Visualise that you have an unlimited number of small cubes (all the size 1×1×1) in different colours. Then, imagine, you are building bigger cubes from these small unit cubes by wrapping layers (like in an onion or Russian nesting dolls) such that each layer has a different colour.Next, imagine the layers of small unit cubes and try to answer the following questions:
Level 1. Imagine a cube, C_{1}, of the size 3×3×3 (each layer has a different colour).a) How many layers does cube C_{1 }have? b) Draw a picture, how the small unit cubes of the outer layer touch the faces of the previous layer inner
cube. How many unit cubes of the outer layer have a face touching the inner layer face? c) How many unit cubes of the outer layer touch the inner cube along the edges? Draw a picture.d) How many unit cubes of the outer layer touch the inner cube at the vertices? Draw a picture.e) How many small unit cubes are there in total? Level 2. Imagine a cube, C_{2}, that has one more layer than the previous one (each layer has a different colour).a) How many small unit cubes did you add to the previous cube C_{1}?
In Level 2, the questions b), c), d) and e) are the same as in Level 1.