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Author Topic: My final review about 18 pieces burrs
Guillaume Largounez
Member # 1726

posted November 07, 2010 01:18 AM     Profile for Guillaume Largounez   Author's Homepage   Email Guillaume Largounez     Send New Private Message   Edit/Delete Post   Reply With Quote
As said in the topic about the making of burrs, I recently spent a lot of time playing with high level 18 pieces burrs. Some commercial puzzles, some wooden prototypes, and some prototypes made of plastic with Live Cube.
The pieces of some are described on Keiichiro Ishino's website.

All these puzzles have the classical 18-pieces burr structure :

They have 8-unit long pieces, except the three "Lange Wapper" ones, that have 10-unit long pieces :

I recall that what is called "level" is the number of moves that are necessary to remove the first piece from the assembled puzzle. If the first piece gets out immediately, then the puzzle is level 1. If it gets out at the second move, it is level 2 etc.

List of the puzzles that I have tried

Coming of Age mkII (Brian Young, 2003. Level 14 or 19)
Disassembling : success (about 3 hours for both levels).

Condor's Peeper (Jack Krijnen, 2008. Level 62)
Disassembling : success (3 hours and a half)

Variants of the Phoenix Cabracan puzzle :
Burrly Sane for Woodworkers (Jack Krijnen, 2010. Made with one mistake. Level 117 instead of 138)
Live cube.
Assembling : failure (30 hours, 108 moves correct out of 117).
Burrly Sane for Professionals (Jack Krijnen, 2010. Level 148)
Live cube.
Disassembling : failure (2 hours).
Burrly Sane for Extreme Puzzlers (Jack Krijnen, 2010. Level 152)
Live cube.
Disassembling : failure (5 to 10 hours).
Phoenix Cabracan (Alfons Eyckmans, 2009. Level 113)
Live Cube.
Disassembling : success, because the solution is entierely contained in the solution of the above Burrly Sane variants.
Tiros (Alfons Eyckmans, 2010. Level 150)
Live cube.
Disassembling : success (about 5 hours, thanks to the experience on the other variants).
Garuda (Alfons Eyckmans, made with one mistake. Level 77 instead of 95).
Disassembling : success (1 hour and a half, thanks to the experience on the other variants)

Albino (Alfons Eyckmans. Level 39 according to burrtools, actually 27 thanks to a rotation);
Disassembling : success (2 or 3 hours).

Lange Wapper 14 (Alfons Eyckmans, 2009. Level 14)
Live Cube.
Disassembling : failure (about 5 hours).

Lange Wapper 35 (Alfons Eyckmans. Level 35 according to burrtools, but 19 thanks to a rotation)
Live Cube.
Disassembling : success (1 hour or less).

Lange Wapper 39 (Alfons Eyckmans. Level 39)
Live Cube.
Disassembling : success (between 1 and 5 hours).

General comments on high-level 18 pieces burrs

Most of these puzzles propose a disassembling challenge only. The puzzle is given assembled, and the goal is to find the way to take the pieces apart.

In all these puzzles, the sequence of moves is not trivial. This is not "one move allows the next one, that allows the next one etc". There are choices to be made. A random exploration of possibilities may be enough to find the solution of the disassembling challenge, but not always.
In Tiros, for example, once you have got the first piece out, after 150 moves, you must find the way to remove a second piece. But this is not easy, and if you only trust chance, you may well, as I myself did, perform the 150 moves back until the initial configuration, with an empty space instead of the missing piece, and find nothing.
Since several choices are possible during the sequence, there are actually more than 150 configurations to try. Some logic must be used in order to find the way to go. In this case, it is easy : restrict the search to moves that go through the hole left empty by the piece that is gone.

Even when you try to remove the first piece of these puzzles, there are some designs were it is easier to use logic than in others. Actually, most of the time, it is just anticipation : you look for a piece that seem to be able to be removed. You look at the moves that could free it, then you search combinations that could make these moves possible.
I especially had to use this kind of thinking in the Phoenix variants (the Burrly Sane series, Tiros, Garuda, Phoenix Cabracan), and in Lange Wapper 39.

Trying to assemble the pieces starting from the disassembled puzzle is likely an inhuman challenge with these kind of burrs, because of the existence of many ways to put all the pieces together, but that are actually impossible to perform because there is eventually no way to put the last piece, however we may proceed.

