6-piece caged burrs

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Pio2001
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6-piece caged burrs

Post by Pio2001 » May 14th, 2016, 6:42 pm

I've always been a big fan of 6-piece caged burrs. I've been looking after the improved version of Stéphane Chomine's Château d'If for quite some time.

All I knew about it was a Burrtools file that I got directly from Stéphane in 2012, when everyone was rushing to design the caged burr with the highest possible number of moves. It was never published because, with a level 44+3, it was beaten by Goh Pit khiam's Congestion, with 59+17 moves before having a chance to be produced.
I did a prototype of it with LiveCubes and managed to solve it. Then it fell into oblivion.

After a break in his puzzle making activity, Maurice Vigouroux decided to go back to the workshop and asked me what intersting designs would be worth making. This improved Château d'If was in my shortlist, and so it came at last into being.

Here is now my collection of 6-piece caged burrs :
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From left to right:

Ishino's Burr In Cage 4 12 (Caged Notchable Unique 4.12 Moves 9 Holes)
Moves: 4.12.2.1.2.2

Stéphane Chomine's Château d'If
Moves: 24.5.2.4.1.3

Donald Osselar's Nickel Box
Moves: 28.18.17.1.1.3

Stéphane Chomine's Château d'If 2 (until a new name is found ?)
Moves: 44.3.5.3.1.2

Goh Pit Khiam's Congestion
Moves: 59.17.5.1.3

I have recently brought Ishino's caged burr at work and some colleagues have tried their wits at disassembling it. Most of them managed to find the first 4 moves and to remove the first piece. But 5 minutes are too short for them to find the 12 next ones.
Some of them, more into puzzles, have managed to disassemble it completely after 15 to 30 minutes.
I disadvised them to try to reassemble it, because this design has 142 false assemblies, and only one that work. Moreover, the right assembly features a piece lying "sideways", i.e. with what seems to be its "back" side NOT facing the outside of the structure. So the chances of finding it among the 143 possible ones (and then finding the assembling sequence that follows) are very thin. I don't know if considerations about the possibility to remove a piece could help assembling the puzzle from scratch, but it seems unlikely. It is probably an inhuman challenge.
My burr-in-cage 4.12 comes from Maurice's realizations done in year 2003, before Arteludes. It is thus varnished instead of waxed. The cage is in wenge, and the pieces are in wenge, difou, niove, padauk, purpleheart and maple. Only the outside of the pieces is varnished.

The Château d'If is one step higher in difficulty. None of my colleagues would be able disassemble it, I think. But the difficulty is not too high if you are good at three-dimentional vision. My uncle and my cosin both solved it. I mean, they disassembled it completely, starting from the solved configuration.
It has one solution for 3092 assemblies. Probably inhuman to assemble from scratch. Since the pieces are more complicated than in the 4.12 burr-in-cage and it has no colours, an effort of memory is required to be able to reassemble it after you have scrambled all the pieces. You have to learn by heart the position of each piece. And that's something that is easily forgotten. Therefore this puzzle is always a bit confusing to reassemble.
My copy is part of a small series that Maurice made for friends, with a superior finish. The cage is in niove, a very beautiful orange wood with dark stripes. The pieces seem to be in padauk, because they are bright red inside, but have turned brown on some outside parts that have been most exposed to light.

The Nickel Box have been one of Maurice most beautiful realisations, with its cage in ebony and dowels in beech. It is a great puzzle to disassemble. I find the labyrinth of possible paths more enjoyable than in the Château d'If. There is a real exploration taking place, not just random trials and failures. And the difficulty remains high even after the first piece is out. Two difficult sequences must be found to remove the second, then the third piece. And there is a quite surprising feature in the sequence for the third piece that must really be remembered when you play the sequence backwards to reassemble the puzzle. It is easy to remember the right assembly thanks to the dowels, that severly restricts the possible configurations.
Most Nickel Boxes made by Maurice have pieces in padauk, but mine comes from a pre-release that featured two ones with pieces in marblewood, two with pieces in purpleheart (the most beautiful of all in my opinion: the association of purpleheart with ebony just looks gothic), and two with pieces in bubinga, including mine. For some monthes, bubinga developed some kind of cheese smell that was a bit unpleasant, but now the smell is gone. Caged burrs have the tendancy of amplifying the natural smell of woods by keeping the pieces trapped inside a closed space.

I have just solved consistently the Château d'If 2, disassembling and reassembling it twice. It is in the same category as the Nickel Box and Congestion : enjoyable labyrinth of possible moves, high difficulty, and configuration easy to remember for the reassembling. Of these three puzzles, it is the one that has the simplest pieces. All of them but one have just one bar linking the two sides, plus one voxel. As a consequence, it is the one with the most repetitive sequence, and with the most dead ends. I have not yet found a real iterative structure in it, but it definitely reminds of Donald Osselaer's Fermium or Ultraburr, with small key sequences to be performed in a given order.
The cage is in ebony, with two different sizes of aluminium dowels, that stand for two different colours in the original design. This time, Maurice used a variety of woods for the pieces. Mine is in dark cuchi, a beautiful, heavy and smooth wood that gives the puzzle a very enjoyable mechanical behaviour.

The Congestion is the ultimate 6-piece caged burr. Not only there are 59 moves to get the first piece out, but there are also dead ends, and the second piece is very difficult to get out too. Things are as difficult as they can possibly be here. Some parts deceivingly look like you are going backwards. Some crucial moves look like they are useless. And the whole thing feel, yes, quite congestionned. The right assembly to use to reassemble the puzzle is easy to remember, but even introducing the four first pieces is difficult. What's amazing is that all of this fits in a simple 6-piece burr with a simple cage. A lot of published designs use extra inner voxels in their cage in order to be more difficult to solve, and in spite of this, don't come anywhere near the complexity of the Congestion.
All Congestions were made with a cage in bloodwood and with aluminium dowels. Normally, the pieces are in purpleheart, but mine is in sucupira. Sucupira, like merbau, is not a very good wood to use in puzzles. It warps noticeably and the end grain is rough. I filed the inner part of both sides of the pieces so that the mechanism of the puzzle feels smoother, and now it works quite well in spite of the warping of some of the pieces. If such a warping had occured in a 18-piece puzzle, for example, it might have been more problematic.



In conclusion, I am so happy with this series of puzzles ! They beautifully match the criterion of unexpected complexity hidden inside a deceivingly simple look. The gradual progression from the easy 4.12 cage to the infernal Congestion is perfect. And they are outstanding pieces of craftsmaship.
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