Saturday 19 April 2014

An N-ary puzzle to N'd all other N-ary puzzles!

So exciting - N more N-ary puzzles!
Over the last 2 years I have developed a bit of an addiction to N-ary puzzles. Yes I know I have developed an addiction to ALL puzzles but I really am trying to narrow down my interests a little bit. I'm struggling but promise that I'm trying really hard. Certainly one group that I am particularly keen to get more of, is the group that are mathematically based - i.e. they are based on Gray binary code.

Ternary Burr
I have written about a few of them before - One of my all time favourites is the Hexadecimal puzzle which is still available and beautifully reproduced by Dave Janelle of Creative Crafthouse - I wrote about it here. It is particularly fun because it has several challenges to keep you going over a long time.  Here I wrote about the Binary burr, recreated by Eric Fuller from Bill Cutler's original design and along with Goh Pit Khiam's amazing Ternary burr which Eric also reproduced a few months later - these were also amongst my favourite N-ary puzzles, partly for the craftsmanship, but especially because they combined my love of burr puzzles with N-ary puzzles. So you see, I am particularly keen when one of these beautiful logical puzzles also combines aspects of another subtype too. I did mention a while ago that I had received another small [sic!] batch from Wil Strijbos - they were the latest designs from the amazing Jean Claude Constantin and I am really pleased to say that some of them are also available from Puzzle Master too.

Of course, some of the puzzles in this group are boxes, but many of my puzzle friends know that I don't collect boxes and so would never have one of the magnificent Kcubes in my collection! Would I? Of course not - I have 2 of them! ;-)
The KCubes MMMDXLVI box has such a small cavity that I decided that it wasn't a box and thus I was allowed to own one. It requires 3,546 moves and is made of Kingwood, Tulip wood, Mun Ebony, and brass inlay with Tulip wood. It usually takes me about 90 minutes to open it because I invariably get lost during the process. Mrs S has admitted that it (and it's smaller brother the K419) are so gorgeous that they can remain on show in our living room on the central coffee table.

I am not the only one to have a huge addiction to N-ary puzzles - my very good friends Michel and Goetz often communicate with me about these particular puzzles and I do get informed of new ones often before they hit the market and then we discuss them a little without giving too much away. For more information about this fascinating group, you really should visit Goetz' Compendium of N-ary puzzles - he has analysed many of them in great detail and also have a look at his treatise on the Kugellager puzzles here - these pages are a tremendous resource for us all.

Having received so many at once I did ask for advice about the order to start them in and I started working my way through them. The first one that I played with was probably the most attractive of all.

This magnificent puzzle is called Uhrwerk and it is absolutely huge at 17.3x17.3x1.8 cm and despite the huge complexity of the construction is 'just' a ternary puzzle requiring a mere 160 moves at which point one of the ball bearings can be removed. It is quite fragile and not suitable for children but is stunning and fun to play with. You get into a nice rhythm and it's lovely to see which ball moves at each change of direction.

Later I moved to something quite a bit harder and certainly more unusual - the Seestern puzzle is a record breaking 11-ary puzzle consisting of a large ball bearing in a track which runs through 3 layers. Each layer must be manipulated simultaneously to allow the ball to roll around the track - it goes back and forth many times and if you don't pay attention or stop for a rest and forget where you were then many more than expected. The total number of moves on this one has been calculated as 1330 but it feels like a lot more due to the micro-adjustments needed continuously during the solve. It is 16 cm in diameter and 1.7cm deep, and a deep red colour. Luckily it has a reset hole for just in case you don't fancy doing it in reverse! I, of course, did it both ways because I'm a glutton for punishment.

So I did promise a review of what I consider to be the best N-ary puzzle of them all and so here goes - my own favourite from this group has taken me many MANY hours to solve and several highs and lows! It meets my criteria for a good puzzle - it is attractive, well made, logical and combining 2 different genre's of puzzles, it gives twice the fun. I introduce for you, the Labynary puzzle by Jean Claude Constantin. This one is available from Puzzle Master as well as from Wil Strijbos.

This puzzle is, like the others, made from laser-cut wood and acrylic and it also has a very small ball bearing inside. It is circular with dimensions 13.6cm diameter and 2.6cm thick. Puzzle Master rate it at the top of their difficulty scale as a 10 (Mind Boggling) which is absolutely correct. At the beginning the ball bearing lies inside a track cut into the puzzle just to the right of the bottom left screw head. The aim of the puzzle is to remove this bearing. Looking at each of the corners you can see an exit hole so it would initially appear that the aim is to navigate a maze to one of these holes. The bottom left hole is a specially designed reset hole so you don't need to backtrack to the beginning having solved it. 3 exit holes would appear to indicate 3 challenges! This was originally what I thought but my excited hopes were dashed - this is one long puzzle as only 2 holes are reachable and one is a false ending! Goetz states that this is a Ternary puzzle but I have no idea how he can tell!

