Challenge Level

Cables can be made stronger by compacting them together in a hexagonal formation.

Here is a 'size 5' cable made up of 61 strands:

How many strands are needed for a size 10 cable?

How many for a size n cable?

Can you justify your answer?

Once you've had a go at the problem, click below to see the diagrams some students produced when they worked on it.

**Do these diagrams give you any ideas for how you could work out the number of strands needed?**

Group 1

Group 2

Group 3

Group 4

The work that these students did using their diagrams is given on the Getting Started page, if you would like another hint.

**Which of the four approaches makes the most sense to you?
What do you like about your favourite approach?**

Can you think of any other approaches?

Hexagonal packings are often chosen for strength or efficiency. To read more about packings, take a look at the Plus articles Mathematical Mysteries: Kepler's Conjecture and Newton and the Kissing Problem