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.