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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?

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?