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How would you find out how many football cards Catrina has collected?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.

This activity will help you get used to the coins you have in your country.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

This task follows on from Build it Up and takes the ideas into three dimensions!