Wednesday, April 5, 2023

Don’t Be A Square – Bent Packing

Bent Packing by Arne Koehn
Tired of working with others that are always right -  angled?  Had enough of cubic dissections?  Looking for a puzzle that has a lot of rotations?  Then it’s time to wrap your mind around the core of Bent Packing.  There are too many squares in this world and Arne Koehn has decided to do something about it.

Bent Packing is an apparent cylinder packing puzzle designed by Arne Koehn.  Not only did Arne design the puzzle but he made the model files available for anyone to print their own copy.  Even selling copies is allowed with the only restriction being to credit the designer.  And on top of all that, the OpenSCAD file used to create the models is included.  Wow! – That’s about as generous as it gets.  You can get everything here:

Before moving on to the puzzle itself, the OpenSCAD file provides a lot of useful information.  Of particular interest, is the code for beveling the pieces using the minkowski function.  It’s absolutely brilliant!  It was posted on the Mechanical Puzzle Discord not too long ago and I’ve already used it a couple times.  In fact, I used it to bevel the pieces for 4 Pack (No Scoop 4U – 4 PAC) and the frame and key piece for Mini Lock (Petits Puzzles – Mini Lock).

Bent Packing Frame Disassembled
The OpenSCAD code also uses the BOSL2 library to provide the threading and lettering.  If you need threaded pieces, the library has a nice set of thread routines that you can screw around with.

Since Bent Packing is an apparent cylinder packing puzzle, you have to pack the pieces inside so that it looks like a complete cylinder from the outside.  There are 3 openings in the frame that need to be filled to accomplish this: the rather large opening in the side used to insert the pieces; a hexagonal window in the side opposite from the piece entrance; and a small window in the top of the puzzle.

So how hard is it to pack the pieces in the frame?  For starters, you can just unscrew the frame, put the pieces in, and screw it back together again.  And before you laugh, this really is a nice feature allowing you to store the puzzle in a non-solved state and safely transport it with all pieces encased without worrying that they will fall out (unless you were foolish enough to pack it in the solved state).

On my first try, I packed the pieces in but failed to fill the hex window.

On my second attempt, I said to myself, Oh, that’s not good.  As the last piece snapped in place, I realized it shouldn’t snap and of course the pieces were stuck.  Good thing the bottom can be unscrewed (I recommend not gluing the frame shut for obvious reasons).  I believe that this move was possible because the pieces were designed with large tolerances to support the widest universal success across a world full of various 3D printers.

Bent Packing Top
Forsaking the use of any force whatsoever, no matter how small, I found myself going around in circles.  That’s pretty easy to do with this particular puzzle.  I eventually discovered that I could pack the pieces in without covering the window on the top.  I was beginning to understand why the windows were placed the way that they were.

Of course, along the way I also found a configuration that can fill all the holes.  Unfortunately, it was not possible to insert the pieces for that configuration.  However, it would make a great way to store the puzzle.  Having run out of time, I had to put the puzzle down for the night and leave it for another day.

Lying in bed the following morning, it suddenly dawned on me what I had been missing.  DUH!  As I sat down at the table with my cup of tea, I quickly solved the puzzle.

As I look at this puzzle, I can’t help but wonder if it could be the next successor to the picnic basket puzzle series.  Could this frame be robust enough to support multiple types of pieces that can be packed within?  Will Arne take on this challenge?  Will others in the puzzle community take on this challenge?  Would it be possible to organize a competition?  These are the things that flitter through my mind as the pieces drift through my fingers.