The
Nine Bed Nightmare,
a new box packing puzzle by George Bell.
You can now purchase a copy for a limited time from
puzzlewood.com
The nine puzzle pieces:
Note that all pieces are 3D, none of them are planar!
Volume of front row: 6, 8, 10, 12 units (total 36 units).
Volume of middle row: 12, 15, 18 units (total 45 units).
Volume of top row: 20, 24 units (total 44 units).
Total volume of all pieces: 125 units.
Another way to sort the shapes:
All nine pieces can be used to build:
A 5x5x5 cube (hard, solution is unique). Or ...
A 5x4x4 brick and a 5x3x3 brick (easy, solution is unique). Or ...
A "big bed". The volume of this bed is 126 units, so there is one hole somewhere
(not visible in this photo). There are two solutions with different hole locations.
Using a subset of the pieces, we can also build:
A 5x5x4 brick (medium, 2 solutions both using the same pieces). Or ...
A 4x4x4 cube (easy, 6 solutions all using the same pieces).
Finally, it is possible to add three larger "beds" of analogous shape and build a 7x7x7 cube with a unique solution. This is the "twelve bed nightmare".