Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
Do you have enough information to work out the area of the shaded quadrilateral?
When drawing trees with 7 vertices, you might find it helpful to start by working out what the sum of the degrees of the 7 vertices must be.