Sunday, 16 February 2020

TICs so Difficult They Cause Facial Pain

Should They Be Called Tic Douloureux?

My usual expression
There have been a bunch of puzzles that I bought from Brian Menold (the published Professor of Wood) that have caused me serious difficulties! I have spent ages and ages on them and was on the verge of giving up. all know me! I keep trying at many puzzles for months if not years and do even occasionally solve them. I was on the verge of having nothing to write about this week due to lack of time and my failure to solve anything which spurred me on to greater efforts. The end result was that my "Plug face" went from one of gormless confusion to one of utter pain as I concentrated ever harder to try and find the position required for these blasted blocks of wood. Mrs S. even started to laugh at me between her coughing spasms!

I developed a Tic!
She thought that I was in pain with my expression of anguish and the odd noises I started to utter. Hence the subtitle of this blog post. In "Tic Dourouleux", severe pain in the face caused by Trigeminal neuralgia can cause facial contortions/spasms but in this case, I developed facial contortions in response to playing with a series of TICs! Of course, all of them had been designed by the "Master of Brain Pain", Andrew Crowell.

I had been carrying PedanTIC around with me for a few months since it arrived and had almost given up on it when Ali asked me about it at the last MPP. It would seem that he also had been stumped by it for a long time. I initially got it confused with another TIC and told him that I had solved it but after getting home, I realised that it was the one in my bag still awaiting its' Aha! moment. Whilst I felt vaguely guilty for not remembering, it was only for a moment - I am sure that Ali had helped with the mass destruction of my Happiness cubes. It did make me appreciate even more how difficult the puzzle must have been - Ali is an assembly machine...if he struggled with a TIC then it would have to have been VERY difficult indeed!

The PedanTIC had been an entry by Andrew in the design competition in Japan. Brian had offered copies for sale a little after the IPP ended. Brian wrote this about it:
This little gem is definitely a challenge. This is probably similar in difficulty to GalaTIC (previously offered) in terms of moves and rotations. At one point you are making 26 moves to add the next piece! Extra joinery was needed for this one too. Lap joints and brass pins keep everything in order. Olivewood, Black Limba, Okoume, Chechin and Bocote are the woods in these.
I have written about GalacTIC and absolutely adored it (despite finding it incredibly difficult) and could not resist buying something of an equivalent challenge and of course, those woods are totally irresistible to me. I did not expect it to be quite this difficult, though!

Finding the correct position for the pieces was not actually that tough for me and it was quickly obvious that 3 of the pieces would just slot into place at the end of the puzzling. This left 2 pieces to place within the frame. Oh boy! What a tremendously tough challenge it was placing 2 pieces! In my desperation to have something to blog about, I spent hours and hours on this one puzzle over the last 10 days. There are lots of possible moves which I find quite hard to remember and ended up taking notes. On several occasions, I had made an interesting move, tried to find a further move and not only could I not find a further move but I could not backtrack out of the position I was in. Aaaargh! I think that last Sunday after publishing my blog, I had my final breakthrough. I was in a new position and suddenly realised that it ould allow the 2 pieces to interact back and forth repeatedly. There was a lovely dance of the pieces and I had achieved the end position without really understanding how. Quick! Take a photo! Over the next day or so, I worked out what I had done and can now repeat it at will. I am very surprised that it did not win a prize.

At last! That is a damn fine puzzle causing a great facial expression
After that, it was time for the next tough challenge - also designed by Andrew Crowell - the Caged Cubes:

Caged Cube #1 (right) and #2 (left)
As soon as I saw a picture of these puzzles on Brian's Facebook page, I knew I had to have it. I have to buy as many of Andrew's designs as possible and this was stunningly made - I chose the Wenge frame. Brian wrote this about it:
This design from Andrew Crowell adds a twist to his usual "rotational madness". Now you must assemble the cubes inside the frame! Two sets of pieces come with one frame for economic reasons. One set of pieces are all the same wood and the other is a variety of exotic and domestic woods. An instruction sheet is included for the proper way to solve the Caged Cube.
I started on this at work this week. Even assembling the pieces into a cube shape outside of the frame is quite a challenge! After about 45 minutes I managed to find the assembly for the multiple wood #2 but could not seem to find the assembly of #1. I left it with a medical student for about an hour in the hope that it would keep him occupied for a bit whilst I did my boring paperwork. He failed too!

Some corners are missing
Having at least found the shape for #2, I decided to begin the true challenge of putting it inside the frame. The space inside the frame will fit a 4x4x4 cube exactly - there are no protuberances inside but the gap in the sides has a corner piece which means there are no 4x4 windows to fit through. Luckily the cube has several of the corner pieces missing which will allow the pieces to slide about once placed inside the frame. It requires rotations just to get the pieces inside let alone making them interlock together.

This puzzle is the perfect mixture of linear movements and rotations. The challenge is immense and fun - I spent 3 days on it having found myself stuck at several points being unable to insert the next piece inside the frame (let alone get it into place in the cube too). Finally, on Wednesday evening I let out a shout and my facial pain was relieved by the presence of a cube in the frame - yay! I think I even know how to remove it and repeat the process! My photo was taken!

