Arranging Your Balls - Pyradox

So, how many different ways are there to arrange your balls.  It turns out that it’s the same as the number of licks it takes to get to the tootsie roll center of a tootsie pop as demonstrated by Mr. Owl – Three.

The summer of 2018 was a time of many fine things, the foremost being the Edward Hordern Puzzle Exchange at IPP 38 in San Diego.  Amongst the many enticing entries was Pyradox exchanged by George Bell, designed by George Bell, made by George Bell, and packaged by George Bell.   I’m specifically calling out the packaging since it’s nice and compact and well laid out within a transparent box.

Packing balls in tight spaces is a niche area of spatial mathematics and ball packing master George Bell has written several articles concerning this topic.  CFF Issue 94, July 2014, includes George’s article on the development and analysis behind Pyradox – Pyradox: A Pyramid Packing Puzzle.  The article also describes how George paradoxically accomplished the impossible when creating this puzzle.

Pyradox consists of 5 plane looking pieces and 3 coasters.  The objective is to fulfill your prayers by fully filling the holey coasters with a pyramid.  Each polysphere piece consists of 4 wooden balls glued together with colored bands.  Each of the 3 colors used, red, blue, and green, identifies a unique piece shape.  On careful inspection, you will notice that one of the 3 types of shapes is different, which may be useful when solving the puzzle.  The 3 base plates are made from laser cut wood with Pyradox engraved on each and I don’t really recommend that you use them as coasters.

Each base plate provides a different pyramid building challenge.  To make it easier for you, one utilizes hexagonal close packing, one a face-centered cubic packing, and the last a warped face-centered cubic packing.  You’re welcome!

George did an amazing job discovering how the same 5 pieces can be used to construct 3 different pyramids with different packing geometries.  I found each to be fun, non-trivial, and not too difficult.  Copies are occasionally available on George’s PolyPuzzles Etsy shop.  Get one and have yourself a ball.

Where Does that F’n Piece Go! - Melting F

When the puzzle arrived, it had pieces nicely packed in a display case.  On close inspection, the packing appeared trivial.  I was able to take them out, mix them up, and put them back into the display case easily.  I also discovered that there were many solutions.  It will be a couple of years before this one will stump me – hopefully.

Hold on – there’s another piece in the shipping box that it came in.  Surely, it doesn’t go in the case with the other 9 pieces.  Since it’s bigger and oddly shaped, maybe it’s supposed to replace one or two of the other pieces.  However, having worked with a puzzle or two and the fact that the word melting is in the name, I suspected that the additional piece had to be crammed in the case with the other pieces.  You may be tempted to just torch that F’n piece and drip it in between the other pieces, but as puzzlers we’re all about doing things the hard way.

Melting F was made by geometric puzzle packing genius, George Bell, and was his entry in the 2020 Nob Yoshigahara Puzzle Design Competition.  This new design is a truncated rhombic dodecahedra packing exercise.  The puzzle consists of 10 3-D printed pieces that need to be packed within a clear acrylic display case.  The 9 identical blue pieces are made from 3 truncated rhombic dodecahedra while the single F piece is made from 5.  You have to squint really hard to convince yourself it looks like an F.

The initial step with these types of puzzles is to determine the type of packing used – in this case, how the truncated rhombic dodecahedra are oriented within the space defined by the display case.  This then defines how the pieces can be oriented within the case.  Then comes the hard part – determining where the pieces have to go.  Although this is not overly difficult, it does take some experimentation to find the solution.

I liked the fact that nine of the pieces were simple identical shapes.  It drops the level of complexity and makes the design approachable for any level of puzzler.  It also displays nicely in the clear acrylic display case.  Melting F can be acquired from George’s PolyPuzzles Etsy Shop when in stock.