### All in the Mind

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface of the water make around the cube?

### Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

### The Old Goats

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?

# Appearing Square

##### Stage: 3 Challenge Level:

Here is a solution from Adam and Chris at Moorfield School:

"A square appears becase the amount of squares on the sides of triangle are more than the sides of the trapezium. The square comes from the triangle.

The sloping sides don't fit exactly so they give you an extra square.