Yeeeeehaw! That was great fun and really quite tough.
Caged Cube #2 assembled
Next, it was on to Caged Cube #1 and it nearly killed me! The interaction of the pieces was so blocked that, for a while, I could only get the 2 larger pieces inside the frame! Every single step of progress with this puzzle was a huge challenge. Getting a third piece inside was difficult which felt like a huge success when done. Then getting the fourth piece inside required me to take everything I had done before apart and start afresh. Ouch! After 2 days I finally managed to get the 4 larger pieces inside the puzzle and could work out how they interact with each other - finally time to add the little L shaped piece - how hard could it be?

Place the L
This is a spectacular challenge! It is quite obvious looking at the surface of the cube that there are 2 places that it can physically fit. The instructions that came with it tell the (by now very agitated and pained) puzzler that the 2 white dots should not be visible on the surface when it is complete. This immediately rules out one of the positions.

It's just under the surface! How hard can it be? Aaaaaargh! I spent 3 days on this and was on the verge of publishing an "I have failed" post when I had the most wonderful Aha! moment of the year so far! No matter which ways you move all the pieces within the frame, you cannot seem to find a position to insert the L piece to allow it to be rotated into place. Everything is blocked. I spent quite a few hours just on this piece placement alone. I even questioned whether I had to dismantle what I had done already and start again.

Then...literally ½ an hour before moving to my study, I found it! OMG! That is a really difficult puzzle! All three of these are also candidates for my top 10(ish) of 2020 - they are simply wonderful! I now feel safe to bring them to an MPP to allow the guys to play!

Incredible! One of my favourites so far!
If you get the opportunity to try either of these three TICs then go for it. They are simply amazing - you will need some time because they are really quite tough. I say that not because I struggled. But if Ali had difficulty then at least the PedanTIC must be a significant challenge!

I cannot wait to see what is coming next!

Sunday, 9 February 2020

Everyone Should Have Some Tray Puzzles...Or Maybe...

Everyone Should Have a Tray of Puzzles?

My Tray of Shame!
It would appear that I have not (yet) committed murder and been carted off to prison! Mrs S continues with the demon cough all night and I continue to have unrequited thoughts of assassination but have so far managed to hold myself back! I have to think of the cats...who would look after them if I killed her and went to the clink? Whack! Ouch! No dear, that's not the only reason I've kept you alive!

Yes, on the floor next to my armchair in the living room I have a tray - it's a nice wooden one which Mrs S insisted on me using rather than spreading out across the whole living room. It is my "tray of shame" - puzzles I have not solved but can't actually put away. I still keep picking up all of these puzzles fairly frequently and getting nowhere with them. Some puzzles have been there for several years! I really need to solve them some time but then, I really need to get better at puzzling! Allard has the puzzling machine (Louis) come over to solve his outstanding failures but I don't have anyone here like that.

The actual subject of this blog is about a group of puzzles that I have very little experience or skill with - tray puzzles. Today, I can report that I have solved a whole series of them and actually enjoyed it. I received a bunch of toys from Tom Lensch late last year and admired them, quickly played with a few and failed dismally so added them to my tray of shame. I tend not to be good at packing puzzles because I have no patience for puzzles that are solved with huge amounts of simple trial and error (especially those that have high numbers of pieces). These puzzles did not have a high piece count and because they were designed by Goh Pit Khiam, I was fairly sure that they would have required a decent bit of thought and understanding with a great Aha! moment. He is a fabulous designer.

Having failed with all three of the "3 in 1" puzzles, I stopped trying until a few weeks ago and had a play with a different set -

This is a series of 5 challenges all marked out by lovely laser etching inside the tray. The aim is to place the start and end pieces as shown in the tray and then place the other pieces so as to create a single continuous pathway to join them together (the walnut squares are blank fillers):

Challenge 1
Challenge 2
Challenge 3
Challenge 4
Challenge 5
It looks easy, doesn't it? I have to say that as a starter for tray puzzles, for someone with very little confidence, this is just perfect! Whilst watching TV with Mrs S, I found solutions to the first 4 in a single evening and struggled with number 5. These are not simply trial and error - it could be solved that way but a little thought certainly cuts down the sheer number of random piece placements required. Having failed for a long time to solve almost anything, this was just the pick-me-up that I needed. The fifth challenge was taken to work and in a quiet moment during a period between operations, I had another go. Yess! After another 20 minutes, I had solved the final challenge and could take another puzzle out of my tray of shame once and for all. Fab! This is perfect for newbies or people like me who need a bit of a boost of confidence.

No, I am not going to show the solutions - it's not so hard as to need to give anyone help.

3 in 1
Next up was the series that had completely beaten me for a couple of months! I just could not seem to think about these in the right way. The 3 in 1 is also designed by Goh Pit Khiam and beautifully made with a Canarywood tray and 3 sets of 5 different shaped pieces - Cherrywood, Maple and Walnut.  Pick a shape and try to insert all 5 of them inside the frame. The tough feature of this is that the frame has a lip and the pieces need to slide under the edge. It is so perfectly made that no piece can be slid inside without lying it flat first. There is no squeezing it diagonally under the edge.

This was the puzzle that I stared with when I first received these months ago...and I completely failed with all three of the challenges. Off it went to my tray of shame and got played with at least weekly without success until well after Xmas. Finally, in exasperation, I took it to work to torture other people with as well as to spend more time with myself. I had a couple of very senior trainees with me who did not help me at all. I was kind of hoping they might solve it for me. I even plugged one of them into Burrtools which told me that it could not be solved - those of you in the know will be aware that that fact is particularly helpful and prevented me spending more time attempting the impossible! As a result, I spent more time trying to place the pieces on the tray whilst it was upside down and ignoring the lip. Only after I had found a possible assembly or two would I then turn the frame back over and try through the limited hole.

One afternoon, waiting for some blood results, I had ½ an hour to play and I suddenly had a breakthrough - I thought about other puzzles by the designer and something went click in my head. Initially, I thought that was my old man's neck going "crack" but it ended with a wonderful Aha! moment. Yess! One down, 2 to go!

The next 2 still took me another week or so - I got my final motivation when someone (I think it was Mike) at the last MPP told me they had solved their copy without a lot of trouble. Damn, I'm thick! I worked on the last ones at work and one of them has an absolutely delicious solution - classic Pit Khiam! The other one came as a huge is solvable by Burrtools and when worked out it is a very nice sequence.

At last, another puzzle series can be removed from my tray! Maybe I can relax and join my boyz in their favourite place, the nice warm conservatory:

Oh, Lord! I want to be a cat!!!!

Sunday, 2 February 2020

Am I Getting Tic'd Off?

Hell NO!

PackTIC #8
By pure luck, I am still here and ready to blog! Mrs S continues to cough her lungs out day and night driving me to thoughts of strangulation and smothering. Despite a move to the spare bedroom and adoption of a pair of rather uncomfortable earplugs, I can still hear her at all hours of the day and night. I have refrained from murder purely because I thought that you crazy puzzlers out there might miss my drivel which would cease if I were to be arrested. Even her laser-burning stare has been weakened and only produces a slight tingling between my eyes.

The question I ask myself and more often that Mrs S asks me frequently is can you have too many Turning Interlocking Cubes (TICs)? Mrs S was moved to ask me that (or something similar) after another box arrived on Friday from Bernhard - a little pre-Brexit treat to myself before customs and duty will be added to packages from Europe.

ElfTIC - needing a little remedial glueing
These should keep me busy for a while unless Mrs S recovers her strength and decides to bump me off!

Obviously, I cannot have too many TICs! Recently I have been fighting with 2 more of Andrew Crowell's amazing designs from the brilliant Professor of wood, Brian Menold and from the Doctor of wood, Eric Fuller. The picture at the top of the article is PackTIC #8 - simply insert 5 pieces into the frame to make the customary 4x4x4 cube. It should be easy right? Maybe for you but not for me! I love these puzzles but even now really struggle with them.

More recently these puzzles have been sent out to fellow sufferers in pieces as assembly puzzles and, despite my lack of assembly skillz, I agree that this is the best choice. I started with the puzzle from Brian because it is a bit smaller and hence possible for me to shlap about to work and back if I get a chance to play in a quiet time. The first out how they form a cube without actually inserting them in the frame. Despite the odd larger shapes, I really struggled to find a cubic assembly. The largest square piece looks like it should be very restricted but, in reality, it can be inserted in several different orientations. Yes, I know I am making feeble excuses but I really am crap at this aspect of puzzling! I blush to admit that it took me over 7 days of trying to find the positions that the pieces need to be in. I usually advise any trainee anaesthetists or medical students that I have got bored with teaching and need to amuse in some way that they should start with the larger pieces and see what

Having finally found the positions it is time to get the cube assembled. I am actually not too bad at this part - it can take a little while but once I know where the pieces should go I usually only struggle a little bit and really enjoy the process. This time it only took me about ½ hour to assemble my cube. This one is rated by Brian as less difficult than some of the others as it has only 15 moves and 4 rotations. I loved it! Very clever and really perfectly made. The fit is snug but not tight - I suspect in the British summer when it gets a bit more humid it may prove impossible without drying it out first but just now it's a stunning challenge. Probably a little tough for an absolute beginner but definitely one to show off and entice someone into the hobby.

Assembled it! A lovely puzzle. Just the right difficulty.
Next up I moved to BioTIC, the TIC that turned Eric off to these puzzles!

BioTIC is one of the most difficult TICs that Andrew has designed - Eric described it like this.
"BioTic is a BEAST! 28 total moves and nine rotations are required to solve it."
I knew I was going to buy this because, well, it's a TIC but, with a description like that I was slobbering all over my keyboard! Sorry for that image! It arrived in December and after a little fiddle and a photo, I put it down to develop my cold and feel sorry for myself.

The puzzle is made from a gorgeous dark Sapelle and Walnut pairing and is seriously chunky (considerably bigger than those made by Brian) - this was to ensure that it would withstand the complex movements required to get the 6 pieces inside the frame. Two of the best puzzlers in the world, George Bell and Goetz Schwandtner wrote rave reviews on the page and said how much of a challenge this is. I decided after reading their reviews that I should solve something else first and started on the PackTIC #8.

