### Doodles

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

### Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

### Snooker

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

# One Basket or Group Photo

##### Age 7 to 18 Challenge Level:

A school photographer is taking a photograph of the two basketball teams. She has to arrange ten people, all of different heights, in two rows of five, one behind the other. Each person at the back must be taller than the person directly in front of them. Along the rows the heights must increase from left to right.

In how many ways can two, four or six people to be arranged in this way for a photo, or eight people? In how many ways can the ten team members be arranged like this for the photo to be taken?

You may even like to generalise the problem to twelve people or to any specified even number.

Now try the problems Walkabout and Counting Binary Ops