Feeding the meter
Problem
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 two 10p coins, then two 20p coins, then four 10p coins, then a 20p coin, and finally three more 10p coins.
This morning I put in four 10p coins, then three 20p coins, then another 10p coin, then two more 20p coins.
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?
There are lots of possibilities. It's going to be really hard to count them all without missing any, and without accidentally counting any twice.
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 some more manageable problems you could work on, to help you to get started?
What other interesting mathematical questions can you think of to explore next?
We have thought of some possibilities:
How can you be sure you've counted every possibility?
How would you work out the number of different ways of feeding the machine when the cost rises to £1.60? To £1.70? To...
How can you be sure that your method will work for all car park costs, not just the ones you've tried?
What if the car park machine also accepted 50p coins? Or 5p coins? Or...
I noticed that I have different ways of putting the money into the car park machine...
Yesterday I put in two 10p coins, then two 20p coins, then four 10p coins, then a 20p coin, and finally three more 10p coins.
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This morning I put in four 10p coins, then three 20p coins, then another 10p coin, then two more 20p coins.
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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?
There are lots of possibilities. It's going to be really hard to count them all without missing any, and without accidentally counting any twice.
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 some more manageable problems you could work on, to help you to get started?
What other interesting mathematical questions can you think of to explore next?
We have thought of some possibilities:
How can you be sure you've counted every possibility?
How would you work out the number of different ways of feeding the machine when the cost rises to £1.60? To £1.70? To...
How can you be sure that your method will work for all car park costs, not just the ones you've tried?
What if the car park machine also accepted 50p coins? Or 5p coins? Or...
We'd love you to share the questions you've come up with. Tell us also how you got started and any conclusions you have arrived at.
Send us your thoughts; we'll be publishing a selection.
Send us your thoughts; we'll be publishing a selection.
Teachers' Resources
Matt likes to keep a diary of some of the interesting maths he comes across. Here are some recent entries:
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What do you think?
What other interesting mathematical questions can you think of to explore next?
Matt and Emmy have thought of some possibilities:
How can you be sure you've counted every possibility?
How would you work out the number of different ways of paying when the cost rises to £1.60? To £1.70? To...
How can you be sure that your method will work for a snack of any price, not just the ones you've tried?
What if the vending machine also accepted 50p coins? Or 5p coins? Or...
How would you work out the number of different ways of paying when the cost rises to £1.60? To £1.70? To...
How can you be sure that your method will work for a snack of any price, not just the ones you've tried?
What if the vending machine also accepted 50p coins? Or 5p coins? Or...
We'd love you to share the questions you've come up with. Tell us also how you got started and any conclusions you have arrived at.
Send us your thoughts; we'll be publishing a selection.
Send us your thoughts; we'll be publishing a selection.