It’s been 6 months since the Penultimate Burr Box Set was released by Cubicdissection. I figured that most people have already solved all 898 of the puzzle challenges by now and that the sets were starting to collect a layer of dust. Instead of generating hundreds of additional 6-piece burr challenges, I decided to determine if I could find a burr puzzle that required more than 6 pieces. In essence, I was looking for the ultimate Penultimate Burr Box Set challenge.
The picture above shows the result of that search. This shape can be constructed with 2 different sets of pieces, each with a unique solution and a 126.96.36.199 level of difficulty. However, the only difference between the 2 sets is the substitution of one piece and the substituted piece is only different by 1 cubie. In effect, there is really only one puzzle. The pieces used are deferred to the bottom of the post in case you wanted to figure out which 8 of the 27 pieces are required to build the shape as part of the solving process. For the sane readers, just keep reading.
To come up with this bonus, I experimented with several shapes using BurrTools until I found this one. Here is a timeline of my experience testing it:
- 0 minutes: With 8 pieces, this looks like a daunting task. Complex Burrs with more than 6 pieces sometimes use different colors for pieces based on their orientation to help the solving process. Of course, all these pieces are of the same type of wood and nothing special has been done to aid the solving process. Then again, this puzzle wasn’t specifically designed to be difficult by an evil (I use this word in the most affectionate way possible) puzzle designer.
- 5 minutes: OK, I think that I know which pieces are the 4 that go together, which I will refer to as frame pieces, and the 4 that cross each other inside it, which I will refer to as cross pieces. I already have 7 pieces in place. How hard can it be to add 1 more? I’ll probably have to shuffle some pieces around, but it shouldn’t be a big deal. I’m also pretty sure what the last piece to be added is.
- 10 minutes: I now have 7 pieces where it looks like the last piece would fit inside. However, there are 48 possible assemblies and only 1 can be constructed. After some fiddling around, this one doesn’t seem to be the lucky one.
- 1 hour: Uh, maybe all this trial and error isn’t the way to go. I keep doing the same thing over and over. Time to break down and start thinking about it. There are 48 different ways to put the 4 frame pieces together and then there are 24,576 ways to place the 4 cross pieces inside, resulting in 1,179,648 different combinations and that is assuming that I was correct in the division of pieces. Given these numbers, most puzzlers take the lazy way out and start thinking about how to solve the problem. It seems that 2 of the cross pieces have to work together and this appears to lock up the 4 frame pieces where you can’t add the other 2 cross pieces.
- 1 hour, 15 minutes: Solved! For me, the trick was figuring out what the second to last piece to be added was and arranging all the other pieces so that this move could be accomplished.
Any excuse to pull out the Penultimate Burr Box Set is a good one. The set is beautiful and well crafted. The pieces are spot on and a pleasure to play with. Cubicdissection did a fantastic job making these sets and I always enjoy spending time with it.
The pieces required to make the ultimate Penultimate Burr Box Set challenge puzzle are: 5, 6, 7, 8, 9, 10, 15, and 12 (or 17 instead of 12).