[i]Imagine you have an unlimited number of small unit cubes (all the same size 1×1×1). From these unit cubes, you start to build bigger and bigger cubes in such a way that a cube will be wrapped into other unit cubes. This “unit cube wrap” can be called a layer. Then you build cube C of the size of 5×5×5 unit cubes and [i][i]try to answer the following questions: [/i][/i][/i][br][i]a)    [/i][i]How many layers of cube C do you have to unwrap to get to one single unit cube? [/i][br][i]b)    [/i][i]How many unit cubes does each layer have? [/i][br][i]c)     [/i][i]How many unit cubes are hidden in cube C that cannot be seen at all? [/i][br][i]d)    [/i][i]How many unit cubes of the visible layer touch the faces of unit cubes of the previous layer? [/i][br][i]e)     [/i][i]Remove the unit cubes from cube C that have just three touching faces with the other unit cubes. How many unit cubes remain in the visible layer? [br][br][/i]To solve the problem you can use the following GeoGebra Applet, where you can also change the colour of individual unit cubes (one click - yellow colour, two clicks - blue colour, three clicks - the original orange colour). You try to colourfully highlight the wanted unit cubes in questions a)-e).