Flushed with my success, I moved onto the BioTIC and BAM! hit a wall! Looking at the larger pieces and working out the theoretical placements proved impossible! I usually can work out where pieces will go by playing with them one piece at a time and the frame. This allows the possible placements to be discovered and helps visualise where other pieces might go. With this puzzle, the biggest piece fits around the outside in several places and is not helpful. Moving to the next pieces, I couldn't find a way to get them inside the frame at all! Gulp! After a week, I went to Burrtools to at least show me the placements. I know it is a sort of cheat but only a tiny part of the challenge is the positions.

Having seen where everything needed to be, I started on the assembly and LORD, that was almost impossible! I could see that 3 of the pieces just slotted into the frame at the end of the assembly but the 3 more complex pieces were going to be an enormous challenge. What order should they go in? How the hell do they even go into the frame? What is the meaning of life? Oh yes, that would be 42! I worked on this for days and days and days and had a huge AHA! moment when I managed to put the largest piece inside the frame and manipulate it into its end position - phew! Next. I need to place another large oddly shaped piece with the first one getting in the way all the time. This took another few days and even Mrs S looked up from her coughing at my exclamation of success. Finally, the last piece needs to be placed and it is really really blocked. Another day or two required and I got it!

OMG! What a challenge!
This puzzle is incredibly tough - the sheer number of rotations is part of it but the main difficulty is the complexity of the pieces and just manipulating them into the frame. It is wonderful and is a candidate for the puzzle of the year 2020 already! Mr Crowell, you are a genius - please keep designing them. Am I getting TIC'd off? Absolutely NOT!

If you get a chance to play or buy these puzzles then don't hesitate - they are fantastic. Brian still has some copies of the Cluster puzzle (another non-cubic rotational design by Andrew) that I reviewed here. Don't miss out - just because it's not a cube, don't underestimate how much fun it is.

I have had a little chat with Eric after I placed my review on his store and he is not planning on making more TICs just now because he feels he cannot make them well enough to be played with and also make a profit without charging a fortune. I am sure that you understand his reasoning, he has an expensive lifestyle to finance as well as several dependent staff to pay. He has not completely ruled out making more in the future but not for a while at least. Here's hoping he does make more.

Sunday, 26 January 2020

The Rua Required a Transformation of my Mind

The 12 Axis Dodecahedron aka the Rua
This might be my last ever post on the blog as I might be arrested and convicted of a murder within the next few days! I have passed on my very minor cold to Mrs S and she has incubated it and multiplied it until it is probably a mix of She-bola/SARs/Chinese coronavirus along with pneumonic plague (even the rats have been seen running in fear away from our house. The sound-effects have been truly grizzly here in PuzzleMad HQ and the incessant coughing has been impairing my beauty sleep. Those of you who have met me, know very well how much I need more beauty! I am on the verge of holding a pillow over the source of the coughing which my years of airway experience tells me is probably not a good idea and might end up with a visit to "Her Majesty's Hotel", Broadmoor. So on to the next/maybe last puzzle review...

I figured it was well past time that I wrote about a twisty puzzle. I've not really had much luck solving them recently and finally, after a change in my mindset, I finally solved one that I have been working on for 9 months on and off. Pictured above is the 12 axis dodecahedron by Lanlan which should really have been called the Rua, the original name given to it by Matt Shepit in 2008. Many people had wanted a copy of this puzzle but could not afford the massive prices that Shapeways had been charging to make one. This is a Dodecahedron like so many other puzzles I have reviewed before but unlike most of them, this is a rhombic dodecahedron which completely changes the approach. We were all very surprised and delighted when LanLan produced this although a little mystified why they had ignored the original name.

I bought my copy from the HKNowstore along with a bunch of other puzzles at the same time way back in May last year and immediately set to looking at the turning and wanting to see if there were any easy algorithms. It certainly is nice and smooth and quite quickly you can see one of the quirks of the rhombic geometry:

A single 180º face turn
A partial face turn allows it to be jumbled - 2 turns only
The rhombic face shape means that a 180º rotation of a face keeps the puzzle shaped like a rhombic dodecahedron, however, it is possible to turn a face a partial turn to align the edges of adjacent sides and then turn the next-door face which creates a very odd shape - effectively the puzzle becomes jumbled as pieces are taken out of their normal orbits.

This frightened me to death so I quickly undid it and made sure that it stayed in true shape for the majority of my puzzling. As is usual I did sequences of 2 face turns and three face turns (L, R, L, R or L, R, U, L, R, U etc) and discovered a nice feature that allowed me to swap about 2 pairs of the small inner triangles. I thought that this might come in handy later. I then tried a few turns of the faces to see what I could do with the corners and, as usual, got lost and scrambled it by accident:

"Just" a 180º scramble
This happened in June and I have been playing with it ever since! I think I have carried it with me everywhere since then and taken it out to play frequently. You guessed it...up until now, I have gotten nowhere with it! My main reason? I am seriously not very bright! Apart from that, I have been trying to solve it either layer by layer complete or layer by layer corners first and just could not work it out at all.

