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Six Jays
Try to fit six J-shaped heptacubes inside a 4x4x4 box. This should be a piece of a cake, as there are 29,617 ways of doing it. The problem is that each J-piece here has a 4x4 panel of Perspex glued to the top of it. These panels form the sides of the cube. You will appreciate that there are many different ways of positioning the square end of the heptacube onto a 4x4 panel. I have three different sets of six pieces, each different piece is coloured differently and there is a large number of different sets of six pieces which will (can?) be assembled to form a cube. The J-pieces are cut from half inch plywood.
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This is a fine example of a way of presenting what is on the surface an overly simple packing puzzle. It is very frustrating and although the 6x7 units leave 22 empty unit cubes inside, it is by no means trivial. As there are so many subsets of the pieces, there are many hours of happy puzzling here. To protect the Finnish designer’s copyright I have not pictured all the pieces, just enough to give the general idea.
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