### Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

### Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

### Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

# Making Cuboids

##### Stage: 2 Challenge Level:

There are lots of answers to this problem, depending on what questions you choose to ask.

Here is some work that Lydia from St Mary's Catholic High School in Chesterfield sent to us:

There must be ten cuboids:

 $6\times6\times6$ $4\times4\times4$ $8\times8\times8$ $6\times8\times8$ $6\times8\times6$ $4\times8\times4$ $3\times3\times3$ $2\times2\times2$ $2\times4\times4$ $3\times4\times4$ $3\times4\times3$ $2\times4\times2$

 $4\times8\times8$ $4\times6\times6$ $4\times6\times4$ $4\times6\times8$ $2\times4\times4$ $2\times3\times3$ $2\times3\times2$ $2\times3\times4$

These are the only possible shapes using the three lines (edges) with $2, 3$ and $4$ units of length.

To make these cuboids I had to double the length of each edge so I ended up with $4, 6$ and $8$ units of length, this made it easier to construct them.

The workings out are on the pictures below.

Thank you, Lydia.  You seem to have worked hard at this challenge.