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# Pocket Money

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Age 11 to 14

Challenge Level

Imagine your family agreed to give you some pocket money every day for a month! You can choose from the following options:

- £10 every day
- £3 on the first day, £3.50 on the second, £4 on the third, and so on, increasing by 50p per day
- 1p on the first day, 2p on the second, 4p on the third, and so on, doubling each day.

**Without doing any working out, which one would you choose, and why?**

In a month with 31 days, how much money would you have by the end of the month, under each system? You may wish to explore using a spreadsheet...

**Here are some questions you might like to consider:**

In which months would option 1 be better than option 2?

If your family stopped your pocket money on day 8, which option would give you the most?

On which day of the month does option 3 become the most fruitful?

If you chose option 3, how many days would it be before you became a millionaire?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?