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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?