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)

Wood

Disassembling : success (about 3 hours for both levels).

**Condor's Peeper** (Jack Krijnen, 2008. Level 62)

Wood

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).

Wood.

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);

Wood.

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 14.21.15.11 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.*