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## 'Little Boxes' printed from http://nrich.maths.org/

I don't know whether you've had the same problem as me. I've
found that I have loads of CDs and DVDs and they are not very tidy.
I decided to collect them all together in their boxes and after
putting them all the same way up I started putting them together
into cuboid-type shapes. I found when I started that just two could
be put together to give three different cuboids. Here's what they
looked like:-

I've used different colours to show each box, just to make it
clearer to see, but we're going to imagine each box is identical.

I then tried it with an extra box making three altogether. I
moved them around and found that again I could make three different
cuboids. These are the ones that I found:-

But, perhaps like you, I've got lots of these boxes of CDs and
DVDs. So I moved on to using four. Again I found three but realised
that there were more that I could find. Here are the three:-

Well, you could try the same ideas. If you have not got CD/DVD
boxes it does not matter. You could use old match boxes or books
that are all the same size. In fact you can use any objects as long
as they are cuboid shaped and you have plenty of them that are
exactly the same. All you have to do is to find out how many
different cuboids you can make when you use fourof them, then five
of them, then six *etc.*

But notice that when you've put them together it does not matter
which way up they are, they count as being the same. For example
these three would count as being the same:-

Now that you've tried some, how about getting other friends and
people at home to have a go and see what they all come up with -
maybe you could work together?

Well, Good Luck.