I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
How many noughts are at the end of these giant numbers?
How many different ways can you arrange the officers in a square?
A "doodle" is a closed intersecting curve drawn without taking
pencil from paper. Only two lines cross at each intersection or
vertex (never 3), that is the vertex points must be "double points"
not "triple points". Number the vertex points in any order.
Starting at any point on the doodle, trace it until you get back to
where you started. Write down the numbers of the vertices as you
pass through them. So you have a [not necessarily unique] list of
numbers for each doodle.