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Paving Paths

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?

1 Step 2 Step

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Even Up

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Pocket Money

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