You may also like

problem icon

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?

problem icon

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..

problem icon

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: Challenge Level:3 Challenge Level:3 Challenge Level:3

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