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 Post subject: Old Fashioned Burr Puzzles
PostPosted: Sat Jun 09, 2012 5:03 pm 
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As a slight distraction for my twisty puzzle obsession, I have become interested in those "old school" puzzles, the classic six piece burr. These consist of rectangular blocks 2x2x6 (or longer) which have had some 1x1x1 blocks removed from the central 2x2x4 section. Traditionally made from wood, the object of the puzzle is to fit the six burrs together to make this shape:
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Anyway, I was reading this article on burs, and was inspired to design some using SketchUp and get some printed at Shapeways:
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They are from top to bottom:

Bill's Baffling Burr (5.1.1.1.1.1)
Burr 305 (1.1.1.1.0.0)
Burr 306 (1.1.1.1.0.0)
Piston Burr (9.3.1.1.1.1)
Unique 10 (12.1.1.1.1.1)

The numbers mean the number of moves to remove the first burr, then the second and so on. I must admit that I am no expert on these things, and had to refer to the IBM site to work out some solutions :(
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This is the Piston Burr (so called because of the backwards and forwards moves the pieces make) solved.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sat Jun 09, 2012 5:17 pm 
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That's incredible! It's so rare to see printed burr pieces. And they look great!

Incidentally, the Piston Burr is my favourite 6-piece design! If you ever consider making any more of them then do let me know. So far I have it in cheap wood, machined aluminium and one preordered in ebony. I'd love a printed one to add to the family!

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sat Jun 09, 2012 5:36 pm 
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Hybrid424 wrote:
That's incredible! It's so rare to see printed burr pieces. And they look great!

Incidentally, the Piston Burr is my favourite 6-piece design! If you ever consider making any more of them then do let me know. So far I have it in cheap wood, machined aluminium and one preordered in ebony. I'd love a printed one to add to the family!
Thanks, I have pm'd you with some more info.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Jun 10, 2012 2:48 pm 
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Great work Gus! Love it.

I own a set with 42 (25 fifferent) notchable piecs in a beautiful woode case, but for a level-burr you usually will need other pieces too.

Will you put up the 3D prints for sale on shapeways? Are you planning to make files for all 369 pieces?

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 5:13 am 
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Just as an interesting addition, here's exactly the same burr (Piston Burr) in machined aluminium by Wil Strijbos.

The top pic shows two different Burrs, the one on the right being the Piston Burr, and the other being Philippe Dubois' Burr, a level 6.4 burr.

The second pic shows the Piston Burr pieces.

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Aluminium Burrs (Wil Strijbos) by Puzzleparadox, on Flickr
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Aluminium 10 Move Burr (Wil Strijbos) by Puzzleparadox, on Flickr

Although Wil called it a '10 Move Burr', it technically has a level 9.3 solution due to simultaneously moving pieces.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 5:27 am 
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I notice that the pieces must have been milled by hand? It's just that the non-notchable pieces have pieces added (e.g. the cylinders) rather than the complete parts milled out of a single piece. Why not just make these pieces from large lumps of Al and then you could have a work-out during the solve :lol:

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 5:55 am 
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Gus wrote:
Why not just make these pieces from large lumps of Al and then you could have a work-out during the solve :lol:

Oh they are plenty heavy anyway! You'll get a workout regardless. You should try juggling the two of them! :lol:

Obviously the non-notchable pieces can't be milled in the normal fashion, so cylinder pieces were used instead. This actually improves the motion of the pieces, especially in such a high level burr as this one. Because the edges are rounded the pieces never catch on each other, but they are still the right width so there is practically no play between the pieces either. More burrs should be made like this!

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 6:05 am 
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I was going to round the edges of my 3D printed burrs, but I think the sharp edges look better, and they rarely lock against each other, especially after a few solves.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 6:16 am 
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The sharp edges do look better. I imagine catching is more of an issue with machined metal than it is with plastic due to the complete lack of give.

So, now that you're into burrs, have you played around with BurrTools yet?

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 7:49 am 
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Yes, I know about this tool, but I am afraid to start using it because it will swallow up vast amounts of my time once I start! For the moment I'm happy to play around with the "simple" six piece burr.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 9:08 am 
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Hi Gus,

Your idea of 3D printing the burr pieces is a good one. Depending on the size you can probably make them fairly inexpensively. Have you tried making them hollow?

Overall, there are 837 distinct pieces at a given length.

You might be interested in a lot more info I have posted here:
http://robspuzzlepage.com/interlocking.htm#trad

BTW, anyone who wants wooden pieces can have some made by a fellow here:
http://www.ebay.com/itm/160729242268#ht_1475wt_1212
(He had asked me to post his auction link.)

And if you want to "branch out" beyond the traditional six-piece burr, George Bell offers several interlocking puzzles at his Shapeways shop:
http://www.shapeways.com/shops/polypuzzles

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 9:35 am 
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Thanks Rob, I got the Unique-10 (length=8) design from your pages. My pieces are only 10x10x60/80mm in size, and they are hollow (as far as Shapeways software is concerned :wink: ), only 1mm wall thickness, so I don't think they could be made much cheaper.

I wish I had the tools and skills to make a nice set of wooden burrs :(

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 1:51 pm 
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Hi Gus,

interesting choice of 6 piece burs you made! :) Additionally to the links that Rob posted, there is also this site:

http://puzzlewillbeplayed.com/

It does not only contain six piece burrs, but also others. If you click on "Interlocking (6 piece burr: traditional)", you'll find some more 6 piece burrs.

My special field of interest are 18 piece burrs, with 6 pieces parallel to each axis, and currently with up to a 152 moves to remove the first piece. There are some listed in my gallery page (see link in my signature).

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 3:56 pm 
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Nice websites, thanks for the links. So a level 152, 18 piece burr, eh? Please have mercy, I've only just started on 6 piece burrs :lol:

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 4:29 pm 
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Gus wrote:
Nice websites, thanks for the links. So a level 152, 18 piece burr, eh? Please have mercy, I've only just started on 6 piece burrs :lol:

I think you should back away carefully from the puzzle, Gus!!! :shock:

Some of these burrs were what got me started on my current puzzle madness. I have a beautiful Tiros 18 piece burr made by Maurice Vigouroux. It is made of 3 different lovely woods. It requires 150 moves to get the first pierce out and I have been trying for 6 months! So far I have managed to make 100 odd moves but can't get any further. God only knows how I would ever manage to put it back together again. :shock:

So Gus, I repeat, "STEP AWAY FROM THE PUZZLE"! Only madness lies over here! :D :D

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 4:33 pm 
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Surely there can't be that many burr puzzles out there to collect though. Right?

Right? :?

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Mon Jun 11, 2012 5:49 pm 
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Hybrid424 wrote:
Surely there can't be that many burr puzzles out there to collect though. Right?

Right? :?:

:shock: :lol: :lol: :lol:

From Bill Cutler's definitive analysis - there are 837 distinct pieces and there are 35,657,131,235 ways that six pieces drawn from this group of 837 fit together in the burr shape (allowing duplicates of pieces within a set, but not rotations and mirror images)! Luckily, of those 35 billion, only ( :shock: ) about 5.95 billion are constructible.

If you only take solid burrs (no internal holes), there are 119,979 of them requiring just 369 piece types needed to produce them. Of those 369, 112 are used in duplicate and 2 in triplicate, making a useful set of ONLY 485 pieces to make all the solid burrs. The rest of those 5.95 billion puzzles are holey burrs.

To cut it down a bit maybe you want to include only the pieces that are easy to make! Blind (or internal) corners (i.e. where the sides of at least 3 cubies meet in concavity) are tough to make. Any piece without any such blind corner can be made using a milling machine and is "millable". There are 78 millable pieces. Maybe you'd like to constrain it further to pieces you can make on a table saw  or by hand without resorting to a chisel, you have to make only cuts running perpendicular to the long axis. These pieces are called "notchable", and there are only 59 of them. Only 25 of those 59 pieces are useful to build solid burrs, and only 314 solid burrs can be made from that set of 25 (with some duplicates, so you need a set of 42 pieces). Overall, the 59 notchable pieces can be used to make 13,354,991 assemblies.

So how many burrs can there be to collect? Not that many!!! :lol: :oops:

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Tue Jun 12, 2012 2:40 am 
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I love the way that Burries (new word!) quaintly ( :lol: ) distinguish between burrs by how hard they are to make using saws and chisels and milling machines. I'm not being sarcastic here, I've done some woodworking in my time, and I appreciate the craftsmanship (craftswomanship?, craftspersonship?). Anywhoo, we now have CAD and 3D printing, so I say ... MAKE THEM ALL :shock:

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Tue Jun 12, 2012 4:35 am 
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Gus wrote:
so I say ... MAKE THEM ALL :shock:

:D :D
Great!
If it doesn't cost too much - make that FULL SET for me too!
:D

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Jul 01, 2012 6:36 am 
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Here's a few fun little comparison pics of daddy burr and baby burr:

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Piston Burr - Aluminium & 3D Printed by Puzzleparadox, on Flickr
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Piston Burr - Aluminium & 3D Printed by Puzzleparadox, on Flickr
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Piston Burr - Aluminium & 3D Printed by Puzzleparadox, on Flickr

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Jul 01, 2012 7:05 am 
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Great pictures. Those Al pieces sure look nice.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Jul 01, 2012 12:39 pm 
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Gus wrote:
Great pictures. Those Al pieces sure look nice.

The two al burrs are still available if you wanted one. Just ask Wil Strijbos. Drop me a PM if you need/want contact details.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Aug 05, 2012 3:56 pm 
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Hi,
I, too, am a big fan of traditionnal 6-piece burrs. Here are some pictures of my collection :

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Here are the puzzles, from left to right, then top to bottom in the first picture.

Philippe Dubois / Gaby Games Burr
Made by Arjeu, probably in stained pine.
2 assemblies, 1 solution. 6+4 moves.
My oldest burr and one of my oldest puzzles. It was it who started my passion about burrs. A perfect introduction to holey burrs for beginners.

Just below it, the Double Cross.
Made by Maurice Vigouroux long ago in Carolina Pine.
1 assembly, 1 solution, 1 move.
It is the easiest design that I know for a 6-piece burr with no internal holes.

