### 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. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..

### 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