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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?

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?

Burning Down

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

Gift of Gems

Age 14 to 16 Challenge Level:


Try writing down what each jeweller has after they have all given their gifts.

These four collections all have equal value.

Use this to deduce other statements you can make about the value of each kind of gem.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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NRICH is part of the family of activities in the Millennium Mathematics Project.