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## 'All Wrapped Up' printed from http://nrich.maths.org/

Well, we're often wrapping up presents - I find that many of them
arrive in boxes that are cuboid. Remember those? A cuboid has 6
faces; each face a rectangle (including squares); each face paired
with one the same on the opposite side and all the angles 90
degrees. So they might look like these:

Now let's talk about the wrapping paper. You are probably used to
using A4 paper for all kinds of things. A4 paper looks a bit like
this:

But two A4s together make A3:

So we have:

Which could look better as:

Now for easiness we'll approximate the size of the A3 sheet to 40cm
by 30cm.

The wrapping paper we'll be using is A3-size, like the picture
above.

So, we're wrapping up a cuboid in this A3 wrapping paper.

The challenge is to find the largest cuboid that can be covered
completely with the A3 sheet - you will probably want to stick to
whole numbers of centimetres!

Rather than wrapping the cuboid like we might do a birthday
present, let's think about it as if we're trying to have as little
overlap as possible.

You might do this practically or you may use diagrams or even a
spreadsheet - it is up to you.