For example, Tiros has 50 impossible assemblies in addition of the right one. Adding more colors, I restricted the number of possible assemblies to 2 only according to the burrtools software. The right one, and another impossible one.
I then studied the differences between the two. Two pieces were swapped. I then realized, still using the burrtools software, that if the impossible assembly existed, it would be possible to perform the 82 first moves of the disassembling sequence before being stuck.

Finding these 82 moves from the right puzzle, properly assembled, is difficult. It should take at least one hour, and possibly much more.
Finding the existence of these moves using only the disassembled pieces is very difficult. For example, it took me 30 hours to find 108 moves using the disassembled pieces of Burrly Sane for Woodworkers.
Realizing that these 82 moves are all that can be done with the false assembly, that we can't go no further and that this is actually not the way the pieces should go, is insanely difficult. That may be possible, but I think that we are leaving the world of puzzle enjoyment and getting into the world of unuseful boring mathematical enumerations.

Starting from the original Tiros pieces and proving the same thing for the 50 false assemblies is practically impossible in my opinion.

That's why I think that in order to maximize enjoyment, and proposing an assembling challenge in addition to the disassembling one, 18-pieces burrs designs should have only one possible solution, but also one possible assembly and no more.

There are exceptions : if, for all false assemblies, not a single piece can move, and the number of false assemblies is less than 100, then the assembling challenge should be possible.
I insist in restricting the number of false assemblies because Coming of Age mkII, for example, has 880 millions of them !
Another exception : the Decemburr puzzle (12 pieces burr, by Goh Pit Khiam, 1999) has 5500 false assemblies, but a clever analysis of the final shape and of the available pieces allows to eliminate 5400 of them at once. Trying the 100 that remain is long, but possible, because in most of the cases, nothing could move if they were assembled.

Trying to restrict the number of assemblies with Burrtools on my two preferred puzzles, Tiros and Lange Wapper 14, I found that in both cases, coloring the three main groups of pieces with different colors, adding grooves in the outer edges of the final shape, and dinstinguishing the opposite grooves of each group of 6 pieces (simple groove on one side and double groove on the other side, for example), was enough to restrict the number of possible or impossible assemblies to one.
In both cases, beveling the corners only, even with two kinds of bevels on each side, was not enough. And grooving uncoloured pieces, even with two kinds of grooves, was not enough either.

Specific comments about the puzzles tried

Usually, the longest the sequence, the more interesting it is. Short disassembling sequences (less than 30 moves) leave little room for logical searching. They are solved with random exploration. Longer sequences tend to be composed of main important steps, that consist in moving key pieces, with casual and often repetitive moves between them. They can be solved by random exploration too, but after some time, their logic becomes apparent.

Among the highest level burrs, Tiros (level 150), and Burrly Sane for Extreme Puzzlers (level 152) were the two ones that I most carefully studied.
They are very similar. The 87 first moves are exactly identical (they are both variants of the Phoenix Cabracan). The sequences are then close for a few moves. The real difference comes at move 109 to 118 of the Burrly Sane for Extreme Puzzlers. An original bit of sequence, difficult to find, that has no equivalent in Tiros. Actually, such interesting moves are also possible in Tiros, but they are unuseful, while they are required in Burrly Sane. But on the other hand, Tiros also has an interesting bit of sequence that Burrly Sane doesn't have : starting with move 147, until around move 168. The lenght of these sequences is meaningless, their real originality is in one or two elegant lateral shifts.
Burrly Sane has the longest total sequence : 209 moves, versus 189 only for Tiros. But after move 150, for me, Tiros looks more difficult than Burrly Sane. Very difficult to choose between the two !

My final preference for Tiros was based on another thing : aroung move 150 or something like that (I have no more a real prototype in order to check) the piece N of Burrly Sane (on Ishino's site) can rotate around two axis at once. Not enough to reach any other position, but it hangs in a quite inelegant way at the back of the puzzle. In Tiros, in the same configuration, the next pieces maintain it in a tighter position, which gives to the puzzle a sturdier look at this stage.

I was also interested in the Lange Wapper puzzles, by Alfons Eyckmans. Their pieces, 10 units long, makes them heavier and a bit more impressive. The Lange Wapper 14 and 39 seem more interesting than Lange Wapper 35.
The number of moves to get the first piece out is not everything. The level including the number of moves for the next pieces are actually for Lange Wapper 14, and 39.8.14 for Lange Wapper 39.
The sequence of Lange Wapper 39 is more interesting. It demands more logic than Lange Wapper 14. And the puzzle remains challenging until the 11th piece gets out, with an original configuration near the end : two groups of pieces interlock each other while being free to slide quite a lot.

