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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?

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

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Burning Down

One night two candles were lit. Can you work out how long each candle was originally?

At a Glance

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Is it?