A week or so ago I tried again and for some reason decided that I should practice my counting (definitely not very bright) and a thought suddenly occurred to me (maybe not so sudden if it has taken 8 months!) - maybe I need to hold the puzzle a different way and think of it as a different shape? What made me think about this? There are 2 different types of corners to the puzzle. There are 4 colour corners (6 of them) and shallow 3 colour corners (8 of them). What does this remind you of? No? Well, it took me a long time as well! If you think of the 4 colour corners as centres of a cube and the 3 colour corners as true cube corners then suddenly a change of image might occur to you. This puzzle is a shape transformed cubic puzzle where the faces that turn are actually edge turns of the cube, like a helicopter cube or curvy copter. In particular, it seems this puzzle is a shape mod of the Curvy copter 3. Have a look at the pictures below to visualise the change of perspective:

Old face up perspective
Turned on its corner
In the right-hand picture, notice that the 4 colour corners are now in a centre position and we can see the top four 3 colour corners which are in the position where a cube's corners should be. The new centres each have 4 small triangles around them and when a face is turned 180º, the 2 corners and centres swap over. Think of this like the curvy copter 3 below:

Notice the centres with 4 triangles around them
The Rua is missing the petal-shaped pieces
Having finally had this wonderful epiphany, I set to attempting a solve. Starting with "corners" aka 3 colour corners first. This was now easy! Until I attempted to place the "centres"! It would appear that the moves of this puzzle MUST be done in a strict order to prevent ruining the orientation of the centres (after all it is effectively a "super-cube". After I ruined it a few times, a little experimentation revealed my error and I just needed to keep track of the order I turned the faces for each algorithm.

I also discovered that in my first attempt using this approach, there was a sort of parity. I managed to create it in such a way that I had either all centres correct and 2 corners needing to swap or vice versa. I spent a day trying to swap things around in multiple directions until I had another epiphany...I had placed the corners in such a way that I had placed a face in the space adjacent to where it was supposed to go. Thinking of the cube above, the centres are not fixed and I had inadvertently swapped the red and the blue colours which ensured the puzzle could not be solved.

I resolved the corners on the correct faces using the methods required for the Curvy copter and using all the same algorithms (but needing concentration to keep my head right) and I was left with only the triangles to place. Recalling my simple 4 or 6 move cycle that I had found initially 9 months previously, I tried to use it to move the triangles where they needed to go bloody way was that going to work! Time to get my Curvy copter 3 out again and play. I had been very impressed with that puzzle all those years ago because it was one of the first puzzles where I had been able to design my own commutator for it.

Cycling triplets
Swap around the front 2 triangle
An L, R, L, R sequence cycles the three highlighted triplets as shown. If we do a B, F, B sequence it splits off the top front triangle from the triplet and replaces it with the one from below. Undoing the 4-move and then the three move sequences, in turn, creates a 3 cycle of triangles. This is exactly what I found in the Curvy copter 3 and worked perfectly for the Rua.

I have a "simple" 3-cycle!
This fun and surprisingly easy sequence can be used with various setup moves to finally solve the puzzle. Yessssss! At last! All it took was to transform my mind into a different orientation! It should have been easy as I have a very small mind and lots of space in my skull for twisting it about. I obviously need more practice.

If I had read the twisty puzzles museum post first then I would have had much less difficulty with this one - the description says the following:
"Rua is a face-turning rhombic dodecahedron and has therefore an axis system identical to an edge-turning hexahedron. Like all puzzle with this axis system it allows jumbling moves."
Knowing this would have made a HUGE difference!

Finally, it was time, under Derek's insistence that I perform a jumbling scramble. Oh boy, it gets very locked up very quickly! I suddenly wished that I hadn't done that:

Oh Crap! What have I done?
Movement becomes very difficult as the pointy triangles impinge on the movement of the edges. Luckily, it only takes a bit of fiddling about doing random movements to get it back to rhombic dodecahedron shape and then the solution to the puzzle is unchanged. It's worthwhile doing the full jumble just the once to say that you have done it but after that, it doesn't add anything to the process.

Overall it is a really fun puzzle and much less of a challenge once I had my perspective shift. What I now need to get is a copy of the Master Rua which SuperAntonioVivaldi showed off on his YouTube channel. Unfortunately, at nearly £300 that is not coming any time soon!

I can heartily recommend this wonderful head twister to all of you with an interest in twisty puzzles.

Now I am off to smother my wife with a pillow!!!! Aaaargh!

Sunday, 19 January 2020

A Great Tonic For When I'm Under the Weather - Dominola

Another vintage puzzle - Dominola
My good friend and the singular PuzzleMad foreign correspondent, Mike Desilets, always comes up trumps for me just when I really need it. I seem to have been poorly for quite a while (12 days and counting) with a spot of puzzler's lurgy that just won't go away! Mrs S is complaining about the 'drowning in mucus' noises at night and keeps asking why I feel the need to gargle with it when she is trying to get to sleep. I, of course, am completely unaware of my horrific sound effects and have to add being woken up multiple times a night by being kicked or shouted at to my woes. Needless to say, puzzling has been a bit tough and every time I settle down to work on something I lose consciousness before I get anywhere. Just as I was getting desperate to find something to blog about, Mike dropped me another wonderful email about an old and interesting puzzle that he has been working on. Over to you Mike...

Aloha Kākou Puzzlers,

This time of year I, like you, fantasise (Ed - we are NOT getting into my fantasies here!!!) about all the puzzling I am going to get done in my time off. That never really happens. Instead, new puzzles flow into the house at an accelerated rate and the backlog grows (OMG! Tell me about it!). I also continually get hung up on certain puzzles that catch my interest. Many of those end up as blog posts, and today I have one such for you. Once again, it isn't the puzzle, per se, that has me hung up, but rather the full family of puzzles it belongs to. We’ll get to all that shortly.

Today’s puzzle is called, rightly enough, Dominola. Not to be confused with my editor’s current Dominola, Mrs S. That is a completely different blog post for a completely different kind of site (We are NOT going there! She won't let me). And you’ll have to pay for it. I am of course referring to the domino-based puzzle designed by Eric Everett way back in 1935, or so. The extent to which it can be considered an original design is open to question, and we will get to that further down. My usual slapdash patent search turned up nothing on the puzzle itself, but the phrase “Dominola, unique puzzles with many solutions” was duly copyrighted on June 10, 1935. Mr Everett then applied for a trademark on the name DOMINOLA in a distinctive if unimaginative san-serif font on June 29, 1935. The name Dominola (in a different font) had been previously registered as a trademark by one John M Haddock on April 7, 1903, for a card game. It appears this earlier trademark had expired by the time Mr Everett applied. Unlike patents, trademarks are considered “abandoned” under US law after three years of non-use. Said use, must be continuous, ongoing, and demonstrable, otherwise the mark goes back into the stew pot. 

Dominola packaging.
Eric Everett’s Dominola puzzle consists of a complete set of double-six dominoes and a two-sided playing board. A double-six set consists of 28 tiles, 7 of each number. In keeping with the times (see Embossing Company post from way back), and likely the target price-point for the puzzle, the tiles are made of embossed wood. If this post makes you want to add a set of dominoes to your collection, I recommend an antique set of bone over ebony with brass spinners. They seem to be plentiful on the British and European Ebays and are reasonably priced considering many are over a hundred years old. Anyway, wooden tiles are quite fit for Dominola and the coloured pips add a nice splash of, well... colour.

Dominola instructions - no surprises here.
So you already have a bargain with this puzzle, in that it comes with a full set of dominoes. You can both play dominoes AND solve Eric’s two puzzles. That’s right, two, because the playing board is two-sided, with a different puzzle on each. Look at the pictures below if you don’t believe me. Now, the objective of the puzzle is to lay down the tiles, ends matching of course, in such a way as to complete a continuous circuit. In essence, this is an edge-matching puzzle. Although the dominoes have “numbers” of pips, there is no mathematical element to the solution. The pips could very well be replaced by symbols or just colours for that matter.

Lack of maths does not mean the puzzle is easy. It actually requires a respectable amount of work. Why? Glad you asked Kevin! (Hahaha!) Picture a simple tile rectangle. It would be pretty easy to make this circuit with the dominoes. Plenty of solutions and only one constraint, continuity. Now picture a figure-eight; one crossing. All of a sudden you have a constraint, though a minor one, and thus slightly fewer solutions. Add more crossings and/or interconnections and you quickly introduce all sorts of complicated co-dependent constraints, and the number of solutions drops rapidly. These new constraints typically involve three, four, and even five-way linkages of same-numbered pips. It's an interesting and underappreciated fact that all of the tiles in a pip-number set are not equal. The double-sided tiles (1-1, 2-2, 3-3, etc.) are, in a sense, unique in the way they function. When you are working on your homework assignments (below), you’ll quickly discover that the placement of double-sided tiles requires especially careful consideration. (Homework? But but but...I'm poorly!)

The complete double-six set provided with Dominola
Mr Everett does offer the puzzler an olive branch of sorts, in that four tiles are pre-set on each board. This gives one a starting point, at least. In the case of the purple side, the fact that two of the pre-placed tiles have one pip is highly significant and immediately rules out certain arrangements. There is still a lot of work to do, but the pre-set tiles at least stimulate thought in an analytical direction, or they should anyway. That becomes the real fun of this puzzle.

I must confess, I have never been a huge fan of edge-matching (Me neither). All too often it is simply a seemingly endless trial and error search tree process; not much to think about other than keeping track of what you’ve already tried so you don’t spin around in circles. I had that mindset and expectation when starting out on Dominola. I quickly realized, however, that domino tiles are not anything like the conventional three, four, or six-sided geometric tilings we are used to. They have, as you can see, two ends, each of which can form three potential connections in as many cardinal directions. They are fundamentally “end-matching” if you will. While most edge-matching puzzles build into a solid shape, domino tile end-matching forms open patterns (and also shapes, if you want to take the maths approach). This makes them intrinsically interesting to a recreational aesthete such as myself. You have to admit, Mr Everett’s designs are quite eye-catching. But more importantly, the properties of domino tiles, and thus how they match, opens up opportunities for true problem-solving.

Purple side
Orange side
So solving Dominola involves more than just trial and error. But don’t worry, If you are a lover of trial and error, there is still plenty of it. Despite what I just said above, I could not find a method to fully “solve” the puzzle through algorithm or artifice. I still think it is out there, I just didn't have the patience or smarts to figure it out before resorting to brute force.