Top center, a variation of Bill Cutler's L46AA (length 10), that is millable instead of notchable.
Made by Maurice Vigouroux in bloodwood, with dowels in ebony.
1 assembly, 1 solution, 10 moves.
The most confusing disassembling sequence that I know of for a 6-piece cross. I don't consider any 6-piece cross to be a real challenge to disassemble for a confirmed puzzlist, but this one might keep some busy for several minutes.

Top right, the Mega Six, a slight variation of Bill Cutler's Computer's Choice level 10.
Made by Brian Young in western australian jarrah.
20 assemblies, 1 solution, 10 moves.
One of the most difficult and impressive 6-piece burr. It has two ambiguous pieces and 19 false assemblies, two of them actually allowing to remove one piece, only to be left with an impossible assembly of 5 pieces !

In the middle row, on the left, Abad's Level 5 Most Assemblies.
Made by Maurice Vigouroux, in bubinga.
896 assemblies, 1 solution, 5 moves.
A very interesting design, as the high number of assemblies allows -and force- the puzzlist to use much more logic than with most other crosses in order to solve it from the disassembled state.

The next one is Abad's level 6.7.
Made by Maurice Vigouroux in bloodwood.
25 assemblies, 1 solution, 6+7 moves.
Might hold the record for the highest total number of moves (16) for a unique solution. I enjoyed very much to solve it starting from the disassembled state. But I find it less interesting once the solution is known. The disassembling sequence is not very complex.

The third one in the middle row is a copy of the Mega Six made by Maurice Vigouroux in curly maple, and without gluing any extra cubes. Maurice always mills the pieces that are not notchable, and he uses a chisel to cut the pieces that are not millable.

The one on the right is Zodiac Burr (Mouse).
Made by Zandraa Tumen-Ulzii, in pine.
1 assembly. 1 solution. 1 move.
The puzzle itself is just a solid burr that opens in two halves, with two symmetric sets of 3 pieces. But the interest of the object is the carved and painted pieces, that represents a rat, one of the 12 animals of the chinese zodiac. This is the only carved puzzle in my collection.

In the bottom row, the left one is a copy of Bill Cutler's Computer's Choice 5-holes.
Made by Maurice Vigouroux in curly maple.
7 assemblies, 1 solution, 9 moves.
I find the disassembling sequence interesting because it features a nice dead end, while the right move is more subtle.

Then, a copy of Bill's Ball Bearing Burr.
Made by Maurice Vigouroux in cherry. It is a bit of an intruder in this list, because it is not a honest 6-piece cross. It features two marbles inside, that prevents any move that we could make to disassemble the puzzle, whatever its orientation. When one of the marbles falls in the position that frees the first move, the other one automatically falls into a position that blocks it !

The third one in the bottom row is Peter Marineau's Piston burr.
Made in padauk by a anonymous french manufacturer that is certainly Dalloz.
10 assemblies, 1 solution, 9 moves.
Also called "Burr B". It has been improved by Edward Hordern under the name of "Modification of burr B". The result has 10 moves, but doesn't have a unique solution, except if you use three colours. It also adds a difficulty in the disassembling sequence by "hiding" one of the moves.
Love's dozen has the same disassembling sequence, with an extra move performed forth and back, which leads to a total of 12 move, the absolute record for a traditionnal 6-piece burr.

The last one is Abad's Level 9 burr.
Made by Maurice Vigouroux in walnut.
2 assemblies, 1 solution, 9 moves.
I like they way the disassembling sequence messes up the puzzle. And I find this kind of dark striped walnut gorgeous.


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 Post subject: About the number of moves
PostPosted: Sun Aug 05, 2012 4:20 pm 
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About the number of moves

There are multiple ways of characterizing a given design. The presence of holes is one. Most of the 6-piece burrs in my collection are indeed holey.
Here are two questions about burr puzzles without internal holes. Try to find the answer before I give the solution :wink:

  • If a burr puzzle has no internal holes, does it mean that it has to got one plain key piece that is removed at the beginning of the disassembly ?
  • If a burr puzzle has no internal holes, does it mean that the first piece can be removed in one move only ?

The three common ways to characterize holeys burrs is to give the number of moves to remove each piece, which is called the "level"; the number of possible assemblies, and the number of solutions.

For example, Philippe Dubois' Burr is level 6.4 (6 moves, then 4 moves), has two assemblies, and one solution.

The definiton of the number of moves for the first piece is not always clear. And for the next ones, the matter becomes even more difficult.

When we talk about the level of a puzzle, we usually mean the level as calculated by the Burrtools software. And since it doesn't take rotations into account, this number is sometimes just wrong.
With 6-piece traditionnal burrs, it is rare to find a design that allow a rotation. Bill Cutler's "Computer's Nightmare" is an example. It is actually impossible to disassemble it without performing a rotation. The software says that it has no solution. The level must be found by hand, playing with the real puzzle.
Burr puzzle like the Xenon or Ultraburr, created by Donald Osselaer, are not traditionnal crosses, but rather "board burrs". They often have a real level that is much lower than the one given by Burrtools, because a piece can be removed with a rotation well below it could be possible without rotation.

