Sunday 26 March 2023

A terrible memory or a fundamental failure to understand?

Juno's Grooved 6 Board Burr number 7
I’ve had a week of annual leave up in Bonny Scotland relaxing and eating far too much good food! (I can heartily recommend Dine at the Traverse  as a fabulous place to eat - afterwards I was only good for a sleep). Of course there was also the customary visit to the outlaws and even a Mother's Day afternoon tea at The Ivy (again, I was only good for a sleep afterwards!) Luckily, I brought a few puzzles to play with and even managed (with a struggle) to solve one… partially at least!
Yay! 6 more!
This week I am showing off the seventh in the series of Grooved Board Burrs by Junichi Yananose. Seven? OMG! But how could I resist? I have the other 6 and absolutely adored them. I have reviewed most of them (#1, #2, #3, #4, #6) over the years as they came out. Number 7 in the series was released a couple of weeks ago and is still available now. Juno himself (he’s a genius) said that the difficulty is extremely high and suggested using the photos on the site to aid with small hints during the search for the solution path.

The first thing I noticed when I unwrapped my lovely parcel was how vibrantly beautiful the puzzle is. As before the puzzle is made using Juno's home made Plywood (this provides strength and prevents warping as humidity conditions change). The wood used are PNG Rosewood and Red Gum which contrast with each other beautifully. This one is slightly larger than the first 6 and is less bevelled to try and prevent inadvertent rotational moves. The immediately obvious difference, however, is that this puzzle has considerably more complex pieces with pins on the external surfaces of the puzzle. These are also there to prevent rotational moves.

Juno wrote in his description:
"The puzzle has a unique solution in a relatively small number of 91 assemblies, and the computer program Burr Tools showed its level to be, 50-18-3-3, the highest number in the Grooved 6 Board Burr series. In the real world, the interlocking of the consisting pieces becomes unstable after around 40 moves from the assembled shape, and it allows a rotational movement shortcut that is theoretically possible. It is yet the largest number ever in the series to release the first piece from the assembled shape."
The pathway is relatively constrained initially but very quickly it becomes apparent that there is quite a lot of movement possible with many choices for what to move and at various points the puzzle gets stretched apart a very long way and still remains stable. Those external dowels/pins really do work to prevent rotations. I managed a good few moves with my usual to and fro approach backtracking to the beginning each time. Then I got stuck for a couple of days. I couldn’t spend too much time on it - we were on holiday and had stuff to do. 

After a bit of a hiatus at one position and wondering whether I had completely mistaken the correct path, I found a spectacular new move which opened up a whole new set of paths but, as is usual I backtracked to the beginning and, yes, as you’d expect I couldn't find the move to get to that place again. I’m an eejit! I spent several hours searching around the same spot desperately trying to find the single crucial move.

The difference was small… I needed to move from this position:

See how stretched out it is?
To this position:

That front board has shifted from one notch to another
This looks trivial to achieve yet it took me 2 days of swearing under my breath! The crucial factor in finding the path was the realisation that the placement of the pegs on the outside forces the puzzle to use ⅓ voxel moves! This is the reason for the title of the blog post - I thought I had just been a victim of a terrible memory but in reality, I had completely misunderstood the complexity of the puzzle. This means that instead of a 6x6x6 grid (with each board being 1x4x6 voxels), a much larger grid was needed. The whole thing would need to be tripled in size!

After that hideous/revealing discovery, it opened up again to a huge new vista of complexity and some seriously scary sequences. The puzzle did begin to become rotationally unstable but unallowed moves were always prevented from being completed by the pins. My to and fro technique worked for quite some time but eventually I got lost. I found myself going around and around in a loop unable to go forward or back until I found my way back to the beginning by accident. Phew!

At this point I stopped for a day to try and regain my nerves! These puzzles are great fun but I’m always frightened with some that I will get stuck in a position and not be able to go forward or back ever again. I have a couple of incredibly complex burrs that are stuck in an odd hedgehog-like shape and I cannot do anything about it - they’ve been stuck like that for years! I did get my courage back, however, as I figured that a 6 piece burr really should not get irrevocably stuck. Once I returned back to the second half of the solution, I systematically tried different sequences until I had my Aha! moment. My first piece came out.

I have to say that Juno's hint pictures were not in any way useful! Each one was taken with a different orientation of the puzzle making it impossible to relate one position to a later one. I tried turning my puzzle at various stages to match the photo but quickly lost any idea of what position I was in whilst rotating it about. 

In removing the first piece, I had to reach to a table to put it down and my grip on the puzzle shifted and the remaining pieces revealed themselves to be very unstable. A bunch of pieces rotated and dropped down. I had no idea how they should have been placed and it was easy to remove a pair in one go from this new position. After that, I took it apart completely for my photo.

Seriously complex pieces!
I would love to tell you that I have managed to reassemble it but there is not a hope in hell of that without Burrtools! I think even the amazing Rich (frequent MPP visitor, who is an incredible burr assembler) might struggle to assemble this from scratch.

I will need to wait until I get home to my computer (this post was done on an iPad) to program it in. It’s going to be a real challenge to enter it as I don’t actually have pictures showing where all the external grooves and pins should be on the assembled puzzle. But, trying to make my BT files is part of the puzzle fun for me. It might take several hours! Oh joy!

This fabulous challenge is still available from Juno now - go buy one before they sell out. It is seriously seriously good.
Thank you, my friend!

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