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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.

Even Up

Age 11 to 14 Short Challenge Level:
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?

You can find more short problems, arranged by curriculum topic, in our short problems collection.