A Puzzle of Two Tales – Soma in Case

I hate it!  No, I love it!  No, I’m pretty sure that I hate it!  But it’s great!

Introducing Soma in Case.  This copy isn’t pretty like the one produced by Cubicdissection in 2018.  The quality of the 3D printed box is rough, poorly fitting, and ugly.  There are a lot of artifacts on the perimeters and places where the printer seemed to completely fail.  The pieces are made from Livecubes, which are great for quickly producing pieces, but unfortunately, only four prong pieces were used requiring the prongs to be cut off of one cube of every piece.  And even though the prongs were removed, the base where the prongs are mounted still sticks out from the pieces.  Ideally, each piece would have used 2 cubes with 2 prongs that can be mated to avoid exposed prongs that need to be trimmed.

My apologies to the maker of this puzzle for criticizing a good deed.  In the end, the construction of this puzzle accomplishes its goal of providing an opportunity to experience this excellent design by Hajime Katsumoto.  In fact, nearly all of the solve time was spent searching for the magical assembly using the pieces without the box.   The box is really only needed to verify piece restrictions and testing potential solutions (I use the term potential loosely here since several of the assemblies that I tried had no potential to evolve into a solution).

The style of the box was modeled after (or perhaps before, I really don’t know) the one built by Cubicdissection.  I find the style a bit odd, but it works.  I did like the choice of the top and bottom fill pattern used.

The pieces of the soma cube (3x3x3) consist of 27 cubes and the box is 3x2x5 which holds 30 cubes.  That’s 3 extra spaces!  But wait – there’s a cube attached to the underside of the lid.  Not only does this keep the lid from coming off, but its main purpose is to get in way of adding pieces to the box.  Only 2 empty spaces left.

It doesn’t take much pondering to determine that the space directly behind (or in front depending on your point of view) the fixed cube needs to be empty.  Otherwise, the box would be bricked – and as hard as I tried, I wasn’t able to brick the box.  The remaining empty space could be anywhere

I must have discovered all the ways to assemble the pieces within the box that aren’t possible.  At least it felt that way.  The Cubicdissection description says there are Over 100,000 solutions, only one is assemblable.  Although as a frequent BurrTools user, I would have said over 100,000 assemblies but a single solution, the point comes across that it won’t be trivial.  In fact, I worked on this one for a long time before I finally found that needle in the haystack.

Of course, it’s not a random process where you have to try all assemblies.  You can narrow the search by knowing where one empty space is within the box and hypothesizing where the other could be.  The cube attached to the underside of the lid also restricts how pieces can be oriented within the box.  You quickly realize that the movement of the pieces is very limited within the confines of the box and that rotations are difficult to accomplish.

This copy of Soma in Case may not be the heirloom puzzle (defined as any puzzle that children are not allowed to touch but someday own) coveted by serious puzzle collectors, but I highly endorse the use of 3D printing, Livecubes, and other materials to experience excellent puzzle designs like this one from Hajime Katsumoto.

No Scoop 4U – 4 PAC

Continuing the trend of designing restricted-opening packing puzzles with 4 simple looking pieces, Hajime Katsumoto has provided us with 4 PAC.  The box has a single slot opening to permit the pieces to be entered and several poke holes for you to insert your fingers for manipulating the pieces.  However, for this packing puzzle, the pieces are round, allowing for new types of rotations within the box.  This novelty helped 4 PAC win a Jury Honorable Mention award in the Nob Yoshigahara Puzzle Design Competition in 2021.

This puzzle looks innocuous.  After all, we’ve solved several of these 2x2x3 packing puzzles with simple looking pieces.  This one looks even easier with the pieces made from cylinders, which support rotations around the cylinder’s axis.  When I first saw a photo of this puzzle, my initial reaction was that it could be trivially solved in several ways.  Deep down, I knew this would not be the case and was summarily reengaged by a comment on the Mechanical Puzzle Discord server: The solution doesn't use the scoop move.  The scoop move?  Was this the move that my trivial solutions were based on.  Indeed it was.  After more thought, this move is obviously (I use the term obviously loosely here since it obviously wasn’t obvious on my first pass) impossible.  However, it would have been possible if the top of the box had a thickness of 0 (that’s mm not inches), which the mental construct within my mind indeed had.

Having cleared its reputation of trivialness, I decided to print a copy to solve.  Given the nature of this type of puzzle, it’s easy to deduce how the last piece goes in.  That only leaves figuring out how to add the first 3 pieces.

No Scoop 4U

As with most of these types of puzzles, I take an out-of-the-box approach and attempt to construct the configuration of the pieces inside an imaginary box and envision how they would be removed.  Unfortunately, sometimes you don’t recognize invalid moves like the scoop move.  This one seemed to require more of an in-the-box approach and I thought that I was clever to have a box with a removable lid so that I could experiment without the top.  I use clever as loosely as obviously since it had all the disadvantages of the out-of-the-box approach as well as the frustration of trying to move round pieces in a tight box in orientations that couldn’t be realized with the top in place.  Having exhausted all the poor ways to solve this problem, I was forced to use the better approach.  With the lid ON, I was able to determine how the pieces could be added one-by-one until the box was packed.  What was once a trivial, unwieldy, frustrating fidgety puzzle, became an interesting puzzle with a solid Aha moment.