The Sweetest Burr

Sweet Sixteen family portrait. The one in the bottom right was made by Eric Fuller from Walnut, Maple and Cherry. Photo courtesy Jack Krijnen

Sweet Sixteen family portrait. Top and left were made by Jack, bottom right was made by Eric Fuller from Walnut, Maple and Cherry

Sweet Sixteen is a level-16 eleven-piece burr from Dutch designer Jack Krijnen. After completing the burr in 2002, Jack was playing with names that related to the number 16. He looked at his daughter who was 16 years old and “Sweet Sixteen” came to mind. The name satisfied his penchant for giving his creations identities with a double meaning.

Created several years prior to the release of Burr Tools, this puzzle was designed completely by hand. While Jack’s current high-level burr designs are created through finding a starting set of pieces that seems promising and systematically adding or removing voxels till the level has increased, his older pre-Burr Tools designs began with establishing a move sequence and then determining the shapes that the pieces would need to enable those moves.

In burr puzzles that have been designed by hand one often perceives that the solution involves a highly intentional sequence of movements that is noticeably different to computer-designed burrs. The particular sequence involved in the opening 11 moves of Sweet Sixteen, which are thematically based on Jack’s all-time favourite six-piece burr, are a big part of its charm.

The solving of this puzzle is not just about finding the correct sequence of moves to remove the first piece (and disassemble the puzzle) but equally about discovering the kind of piece sequence the puzzle contains. There’s a nice moment after move six when you realise that you can’t go “forward” any more and have to retrace the steps you’ve made (albeit with one piece shifted). This backward and forward repetition of a move sequence can be found in higher level burrs and, to me at least, makes for a very satisfying burr to play with.

In February 2014, I caught up with Jack via email and chatted about the birth pangs of this puzzle.

Saul Symonds: You have said that when designing Sweet Sixteen, as with other burrs you made at that time, the first thing you did was establish the move sequence. How do you choose the pieces for this: do you play with random pieces or do you target specific piece combinations?

Jack Krijnen: I have used both approaches. Just playing with pieces may lead you to an interesting movement pattern to use in a puzzle. Next you determine a move sequence containing this pattern. Elevenses, for instance, was designed around a double interrupted slide I incidentally found.

In the case of Sweet Sixteen the design started with a specific idea. My all-time favourite 6-piece burr is Peter Marineau’s Piston Puzzle. The first two moves enable a piece to move two units and are subsequently taken back. This leaves the puzzle in a state with just one piece shifted. After that, a four-move sequence frees the first piece. Would it be possible to embed the Piston Puzzle in a larger burr, and lengthen the to-and-fro series of moves?

Sweet Sixteen 1

In the picture (right) the dark pieces represent the Piston Puzzle. The light pieces are ‘free’ to participate in the series.

SS: In Sweet Sixteen moves 1-5 and 7-11 mirror each other. Which of these five moves was the original sequence that you created?

JK: What charmed me most in the Piston Puzzle was the to-and-fro movement: because the first move disables the key sequence, you have to undo respectively move 2 and move 1 later on. I wanted to keep this concept intact, with a longer move sequence. So there’s no separate creation of move 1-5 and move 7-11. The concept of the puzzle implies the mirroring.

The first Sweet Sixteen made by Jack back in 2002. As he explained, “At that time I lacked sophisticated tools. I even did not have a circular table saw. And I hadn’t found a decent wood shop in the vicinity yet; so it’s made from ordinary pine wood bought at a do-it-yourself shop. You can see at the pieces the wood coloured with age.” Photo courtesy Jack Krijnen

The first Sweet Sixteen made by Jack back in 2002. As he explained, “At that time I lacked sophisticated tools. I even did not have a circular table saw. And I hadn’t found a decent wood shop in the vicinity yet; so it’s made from ordinary pine wood bought at a do-it-yourself shop. You can see at the pieces the wood coloured with age.”

Sweet Sixteen made by Jack from beach. Photo courtesy Jack Krijnen

Sweet Sixteen made by Jack from beach

SS: So was it used as a way of increasing the level of the burr?

JK: Of course it raises the level, but my main objective was to keep this concept intact with a longer move sequence. Because of the mirroring every extra move increases the level with two. Maybe I should put it this way: I aimed at as high a level achievable preserving the character of the puzzle.

SS: Were there other to-and-fro move sequence you created whilst designing this puzzle that were discarded in favour of the one that was eventually used?

JK: There must have been. I didn’t keep design documentation, and it was 12 years ago. Finding a to-and-fro move sequence is not a deterministic process leading to the one-and-only. It is looking at a picture of the shape, and imagining what moves are subsequently possible. And even then, the final proof is when you have deduced the shape of the pieces and have performed an analysis proving you were right.

SS: Did the shape of the puzzle and the particular configuration of pieces on each axis, arise out of the search for the to-and-fro sequence, or was it there from the start? It is very similar to your previous Elevenses.

JK: Shape of puzzle and to-and-fro sequence are different things. A to-and-fro sequence is an idea you want to use to lengthen the solution path. The shape may be a design objective (one of my puzzles is an elephant), or a design restriction. At the time I was interested in high-level designs for known rectilinear burr-shapes. My fascination with the Piston Puzzle was projected at the 2x4x5 shape. For the double interrupted slide the 2x3x4 shape was a nice starting point.

Piece J

Piece J

SS: While some designers try to avoid non-notchable burr pieces you seem to relish the possibilities their internal corners offer. One example can be seen in the third and fourth moves of Sweet Sixteen in which piece J (using the lettering on Ishino’s website) moves upwards allowing piece D to slide into its isolated internal corner. Do you have a preference when it comes to choosing burr pieces and how does this choice affect the types of moves in your puzzles?

