You may wish to take a look at the related problem Pennies and Tuppences first.
Alison has some 1p, 2p, 5p and 10p coins, and has been working out different ways of making 12p.
"If I use a 10p, I will need 2p more, so there's 2 ways of doing that.
If I use two 5ps, I will also need 2p more, so there's 2 ways of doing that.
Or if I use..."
| 10p | 5p | 2p | 1p | Number of ways |
| 1 of these | none of these | 2 | ||
| none of these | 2 of these | 2 | ||
| none of these | 1 of these | |||
Can you help Alison finish her table? You should find there are 15 ways altogether!
Is there a method for working out how many ways there are of making any amount using 10p, 5p, 2p and 1p coins?
What if you also had 20p and 50p coins?
It might get very time-consuming, even if you have a good method!
If you know a little programming, perhaps you could write a computer program to help.