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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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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:

Four jewellers had respectively 8 rubies, 10 sapphires, 100 pearls and 5 diamonds. 

Each gave one gem from their collection to each of the rest.

Afterwards they noticed that they all had collections of gems of precisely equal value.

Can you work out the relative values of each gem?

Can you then work out how much each jeweller gained or lost?


This problem comes from Lilavati , a standard work on Hindu mathematics written by Bhasakaracharyya, who lived in the twelfth century of the Christian era. The book is written as instruction for a young and beautiful woman called Lilavati and it is thought that she was Basakaracharyya's daughter.