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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?


A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Gift of Gems

Four jewellers share their stock. Can you work out the relative values of their gems?

Eight Ratios

Age 14 to 16 Challenge Level:

Oliver, from Nottingham High School, and Jonathan, both sent in very good solutions to this problem.

Here is Jonathan's solution:


Oliver's solution is below:


Well done to both Jonathan and Oliver for their excellent solutions!