### Four Points on a Cube

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?

### Instant Insanity

We have a set of four very innocent-looking cubes - each face coloured red, blue, green or white - and they have to be arranged in a row so that all of the four colours appear on each of the four long sides of the resulting cuboid.

### Classic Cube

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

# Plane to See

##### Stage: 5 Challenge Level:

Where does the plane $PDQ$ meet the line $EH$?

Imagine a vertical line through $A$. Where does the plane $PDQ$ meet this line?

The method only needs similar triangles and similar 3D shapes.

It is not necessary, but it may help, to use coordinates with the origin at $A$.