JK: Notchable pieces are beneficial for puzzle makers. Now there is nothing wrong with making life easy for them, but as I wrote to Eric Fuller (who recently made a batch of Sweet Sixteen) “You will have noticed a couple of complicated pieces to make. Just to challenge you…”.

Photo courtesy Jack Krijnen

Non-notchable burr pieces may be beneficial for designers, for instance when they are aiming at high-levels. Or allow for interesting move patterns. I already mentioned the double interrupted slide in Elevenses. This can be achieved with two relatively simple, but non-notchable pieces (see the picture on the right). In my design perspective notchability of pieces comes second place. When finalising a design I try to reduce the number of “sins against notchability”. That’s also in my own interest, as I’m a puzzle maker too.

Another action at the end of the design is filling up voids where possible, to increase the stability of the puzzle, in assembled state and during assembling.

SS: I would like to ask you about the reference you made at the bottom of the “Tipperary” article [1] to Tim Krabbé’s book on the Babson task as this wasn’t mentioned elsewhere in the text. It wouldn’t be hard to make a link between the search for the Holy Grail of chess puzzles and the search for highest possible burr level. What was its influence on your search for ever-higher level burrs?

JK: Krabbé’s essay on the Babson task (translated from Dutch the English title would be: “The man who wanted to make the Babson task”) is a great book describing the quest of Pierre Drumare for the most challenging chess puzzle one can imagine. An obsessive quest lasting 20 years with a disappointing end.

The design of Tipperary took me six months with an average of one to two hours daily. Later high-level designs also took lots of time. Pierre Drumare made me keep my feet on the ground (and sufficient attention with my wife and children…).

SS: As the level of burrs gets higher and higher it seems that the only feasible challenge is to disassemble them with the reverse procedure often done with the help of Burr Tools. In Sweet Sixteen do you consider the assembled state to be the correct starting point or is disassembled equally valid?

JK: It depends on the number of pieces and the number of possible assemblies. There’s always the disassembling challenge. But an average 6-piece burr will provide an assembling challenge too. In general, with increasing number of pieces, it’s more likely to be a disassembly challenge only. Even with a low number of assemblies it soon becomes undoable; where do you place each piece?

Let’s take Condor’s Peeper as an example. If you neglect the colours, what will the level be? Still 62? I really don’t know. I had Burr Tools run for over a month, only counting the number of assemblies. At 7 billion I stopped the program. Quite an assembling challenge you have here!

On the other side you will find Assembler’s Challenge. I made this design after a discussion I had on a puzzle forum about the 18-piece burr as an assembling challenge. It has one assembly, one solution and only three different pieces. So it is well within the capabilities of most puzzle solvers to start with the disassembled state.

Sweet Sixteen has three assemblies. Four of the pieces are easily identifiable as part of the five pieces in the cross. I think both starting points are valid. It’s for the puzzler to choose.

SS: My version of Sweet Sixteen, which was made by Eric Fuller, has a different coloured wood on each axis which of course aids in assembly. Do you believe this is essential for this puzzle’s assembly?

Sweet Sixteen pieces

Sweet Sixteen in its disassembled state

JK: Of course, different coloured woods lighten the assembling challenge, but for Sweet Sixteen it’s not really necessary. It has a limited number of pieces and of assemblies. There’s another virtue in using different kind of woods though: the joy for the eye. Especially contrasting woods give the puzzle a nice appearance.

SS: When I googled Assembler’s Challenge to have a look at the pieces I came across a forum post discussing a race between you and Maurice Vigouroux to see who could make the smallest puzzle. This isn’t too dissimilar from the race you had with Alfons Eyckmans to see who can make the highest level 18-piece burr. To what extent does competition factor into your burr designs?

JK: Funny as it may sound: I myself am my main opponent in the burr competition. I like to explore my limits, in designing high levels as well as in wood crafting. So I made a small burr, and Maurice made an even smaller one. We discussed limitations, such as the width of the saw blade. And we discussed the woods appropriate for small puzzles; it has to be fine grained. I’m not saying I dislike winning or leading; this is a competitive world, and I am part of it (just a complicated way to say I do like it). But it was Guillaume Largounez who made it into a race.

SS: And when you made Sweet Sixteen where there other designers/designs that you were competing against?

JK: Not for the 2x4x5 shape. I wasn’t familiar with any existing puzzle of this form at the time of the design. Sweet Sixteen still is the only one with this shape at Ishino’s site.

SS: On a similar note, what attracts you to burr puzzles? Your designs are mostly burr puzzles that push the limits of what was previously possible.

JK: To be honest, I never really thought about that. It must be that I’ve always been attracted to problems firing one’s imagination, not only within the puzzle world; we talked about the Babson task earlier. It is curiosity to what is possible and achievable. There’s no challenge in designing a burr with 2 pieces and a level of 100. The 18 piece burr offers all you want: a prescribed shape, yet a number of piece variations and combinations of pieces that makes a brute-force approach (as Bill Cutler did back in the nineties for the 6-piece burr) by far illusive. So how do you find a promising approach to a high-level design? That’s the provocation I can hardly resist.

[1] Jack Krijnen, “It’s a Long Way to Tipperary”, CFF 66

My copy of Sweet Sixteen was made by Eric Fuller at Cubic Dissection and is sold out

All photos and images courtesy Jack Krijnen

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