A Christmas Present For You 2! – Penultimate Burr Box Set 7-Piece Burr Challenges

I know that by now, most of you have completed all 898 Penultimate Burr Box Set challenges including last year’s Christmas Challenge and were wondering what to do with that old dusty box.  In the event that you haven’t sold, traded, or regifted your stick collection, there is now an entirely new set of challenges for you.

6-Piece burrs have been all the rage with everyone amassing large quantities of this venerable puzzle and all its variants.  However, the 6-piece burr is so 2020!  As we leave 2020 behind us, a new set of challenges is needed for 2021.  Enter the 7-piece burr, 6’s lesser known brother.

Of course, there are multiple ways to construct a shape with 7 burr pieces.  With the construction that I chose, BurrTools indicated there are 3,232,523 assemblies and 184,687 solutions.  In English, this means that there are 3,232,523 ways that 7 of the burr pieces from the set can make the 7-piece burr shape, but only 184,687 of these assemblies can be taken apart.  Further analysis indicates that 471 of the solutions are unique.  A unique solution is one where the 7 pieces cannot be rearranged to make the 7-piece burr another way.  Of the 471 unique solutions, 38 are level 2 and the remaining 433 are level 1, where the level is the number of moves required to remove the first piece or set of pieces from the puzzle.

I haven’t completed all 471 solutions yet.  OK, I’ve only done the first one so far.  I didn’t find it that difficult but it does require some different thinking.  In the 6-piece burr, all the pieces basically perform the same function, however in the 7-piece burr, 2 of the pieces now function differently.  This can be leveraged during the solution process.

First Attempt: During my first attempt, I managed to assemble 6 of the pieces into an assembly that would have accommodated the final piece, but there was no way to add that piece.  Some extra thinking was required to find an assembly that can be constructed.  

Second Attempt: My second attempt was close, but the parity of the last piece was wrong for the assembly that I was constructing.  (sheesh, what does he mean by parity? – Basically, the assembly had a hole on the left and the piece had a cube on the right).  

Final Attempt: Assuming that the final piece was correct, I rebuilt the assembly with a parity to match the piece and it finally went together.

Some of the puzzles will be very similar to each other and you may want to cherry pick ones that look interesting.  Then again, 2 puzzles may only differ by 1 piece yet be entirely different. If you would like to give these a try yourself, the pieces required for the unique solutions are below.  Hopefully, these challenges will keep your set from joining the yuletide log.

Level 2 Unique Solution Piece Sets:

6,7,9,10,15,17,19	6,7,9,10,15,17,20	5,6,7,12,17,22,24	5,6,7,10,21,22,24
5,6,7,12,15,20,22	5,6,7,15,17,23,24	3,5,6,7,8,22,24	6,7,9,10,11,17,24
5,6,7,9,16,19,24	5,7,10,12,15,18,24	5,6,7,9,19,24,25	5,6,7,10,15,23,24
5,7,10,12,17,22,24	5,6,7,9,17,24,26	4,5,6,7,8,22,24	4,5,6,7,11,15,24
5,6,7,15,17,18,24	5,6,7,12,15,17,22	5,6,7,15,17,20,22	6,7,9,10,14,15,19
6,7,9,10,14,15,20	5,6,7,10,20,22,24	5,6,7,10,19,22,24	5,6,7,12,15,23,24
5,7,10,15,17,18,24	6,7,10,11,12,15,17	5,7,10,12,15,17,22	5,7,10,12,15,17,24
5,6,7,10,15,22,26	5,6,7,10,15,24,26	6,7,10,12,14,15,17	5,6,7,17,20,22,24
5,6,7,9,17,23,24	3,5,6,7,11,15,24	5,6,7,12,20,22,24	4,5,6,7,10,15,24
5,6,7,12,15,18,24	6,7,10,13,14,15,17

Level 1 Unique Solution Piece Sets:

