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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?

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Contact

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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Gift of Gems

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

Flower Show

Age 14 to 16 Short Challenge Level:

It takes four gardeners four hours to dig four circular flower beds, each of diameter four metres.

How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.