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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?

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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?

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Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

Odds, Evens and More Evens

Age 11 to 14 Challenge Level:

For Alison's approach:

What happens to the numbers as you go down the rows?
What happens as you go up the rows?



For Bernard's approach:

Which numbers end in a 0 in row $A_2$?
Which numbers end in a 0 in row $A_3$?
Which of these sequences will hit 1000?
 


For Charlie's approach:
 
Can you find a similar method to Charlie's to describe the other rows?
Which descriptions include 1000?