Imagine you have a blank map of the world. How many colours do you think you’d need to colour it so that no two countries sharing a border are the same colour?
The answer is surprisingly low, just four! If you were to draw a very twisty shape, you’d still only need four colours to make each segment touching another a different colour. This rule is called the Four Colour Theorem.
Rules of the Four Colour Theorem
Two areas count as neighbours only if they share a border line. Touching at a simple point (like a corner) is fine.
Each country or segment on a drawing must be a single shape.
The drawing must be flat, not 3D.
Who discovered the Four Colour Theorem?
In 1852, a student called Francis Guthrie noticed that four colours were always enough to stop neighbouring counties clashing when colouring a map of the counties of England. He wondered whether this was true for all maps.
For a long time, people struggled to prove the theorem until a supercomputer confirmed in 1976 that 4 colours are always enough.
The Four Colour Theorem is a great example of how a simple observation can lead to an important discovery.
Uses of the Four Colour Theorem
The Four-Colour Theorem is represented as a graph colouring problem, where colours are assigned to items so no two items that share a connection are the same colour.
- WiFi and Mobile Phone Towers – cell towers and WiFi routers interfere with each other if they are too close. Colour rules are used to assign frequencies so towers close to each other don’t share the same channel.
- Managing Timetables and Schedules- school timetables require scheduling so lessons aren’t in the same room at the same time.
- Managing Traffic Lights
- Allocating Computer Memory – helps computer chips manage their memory effectively.
Try it out
Use the free worksheets below to test the Four Colour Theorem.
Last Updated on September 9, 2026 by Emma Vanstone
