Maths on the Map

How many colours do you need on a map?

How it Works

Place tiles to create coloured regions on a map. Can you place the tiles such that no two areas of the same colour touch?

Things to Try or Ask Around the Exhibit

  • How many colours do you need to complete this challenge?
  • Do you need more colours if the map gets more complicated?


This type of map-colouring problem is a famous solved problem in mathematics. The related four colour theorem was the first major theorem to be proven using a computer.

Finding the Science in Your World

Problems like this one occur in a surprising number of places, from colouring actual maps to deciding where to place mobile phone towers.