Even for these puzzles, giving the real level "by hand" can be ambiguous. The Millenium, for example, is a 13-piece board burr supposed to be level 521.479 according to Burrtools (521 + 479 = 1000, hence the name). It has been manufactured three times to my knowledge. I had the opportunity to test two of them. One of them was clearly level 348.306, thanks to a rotation allowing to remove the first piece after 348 moves, and that leaves the puzzle in a configuration that is 306 moves away from the removal of the second piece, instead of 479.
However, this rotation was clearly impossible in a second identical Millenium manufactured at the same time in another wood ! The difference is that the rotation is actually impossible in theory, but the first puzzle had enough room between the pieces to allow it, the second one not.

This is not an exception. The rotations that are at the limit are very common. In fact, the most common one, that consists in rotating a square stick in a L-shaped space made of three squares is illegal. The space is eactly 1.414 units, while the needed space would be 1.5 units.
On the Mega Six, a 6-piece burr made by MrPuzzle with slightly rounded edges, such a rotation is possible when the weather is dry and hot, and not possible when the weather is cold and moist, because of the transverse dilatation the wood.
In order to legally rotate a square stick, we need at least a T-shaped space made of 4 squares.

In 18-piece traditionnal burrs, rotations are not very common. Accordign to my experience, they seem to be present in about 1 design out of 10, or a bit more. Goetz and Rob, who also has got a lot of 18-piece burrs in their collection, might have a different experience.


The problem of the second piece

Even if we restrict the level calculation to the sequences without rotations, the matter isn't settled ! As I said, things are clear as long as we only deal with the first piece.

Rafael Abad is a designer who is interested in traditionnal 6-piece burrs with the highest possible of moves for the second piece. A field mostly unknown, as Bill Cutler gigantic and exhaustive analysis of 6-piece burrs only took into account the number of moves for the first piece.
Abad's Level 6.7 Burr, for example, might be the current record holder for the highest total number of moves (16) and a unique solution (Love's Dozen, with a total of 18, doesn't have a unique solution). No computer analysis has ever been run to look for the highest total number of moves in a burr puzzle.

Abad also created a burr that is level 4 (don't look for it on the web, it is yet unpublished). You can remove the first piece in 4 moves. This is plain and clear.
For the next piece, Burrtools says the level is 9 moves. Great ! A level 4.9 burr must be something !...

But the truth is that the puzzle is also level 5.2 !

Here is the explanation : the second piece is blocked by another one, and this one can only be moved out of the way at the very beginning, when the puzzle is completely assembled. It's the first of the 5+2 moves.
If you want to remove your first piece as fast as possible, you can ignore this move, a get it out in 4 moves only. But then, in order to get the other piece out of the way of the second one, you need to go back to the beginning to perform the move that you skipped, and then perform the sequence again in the forward direction, which costs you 3+3 = 6 extra moves.
That's why the Burrtools sequence show 6 more moves (4+9 = 13) than the real one (5+2 = 7).

Performing extra moves at the beginning to get a given piece out can thus allow to leave the puzzle in a much easier configuration than if you insist on using the absolute shortest path to remove a given piece alone. That is also why the total number of moves given by Burrtools can sometimes vary if you solve the same puzzle in a different orientation : it can choose a different sequence of the same length for a given piece, which leaves the puzzle in a different configuration, leading to a different disassembling sequence for the rest of the pieces.

If Burrtools was to take this into account, the computation time would grow very very fast. It may work for 6-piece burrs, but might become a problem for 18-piece burrs, or more complex ones, like board burrs or framed burrs.


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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Aug 05, 2012 4:30 pm 
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Welcome Guillaume!

I knew that a forum with burrs mentioned in it would attract you sooner or later!

To all the other forum members out there - this gentleman is one of the greatest solvers of burr puzzles there is! He has even written a very interesting paper on how to go about it. He as even solved the ultra-difficult Tiros 18 piece which requires 150 moves to take out he last piece!

If any of you are interested in difficult burrs then take a look at Arteludes a French site with some fabulous burrs and other puzzles. I have just bought the Fermium board burr (102 moves to extract the first piece) and Nickel box (a boxed burr requiring 28 moves to extract the first piece). They are all made by Maurice Vigouroux who is a tremendous craftsman.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Aug 05, 2012 4:48 pm 
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About the real difficulty level

I have written an article about the difficulty of 6-piece burrs in the Puzzle Place forums.

Here are some highlights :

It seems natural to assume that the higher is the level, the more difficult is the disassembly, and the higher is the assemblies(*) / solutions ratio, the more difficult will be the assembly.

(*) An assembly is geometric way to pack the pieces into the final shape, but it doesn't mean that it can be assembled in practice. For example, Philippe Dubois' Burr has two assemblies and one solution. Which means that for one of the two assemblies it would be necessary to break at least one piece in order to get it into the puzzle.
There is enough room inside, but the opening is too small. Eliminating all the wrong assemblies can be a very long process when sovling a burr puzzle from the disassembled state.


However, this is not completely true. There are many exceptions.

