Many students over the years have investigated the painted cube. They have imagined a 3 by 3 by 3 cube, made from 27 identical smaller cubes having a paint job. All six faces of the large cube are painted blue.

Consider the 27 individual smaller cubes. How many of them:

Do not have any blue paint on them;

Have one of their faces painted blue;

Have two of their faces painted blue;

Have three of their faces painted blue.

Students have then gone on to generalise for different large cubes and cuboids.

You are invited to be one of the many students over the past 50 years who has investigated the painted cube!

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