Orange in play.
There are certain rules that should be helpful, though. For example, given the layout of Everett’s purple board, every tileset (7 tiles of a given number/colour) must necessarily connect its tile ends in patterns of either 2-2-3, 5-2, or 3-4 (3-4, for example, means 3 interconnected tiles connected in one place and 4 in another). These are the only possibilities, and they apply to all seven tile sets. So if you find you have laid down, say, two connected tiles of a certain type, you cannot then lay down four connected tiles of that type, or else you will have one lone member leftover with no partner. You would need to go with a 5 or a 2 and a 3, assuming the circuit allows for these. Keeping this in mind, and constantly checking against the three fundamental set patterns, you can prevent yourself from creating some clear dead ends. It should allow you to select out a large number of losing arrangements as you work a certain approach. That said, there are still an infuriatingly large number of ways to get it wrong, even avoiding the obvious dead ends, and you won’t often find out until you get to the last few tiles. (My goodness that is a complex thing to think through!)

Consider, if you will, the perplexing lattice design below. I concocted this mostly for the cool interior-exterior optical illusion. I also thought that it would make a challenging puzzle. But is it actually solvable? Take a moment and analyze; see if you can figure it out in principle, without laying down any tiles.

Mike's Lattice Challenge.
The way to figure this one out is to first break the puzzle down into its components and analyze those first. You’ll notice if you stare at it long enough that the lattice is composed of two equivalent halves, mirror reflected. Looking at either instance, you will also eventually see that the layout necessitates a string of seven connected tiles (six is technically possible, but this doesn't help the situation at all since it leaves an orphan). You can arrange a seven-string once on a layout, but you cannot do it twice (which becomes increasingly necessary with two mirror lattices) unless the two strings are interconnected. There is one way to connect the seven-strings of each half, but it creates an insoluble dead-end. That explanation probably won’t make sense until you dig into the problem. The bottom line is that this lattice cannot be completely tiled, and more importantly, that you do not need to systematically attempt every possible tile combination to know this. (I'm pleased that you told me that! I am fairly certain I would have spent many hours trying it!)

As my indefatigable editor and I have said to you many times, Puzzlemad is a full-service blog. No, we won’t check your car’s oil level, but we do enthusiastically support our fellow travellers. Thus, we present you with a free digital copy of Dominola for your use and enjoyment. The purple side is downloadable here and the orange side is here. I drafted these on an 11x17 board, so use your best judgment when printing them out at work. I used the Dominola tiles as a gauge, and they are a bit smaller than modern standard tiles. Fiddle with the enlargement/delargement (ed - is that a word?) settings and it should work out. You get what you pay for, so please don’t bother contacting the Puzzlemad customer service department. It's Mrs S’s mobile. (Whack! Ouch!

True metagrobologists are by this point wringing their hands and scowling mightily.  Of course, they are correct, Eric Everett did not invent this type of puzzle, and it is less than certain that he even originated the Dominola designs. I haven't seen them anywhere else, but of course, I have a meagre puzzle library. Those of the readership that have shelves and shelves of puzzle books, old ones especially, please feel free to research this issue (Ed - I actually have almost no books of puzzles at all). But regardless of Dominola design origins,  the idea of making symmetrical circuits using dominoes has been around a very long time, probably nearly as long as dominoes themselves.

One puzzle book that I do own is Slocum and Botermans’ The Book of Ingenious & Diabolical Puzzles. It contains a selection of eight historical domino circuit puzzles (see page 59). I haven't tried all of these yet, but they look very interesting. The important thing to remember is that each one has its' own dynamic. They do not all behave the same way, and rules you might have developed to help you solve one will not necessarily be useful on another. You really have to think about each one on its own terms.

Since my decades-old copy of Adobe Illustrator CS3 was all warmed up making the Dominola boards, I went ahead and drew the Slocum and Botermans set, just for you. FULL service, my friends. Now you have no excuse at all. Tramp out to the corner market and order up a double-six set and some chips get puzzling. These eight designs will unquestionably keep you busy. Download them all in a single zip file from here.

Although none of the puzzles in this post requires arithmetic, there exists a whole array of domino puzzles that do. If you have that Slocum and Botermans book I’ve been referring to, you can study several pages of them. I would also like to make special mention of a third sort of domino puzzle. This is the use of dominoes to perform simple computation. Here’s a quick link to get you started - a half-adder from 2007. I think others have improved on it since. This will be VERY interesting to a certain narrow segment of the puzzle community.

Even the great Sam Lloyd had something to add to the Domino puzzle sphere - he published an article which you can read below:

I hope you have good eyesight!
To wrap up, I found Dominola, and the whole family of domino tile-matching puzzles, to be both fun and challenging. They go a step beyond any edge matching puzzle I’ve done previously, in a good way. Eric Everett did what many puzzle producers do, take an existing idea, tweak it a little, and package it in a way that is attractive to consumers. It is a great puzzle to own for the collector, although I suspect there are not many copies floating around, even fewer in good condition. More importantly, Dominola led me into the larger, deeply historical world of domino-based puzzles. This has not only caused joy (and frustration) but has saved me a significant amount of cash. If Mrs S finds out about this, I think Kevin will also save a lot of money, and also curse me to the grave. (Luckily for me, she doesn't read any of my drivel at all - otherwise, I am a dead man!)

Ok boss, bring us home...

My goodness! You have completely opened up a new sphere of puzzling to me! I had never even contemplated dominoes as a source of puzzles! I will need to get myself a nice set and have a play once my post Xmas finances have settled down a bit. The nice vintage domino sets I have found on eBay are quite pricey!

Thank you so much, Mike, as always, for helping me out in my hour of need! I will hopefully be back to full strength puzzling very soon or Mrs S may well euthanase me with her bare hands and teeth!

I hope that this has been of interest to all you puzzlers out there? I certainly found it quite fascinating and will certainly be trying some of these challenges myself.

Follow up - the reference given above to Slocum's book was an error - it should have been to Van Delft and Botermans' Creative Puzzles of the World. The page numbers are correct. Sorry if we confused anybody.

Sunday, 12 January 2020

Juno's Ring Case

But Why Is The Ring Outside?

Ring Case by Junichi Yananose
Yukari announced that there was going to be a couple of new puzzles released on Boxing Day and with the description of the puzzles posted I knew that I would be spending my money and hopefully Mrs S wouldn't be watching me! Quite a few puzzlers that I had been in touch with were eagerly awaiting the day and several of them failed to realise that Juno lives in Australia and is thus 12 hours ahead of the UK and 17 hours ahead of the US. So whilst watching TV on Xmas day and idly surfing on my iPad, I suddenly noticed that the new releases had gone live and BAM! I had 2 new puzzles on the way - Mrs S had not even noticed me move my fingers...I blame the champagne for that!

A nice big box cleared customs quite quickly (after a ransom was paid) and the lovely little beauty above was revealed. It is apparently designed to hold a ring - hence the name Ring Case. I showed it to Mrs S and suggested that we put one of her nice rings inside for safe-keeping and to give her a nice fun challenge if she wanted to wear the ring. She stared at me for a few seconds and suddenly I lost consciousness! A few hours later when I woke up she told me never to blaspheme like that again - she suggested that certain pieces of my anatomy could be put in the case - she would be happy to put it/them through a mincer to help with any "fit" issues! Gulp! I decided against going any further with my foolhardy idea. I also had a nice look at the other puzzle in the box, the Unbalanced 6 board burr which I could not resist at the same time:

Unbalanced 6 board burr
A ring found in the packaging
During quite a bit of 2019, "She who frightens me to death" has frequently complained about me not collapsing down the boxes I receive and leaving a pile of them (with packing peanuts or bubble wrap) in our dining room/storage area. At one point she got quite annoyed and after a series of Whack! Ouch!s I took them to the recycling and vowed to keep everything tidy in the future. Thus I took Juno's box and emptied out all the bubble wrap and dismantled the box and put it somewhere to be disposed of. Whilst flattening the bubble wrap I found a small bubble wrap envelope which looked and felt odd. I unfolded it to find a very nice looking (but probably fake) pink sapphire ring - it was probably a lot cheaper than the lovely ring with a similar stone that Mrs S received when my mum died. I was perplexed! Why is there a ring outside the ring case? Very odd indeed.

The lovely puzzle is made from Victorian Ash (main body) with side panels of Jarrah and the lid a combination of American Rock Maple and Jarrah (apparently inside there are more pieces made from Burmese Teak, Jarrah and metal. It really is a very attractive thing and a nice size at 81 x 81 x 53mm. It actually would be perfectly at home in a woman's jewellery collection.

On Facebook, a few people who had already received their copies had enjoyed opening the case but were struggling to remove the ring (which I already had) so I set to exploring. I realised that the lid would eventually slide off revealing a, dare I say it...cavity. But it is a case and NOT a box! There is almost no movement in the lid but some interesting things happen to the feet. In fact, the things that happen to the feet depend on the orientation of the puzzle when you manipulate them.

Over about 30 minutes I played with my feet and made some lovely fun discoveries. It is absolutely beautifully made - everything works well with the clever use of magnet in places and I suddenly managed to slide the lid back part way only to have it stop dead. Finding the move to remove the lid completely was what I thought might be the final step. It certainly stopped me dead in my tracks!!! I suddenly realised why the ring had been on the outside. Juno has had another laugh at my expense! Apparently, the Ring case IS a box - how do I know? Because there was a loaf of bread in there!

Aaaargh! Juno made me a bread ring!
I roared with laughter at this! The joke that was started by George Bell has continued for 2 years now and is a fantastic little source of fun between Juno and me! He has actually created a little loaf of bread and stuck it to a ring shank - even Mrs S found it funny!

Despite having gotten this far, I could see that the ring was still held captive by a steel rod. I needed to find a way to shift that rod to retrieve my precious ring. This step took me a good 20 minutes extra and was very unexpected and exceptionally clever. It involves a mathematical object which I particularly like. Eventually, I had my box/case fully solved:

Which should I put back inside?
The sequence of moves that are required is very lovely - it is not a really difficult sequential discovery puzzle, taking only about an hour in total but it is great fun and very nicely made. It genuinely could be used to hold some jewellery even though Mrs S declined - I put both rings back inside:

Both held nicely by the rod
I have enjoyed solving and unsolving the puzzle many times over the week. At £95 it is a bargain and I think that those of you who have not bought it should do so quickly - there are 14 left as I write. This is a sequential discovery case/box (grrrr!) with anything from 172 to 348 steps to completely solve and made from beautiful woods. Once finished, you will have 8 separate pieces plus several held captive in the case. Below is a photo of all the pieces - it is hidden behind a spoiler button - DON'T click the button if you don't want to see all the parts - you have been warned!


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