April 7, 2011

Tipperary by Jack Krijnen

Jack Krijnen was kind enough to send me a copy of a puzzle he designed named Tipperary. He sent it from The Netherlands in December and it finally arrived in February after we both thought it had been lost! Needless to say, we were both quite relieved. Thanks Jack!

It is an 18 piece burr which requires 43 moves to remove the first piece. Jack designed this burr back in 2003 and at the time it succeeded Burrloon (33 moves by Goh Pit Khiam) in highest level. Indeed, it is a long way to Tipperary!
As you may imagine with this number of moves, it was fairly difficult to get it apart. However, the solution does have a pattern to it that makes it pretty easy to remember once you get the hang of it. I think it took me a good 30 or 40 minutes to get the first piece out, and after that it is fairly easy to disassemble the rest of the burr.

As usual, with a burr of this complexity, I took great care to keep the pieces in the correct orientation as I removed them and also kept track of their position. However, when I tried to reassemble it, I arrived at a position where I couldn't figure out how a piece could fit in. Damn! I sweat it out for a while, but it soon became evident that I wasn't going to be able to figure it out. Abandoning hope, I mixed up the pieces in frustration, and then proceeded to sort them by shape. It was actually an interesting exercise, since I previously didn't really understand its construction. Here's a photo of one of the more complex pieces.

If you look at the cluster of six pieces going in the same direction, the two outer pieces and the two inner pieces are essentially the same, which gives the solution a nice symmetry. However, figuring out the location of the remaining six 'inner' pieces is still quite a challenge.

Jack actually wrote an article for Cubism for Fun that described his the design process for this burr, which was quite interesting to read. This "cage" concept for the outer pieces was actually created by Willem van der Poel way back in 1953! The article describes how Jack originally discovered a short sequence of move involving two pieces, and how he drastically increased the move count by adding in a second sequence of moves that interferes with the first sequence. This essentially multiplies the two move counts together, resulting in the length.

The real challenge was to figure out how to make the solution unique, and for this he used a computer to evaluate over a half-million potential assemblies for uniqueness. In the end, he did discover a version that had a unique solution, which is the version posted on Ishino Keiichiro's site, Puzzles Will Be Played. The version he sent me, however, is a bit easier to construct and has four solutions, all of level 43.

So, I was left with a bunch of pieces and no idea how to put them back. Fortunately, there's a great tool named Burr Tools that can solve puzzles like this quite quickly. To my surprise, it actually took a while to solve, about 20 minutes. Usually, it can come up with a solution to a simple puzzle after only a few seconds, so that shows you how complex a process it can be to solve an 18 piece burr!

Using the solution generated by Burr Tools, I carefully put the puzzle back together. It was a bit of a dexterity challenge though, since I had to keep reaching for the keyboard to navigate through the solution while holding the burr in my other hand, hoping it wouldn't fall apart! Eventually I did get back to a position where I could finish it off: I still remembered how the last few pieces went in. Phew! It was quite a relief to get it back together.

Jack did an excellent job constructing this burr, the fit is quite good, and it is not an easy burr to make either! The piece shown here has an inside corner that must have been made square with a chisel. Very nice! The wood he used was Meranti, which Jack says is actually not a very good wood due to tearout when cutting. It has a somewhat unusual aroma, too.

I had a great time with this puzzle, though burrs aren't my specialty, it was fun to play around with this one for a while. About a year ago, Jack developed the Burrly Sane series of 18-piece burrs, that have outrageously long move sequences to remove the first piece:
I will have to try to tackle one these some day, I'm quite curious how they work. Interestingly, they actually have fewer assemblies than Tipperary (which has more than half a million). These have somewhere between 1 and 40 assemblies, which is much more reasonable to evaluate by hand. Of course, finding the assemblies to evaluate in the first place, and then eliminating the ones that don't have valid disassemblies is another problem! A puzzler named Guillaume Largounez has been posting on the Puzzle World Forums about his experiences with various extremely difficult burrs, so check that out if you're interested in reading more. Also check out this section of Rob Stegmann's Puzzle Page for more information on 18-piece burrs.

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