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A wooden cube has three of its faces painted red and the other three of its faces painted blue, so that opposite faces have different colours. It is then cut into $27$ identical smaller cubes. How many of these new cubes have at least one face of each colour?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.