The front consists of 4 horizontally oriented sliders which can only move if the pins that stick through them are lined up with the cut out paths. The back consists of another 4 sliders but they are arranged vertically. These can move up and down, but again, only if the gaps in the top boards are in the correct place. Sounds fairly easy so far doesn't it? Well not so fast, young Paduan! At the extreme top, bottom, left and right are independent sliders that act purely as extra blockers and even locks of the sliders and some of them are joined together meaning everything needs to be positioned in the right place at the right time. There are a number of holes and grooves cut into the boards on the front and a few more cut into the back parts - these holes and grooves form parts of the maze track that the ball needs to navigate.

Reverse of Labynary showing maze tracks and blockers
Looking at the reverse shows how some of the locking mechanisms work and also shows how the maze parts don't meet up. So we have an N-ary puzzle, a maze that is disjointed and an unknown exit point. All we need now are dead ends!! Yep!!! Got them too!!!

When I first started to play, I had not had the benefit of a kind blogger telling me what the aim was - I had to work that out. Initial movements showed that the ball bearing moved up a slot and quite quickly I was able to extend that slot my moving a slider - the penny dropped! So where was the next part of the track for me to jump to? There are choices - so choose well. Having made your choice, it is time to actually make the pathway and now comes the N-ary part of the puzzle - as you move further from the start point it requires more and more complex series of moves of multiple sliders and blockers to get the paths to form. I, of course, chose wrongly and set out along a nice fun route. I was full of hope and happiness only to have it dashed by a dead end when I was so near and yet so far! So back I went and had to think of where there was an alternative pathway. It wasn't so obvious at all which was why I had missed it the first time.

I worked and worked on this over about 3 weeks (probably 20 odd hours or more) and got to a point where I was finally understanding the system. But it never got to the point where I was able to just blindly and rhythmically make my moves as you can with many of the other N-ary puzzles. You need to break each section into small subsections and solve them one at a time without forgetting what you were trying to do! This, I found very hard and often reached a point where I had no idea what I was trying to achieve or why I had just done a sequence. Each time it's important to sit back and take stock of the aim. Suddenly I was sooo close and then nooooooo! Hopes dashed yet again! Now where? Backtrack again and Aha! (We puzzlers live for that Aha! moment) Another pathway I had not noticed earlier and off I went. Finally I let up a shout and the ball was free! Did I dare to do it in reverse? Hell no! I had a blog post to write which required photos etc so I reset the ball in the reset hole and quickly put the sliders back.

Reset hole - I'm not going to show you the exit!
Should you buy this puzzle? I would say absolutely! It is not for N-ary beginners and not for children but I can categorically say that it is the best puzzle in it's class that I have ever tried. I love it and can't wait to solve it again. Buy it from Puzzle Master from the link above or direct from Wil Strijbos. It's very good value for money at $54CAD.


  1. Kevin, thanks for the interesting article and photos. That Uhrwerk is beautiful and the challenge of the Labynary is SO tempting. How do you store these? Could they be displayed on a wall as art?

    1. I guess you could use mounts for decorative plates to wall mount them. But for myself they are in a rather large pile on my desk along with another 25 burr puzzles and some twisties all awaiting either solving or storage! I seem to have run out of space and will need to have yet another reorganisation!

  2. Great article Kevin. Need to get hold of Will to see if he knows where I can obtain a special ODD puzzle :-) Fantastic read tonight!

    1. I've asked mate because I really want one too! But there are absolutely none available! Need to try at auction then!

  3. Nice write up Kevin. All appear to be really great puzzles, but I am not sure if I have the patience to get through one like the Labynary!

    1. Thanks! Each to their own. But if you ever felt the urge then you would not be disappointed with this one!

  4. Very nice blog post! Recently I had a discussion with other puzzle experts on this topic and now believe the Labynary is binary, not ternary. It is still refusing a thorough analysis, because of the a bit irregular pattern of all those switches. The mechanism looks similar to "Six Bottles" and "Steuerrad" (both ternary), but this one seems to be binary only. Most obvious difference to these other two: the pieces only have two positions, not three. :) Now after reading your post I feel like pulling Labynary out again and solving it -- will take some time! ;)

    1. Good luck solving it again. At least you now know the path to take.

      I'm really not sure how you can tell with some puzzles what level it is. I did think it was binary myself but there's so many extra sliders and blockers and locks that I wondered whether that made a difference.