### 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.

### Let's Face It

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

### Cubic Conundrum

Which of the following cubes can be made from these nets?

# Christmas Presents

##### Stage: 2 Challenge Level:

No one has sent in a complete solution for this problem, so please send one in if you think you have it. These two partial solutions from Joanne and Jill might get you thinking!!

Joanne, West Flegg Middle School says:

I first took your plans and developed them.

After that I thought about what didn't work in the patterns and I found that groups of 4 squares together in a square didn't work:

These shapes do not work

These shapes do work. They are nets of a cube:

I think there are 6 different ways of covering this parcel.

Task 2: To make a net for a cuboid.

These did not work.

I found that you could not have the 2 end squares on the same side.

These are the nets that did work:

I found 6 nets that will cover this parcel.

I predict that for the present that is different from a cube in 2 directions the number of nets is 3.

Jill, also from West Flegg Middle School, says:

First of all I found several different ways of the non net (reflected, upside down, sideways). Here are two that I found the most:

But then, when cutting out the card to test it, I cut it wrongly.
Then a brainwave struck me: if I move one segment over a bit it would work!

Here are some I investigated:

But then, when I came to this one which didn't work, I realised something: the squares that are moved have to be on the same side.

This led to some interesting thoughts:

• How many other nets can be made?
• What would happen if there weren't two squares on different sides?
• Can we do this with other 3D shapes?

Well, the truth is there must be answers out there somewhere.