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?
How many noughts are at the end of these giant numbers?
A walk is made up of diagonal steps, starting at the bottom left
and ending up back on the bottom line (x-axis). You can move
diagonally up and down towards the right but you cannot move towards the left.
A diagonal must go from a left-hand corner of a square to the
opposite right-hand corner of the same square.
The examples above all show 10-step walks. So let's look at a
2-step walk in more detail:
There is only one
way to make a 2-step walk - from A up to x and down to B:
Here are two 4-step walks:
Are there any more 4-step walks?
How do you know you have them all?
How many 6-step, 8-step walks are there?
Can you find a general rule?