But I finally preferred Lange Wapper 14. In fact, Lange Wapper 39 has the same qualities as Tiros, but to a much lesser level, while Lange Wapper 14's sequence seems to highlight more specifically the heavy look of the long pieces, with moves often involving several pieces at once.

If we look at the dates of creation, many of these puzzles were made after 2008. Maybe other, better designs wil be found in the future. But for the time being, from the small selection that I studied, my vote goes to Tiros and Lange Wapper 14.
And if I had a third one to choose, it would be Lange Wapper 39.

Edit : the time spent on Coming of Age mk II was rather 3 hours than 1.

[ November 16, 2010: Message edited by: Guillaume Largounez ]

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Jack Krijnen
Member # 402

posted November 07, 2010 02:43 AM     Profile for Jack Krijnen   Author's Homepage   Email Jack Krijnen     Send New Private Message   Edit/Delete Post   Reply With Quote
Hi Guillaume,

I'm highly impressed by your extensive analyses and your solving abilities. For me, these burrs are merely a quest for each time a higher level. I did never expect someone serieusly trying to solve these extremities. I'm really pleased that I'm wrong in this aspect: apparently you find your joy in playing these puzzles.

Keep the happy puzzling going!

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John Devost
Member # 792

posted November 07, 2010 07:53 AM     Profile for John Devost   Author's Homepage   Email John Devost     Edit/Delete Post   Reply With Quote
Hi Guillaume,

That's quite an impressive study!

I have one of Pit's 'Burrloon' puzzles made by Jerry McFarland in case you'd like to try it out...if so send me an email:

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Guillaume Largounez
Member # 1726

posted November 07, 2010 09:48 AM     Profile for Guillaume Largounez   Author's Homepage   Email Guillaume Largounez     Send New Private Message   Edit/Delete Post   Reply With Quote
Hi guys,
Thanks for your comments.

Since this kind of puzzles are not widely commercialized, it is difficult to know if people would really be interested. Live Cube is quite expensive for the casual puzzlist, not really suited for 18 pieces burrs, and when some wood models are sold on Puzzle Paradise, their price targets puzzle collectors only.

Coming of Age mkII, Condor's Peeper and Gordian Knot, seem to have a significant commercial distribution.

But Coming of Age is not as interesting as the other 18 pieces burrs. The existence of several solutions is disappointing. You don't feel to have "solved" anything when it is done. It's a bit like if someone would have stolen your reward away from you.

Gordian Knot (level has 6 solutions, also. I found a picture of the pieces on the web, made them with Live Cube and tried to assemble them.
After a lot of efforts, I succeeded. Launching Burrtools in order to see if my solution was optimal, I was disappointed to see that, not only it has several solutions, but the one I found was a ridiculous level
On the other hand, it was very interesting that it only took me several hours to find a valid solution among... 10752 false assemblies !
I just tried to assemble the pieces through the openings that left the biggest move liberties. For example, if you see that a piece can fit in 9 different holes, but slide into only one of them, you may discard 90 % of the false assemblies at once. If you are lucky enough to be able to repeat this operation with two other pieces, that's about 99 % of the false assemblies that are discarded.

Among these three puzzles, Condor's Peeper is the only one that gives the real enjoyable feeling of high level 18-pieces burrs. It is something similar both to labyrinths, and chess game.
Like in labyrinths, you explore paths, with crossings, where you have to choose between two or more ways to go on, without knowing which is the right one. Like in a labyrinth, some ways seem to bring you closer to the exit, but things are not always what they seem. You find many dead ends, and must go back in order to try another ways. Sometimes, after a long way, you realize that you are back in the position that you already were before.
And sometimes, when you feel lost, this is like a chess game. You tell yourself "Enough with trusting chance ! I know better than that !". Searching for useful moves, finding the way they could be allowed, sometimes combining useful sequences that you remember, is like trying to gain an advantage over your opponent : if you play that pawn, you threatens the ennemy bishop, but leave your knight undefended. Isn't there any other way than attacking the bishop ?
And don't imagine that when you are trying to move a given piece of your puzzle, the necessary 12 moves are something impossible to remember. After three hours repeating the same 60 moves over and over, back and forth, moving again any of these pieces for any another purpose has become a second nature.

There is also another thing : Live Cube voxels are 15x15x15 mm, while most 18 pieces burrs are made with 9 or 10 mm voxels. The difference in volume is huge, and for me, playing with a large sized burr in much more fun than playing with a small one.
Maybe it is even worse for someone wearing glasses.

I don't think that I would be the only one interested in such challenges. In forums, it is not uncommon to see people spending days trying to disassemble Hanayama's most difficult puzzles.
For me, disassembling Condor's Peeper is no more difficult than to re-assemble Hanayama's Vortex : it took me 3.5 hours to disassemble Condor's Peeper, but 5 hours to rebuild Vortex !

And think about the Rubik's Cube. Today, everyone learns the method by heart from a book or a magazine, but at the beginning, someone had to solve it and write the general method ! And that was much, much more difficult than to solve a high level burr.

That's why I took the time to try the most possible designs. It was Condor's Peeper that enlightened me. I immediately thought about having a bigger version made for me, but when I saw all the designs on Ishino's page, I knew that there were certainly other more interesting ones among them, and I didn't want to miss them.
Of course, there may be some exceptionnal ones among those that I didn't try, and there are certainly thousands of other ones, that have not been found yet.
But I did the most that I could do, and I am happy to have found the ones that I found.

Jack, your search for the highest possible level have given very interesting results.
But among the 12 puzzles above, we can see that the level given by burrtools is actually wrong for two of them because of the presence of a rotation in the middle of their sequence.
This is also true for the Triple Cross, of which I didn't speak here because I solved it 23 years ago, and I can't compare my feelings or the resolution time with todays'.
That's 3 rotations found out of 13 puzzles.

Therefore, creating new designs, after Burrtools analysis, the minimum is to check that no rotation spoils the sequence found.
But it causes another, more difficult problem related with false assemblies : how to be certain that an unseen rotation does not make a given false assembly actually possible ? Burrtools can't check for rotations. This may turn a mighty high level burr into a poor puzzle !
Unless the puzzle can be completely analyzed "by hand", this is another argument in favour of 1-solution 1-assembly designs. At least, the solution can be completely checked by manual exploration.

John, thanks for the offer about the Burrloon, but I am going to rest a little, now ! Maybe one day I'll make a model of it with Live Cube and see if the sequence is interesting (if I can solve it, of course), but for the time being, I'm going to write some specifications that describe how I would like Tiros and Lange Wapper 14 to be made.

[ November 07, 2010: Message edited by: Guillaume Largounez ]

[ November 07, 2010: Message edited by: Guillaume Largounez ]

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John Devost
Member # 792

posted November 07, 2010 01:08 PM     Profile for John Devost   Author's Homepage   Email John Devost     Edit/Delete Post   Reply With Quote
Again Wow! I definitely think you're in the minority when it comes to your fascination with high level burrs...keep on puzzling!
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Guillaume Largounez
Member # 1726

posted November 14, 2010 07:20 PM     Profile for Guillaume Largounez   Author's Homepage   Email Guillaume Largounez     Send New Private Message   Edit/Delete Post   Reply With Quote
Frank Worrell has just published a level 217 puzzle : 10 super sticky sticks.

However, I think I wouldn't like playing with two-dimentional hidden sticks like these as much as with three dimentional visible interlocked sticks, like in traditionnal burrs.

By the way, if you want to turn mad someone who owns a copy of the Tiros burr, disassemble it until pieces J and K are out, swap them, and rebuild the whole puzzle without the piece G (it can't fit if J and K are swapped).

If the way Burrtools gets pieces J and K out is the shortest, solving the puzzle back to its assembled configuration should take 331 moves

[ November 14, 2010: Message edited by: Guillaume Largounez ]

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John Devost
Member # 792

posted November 15, 2010 06:40 AM     Profile for John Devost   Author's Homepage   Email John Devost     Edit/Delete Post   Reply With Quote

I think I wouldn't like playing with two-dimentional hidden sticks like these as much as with three dimentional visible interlocked sticks, like in traditionnal burrs.

I wonder if the cover was made clear (plexiglass) if that would give too much away?

I really do like the simplicity of the pieces...nice design by Frank!

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Guillaume Largounez
Member # 1726

posted November 15, 2010 07:14 AM     Profile for Guillaume Largounez   Author's Homepage   Email Guillaume Largounez     Send New Private Message   Edit/Delete Post   Reply With Quote
Originally posted by John Devost:

I wonder if the cover was made clear (plexiglass) if that would give too much away?