For example, Bill Cutler's L46AA Notchable length 8 is a level 6 puzzle, but it is much more difficult to disassemble than Philippe Dubois' Burr, that is also level 6. It is even harder than most other burrs of higher level, like Peter Marineau's level 9, in my opinion.

The presence of dead ends in the disassembling sequence is clearly an important factor, and the L46AA has a lot of them.

The determination of the number of dead ends, however, is even more tricky than the determination of the real level of a burr puzzle. It's not that it is difficult to define. It's just that if we carefully count them, we find that, contrary to what we just said, the L46AA and the Philippe Dubois feature exactly one dead end each !

The explanation lies in the list of all possible moves. We can draw the configuration tree of these moves, representing one configuration of the puzzle with a dot, and the moves with lines allowing to get from one configuration to another.

Here is the configuration tree of philippe Dubois' Burr, from the initial state to the removal of the first piece :

Attachment:
Legende.jpg
Legende.jpg [ 39.65 KiB | Viewed 8564 times ]


The numbers represent the moves as Burrtools counts them. The 1 is doubled because the move is 2 units long, and the 4 is doubled because it involves two pieces that can also move one after the other. Therefore the puzzle goes through 2 distinct configurations when these moves are performed.

And here is the configuration tree for the L46AA length 10, that is level 10 (it is level 6 if the pieces are 8 units long). The cross on the left is the initial state, and the arrow on the right is the removal of the first piece :

Attachment:
L46AA.jpg
L46AA.jpg [ 30.28 KiB | Viewed 8564 times ]


Indeed, there is only one dead end, but there are 4 closed loops before reaching the 6th move ! (the left part of the tree is the same for the level 6 and the level 10 versions). It is exactly like a labyrinth. We are at the starting point, and must cross the maze until we find the exit. And the difficulty of a labyrith doesn't depend only on the number of its dead ends !
The psychological factor is important. Some crossings can be very well hidden, for example in the middle of a move that is several units long. Some paths might lure the puzzlist into thinking that he or her is making progress, while it is only a long dead end.

On the opposite, the dead end in Philippe Dubois' Burr is trivial. It is when the piece is actually free to get out, and you move it in the direction opposed to the exit !

Another extreme example is Bill Cutler's 139 burr. The disassembling tree has 139 nodes. It should therefore be a very complex labyrinth, with a lot of dead ends and loops.
In fact, it is a level one puzzle. The first piece comes at once, and you have to keep it in place on purpose if you want to explore the other possibilities.
So the number of nodes is not a good information.

In last resort, the only way to know exactly how difficult is a puzzle to disassemble, is to play with it.


The assemblies / solution ratio usually gives a better indication about the difficulty of the assembling challenge. But in this direction, there are still exceptions.

With most of the traditionnal 6-piece burrs, the method to find the solution, given the disassembled pieces, is to try all the possibilities until we find the right one. I wrote an article giving the step by step instructions in order to perform this search in the Puzzle Place wiki.

Following this method, we go through all possible assemblies one by one. However, it is very difficult to predict in which order we are going to meet them. With luck, we might find the right one at the beginning, or, on the opposite, have to browse through all the other ones before finding the solution.

With the order that I personally use for sorting my pieces, I find Bill's Baffling Burr solution at the second try out of 24 assemblies... but I must go through 16 assemblies of Abad's level 6.7 out of 25 in order to solve it.

In order to increase the difficulty of the challenge, it would be interesting to place the right assembly near the middle of an ordered list, so that whatever order we choose to try the posibilities, we need to run through at least half of the false assemblies. But the order in which we encounter the assemblies depends on the way we sort our pieces, positions and orientations. It can't be predicted, and I see little hope in doing so.

Anyway, the assembly / solutions ratio is only a part of the difficulty. The number of posibilities to try before completing any assembly is also a determinant factor. I gave an example in the article about the difficulty of burr puzzles, with Philippe Dubois' Burr, where I show that replacing the sorting order of the orientation of the pieces with another one, seemingly equivalent (in fact slightly worse at first sight), the number of steps in order to reach the first assembly, which is the right one in both cases, is divided by 4 !

Therefore, if the assembly / solutions ratio is a useful information, it doesn't rule out surprises.

There is also another case, rarely encountered in 6-piece burrs, but very interesting, where a high number of assemblies doesn't necessary mean a difficult puzzle.

Besides the race to design the 6-piece cross with the highest possible number of moves, designers also have put their attention to the highest possible number of assemblies. Bill Cutler came with the L5 Notchable Most Assemblies. It has one solution for 480 assemblies.
Then Keiichiro Ishino found the Notchable Unique Most Assemblies, one solution, 688 assemblies.
Rafael Abad holds the record. The Abad's Level 5 Most Assemblies Burr has one solution and 896 assemblies.

The goal was maybe to design the most difficult 6-piece burr ever. Indeed, the systematic exploration of all possibilities doesn't seem to lead fast results, and it is quite possible that tens of hours would be needed to solve these puzzles this way.

Surprisingly, this goal was entierly missed, but the resulting burrs are nonetheless very interesting ones. Their structure, probably because of the necessity to make nearly all assemblies impossible, allow the use of a completely different way of resolution, that involves more logic than just taking the pieces one by one and trying them all.

