Four Colours Theorem<\/h1><\/span><\/div><\/div><\/div><\/div><\/div>Skills: spatial and problem solving skills<\/p>\n
Resources: templates, coloured pencils or markers<\/p>\n
Activity: Can you fill the pattern that no two shapes connected by the same border have the same colour? What is the smallest numbers of colour needed? Is that possible with only 4 colours?<\/p>\n
These puzzles challenge our spatial and problem solving skills. They are from an area of maths called Graph Theory, which is concerned with networks and connections. This sort of maths helps us understand large networks like social media and mobile phone networks.<\/p>\n
Thanks to the Graph Theory we know that any pattern or map can be filled with 4 colours maximum (it could be less)!<\/p>\n
Click on each picture to see the puzzles in more details and\/or download them. Download the all pack and answer at the bottom of the page.<\/p>\n<\/div><\/div><\/div>
![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/pattern-graph-4-colours.jpg\" "\\"pattern")
<\/span><\/div><\/div><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_Counties-Ireland-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_City-Map-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_Patter2-copie-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_Pattern2-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_Pattern3-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_Pattern4-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>
Skills: spatial and problem solving skills<\/p>\n
Resources: templates, coloured pencils or markers<\/p>\n
Activity: Can you fill the pattern that no two shapes connected by the same border have the same colour? What is the smallest numbers of colour needed? Is that possible with only 4 colours?<\/p>\n
These puzzles challenge our spatial and problem solving skills. They are from an area of maths called Graph Theory, which is concerned with networks and connections. This sort of maths helps us understand large networks like social media and mobile phone networks.<\/p>\n
Thanks to the Graph Theory we know that any pattern or map can be filled with 4 colours maximum (it could be less)!<\/p>\n
Click on each picture to see the puzzles in more details and\/or download them. Download the all pack and answer at the bottom of the page.<\/p>\n<\/div><\/div><\/div>
<\/span><\/div><\/div><\/div><\/div><\/div><\/a><\/span><\/div><\/div><\/div><\/a><\/span><\/div><\/div><\/div><\/a><\/span><\/div><\/div><\/div><\/a><\/span><\/div><\/div><\/div><\/a><\/span><\/div><\/div><\/div><\/a><\/span><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_Pattern5-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2023\/10\/MathsColouring_Pattern1-400x566.jpg\")
<\/a><\/span><\/div><\/div><\/div>