### Christmas Presents

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

### Platonic Planet

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?

### Face Painting

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.

# Cubic Conundrum

##### Stage: 2, 3 and 4 Challenge Level:

The solution below has the cubes in this slightly different order:

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.