Knuth's packing puzzle

prusaprinters

In case you found the Hoffman packing puzzle to easy, here is the Knuth version.In 1978 Hoffman proposed that a if you take cuboids with size AxBxC, you can always pack 27 into a cube that has edges of length A+B+C.In 2003 Knuth showed that for a special subset you can fit 28 cuboids into a cube. As you can see in the pictures the short side of the cuboids fits 4 times into the cube. Therefor design falls into this subset and should therefor be solvable for 28 pieces instead of the typical 27. Good luck.Warning, this is a really hard puzzle. There are solutions to be found online though. Or you can throw away one piece and solve it like a Hoffman puzzle (which it technically is not).Very similar easier puzzle: https://www.printables.com/model/221120-hoffman-packing-puzzle47All parts have 0.2 mm play in the design. I would not recommend to scale it down. A parametric fusion file is included, if you want a smaller version use the "scale" parameter from the list.You need to print the cube, the lid and 28 cuboids:1 x 'Cube.stl'1 x 'Cube lid.stl'28 x 'Cuboid.stl' or 1 x 'Cuboids.stl'There is also a single stl file with all parts if you have a big build plate.I printed the blocks in various colors for fun.Notes:Make sure your 3D printers is accurate and print the outside walls slow.GrindingThe play in the parts was fine, but the blocks tend to grip when the print layers rub over each other in the not parallel direction.I took all blocks and ground then on an old 320 grit whetstone for a few seconds. This makes the sides slightly dull, but they now slide the same in all directions. Making the puzzle more enjoyable.Use water to keep the material cool, if you do not, the grit of the sandpaper/stone will get into the plastic and stain it. By rubbing it you heat and soften the PLA and dirt gets trapped in it. With water it stays cold and it stays clean (although slightly matte finish).Grind the Cuboids on a whetstone for a few seconds each side.Before (left) and after (rigth), color remains the same, but the finish is less shiny.How I Designed ThisFor the detailed design, just open the fusion file. For the story behind the ratio between the sides of the cube and cuboids, there is the following:As you can read in Wikipedia, a Hoffman packing puzzle has an inequality:The 3 sides of the cuboids must each have a different size and the sum of the sides must be less then 4 times the smallest size (x+y+z < 4*min(x,y,z)).Because for (x+y+z > 4 min(x,y,z)), the cuboids could be stacked to easily in the cube. Resulting in trivial solutions. While solving this puzzle Knuth discovered in 2003 that for (x+y+z = 4 min(x,y,z)) there are three solutions which fit 28 cuboids. There are also still the same solutions for 27 cuboids.I took the parametric file I made for https://www.printables.com/model/221120-hoffman-packing-puzzle, and included the equality into the parameters. So it will always satisfy the equality above.