Once I realized this other method could work, I solved Abad's Most Assemblies in 10 minutes !
OK, I was lucky. It took me more than 30 minutes to reassemble it the second time.

I won't tell what is the solution in order not to spoil these puzzles, if they are released one day.
But we can see, again, that mere numbers can be very misleading.


Last edited by Pio2001 on Sun Aug 05, 2012 5:24 pm, edited 5 times in total.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Aug 05, 2012 4:57 pm 
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About the woods

I hope you don't mind if I add another few words about the woods used to make burr puzzles...

The first thing that I look in a wood is if it is an endangered species. Many of the exotic woods used in puzzles are endangered species, some are even considered as critically endangered accordign to the IUCN red list of threatened species. It is the case for wacapou, for exemple.
To find if a wood is listed as endangered, look for its commercial name in Google. Most retailers give its scientific name in their catalog. You can then search for its scientific name in the IUCN search engine.
Some are not on the IUCN red list, but when the wood is rare, grows in only one small location in the world, and is looked after by collectors, it is not difficult to get an opinion. I'm sure that marblewood, for example, that only grows in Guyana, would deserve a good place in the list. As thousands of other species, it just has not been evaluated yet.

It can be useful to remember that international trade of brasilian rosewood, or any object made in this wood, is forbidden by commercial treaties (see the CITES).


A plague with some woods is that they loose their colour over time. It seems related to the exposition to ambient light. Padauk is the worst. After several years, it can completely loose its red tint and become grey-brown, or even green-grey.
This is why I keep all my padauk puzzles in closed boxes.
Bloodwood and bubinga seem to behave the same way, though much more slowly.
Purpleheart is special. First, it becomes more coloured, changing from purple-grey to deep purple, then it looses its tint again, becoming rather brown-purple.
Some woods change colour without necessarily becoming worse. Difou quickly turns from bright yellow to orange. Cherry's orange tint deepens with time. Walnut also gets darker. But these changes can be for the better.
Some woods are slow to change. Beech, maple or ash, for example.
And there are some that doesn't seem to be affected in any way, like marblewood.

Queensland silver ash, western australian jarrah and vitex, woods used by MrPuzzle, also seem completely insensitive to light. But it can also be the beneficial effect of the varnish that Brian Young uses to coat them.
On the opposite, it seems to me that Vinco's wax turns yellow in itself. It can be seen on pieces made in maple... or is it my imagination ?


Besides conservation concerns, the choice of the wood affects the feel of the puzzle. I prefer heavy woods over light ones, neither too hard, nor too soft.
I find bloodwood too hard for large 6-piece burrs. The pieces don't "slide". They either get stuck, or fall into place with brutality.
On the opposite, I find maple too soft. It sometimes feels like if the puzzle was made in a kind of dense foam.

The resulting feel on a given kind of puzzle, however, is very difficult to predict. Maple's softness is not a problem for board burrs, and I've got a different kind of puzzle in bloodwood that looks and feels gorgeous.

For 6-piece burrs, my preferred ones are western australian jarrah (though the varnish of MrPuzzle gets a bit dull after repeated manipulations), dark walnut (difficult to sort out from light walnut, also present into the same boards), and hornbeam, a white wood rarely used in puzzles, surprisingly heavy and hard for a tree growing under temperate regions.

I would like to have a burr made in niove. An orange exotic wood. I only have a box, and some isolated pieces in this wood.
Seeing the craftsmanship found in Indonesia or Thailand, I'm sure that coconut wood would also be great for puzzles.

But sometimes, the simplest solutions are good. Mere pine, with its apparent stripes, gives a nice rustic touch to a puzzle (it doesn't polish well at all, though). Beech also looks very traditionnal, while having an excellent polish.

And the most beautiful wood in my collection may well be Vinco's plum ! If it was a bit heavier, it could rivalize with the finest exotic woods...


Last edited by Pio2001 on Sun Aug 05, 2012 5:31 pm, edited 1 time in total.

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Aug 05, 2012 5:15 pm 
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Puzzlemad wrote:
To all the other forum members out there - this gentleman is one of the greatest solvers of burr puzzles there is! He has even written a very interesting paper on how to go about it. He as even solved the ultra-difficult Tiros 18 piece which requires 150 moves to take out he last piece!

Thank you for your words, Kevin.
But this is unfair : I first failed to solve Burrly Sane for Woodworkers, and looked at the solution, which gave me a hint that was later useful to solve Tiros :wink:

I solved the Century all by myself (a level 100 18-piece burr by Jack Krijnen), true, but Goetz and Aaron did the same.

Puzzlemad wrote:
I have just bought the Fermium board burr (102 moves to extract the first piece) and Nickel box (a boxed burr requiring 28 moves to extract the first piece). They are all made by Maurice Vigouroux who is a tremendous craftsman.

You won't be disappointed with the Nickel box, I can tell you. It's a masterpiece in my collection ! Which version did you choose ? The one in padauk ?


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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Sun Aug 05, 2012 5:40 pm 
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Pio2001 wrote:
You won't be disappointed with the Nickel box, I can tell you. It's a masterpiece in my collection ! Which version did you choose ? The one in padauk ?

