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Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?

Anna, Ben and Charlie have been estimating 30 seconds. Who is the best?

Which numbers can we write as a sum of square numbers?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.