Problems worthy
of attack
prove their worth
by hitting back
– Piet Hein

The 3x3x3 cube puzzle, which you have seen at the club, is properly known as the Soma Cube, and was invented in 1933 by Piet Hein, who is also known for his little poems called Grooks. He actually invented the cube during a lecture on quantum mechanics given by Werner Schrődinger (which I imagine would not have left a lot of free thinking time, but what do I know!). The six four-cube pieces are all the 'interesting' (non-straight) ways of joining four cubes, and they come with the one interesting way of joining three cubes (which is the core of all the other shapes).

Piet Hein worked out (during the lecture!) that they should fit together to make a 3x3x3 cube (but he did have to go home and make a set before he was sure). The cube is not the only shape you can make, and each shape is another puzzle. Martin Gardner gave a set of shapes that I enjoyed trying to make in one of his collections of Scientific American columns, and I've since found more. Let me know when you have solved them all! – and I'll know then you are fibbing, because Gardner included one shape that cannot be made!
http://puzzler.sourceforge.net/docs/polycubes.html#soma-cubes
http://www.leptonica.com/cachedpages/grooks/grooks.html

P.S. Too hard? A top tip for making the cube is to start with the most awkward shapes first: those that do not lie flat. If you're totally, totally stuck, see http://exeterchessclub.org.uk/juniors/soma for one of the 240 solutions.

P.P.S. Too easy? Try Solomon Golomb's pentominoes, the 12 flat ways of combining 5 squares, known as FILPNTUVWXY&Z. (Tetris uses the tetrominoes, which number seven, with rotations and reflections.) I've got a set in the KPQ box (Keep Players Quiet) and you can find instructions to make your own. Together, they make rectangles of sizes 6x10, 5x12, 4x15 and 3x20. If you throw in a 2x2 square as well, you can make an 8x8 square, and that's what the large and small chessboard jigsaw puzzles are made of.

Make pentominoes out of cubes instead of squares, and you can make cuboids sized 2x3x10, 3x4x5 and 6x2x5 (and 3x20x1, if that counts!). All puzzles have more than one solution, not counting rotations and reflections, except the 3x20.

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