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A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

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According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

The Genie in the Jar

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess. For how many days did the whole jar last? The genie's master replied: Five hundred and ninety five days. What three numbers do the genie's words granid, ozvik and vaswik stand for?

Chocolate Cake

Age 11 to 14
Challenge Level


Toby is 2 tomorrow and he wants a big sticky chocolate cake for his party! The problem is that my recipe specifies a 20cm round tin with a depth of 7.5cm, but I haven't got a 20cm round tin.

I do have a 23cm round tin, and I've also got a square tin, which has a side length of 15cm and a depth of 6 cm.

Which one do you think would be best?  Or should I go out and buy a new cake tin?