoy some puzzling experimentation.”

I think that sums it up. Unfortunately, it means that the puzzle is effectively, for the average Joe or Jane Puzzler, an irreversible process. The difficult state will be partially solved (unlinked) and the puzzle will thereafter almost certainly be returned to the simpler solution state for 99.9% of casual puzzlers. It would take tremendous foresight to observe and document the correct starting state prior to disassembly, and truly exceptional motivation to systematically attempt each theoretically possible configuration. I guess with this blog post the odds of the former increase, to the extent that Joe and Jane Puzzler are reading.

I should acknowledge that Kevin, for some unknown reason, DID know the original configuration and could differentiate that from when he had mistakenly achieved an alternative configuration. It will be no surprise to anyone that Kevin is a more advanced solver than myself, by an order of magnitude (Ed - nope I just take photos and get very VERY lucky!). So perhaps it all makes sense. One commentator to Kevin’s original post mentioned that the pieces if in the correct configuration, will lie more or less flat. This is a great observation, and may very well be true, but I seem to recall at least one of my alternatives lying pretty flat as well. I don’t know. If true, it seems like this would have been critical information to include with the puzzle.

If I have some free time (unlikely), I will try to find that really tricky (correct) solution again. Or maybe just mark each of the arms with coloured tape to keep them straight and then explore some other combinations. The original colour scheme from the IPP entry would have been helpful for this.

Realistically, I will likely leave it in the simple solved state. This makes the puzzle effectively a level 3 to 4 on the Hanayama scale. Puzzles at this level are some of my absolute favourites. They can be tricky and I would guess that for most people, as a general rule, they receive much greater replay than the high-level stuff. The puzzle industry, and I guess a goodly portion of the general public, seems to have a fetish for difficulty. It's a psychological issue that bears closer consideration. Most people I know actually give up on hard puzzles surprisingly quickly. But that packaging language is pretty seductive in the store. As a piece of friendly advice to the novice puzzler, the sooner you get beyond this fetish, the more enjoyable your puzzle experience will be. I do like to solve very difficult puzzles, but that kind of hard-won triumph is just one aspect of the puzzle experience and not the most important by a long stretch. There are cheaper and more enjoyable ways to punish oneself.

This is the part of the blog were I say that the statements of the guest blogger are his own and do not reflect the opinion or policy of Puzzlemad. Especially for a post on a previously reviewed puzzle! These are just my thoughts at the moment. Ask me about it tomorrow and I may have a completely different take. For now, I will just conclude that you SHOULD get a copy of Trinity and have a crack at it. This is a very interesting little puzzle, and as you can see from the above, it has obviously captured my attention.

Buy it for the level 6 initial challenge, keep it for the more accessible level 3-4 replay. Take Hanayama and Mr Wong’s advice and do some exploration. Your discovery process will likely be as organic and unpredictable as the design itself. Back over to you for the wrap-up Kevin...


Thank you so much, my friend! I enjoyed your struggle and your discussion - I am pleased to hear that others also spend a lot of time failing to solve things and that they still enjoy them despite that. I have not yet recovered from my computer support experience. Gin gin gin here I come! Splash!

Enjoy the rest of your weekend everyone.