5,7,9,10,18,21,24	5,7,9,10,15,18,23	5,7,9,10,15,18,26	5,7,10,11,15,16,19
5,7,10,11,15,16,22	5,7,10,11,15,16,24	1,5,7,8,10,18,22	4,6,7,8,9,10,22
4,6,7,8,9,10,24	1,3,5,6,9,10,15	5,6,7,15,17,21,23	5,6,7,15,17,21,26
5,7,9,10,13,16,19	4,5,7,9,10,15,22	4,5,7,9,10,15,24	5,7,9,10,13,16,20
6,7,9,10,13,15,23	6,7,9,10,13,15,26	1,5,7,9,10,12,19	1,5,7,9,10,12,20
5,6,10,13,17,24,25	5,6,7,11,13,24,26	5,7,10,11,15,18,19	1,5,6,9,10,21,24
5,7,10,14,15,17,18	5,7,9,10,14,19,22	5,7,9,10,14,19,24	5,7,9,10,14,19,25
5,7,10,14,15,17,21	5,6,10,14,15,16,17	1,5,6,10,15,16,17	1,4,5,6,9,10,15
5,7,9,10,16,21,24	5,7,9,10,13,18,19	5,7,9,10,13,18,20	1,5,6,10,14,15,18
1,5,6,10,14,15,19	1,5,7,9,10,14,19	5,7,10,11,13,16,24	1,5,7,9,10,14,20
5,6,10,11,15,19,22	5,6,10,11,15,19,24	5,7,10,11,12,15,21	5,7,10,14,15,19,22
5,7,10,14,15,19,24	5,7,10,14,15,19,25	5,7,9,10,11,16,19	5,7,9,10,11,16,20
5,6,10,14,15,18,22	5,6,10,14,15,18,24	5,7,10,11,17,22,24	3,5,6,7,8,24,25
1,5,7,10,15,16,17	6,7,9,10,11,15,23	6,7,9,10,11,15,26	5,6,7,13,15,18,23
5,6,7,13,15,18,26	5,6,9,10,21,22,24	5,7,10,11,13,18,24	5,7,9,10,15,22,23
5,7,9,10,15,22,26	4,5,6,7,9,17,19	1,5,7,10,14,15,18	1,5,7,10,14,15,19
1,5,7,9,10,16,22	1,5,6,10,11,12,22	4,5,6,7,9,17,20	5,7,9,10,12,19,24
5,6,9,10,17,19,22	5,6,9,10,17,19,24	5,6,9,10,17,19,25	5,7,9,10,14,21,24
1,5,7,8,10,22,25	5,7,9,10,11,18,19	5,7,9,10,11,18,20	4,5,6,7,8,16,24
6,7,8,9,10,22,23	6,7,8,9,10,22,26	5,6,9,10,16,18,24	5,6,7,9,21,23,24
1,5,6,10,12,15,16	1,5,6,10,12,15,19	1,5,6,10,12,15,21	5,7,9,10,13,20,25
5,6,9,10,18,20,24	4,6,7,8,10,14,15	5,7,10,12,15,16,21	5,7,10,12,15,16,22
5,7,10,12,15,16,24	5,6,7,9,20,22,23	5,6,7,9,20,22,26	1,5,6,7,9,13,23
5,6,7,13,17,22,23	1,5,6,7,9,13,26	5,6,7,13,17,22,26	5,7,9,10,15,24,26
1,5,7,9,10,18,24	1,5,6,10,11,14,24	1,5,7,10,11,12,22	5,7,10,11,15,22,25
5,7,10,12,14,15,21	5,7,10,15,17,19,22	5,7,10,15,17,19,24	5,6,10,15,17,18,19
1,5,6,8,10,16,24	1,5,7,8,10,24,25	6,7,8,9,10,24,26	1,4,5,6,7,9,12
5,6,10,15,16,17,18	5,6,10,15,16,17,19	1,5,7,10,12,15,16	1,5,7,10,12,15,19
5,6,10,15,16,17,22	5,6,10,15,16,17,24	5,6,10,15,16,17,25	5,6,9,10,18,22,24
1,5,7,10,12,15,21	5,7,10,12,15,18,21	3,5,6,7,9,12,19	3,6,7,8,10,15,17
3,5,6,7,9,12,20	1,5,7,10,11,14,24	5,7,10,11,15,24,25	4,5,6,7,15,17,19
1,5,6,8,10,18,22	1,5,6,7,8,14,23	1,5,6,7,8,14,26	5,6,10,12,14,16,24
3,5,6,7,15,16,17	5,7,9,10,11,20,25	5,6,9,10,16,20,24	4,5,6,9,10,15,16
4,5,6,9,10,15,17	4,5,6,9,10,15,18	4,5,6,9,10,15,22	4,5,6,9,10,15,24
4,5,6,9,10,15,25	3,5,6,9,10,14,15	5,6,10,11,14,22,24	5,6,9,10,18,24,25
5,6,9,10,12,16,19	1,5,6,9,10,12,19	5,6,10,12,15,19,22	5,6,10,12,15,19,24
