Sunday, 26 March 2017

Hey Bud! It's Time to Be N-ary

The title of this blog post is a little play on words to introduce a couple of puzzles I have played with over the last month or so. Late last year a few of the guys who got to go to the Dutch Puzzle Party managed to come back (as usual) with lots of new toys and the B-Nary puzzle by Jean-Claude Constantin particularly caught my eye. Several people were very enthusiastic about it but unfortunately there were none left for me! Sob! It was a particularly big birthday for me when the DPP was on and I could not attend - I could not risk the wrath of she who must be feared and obeyed. I did ask Mr Strijbos about obtaining a copy of the B-Nary puzzle and he worked his magic on JCC. My copy arrived about 4 weeks ago.

I love these puzzles! Not only are they N-ary puzzles based on Gray code but they also smell nice - I lurve the laser burnt wood smell that arises when you open the package. This puzzle may be called B-Nary because of the shape (B on the front and N-A-R-Y etched on the sliders) but I discovered straight away that there are 3 positions for each of the sliders and hence it is not binary, it is ternary as confirmed by Goetz' list.

Apart from the interesting shape, the next thing that immediately is noticeable is that there are ball bearings visible in the holes down the left side of the B. It is not clear what they are for but they move in and out of view as the puzzle is rotate top down or back upright. Also there is another ball bearing visible in the oddly shaped hole at the top of the B. The ultimate aim of the puzzle becomes clear as soon as you see that hole and bearing. If you've never done these puzzles before then I can tell you that these are a reset mechanism that allows you to insert the bearing back into the start position without having to retrace your steps through the puzzle - basically it is for the lazy puzzler! Seeing this immediately tells me that the aim is to manipulate the puzzle sliders to open a pathway from that start hole to another hole where the bearing can be removed. After that it should be put back to the beginning. I presumed that the exit hole was the one just to the right of the start as there seemed no other reason for it to be there. As with all these puzzles the trick is to work out the N-aryness of it (how many positions for each piece and how they interact with each other.

The B-Nary is actually fairly straightforward in its pattern - luckily each of the sliders moves the same way as the previous one and there are no weird patterns to it. The sliders interact by way of slots which accept ball bearings and force a stop to movement. A nice surprise was after the first move to discover that there are more ball bearings inside the puzzle which only come into view after pieces have moved. Each of the bearings and sliders need to be in an appropriate position before the next move can be made. Once the pattern is understood then it is actually a really nice rhythm and the whole thing can be sped through in a few minutes.

After 54 moves of the sliders plus a good few more tiltings of the puzzle to roll the bearings around then all the sliders have been moved across to the left and then the bearing in the start hole suddenly drops down inside. So how does one get it to move on to the end hole? I presumed that I needed to try and keep the ball down at the bottom and reverse the 54 moves and then direct it back up again along a parallel track. This proved a real task the first time - the bearing was able to roll about freely inside and kept getting in the way of the movements of the sliders! At times I couldn't move anything and would need to backtrack. Then after I had managed to position them all at the start I tilted the puzzle forwards expecting to see the ball at the exit hole but nope!! Your friendly puzzling idiot had locked the ball up somewhere inside! Doh!

After a little backtracking all the way to the beginning I proceeded to try again and failed and afiled and failed! I kept losing the ball inside somewhere! I was beginning to think I was truly rubbish at puzzling or maybe had totally misunderstood the puzzle when I suddenly managed this:

Finally got the damned ball out!
It must have taken me 2 hours! The sequence is possible in about 10 minutes each way but I kept losing the ball. At this point it was time to see what was going on inside. Flipping the puzzle over reveals screws which can be undone and I dismantled the puzzle layer by layer and not only saw the beautiful design in all its glory (I'm afraid you need to buy it for yourself to see that) but it also showed why I had had so much trouble - there was a disk magnet inside alongside the bearing track which was meant to trap the bearing in the down position. In my puzzle the disk had slipped out and was too far away to work. I placed it into the correct hole and reassembled it. After that I moved the puzzle back to the start without using the reset hole. This puzzle is lovely! Very nice logic, very well implemented and when the magnet is in place then its a rather therapeutic process. I have done it many times since then and now have it in my collection, N-ary section.


Binary Bud

Binary Bud - this is the solved position with the white disk blocked by the green leaves
The other reference in my title is the Binary Bud puzzle. The designer and maker of these puzzles, Namick Salakhov, knows that I adore these mathematical logic type puzzles (even if I can not understand his maths) and he contacted me to ask if I was interested in buying a new copy of the Binary Bud puzzle. He makes very few puzzles at a time because they are done by hand and this is very time consuming. I hesitated for a fraction of a millisecond before replying in the affirmative and sending some paypal A few weeks later a nice box with LOTS of polystyrene packing arrived and inside the HUGE package was a very small but beautifully formed package.

When it arrived the top white plate was able to rotate freely and I was a little worried that it had been damaged in transit despite so much padding. After rotating it around a few times it suddenly snapped down into place and then I could see how it interacted with the green leaves. This puzzle had been Namick's entry into the 2013 IPP design competition.
The instructions are:
Rotate each of the "leaves" from the open position to the close (blocking) position.
And then vice-versa.
Find the shortest solution with the minimum number of moves.
Notes: The top piece can block and be blocked by the leaves; and the leaves can block each other
My initial investigation showed this to be rather confusing. 5 of the leaves were the same interesting shape and a 6th one had a flattened edge as well. The top w as able to rotate and depending on where it stopped it would allow just 2 of the leaves to be rotated upwards. Except....not all the leaves could move because of the way they intercepted each other. When you find one that can move it may release or block other ones but it also gets in the way of the top white disk and thus a freed up leaf may be able to move up due to the adjacent green leaf positions but it is blocked by the top disk! It is clear that each of the leaves has only 2 positions and the puzzle must therefore be binary (the name was also a big clue!)

This was a very confusing puzzle for me! During my discussion with the "king of N-ary puzzles" Goetz, I said that I was struggling to find any repeating sequences. He reassured me that it would become clear that there are several short sequences in the pathway. I persevered for a week or so (halfway through my exploration I am ashamed to say that I might have gotten sidetracked by a few of my New additions (especially the wire puzzles from Wang Yulong and the Slant cube reviewed last week). Eventually it suddenly clicked and I was able to see the little sequences - and I was then able to find the shortest solution (it's 15 moves). The fun thing is that with all the leaves pointing down the disk can spin freely and it is possible to start in a different place and work out the sequence until the disk is trapped again by all the leaves pointing up. I have not yet found all possible solutions to the puzzle yet and to be honest will not know when I have (this could keep me going around in circles for years!)

It is a lovely diversion and I can't wait to hear from him again with another N-ary puzzle for me to be confused with! Thank you so much Namick - I love it!


A box of blocks!
A hint of N-ary-ness
At the beginning of the year the hugely talented Jack Krijnen sent me a box of bits of wood - this is the Merry-go-round. Unlike Allard (partly due to naivete) I didn't order everything up to Non-ary! I asked for ternary, quaternary and quinary pieces with a 6 hole pillar. It took me quite a while to understand how to get started and then I was off! Starting with just ternary and then working my way up I have managed the final moves on the quinary with 7816 moves to assemble! I am sure that I actually did quite a few more than that and have not dared start the disassembly yet. Soon I will start on the mixed N-ary puzzles and see how much fun that it but......maybe later!

You get the idea!
I cannot wait to see what Jack comes up with next.

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