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Wednesday, June 29, 2022
Arranging Your Balls - Pyradox
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.
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.
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Don Knuth looked into this puzzle and even found a piece which can build FOUR different pyramids, the fourth one being the 7x2 "roof". I had thought this was impossible, but the piece he found is non-planar, which I hadn't considered. He mentions this puzzle in his latest volume of The Art of Computer Programming.ReplyDelete
Thank you for the update George! Perhaps we'll see a Don Knuth inspired exchange puzzle in the future.Delete
For the Knuth work, the Wiki shows a multi-volume work with some complete and the rest is planned. Which chapter, please? And do I need this in my library?Delete
For the puzzle, I can also attest that the three challenges are fun to solve. It is a good one to leave on the coffee table, for guests.
You want The Art of Computer Programming, Volume 4, Fascicle 5: Mathematical Preliminaries Redux; Introduction to Backtracking; Dancing Links. It has Dancing Links in the title, the algorithm used by Burr Tools.Delete
I was afraid that the post would discourage people from leaving the puzzle on a coffee table.Delete
Actually, all are subsets of face-centered cubic, surprisingly!ReplyDelete