5,7,10,11,13,22,24	5,6,7,9,14,19,23	5,6,9,10,12,16,20	5,6,10,12,15,19,25
5,6,7,9,14,19,26	1,5,6,9,10,12,20	1,5,7,9,10,20,22	1,5,7,9,10,20,24
5,6,7,11,15,19,23	5,6,7,11,15,19,26	5,7,10,15,17,21,22	5,7,10,15,17,21,24
5,7,10,15,17,21,25	5,6,7,14,15,18,23	5,6,7,14,15,18,26	5,6,10,12,14,18,24
4,5,6,7,12,14,24	5,6,9,10,16,22,24	4,6,7,9,10,12,15	5,6,9,10,13,19,22
3,6,7,9,10,11,15	5,7,10,13,17,18,22	5,6,9,10,12,18,19	1,5,6,9,10,14,19
5,6,9,10,12,18,20	5,7,10,11,13,24,25	1,5,6,9,10,14,20	4,5,6,7,13,17,24
5,7,10,13,16,17,22	5,7,10,13,15,16,18	5,7,10,13,15,16,19	3,5,6,7,12,15,16
3,5,6,7,12,15,19	3,6,7,9,10,13,15	5,6,9,10,15,23,24	3,5,6,7,9,18,24
1,5,6,9,10,16,22	5,6,10,12,15,21,22	5,6,10,12,15,21,24	5,6,9,10,11,19,22
5,6,9,10,11,19,24	1,5,6,8,10,22,25	5,6,7,9,13,20,23	5,6,7,9,13,20,26
4,5,6,7,8,24,25	5,7,10,13,15,18,19	5,7,10,13,15,18,22	5,7,10,13,15,18,24
5,7,10,13,15,18,25	5,7,9,10,21,22,24	4,5,6,7,11,17,24	1,5,6,9,10,18,24
5,6,9,10,12,20,25	5,7,9,10,17,19,22	5,7,9,10,17,19,24	6,7,8,10,14,15,23
6,7,8,10,14,15,26	5,6,7,11,15,23,25	3,5,6,7,10,15,24	1,5,6,8,10,24,25
5,6,7,8,22,23,25	5,7,9,10,16,18,22	1,3,5,6,7,9,12	5,6,10,13,15,19,22
5,6,10,13,15,19,24	5,7,9,10,18,20,22	5,7,9,10,21,24,25	5,7,9,10,15,17,23
5,7,9,10,15,17,26	5,7,10,13,17,22,25	3,5,6,7,9,20,24	5,7,9,10,14,16,19
5,6,7,9,11,20,23	5,6,7,9,11,20,26	5,7,9,10,14,16,20	5,6,7,11,15,25,26
5,6,7,8,22,25,26	5,6,10,12,14,24,25	5,6,10,11,17,18,24	5,6,7,11,14,24,26
5,7,9,10,18,22,24	5,6,10,11,16,17,24	1,5,7,9,10,11,19	4,5,6,7,9,12,19
1,5,7,9,10,11,20	4,5,6,7,9,12,20	5,6,7,11,13,23,24	1,5,6,9,10,20,22
1,5,6,9,10,20,24	5,7,10,11,15,17,21	5,7,9,10,14,18,19	5,7,10,14,15,16,18
5,7,10,14,15,16,19	5,7,9,10,14,18,20	5,6,10,11,15,16,22	5,6,10,11,15,16,24
5,6,7,11,12,22,23	5,6,7,11,12,22,26	5,6,7,10,15,16,20	5,7,10,11,14,16,24
5,7,9,10,16,20,22	3,5,7,9,10,15,22	3,5,7,9,10,15,24	5,6,7,8,18,22,23
5,6,7,8,18,22,26	1,5,7,9,10,13,19	1,5,7,9,10,13,20	5,6,7,12,15,21,23
5,6,7,12,15,21,26	5,7,10,11,15,19,22	5,7,10,11,15,19,24	5,7,10,11,15,19,25
6,7,9,10,12,15,23	6,7,9,10,12,15,26	5,7,10,14,15,18,19	5,7,10,14,15,18,22
5,7,10,14,15,18,24	5,7,10,14,15,18,25	1,5,6,10,15,17,19	1,5,6,10,15,17,21
5,6,7,10,15,18,20	5,7,10,11,14,18,24	5,7,9,10,16,22,24	5,7,9,10,16,22,25
5,7,9,10,13,19,22	5,7,9,10,13,19,25	1,5,7,9,10,15,23	1,5,7,9,10,15,26
5,6,9,10,17,18,19	5,6,9,10,17,18,20	1,5,6,10,13,15,18	1,5,6,10,13,15,19
5,7,10,11,12,16,22	5,7,9,10,14,20,25	5,6,7,12,14,22,23	5,6,7,12,14,22,26
5,6,9,10,16,17,19	5,6,10,14,15,19,22	5,6,10,14,15,19,24	5,6,9,10,16,17,20
5,6,10,11,17,22,24	1,5,7,10,15,17,19	1,5,6,10,12,14,22	1,5,6,10,12,14,24