Good idea.
What I wonder myself is wether the disassembling sequence is purely iterative, like with Hanoļ's tower.

[ November 15, 2010: Message edited by: Guillaume Largounez ]

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Goetz Schwandtner
Member # 1787

posted December 08, 2010 06:04 PM     Profile for Goetz Schwandtner   Author's Homepage   Email Goetz Schwandtner     Send New Private Message   Edit/Delete Post   Reply With Quote
After reading this forum for quite a while, I finally registered to post a reply to this thread. I am a German puzzle collector with a special interest in high level Burrs. That's why I followed this thread and also the 18pc-Burr-prototyping thread with high interest.

Guillaume, thanks for sharing your experiences and detailed thoughts in this area!

At the moment I am having a closer look at the three "Burrly Sane Puzzles" which I am proud to own. It's fascinating how similar and yet how different the solutions are! But of course, that can all be found in the thread above ...



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Guillaume Largounez
Member # 1726

posted December 08, 2010 07:00 PM     Profile for Guillaume Largounez   Author's Homepage   Email Guillaume Largounez     Send New Private Message   Edit/Delete Post   Reply With Quote
Hello Goetz,

Thank you for posting. It is nice to see that I am not alone enjoying these kind of puzzles

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Donald Osselaer
Member # 1852

posted June 13, 2011 02:21 PM     Profile for Donald Osselaer   Author's Homepage   Email Donald Osselaer     Send New Private Message   Edit/Delete Post   Reply With Quote
Hi there.
I see you are deeply interested in extreme high level burrs.
I have once created such things about ten years ago. They were created completely in my head and in theory on paper and no computer was used for the designs. I lived in a remote village in the mountains in the south of Spain at that time and did not have access to a computer. There wasn't even running water or electricity. This is why the designs were left untested at the time because I didn't know of any software that could be used to test them. I knew "puzzle solver 3D" but it couldn't do it.
The puzzles are both based on "Torture" by Frans De Vreugd and I added more pieces to make things more complex.
Yesterday, I found this neat freeware "burrtools" software and so I dug up my old puzzle cookbook and finally tested my designs.
To my own surprise ... they worked!

The first one is a 9 piece board burr level 54.49 ... it isn't unique but I found that by adding 3 colors it became unique

Then I tried to really make an insanely complicated burr ... it is a 12 piece board burr in the same fashion ... the level is 220.196!
Burrtools comes up with level 214.190 but burrtools sometimes makes 3 moves at the same time by pulling the whole burr and leaving 3 pieces in their place ... in reality this ins't feasible and humans will keep the burr in it's place and move the 3 pieces seperately ... that's how I come to the 220.196 level of it.
I do not know if it is unique ... there are 8036313307545600 theoretical possible assemblies and that would take millions of years to calculate ... even just calculating the actual possible assemblies would take 2000 years on my PC. ^^

Even colouring the pieces in three colors like with the level 54 it is impossible to calculate all the possibilities.
A test with 6 different colors is running as I'm typing this but will take 5 more hours.
Who knows ... it could be unique by itself

The way you explain the 18 piece burrs and their "logic" way of solving is very much how these puzzles work since they were made by my human brain.
I first thought out the "ideal combination" being 1-2-1-3-1-2-1-4-1-2-1-3-1-2-1-5-1-2-1-... etc. and then I tried to make a puzzle that forced this solution.
I find this type of puzzle to be much more pleasant compared to purely computer random based designs.

I haven't actually made one of these puzzles yet as they are very hard to make
If you are interested I'll post the design and maybe you could have a go at them

[ June 13, 2011: Message edited by: Donald Osselaer ]

[ June 14, 2011: Message edited by: Donald Osselaer ]

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Guillaume Largounez
Member # 1726

posted June 20, 2011 05:01 PM     Profile for Guillaume Largounez   Author's Homepage   Email Guillaume Largounez     Send New Private Message   Edit/Delete Post   Reply With Quote
Hello Donald,
Thank you for your message. Given the way you created them, your puzzles seem to be very interesting.

I may try the small one with LiveCubes, but I think that the pieces of the big one might be too fragile.
They may even be too fragile in wood.
There is an online game where we can play with 3D burrs ( ) but it is unlikely that we can propose them our own designs.

Funny coincidence, I visited some remote villages in the mountains of Spain not long ago

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