Three Cubes of Three Colours: Upper Primary Mathematics Competition Question

You have three cubes, each one with a different colour. You are going to glue together the cubes so that one face fits perfectly against another face. No face can be attached to more than one other face, and no face can be turned so that part of it is not covered.

How many different 3-cube shapes can you make?

Now, remember that these are three-dimensional objects that you can pick up and rotate in space. So, make sure that your arrangements are truly different from each other even after rotating them. One possible arrangement is shown in the diagram below.

So the real question is, how many unique shapes can you make using these three cubes of three different colours?

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