5,6,7,13,15,19,23	5,6,7,13,15,19,26	1,5,7,10,15,17,21	1,3,5,7,9,10,15
1,5,7,9,10,17,19	5,7,9,10,15,23,24	5,7,9,10,15,23,25	1,5,7,9,10,17,20
1,5,6,10,11,13,24	4,5,6,7,9,18,24	1,5,6,10,13,17,22	5,7,10,15,17,18,21
1,5,6,10,13,17,24	5,7,10,11,12,18,22	1,5,6,7,8,11,23	1,5,6,7,8,11,26
1,5,7,10,13,15,18	1,5,7,10,13,15,19	5,7,9,10,11,19,22	5,7,9,10,11,19,24
5,7,9,10,11,19,25	6,7,8,9,10,23,24	1,4,5,6,7,8,17	5,6,7,9,21,24,26
5,6,10,11,17,24,25	5,7,10,15,16,17,21	5,7,10,15,16,17,22	5,7,10,15,16,17,24
5,7,9,10,13,21,24	1,5,7,10,12,14,22	1,5,7,10,12,14,24	4,6,7,8,10,15,17
5,6,10,12,15,16,18	5,6,10,12,15,16,19	1,5,6,10,11,15,16	1,5,6,10,11,15,19
3,6,7,8,10,14,15	5,7,9,10,15,25,26	5,6,10,12,15,16,22	5,6,10,12,15,16,24
5,6,10,12,15,16,25	1,4,5,7,9,10,15	1,5,6,10,11,15,25	5,6,9,10,17,20,25
5,6,9,10,20,24,25	1,5,7,10,11,13,24	5,6,7,11,15,16,23	5,6,7,11,15,16,26
5,7,10,12,14,16,22	4,5,6,7,15,16,17	3,6,7,8,9,10,22	3,6,7,8,9,10,24
5,6,10,11,15,22,25	5,6,10,15,17,19,22	5,6,10,15,17,19,24	5,6,10,15,17,19,25
1,5,7,10,13,17,22	1,5,7,10,13,17,24	5,6,7,10,15,22,23	4,5,6,9,10,14,15
5,7,10,11,14,22,24	5,7,10,12,13,15,21	5,7,10,12,15,19,22	5,7,10,12,15,19,24
5,6,10,12,15,18,19	1,5,6,9,10,11,19	1,5,6,9,10,11,20	1,5,6,10,11,17,24
4,5,6,7,9,20,24	1,5,7,10,11,15,16	1,5,7,10,11,15,19	1,5,7,10,11,15,25
5,6,9,10,14,19,22	5,6,9,10,14,19,24	5,7,10,12,14,18,22	5,6,10,11,15,24,25
3,5,6,7,15,17,19	5,7,9,10,11,21,24	4,6,7,9,10,11,15	5,7,10,11,14,24,25
3,5,6,9,10,15,16	3,5,6,9,10,15,17	3,5,6,9,10,15,18	3,5,6,9,10,15,22
3,5,6,9,10,15,24	3,5,6,9,10,15,25	1,5,6,9,10,13,19	1,5,6,9,10,13,20
1,5,7,9,10,21,24	5,6,10,11,13,22,24	1,5,7,10,11,17,24	5,6,7,9,16,22,23
5,6,7,9,16,22,26	5,6,7,14,15,19,23	5,6,7,14,15,19,26	5,6,7,9,13,19,23
5,7,10,11,12,22,25	5,6,7,9,13,19,26	4,5,6,7,12,15,16	4,5,6,7,12,15,19
5,6,10,15,17,21,22	5,6,10,15,17,21,24	4,6,7,9,10,13,15	3,5,6,7,12,14,24
3,6,7,9,10,12,15	5,6,9,10,15,22,23	5,6,9,10,15,22,26	5,7,10,12,15,21,22
3,5,6,7,9,17,19	5,6,10,13,17,18,24	5,7,10,12,15,21,24	5,7,10,12,15,21,25
3,5,6,7,9,17,20	5,6,9,10,12,19,24	5,6,9,10,12,19,25	1,5,6,9,10,15,23
1,5,6,9,10,15,26	5,6,7,9,14,20,23	5,6,7,9,14,20,26	3,5,6,7,13,17,24
5,6,10,13,16,17,24	3,5,6,7,8,16,24	5,7,10,13,15,17,21	5,6,9,10,15,24,26
1,5,6,9,10,17,19	1,5,6,9,10,17,20	5,6,7,9,11,19,23	5,6,7,9,11,19,26
5,7,10,12,14,22,25	1,3,5,6,7,8,17	5,7,10,13,15,19,22	5,7,10,13,15,19,24
5,7,10,13,15,19,25	5,6,10,13,15,18,22	5,6,10,13,15,18,24	5,7,9,10,15,16,23
5,7,9,10,15,16,26	6,7,8,10,15,17,23	6,7,8,10,15,17,26	3,5,6,7,11,17,24
5,7,9,10,20,22,25	5,7,9,10,14,15,23	5,7,9,10,14,15,26	1,5,7,8,10,16,24
5,6,7,11,14,23,24

A Christmas Present For You – Ultimate Penultimate Burr Box Set Challenge

 

Merry Christmas!  Hopefully, Santa left you many puzzles under the tree.  And if you don’t celebrate Christmas, a Happy Whatever You Celebrate to you!

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 1.2.2.2 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.

• 

  Wrong Orientation!

  15 minutes: I’ve got them all together!  Wait a minute.  They aren’t in the correct orientation.  However, I’m pleased to have found another symmetric target shape.  I decided to check out my clever new shape in BurrTools.  In seconds, BurrTools started laughing and informed me that there at 92 different ways to construct that shape with those pieces.  92 different ways!  If you dropped the pieces on the table they would probably fall into that shape.  OK, so let’s call that the easy, warm-up objective.
• 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.

Is this a good puzzle?  Yes and no.  It was a lot of fun to work on and well worth doing.  If you have the Penultimate Burr Box Set, definitely pull it back out, dust it off, and enjoy this ultimate challenge.  It’s a great puzzle!  If you don’t have the set and someone offers to sell you this puzzle, don’t buy it.  It’s a terrible puzzle!  This puzzle was not specifically designed to be a clever 8-piece burr puzzle and would be scoffed at by any discerning puzzle collector.  It’s fine as a puzzle challenge in a large burr set, but not good enough to justify as a standalone puzzle.

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).

Penultimate Burr Box Set

When is a puzzle set a better puzzle set.  When it has more puzzles of course!  This was the goal of the Penultimate Burr Box Set in Cubicdissection’s latest offering by master craftsman Eric Fuller.

Eric just gave notice that he is entering the next stage of Cubicdissection’s evolution by discontinuing the GEM series and most of the Artisan series to focus on the high-end Signature series of puzzles.  This news was punctuated with the release of several stunning puzzles, the king of which was the Penultimate Burr Box Set.

