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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.

More Christmas Boxes

Age 7 to 11
Challenge Level

Start with a $10$ by $10$ grid.

If you cut out each corner square, it could be folded into an open-top box that had an $8$ by $8$ base and was $1$ square deep. That means that the box would be able to hold $64$ cubes.


What size square should you cut out of each corner to make the box that would hold the greatest number of unit cubes?

(Another way to ask this question is 'Which box has the greatest volume of space available?'.)