Try this: Soma cube

Safety: This activity uses hot glue. Younger mathematicians should ask an adult to help.

You will need

  • 27 small cubes – cheap dice are good
  • Hot melt glue

Making the puzzle

  1. This puzzle consists of seven pieces arranged to form one large cube. Each piece is made of three or four smaller cubes glued to form shapes. Click here to download a diagram showing all the pieces you will need to make.
  2. Clean your cubes with detergent and dry them thoroughly – this will make the glue stick better.
  3. Stick three cubes together in a straight line. Then stick a fourth cube to the side of the end cube. This piece looks like an ‘L’.
  4. Stick three cubes together in a straight line. Then stick a fourth cube to the side of the middle cube. This piece looks a bit like a ‘T’.
  5. Stick two cubes side by side. Then, stick another cube on the top of one of the cubes. This piece looks like a short ‘L’, and only uses three cubes.
  6. Stick two cubes side by side. Stick another cube to the top of the right hand cube. Finally, stick a cube to the right of the top cube. This shape looks a bit like an ‘S’.
  7. The remaining three pieces are a bit more complicated. Start by making three short ‘L’ pieces out of three cubes each. Then arrange them so they are all lying flat, and facing the same way.
  8. On each short ‘L’, glue an extra cube on a different cube in the ‘L’. You will now have three shapes, each made of four cubes. Two of them will look like mirror images of each other.

The Soma cube

Using the seven pieces you have made, make a large cube. The large cube will be three small cubes wide, three deep and three tall.

What’s happening?

This puzzle can be hard, but if you keep trying, you will find the answer. Many people find it easier if they put the more complicated parts together first.

The final solution is a cube with eight corners. There are only seven pieces, so at least one piece has to be in two corners at once. There are only two pieces that can go in two corners – the long ‘L’ and the ‘T’, so at least one of these pieces has to go in two corners.

There are two twisty pieces that look very similar. These two are called the ‘left screw’ and the ‘right screw’. These two are mirror images of each other, but one twists left, and the other twists right. Any shape that is not the same as its mirror reflection is called a chiral shape. Many other shapes are chiral, including snail shells, and DNA.

soma1.1

What you will need

soma2.1

Use hot melt glue to stick the cubes together

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The first four shapes

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The final three pieces

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The completed puzzle