The Penultimate Burr Box Set was provided in 4 different types of wood combinations with a total of 74 being offered.  They quickly sold out and those lucky enough to acquire one will not be disappointed.  Mine has a Quatersawn Curl Jatoba box with Wenge top and Figured Walnut bottom, Ash pieces, and a Padauk logo.  It’s absolutely stunning and obvious that Eric was looking to make a big statement with this collectible piece.

What I really like about Eric’s approach to selecting and producing puzzles is that he thinks outside the box, or in this case, thinks outside the box inside the box.  Since there were 27 pieces, I assumed that the box would have 3 rows of 9 pieces each.  I was pleasantly surprised to see that it had a nicer shape consisting of 4 rows of 7 pieces each with the Cubicdissection logo in the center of the bottom row in contrasting wood.

Contents of the Secret Drawer

But where are the instruction?  Did I mention what a phenomenal undertaking this effort was?  Did you notice the word Penultimate in the name?  If you were assuming that Penultimate only referred to the large number of puzzles you can construct, you’d be wrong.  Eric wasn’t satisfied with simply making a nice box holding 27 pieces, he wanted more, much more.  In addition to the beautiful set, he added one more hidden touch – It’s a puzzle box!  The instructions for the set are stored in a hidden compartment within the set that must be solved to gain access to the instructions along with a Cubicdissection sticker.

The Penultimate Burr Box Set’s 27 pieces can be used to make a multitude of 6 piece burrs.  Each piece requires phenomenal accuracy since it is not feasible to test every 6 piece burr that can be made with the set to ensure a good fit.  The set of burr pieces was originally defined in Creative Puzzles of the World by Peter Van Delft and Jack Botermans.  Along with the description, they provided solutions for 69 burrs that can be created.  Unfortunately, Van Delft and Bottermans defined the 6 piece burr as being solid with no internal voids, which left most of the set’s potential untapped.

Knowing that Ken Irvine (it’s strange talking about myself in the 3rd person - I hope it doesn’t become a habit for Ken) did an analysis of this burr set in the past with pieces that were 8 units long for the Ultimate Burr Set, Eric requested that the analysis be redone with pieces that were 6 units long for the Penultimate Burr Box Set. 

The Penultimate Burr Box Set analysis showed that 708 burrs with internal voids could be constructed with unique solutions, i.e., the 6 pieces can’t be reconfigured for another solution.  This is an additional 173 burrs compared to the 535 supported by the Ultimate Burr Set.  Each solution requires from 1 to 5 moves to remove the first piece as shown in the following table.

Moves to Remove First Piece	Unique Burrs
1	256
2	156
3	191
4	100
5	5

After rescuing the analysis paper from its well-hidden secret compartment in the box, I was wondering which of the 708 puzzles I should start with.  Having rapidly worked through other sets in the past I was feeling cocky and thought that maybe I should just jump to the 4 and 5 move puzzles and initially thought that I wouldn’t bother with the 1 move puzzles at all.  In the end, I decided on picking a 1 move puzzle to get things going.

After selecting a 1 move puzzle, I took the 6 pieces and quickly determined that burrs with arbitrary holes are more difficult to solve than ones that only have meaningful holes supporting specific movements.  This has been proven before when Bill Cutler and Brian Young took a perfectly difficult 6 piece burr, Computer’s Choice Unique-10, and removed another cube to make it even harder as Mega Six.

At one point, I panicked and thought that maybe the pieces of the set didn’t match the pieces in the analysis.  I assuaged my fears by pulling out my copy of Creative Puzzles of the World and verifying that the pieces did indeed match.

Instead of simply putting it together, I had to resort to thinking.  This is usually the last resort in puzzle solving but sometimes comes in handy.  Now armed with a process for solving the 1 move puzzles, I made quick work of that first puzzle.  For the puzzle that I selected, the first move separated the puzzle into 2 sets of 3 pieces.  I suspect that this process will stand up well for the other 255 1 move puzzles but will need to be updated for the puzzles requiring multiple moves to remove the first piece.

For those not daunted by building all 708 unique burrs, there are another 20,322 6 piece burr combinations that have multiple solutions.  The analysis identifies combinations of pieces for an additional 190 non-unique burrs requiring at least 4 moves to remove the first piece.

The full Penultimate Burr Box Set Analysis can be found here.