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Correct solutions to the first part of the question were received from: Alastair H (Forres Academy), Andrei L (School 205, Bucharest). The solution below is based on Andrei's submission. Well done to both of you.
First I created a small cube from the net in the figure and observed the cubes from the problem:
The first cube cannot be formed from that net, because the square marked with a red arrow should be in the position marked with a blue arrow:
Looking at the cube made from the net: It is possible to see that the second cube (horizontally) can be made from that net and also the last three
In conclusion, the 4 cubes denominated before are the same one, created from the net (B, D, E and F below).
The second part of the problem:
First shade the three faces of the view B of the cube which are not visible. Then do the same with the other three views of the same cube (D,E and F).
A B C D E F
You end up shading all the faces. This means that you can see all the faces of the cube in the four views B, D, E and F so there are no hidden faces where you can shade additional sections.
We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.