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.

Off With Her Head! - Guillotine

AAAGGGHHHHHHHH!!!!!!!!!  Off with her head!  The only puzzle that I left unsolved at RPP that tormented me was Guillotine (aka Harun) designed by Volker Latussek.  Just when I thought that I had left all that stress behind me, a package arrived from the UK.  Allard Walker, somehow sensing that I would be starting to recover from my traumatic experience at RPP, strategically mailed me a copy to arrive just in time to prolong the frustration.  I’m lucky to have such good friends.

It turns out that Guillotine was Allard’s exchange puzzle for the Edward Hordern Puzzle Exchange at IPP39 this year.  For those not familiar with the exchange, each participant brings up to 100 copies of a new puzzle design that has not been released in the wild yet, to exchange with the other participants.  This year there were just over 70 participants, so each participant left with 70+ new puzzles.  In addition, a copy of each puzzle is donated to the Lily Library at Indiana University, which now houses more than 34,000 puzzles, generously donated by IPP's founder, Jerry Slocum.

As I explained in A Decade of Puzzling – RPP 2019, when I got back from RPP, I had an epiphany on how to finally solve this bugger.  Overjoyed to finally be able to validate my hypothesis, I eagerly unpacked Guillotine and began to arrange the pieces.  Unfortunately, epiphanies are cheap and this one wasn't worth much.  It wasn't even close.

Guillotine consists of 12 pieces that have to be packed into a 5x5x5 box.  There are 6 planks that are 4x2x1 and 6 additional 4x2x1 planks that have 2x1x1 pieces added on each end (or you can think of it as a 4x2x2 burr piece with a 2x2x1 notch taken out of the middle).  The box has a sliding lid that covers half the box.  It only covers half to allow the pieces to stick out in the unsolved state that it comes in.

After giving up on my erroneous hypothesis, I called it a night to get some sleep before attacking it again.  I resumed the effort again in the morning, and after a short time finally managed to find a solution. Very clever puzzle!

Peter Wiltshire mentioned that there were 2 solutions at RPP, a hard one and an easy one.  I assumed that after all the struggling that I did, I finally managed to find the easy solution.  After another 5 minutes, I found the second solution.  Having both solutions, I’m now assuming that I found the harder one first and that’s why I found the second solution so fast after the first one.

The copy that I played with was made by Eric Fuller and went by the name Harun, which I assume is the name that Volker Latussek gave the puzzle.  Allard’s exchange puzzles were made by ROMBOL GmbH, and I’m told that they sometimes change the names of puzzles for marketing reasons.  So Harun became Guillotine.  Either way, this one is a tough one to get your head into, or maybe I should say out of.

Thank you Allard!