This puzzle is so remarkable that it is almost strange that nobody has invented it before! The popularity of cube assembly puzzles with the Dutch people is well known, and while the letter shapes of some chequerboard and assembly puzzles are a little contrived, that is clearly not the case here.
This set comprises a tetracube, 3 pentacubes, 5 hexacubes, a heptacube and an octacube.
My personal purist view is that all the pieces of a chequerboard puzzle should be different, and this is the case here.
The complete set of pieces can form an 8x8 board in 2 ways, without turning the pieces over from the positions shown above! There are no others.
The complete set of pieces can form a 4x4x4 cube in 87 ways.
By removing the straight tetracube which forms the letter “i” you have a subset of 60 unit cubes.
This set of pieces can form a 5x4x3 block in 13 ways. 12x5, 10x6 and 6x5x2 shapes are not possible. Nor is a 8x8 shape with a central 2x2 hole.
Finally after solving all these puzzles you can use the letters to make anagrams! Advice on what to do in a damaged submarine? DITCH CUT SUB. Or if you wondered about that skin irritation you got from the air conditioning on public transport? It’s BUS DUCT ITCH. Or perhaps you are a STUD BUT CHIC!