*You may wish to look at the related problem Heavy Pockets first.*

Imagine a world where we only had 1p coins. It would get really inefficient as soon as we needed to pay large amounts...

If we introduce a second coin, it might make life a bit easier.

**If we need to be able to pay any amount up to £2, without needing change, what could we choose as our second coin?**

**What's the best choice, if we want to minimise the total number of coins we have to carry?**

**What about if we needed to be able to pay any amount up to £3?**

Is there a general rule?

**Which two denominations would it be best to choose if we needed to be able to pay any amount from 1p to Np?**

What if we could choose 3 denominations of coin? Or 4? Or...