### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

# One Out One Under

##### Stage: 4 Challenge Level:

This is a three star problem so hopefully it will keep students thinking and testing their reasoning for some while.

Working systematically helps greatly. A table of results shows a very clear pattern, and from there the challenge is to find a way of accounting for that pattern.

This problem offers an excellent opportunity for reasoning from the n case to the n + 1 case.
Seeing the n case result embedded within the n + 1 starting line up.

You may be interested to know that this problem was taken from the book called Maths trails - Visualising