Given a supply of wooden cubes, how many shapes can you make by combining cubes such that 1) you cannot use more than four cubes, 2) rectangular prisms are not allowed, and 3) faces of cubes must match completely (no halfway or other fractional meetings). Turns out there are exactly seven different shapes.
So, if you glue the wooden cubes together into these shapes, and count them up, you have used exactly 27 cubes. By coincidence, 3^3 is 27. Can you arrange these shapes into a cube?
Yes, you can. Apparently there was a product sold decades ago called a Soma cube. It makes an interesting exploration into 3D geometric transformations. You can make the same pieces from correctly dimensioned cardboard boxes.
But you aren't limited to just a cube shape. You can make a snake, or a doggy, a dinosaur, and other shapes. Providing hours of exploration, all for a few dollars in materials.
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