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Boxed In

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

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Plutarch's Boxes

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?

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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?

Sending a Parcel

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The Post Office used to have a strange way of limiting the size of parcels. The maximum allowed was "$6$ feet combined length and girth". That meant you added together the distance round the middle of the parcel (that's the girth) and the length.

cuboid shaped parcel showing length and girth


I used to imagine sending a fishing rod very nearly $6$ feet long and just a few inches round the girth!

This problem is more up-to-date:

We will call the maximum combined length and girth $2$ metres (which is a bit more than $6$ feet).
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are $2$ metres and measurements are all made in whole centimetres?