Until yesterday I had not really thought about using colours for maths, then some maths created this colour matrix.

I recently watched a great Numberphile episode on YouTube titled “A Breakthrough in Graph Theory” where Erica Klarreich describes how Hedetniemi’s conjecture has been challenged.

The title caught my attention as I have always been interested in Graph Theory and I have solved many problems using this branch of mathematics.

Overall the video is interesting and proposes numbers so large you can not imagine them. But what caught my attention was Erica’s description of using colours with Suduko instead of numbers.

For those not familiar with classic Suduko you have a grid of 81 squares, arranged 9 wide by 9 high, this is further broken into 9 smaller grids each 3 high by 3 wide. You fill in the numbers 1 to 9 in each overall row or column but each number can only appear once in a row or column, and only once in each of the smaller grids. A better description is available here https://brilliant.org/wiki/sudoku/.

Hearing Erica’s description I wondered what would a coloured Suduko look like. To get started I created a table with 81 squares and completed the simplest form of Suduko, I could see the pattern with the numbers.

I then found a simple colour chart which included Red, Green and Blue along with the lighter and darker shades.

• Dark Red
• Red
• Orange
• Yellow
• Green
• Dark Green
• Light Blue
• Blue
• Dark Blue

I selected a number for each of the colours so that each group of three’s would have one of the primary colours, but using some of Erica’s logic I did not want certain colours to touching in the initial colouring. This resulted in the following arrangement:

 Number Colour Colour Group 1 Dark Red Red 2 Dark Blue Blue 3 Green Green 4 Orange Red 5 Light Blue Blue 6 Yellow Green 7 Red Red 8 Blue Blue 9 Light Green Green

This arrangement meant that in the first row colours side by side on the list would not touch. I wanted to create the appearance randomness in what was going to have a pattern.

Overall I am pleased with the pattern if I find any time I might write some code to generate these automatically so I can try different colour schemes.
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