The Four Colour Map Theorem

The Most Epic Book of Maths Ever explains how the four-colour map theorem works.
It gives us a problem that's supposed to be impossible, but nobody is absolutely sure!

Let's see what it's all about:

* A MAP is a diagram divided into areas by lines. It can be any size and have any number of lines.

* The map has to be coloured in so that no two areas that share a border are the same colour.

* The theorem says that the maximum number of different colours you should need is FOUR.

* Could you be the first person in the world to design a map that needs five or more colours?

Of course lots of Murderous maths readers have decided to try and disprove the theorem by sending us their maps which they claim need more than four colours.

One of the first was Edgar Pierre Burkart who sent this cute little map with five colours...

...but it only needed four!

This one with five colours came from Edison Fu in Hong Kong...

...but it only needed four!

Here's a cute triangular map using five colours from Patrick...

...but it only needed four!

Here's a very neat five-colour map from Kiron Dutton...

...but it only needed four!

Ilan Feron sent us this five-colour map. The letter "m" shape makes things a bit more complicated...

...but it only needed four!

"Math Machine" thought that the curious blue stripe made five colours essential...

...but it only needed four!

Rishi spent an evening coming up with this five colour map...

...but it only needed four!

This very clever five colour map came from Edison. It took us a while ...

...but it only needed four!

Marcus from Hong Kong thought this map needed five colours. We LOVE chequer boards so we hoped it would work ...

...but it only needed four!

Mahjabeen and Rachel used five colours on this map ...

...but it only needed four!

So if YOU think you've got a map that needs FIVE or more colours...

  • draw out a few black and white versions
  • try colouring them in different ways
  • ask your friends to have a go too

... and if you're SURE it's impossible then you can tell us at our MAILROOM.

Good luck!

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