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.

You Only Have to - Pack 6

There I was, minding my own business at the IPP34 banquet, when Neil Hutchison plunked down a puzzle in front of me.  It was a beautifully made 6 piece packing puzzle with box and a felt marker.  It was rather large and decorated with multiple signatures.  Neil had the brilliant idea of making a puzzle to bring to IPP for puzzlers to solve and sign as a nice keepsake from the event.  At least that was the objective.  In my case, it was signed without solving.

The puzzle was Eric Fuller’s Pack 6.  It consists of 6 pieces that can be packed into a 4x4x2 shape.  Attentive readers may ascertain how the puzzle’s name was derived.  Although this is not a very difficult puzzle, there is only one solution and it may cause some blameless individuals more than a few minutes to solve while under stressful scrutiny.

I never had an interest in Pack 6 until it embarrassed me that night at the banquet.  Upon returning home from IPP, I immediately made a set of pieces from ¾” red oak stick stock from the local home improvement store to attack the problem again.  I started to analyze the puzzle and determine how the pieces should be oriented to provide 16 cubes on each of the 2 layers but eventually decideded that it would be just as quick to determine how a few key pieces could be oriented within the solved state.  Soon thereafter, I had a nice 4x4x2 shape.


With over 1000 finely crafted puzzles in my collection, Pack 6 is the one that adorns my kitchen table.  Why is that?  Because it is the go to puzzle for my little grandson to play with.  It may not be fancy, but it’s fairly robust for the solving techniques of a 3, now 4, year old.  My goal is to expose my grandchildren to puzzles that they can handle and mentally process as they get older.  So far, Pack 6 has been a skyscraper, a bridge, and even a truck.  Someday it will be a 4x4x2 block.

Eric made the original Craftsman run of Pack 6 in June 2003 and a second run in December 2006.  If you are interested in getting your own copy of the puzzle, Eric sells them on his Cubicdissection Artisan Puzzles page.

Identity I A

Every year, serious puzzle collectors from around the world gather to buy, sell, swap, and discuss puzzles at the International Puzzle Party (IPP).  A major part of the IPP is the puzzle exchange, where participants bring copies of a new puzzle design to exchange with up to 100 other participants.  At the end of the exchange, each participant then has a new puzzle from each of the other exchangers.   You would think that this would be enough puzzles to keep them busy till next year, but for these collectors, it is not even close.

After the puzzle exchange, leftover puzzles are frequently sold at the following puzzle party, which is a large puzzle market featuring a wide variety of the worlds finest puzzle masterpieces from the best craftsmen in the world.  I use the term craftsmen loosely since a few of these renowned craftsmen are women.

One of my primary goals every year is to acquire the puzzle exchanged by Frans de Vreugd.  The designs by Frans hit my sweet spot in terms of puzzle complexity and enjoyment.  When Frans does not provide a puzzle of his own design, he makes sure to provide one of the same caliber.

Frans’ exchange puzzle for last year was Identity I A designed by Andrey Ustjuzhanin.  It consists of four identical pieces packed into a U-shaped frame.  Although many exchange puzzles may be of a slightly lower quality than a craftsman would make to sell, the Identity I A puzzle is of top notch quality.  The frame is made from wenge, one of my favorite types of wood for puzzles.  The pieces are equally nice, but I’m embarrassed to admit that I don’t know the exact type of wood used.  The puzzle is nicely finished and the frame even uses dowels to reinforce the joints.  The color of the pieces and dowels contrast nicely with the dark wenge frame.

The puzzle came assembled and I quickly removed the pieces from the frame and let it sit for a while.  I like to provide enough time to forget any of the disassembly process to make the assembly more challenging.  After all, it’s only five pieces that have to go into the frame and they are all identical.  How hard can it be?

I sat down with the puzzle expecting a short session to get those few identical pieces in the frame and was chagrined that I didn’t allocate enough time to get it assembled.  It took another longer session to figure out how all the pieces go back in the frame.

Usually when solving this type of puzzle, I like to determine how the pieces would be combined outside the frame and then determine the order that they need to be inserted into the frame.  I found this approach more difficult than usual with this particular puzzle due to the large number of voids in the final assembly and abandoned it in favor of simply working with the pieces within the frame.  The frame can hold 40 cubes and the pieces only use 30 or 75% of the space within the cube.

It turns out that there is only one way that the pieces can reside within the cube but the pieces can be added in different orders.  The ordering that requires the least number of moves provides a difficulty of 4.3.3.2.2, i.e., 4 moves to take out the first piece, 3 to take out the second, etc.

Packing puzzles where all the pieces are the same are not new but this one is particularly elegant given that it only has 5 pieces and is a non-trivial packing/interlocking puzzle.  The fact that it is so nicely made makes it even more special.  I’m looking forward to this year’s exchange puzzle.

In The Beginning – The Kimiki Cube

A long, Long, LONG time ago, a little boy took a school field trip to the Museum of Natural History in New York City.  This was a wonderful experience for the little boy who had never been to NYC before and certainly not that far from home without his parents.  Even better, he had 2 dollars in his pocket that his mother had given him that morning to buy something that might catch his interest.

As magical as the museum exhibits were, the little boy was amazed at all the wonderful items on display within the museum gift shop.  Amongst all the fantastical scientific displays, ferocious looking dinosaur figurines, and astronomical paraphernalia, he found himself transfixed by a simple cube, which became his grand purchase.

The cube was obviously made of wood and appeared to be comprised of multiple pieces that interlocked together.  It was even stamped with “JAPAN” on it, which even the little boy knew was all the way on the other side of the world.

After cajoling the first couple of pieces apart, the entire cube disassembled into 12 pieces.  Excited, the little boy ran to show his mother the 12 pieces and explained that she needed to put it back together, which she did.  Little boys don’t like to ask mothers for help and he made sure to never do that again.  His mother is still fearful when he approaches with a puzzle in hand.

He was now on the path.  This puzzle and the many that came afterward, warped the little boy's mind and he had no other recourse than to become an engineer.
 
More than 1000 puzzles later, this first puzzle, the Kimiki Cube, is referred to as Ground Zero.