Nine Bed Nightmare Puzzle

A difficult packing puzzle and a demonstration of the Pythagorean Theorem. Pack all the pieces in the two smaller boxes, or pack all the pieces into the large box.

The pieces are all different and resemble tiny beds. The volume of the pieces is 6, 8, 10, 12, 12, 15, 18, 20, and 24 units, which sums to 125 or 5 cubed. The two smaller boxes are 4x4x5 and 3x3x5. Packing the pieces in the two smaller boxes is not too hard, the large box is the real "nightmare" with only one solution. It is also possible to pack a subset of the pieces, completely filling a 5x5x4 box or a 4x4x4 box.

This puzzle is based on a 1 cm voxel size. The pieces and boxes are easily printed without support. Feel free to scale everything larger if you like, but do not scale it smaller or the box walls will become too thin for printing. The box walls are already at the absolute minimum (1.8 mm) for fast printing.

The photos also show a wood version made by Bernhard Schweitzer. See also https://puzzlewillbeplay