[i]Visualise that you have an unlimited number of small cubes (all the size [/i]1×1×1[i]) 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.[/i][br][i]Next, imagine the layers of small unit cubes and try to answer the following questions:[/i][br][b][i][br]Level 1.[/i][/b][i] Imagine a cube, C[sub]1[/sub], of the size [/i]3×3×3[i] (each layer has a different colour).[/i][br][i]a)   [/i][i]How many layers does cube C[sub]1 [/sub]have? [/i][br][i]b)   [/i][i]Draw a picture, how the small unit cubes of the outer layer touch the faces of the previous layer inner[br]cube. How many unit cubes of the outer layer have a face touching the inner layer face? [/i][br][i]c)   [/i][i]How many unit cubes of the outer layer touch the inner cube along the edges? Draw a picture.[/i][br][i]d)   [/i][i]How many unit cubes of the outer layer touch the inner cube at the vertices? Draw a picture.[/i][br][i]e)   [/i][i]How many small unit cubes are there in total? [/i][br][br][b][i]Level 2.[/i][/b][i] Imagine a cube, C[sub]2[/sub], that has one more layer than the previous one (each layer has a different colour).[/i][br][i]a)   [/i][i]How many small unit cubes did you add to the previous cube C[sub]1[/sub]?[/i][br][br]In Level 2, the questions b), c), d) and e) are the same as in Level 1.