I think mine is Padauk. I dealt with Jean-Baptiste direct and he did not give me a choice. The wood is darker than my other Padauk puzzles but also not as deep purple as the Purpleheart in my Tiros. So I am not exactly sure.

It is stunningly beautiful however, and very heavy with the huge amount of ebony in it! So far I have mapped out about 20 moves but not yet found the exit! I strongly doubt that I will be able to reassemble without Burrtools - but I love using that program - it is as much fun as the puzzle itself!!

I really doubt whether I will ever be able to open the Fermium by myself! :shock:

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 Post subject: Re: About the number of moves
PostPosted: Mon Aug 06, 2012 2:30 am 
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Nice to read your thoughts here! :)

Pio2001 wrote:
In 18-piece traditionnal burrs, rotations are not very common. Accordign to my experience, they seem to be present in about 1 design out of 10, or a bit more. Goetz and Rob, who also has got a lot of 18-piece burrs in their collection, might have a different experience.


Of the 18 pieces burrs I have in my collection, I only remember one with a rotation (the level 1 "Super Cross"). In the other Burrs there don't seem to be rotations supporting the solution, while some pieces are quite close to rotations. So, I guess the percentage of rotations is lower in my collection, but maybe that is due to my way of solving them (not actively looking for rotations). If you wonder, which 18 piece burrs I am talking about, here is a list: http://puzzles.schwandtner.info/group_burrs18.html

Pio2001 wrote:
The problem of the second piece


Interesting comments about the second piece and the influence of the level on the removal of the second piece. If I remember right, I also stumbled in a case where two different move sequences for the first pieces were nearly the same length, and depending on which you chose the second piece came out directly together with the first one or only after a few more moves. I believe it was the "Phoenix" or "Phoenix Cabracan".

A different experience I had with the Tiros: I found a solution with 6 moves for the second piece (after the first), while there is a more complicated one with 10 moves for a completely different second piece that others (Guilleaume, Aaron) found first.

In general, the second piece seems more complicated, because you may have to "walk back the solution path" a few steps and decicde where to start the search for the next piece.

Pio2001 wrote:
You won't be disappointed with the Nickel box, I can tell you. It's a masterpiece in my collection !


Indeed, a very nice boxed burr! I especially like the way the color scheme was implemented with the little "dots".

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 Post subject: Re: About the number of moves
PostPosted: Mon Aug 06, 2012 6:16 am 
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goetz wrote:
Of the 18 pieces burrs I have in my collection, I only remember one with a rotation (the level 1 "Super Cross").


Yes, I've got it too.
The level without rotations is 1.1.3.3.6.1.2.5.1.2, and the level with the rotation is 1.1.3.3.3.1.1.1.2.1.2.

I've got another one : Albino, by Alfons Eyckmans. level 39 without rotation, 27 with rotation.

And I tested an unreleased design by Alfons that also features a rotation : Lange Wapper 35. Level 35 without rotation, 19 with.

goetz wrote:
A different experience I had with the Tiros: I found a solution with 6 moves for the second piece (after the first), while there is a more complicated one with 10 moves for a completely different second piece that others (Guilleaume, Aaron) found first.


It is more complicated, but it only uses pieces and moves already seen previously, while the short one uses a completely new move that is very well hidden. That is why I missed it.

goetz wrote:
In general, the second piece seems more complicated, because you may have to "walk back the solution path" a few steps and decicde where to start the search for the next piece.


Yes, especially in very high level burrs. In the Millenium, the information that the level is actually 521.479 is essential. Since the sequence of moves is mostly linear, it gives more or less the position where the second piece can go out, i.e. after you have undone everything you just did :mrgreen:

By the way, Kevin, you may be able to get the first piece out of the Fermium, but you will face the same problem for the second one. So, knowing that the level is 102.95 without rotations, or 100.80 with rotations, you know what you have to do !


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 Post subject: Re: About the number of moves
PostPosted: Mon Aug 06, 2012 6:30 am 
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My approach to Tiros' 2nd piece was different: look for new moves that have not been possible before. That way I found these quite strange moves. :)

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 Post subject: Re: About the number of moves
PostPosted: Wed Aug 08, 2012 6:18 am 
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Pio2001 wrote:
  • If a burr puzzle has no internal holes, does it mean that it has to got one plain key piece that is removed at the beginning of the disassembly ?
  • If a burr puzzle has no internal holes, does it mean that the first piece can be removed in one move only ?


No one ?

Here is another riddle :

Is it possible to decrease the number of moves of a burr puzzle adding one more voxel to the existing pieces ?


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 Post subject: Re: About the number of moves
PostPosted: Wed Aug 15, 2012 4:24 pm 
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Pio2001 wrote:
Pio2001 wrote:
  • If a burr puzzle has no internal holes, does it mean that it has to got one plain key piece that is removed at the beginning of the disassembly ?
  • If a burr puzzle has no internal holes, does it mean that the first piece can be removed in one move only ?


No one ?

Was away on IPP business, so could not answer -- previous post was at the airport when I left Germany. ;)

  • A 6 or 18 piece burr may have no internal holes and no solid "key" piece. The first move would then be a move of groups of pieces, for example the 6 piece burr could be split up into two "halves" with three pieces each after the first move.
  • Same situation as above for the second question. If the puzzle comes apart into two "halves", then these groups have to be disassembled to remove the first piece, leading to 2 moves or more in total for the first piece.

The situation gets worse if you allow 24 piece burrs like the S/M24 or "Lost Day". These don't have internal holes, but you need 7, respectively 3, moves to remove anything from the burr at all.

Quote:
Is it possible to decrease the number of moves of a burr puzzle adding one more voxel to the existing pieces ?


I say no: The solution with the extra voxel would also work with the voxel removed. Thereby the level is the same or increased, not decreased with the extra voxel. Have I overlooked something? :roll:

I am getting the feeling that we are hijacking a forum dedicated for twisties for some other puzzles, but it is in the right section, so I hope the moderators don't mind. 8-)

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 Post subject: Re: About the number of moves
PostPosted: Wed Aug 15, 2012 6:10 pm 
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Hi Goetz,
I hope you enjoyed your trip. Is it you, in the last picture of the "IPP Day 0" message, in Katsmom's blog ?

goetz wrote:
  • A 6 or 18 piece burr may have no internal holes and no solid "key" piece. The first move would then be a move of groups of pieces, for example the 6 piece burr could be split up into two "halves" with three pieces each after the first move.
  • Same situation as above for the second question. If the puzzle comes apart into two "halves", then these groups have to be disassembled to remove the first piece, leading to 2 moves or more in total for the first piece.

The situation gets worse if you allow 24 piece burrs like the S/M24 or "Lost Day". These don't have internal holes, but you need 7, respectively 3, moves to remove anything from the burr at all.


All correct ! The splitting of a solid burr without plain key doesn't even need to be in two halves. In some burrs, it is a pair of pieces that comes out.

For the number of moves, I mean the number needed to remove "something", not necessarily a single piece. But you spotted the trap and quoted the S/M 24 of Bill Cutler, a level 7 burr that has no internal hole... or has it ?

Let's look at it less carefully. Isn't there an enormous hole right in the middle ? Yes there is ! The same is however not possible for traditionnal 6-piece or 18-piece burrs. If they have no internal holes, then something must come in one move only.

So what is the exact condition for a burr to have a part that comes out in no more than one move ? I've read somewhere that the burr must be solid, and convex. It works, but the condition is too restrictive. 6-piece burrs are concave, while solid ones always have a part that comes in one move.

I think that the condition is that there must not be two parts of the surface facing each other.

goetz wrote:
Is it possible to decrease the number of moves of a burr puzzle adding one more voxel to the existing pieces ?

I say no: The solution with the extra voxel would also work with the voxel removed. Thereby the level is the same or increased, not decreased with the extra voxel. Have I overlooked something? :roll:


Yes you have.

The answer is, surprisingly, yes ! I couldn't believe it, but it was found accidentally by Stéphane Chomine with the Burrtools software. He was working on a new design, and he had the surprise to see that, adding one voxel to a given piece, the level dropped from 9 to 1. He thought that the software was bugged, but he couldn't find the error. Both solutions being valid. He sent me the Burrtools file, and I quickly saw what was happening. The software was right. You can add a voxel to an existing burr and decrease its level.

The question is how ?

Hint : it can happen in a traditionnal 18-piece burr, but it is impossible in a traditionnal 6-piece burr.


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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Thu Aug 16, 2012 8:10 am 
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Yes, I had a very good trip to IPP and met many nice people there. And yes, I am in the last picture of this blog post. We were having dinner and much fun with puzzles there.

I am still not convinced about the "adding voxel loosing moves" question. Maybe you could e-mail or PM me the Burr-Tools file (if Stéphane is fine with it, I won't publish it)?

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Thu Aug 16, 2012 2:10 pm 
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File sent !


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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Fri Aug 17, 2012 9:22 am 
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Thanks, file received!

This is indeed an aspect I did not think about: Adding a voxel would allow the piece to appear at a different place because of the outer shape of the puzzle and no holes visible from the outside. It's amazing that the level drops from 9.5... to 1.2... in this case. Would not have expected that!

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 Post subject: Re: Old Fashioned Burr Puzzles
PostPosted: Fri Aug 17, 2012 1:23 pm 
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That's it. As I explained to Goetz in my mail, for this phenomenon to occur, the puzzle must have at least two different kind of pieces.

For example, in a 18-piece burr, there are 6 inner pieces, and 12 outer pieces. When the puzzle is complete, we can only see 8 voxels of each inner piece, while 4 more are visible on the side of the 12 outer pieces.

If you remove one of these 4 voxels, you leave a visible hole on the surface of the puzzle. But the resulting piece might still fit in the center, where this hole would be hidden, while the inner piece replaced may stand in the outer position.

If these conditions are met, and the respective pieces only allow the puzzle to have one solution after they are swapped, then, removing or adding the voxel implies that the pieces must be swapped for the puzzle to have a solution, and these solutions have nothing to do with each other. Their number of moves are not related, and it can very well decrease when you add the voxel.


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