# Feeding the Meter

The car park at work costs £1.50. The machine only accepts 10p and 20p coins.

I noticed that I have different ways of putting the money into the car park machine...

Yesterday I put in: 10p, 10p, 20p, 20p, 10p, 10p, 10p, 10p, 20p, 10p, 10p, 10p.

This morning I put in: 10p, 10p, 10p, 10p,  20p, 20p, 20p, 10p,  20p, 20p.

I think I could probably go for the rest of the month without feeding the machine in the same way twice...

Can I feed the machine in a different way each day of the year?

Sometimes mathematicians like to tackle a big task by starting with a more manageable one, to get some insight into the bigger problem.

Can you think of a way to make this problem more manageable?

We have thought of some possible follow-up questions...

• How can you be sure you've counted every possibility?
• How would you work out the number of different ways of feeding the machine if the cost rises to £1.60? To £1.70? To...
• What if the car park machine also accepted 50p coins? Or 5p coins? Or...