A cube can be made from these seven coloured pieces.
|Can you work out the size of the cube?|
|Form a cube out of the seven coloured pieces.|
|Given a solution, how many different solutions can be obtained from rotating the cube? How many different solutions can be obtained from rotating pieces?|
The Soma Cube is made from seven pieces. Each piece contains three or four units. In total the pieces have 27 units, which form a 3×3 cube.
There are 240 possible solutions (not including rotations). Each solution has 24 rotations of the cube. Each solution has 96 rotations of the pieces.
Every solution can be rotated so the T piece is in the bottom layer. If the T piece was in the centre layer, then it is impossible for the remaining pieces to fill all 8 corners of the cube.
The Soma cube was invented by Piet Hein in 1933 while listening to a lecture on quantum mechanics by famous physicist Werner Heisenberg. Hein was clearly distracted. It became a popular puzzle, and small wooden or plastic versions are still available to buy. Mathematician John Conway thoroughly analysed the puzzle in 1958.
Maths at Home
You can make your own Soma Cube at home. You will need to make unit cubes, and attach them to make seven pieces like this: