Post #1209934

@robinhouston All the details I was able to find, based on these: https://market.cubicdissection.com/listing/perfect-packing/120685 http://www.ageofpuzzles.com/Masters/DonaldEKnuth/DonaldEKnuth.pdf (has solutions / spoilers) https://puzzlewillbeplayed.com/Brick/Hoffman/ https://www.printables.com/model/221119-knuths-packing-puzzle https://en.wikipedia.org/wiki/Hoffman%27s_packing_puzzle In 1978, Dean G. Hoffman posed this puzzle "to a conference at Miami University": Can 27 identical cuboids of dimensions a×b×c be placed into a cube of side length a+b+c? To avoid easy solutions that occur when min(a,b,c)(a+b+c)/4. Hoffman wrote in 1981 that this puzzle typically takes "20 minutes to multiple hours" to solve, and it was first solved by David A. Klarner (his doctoral advisor). There are 21 solutions. In 2004, Donald Knuth looked into the case where min(a,b,c)=(a+b+c)/4, and discovered three solutions (easy, medium, hard) that accommodate not 27 but 28 a×b×c cuboids. This puzzle was George Miller’s exchange gift at the International Puzzle Party 25 held in Helsinki, Finland 2005.