Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .