Greenwich Maths Challenge 4 result

Congratulations to Mike Wakeling who provided the first correct answer to GMC4. This one attracted a lot of interest with many attempted solutions. Many people thought the problem was insoluble (as I did when I first saw it!) This problem came from the late Martin Gardner, and I think it's a gem. If you haven't tried it yet, have a go at the problem before reading the solution below.

Here's the solution. You have the given quantities of red, yellow, green and blue paint and have to colour the diagram in four colours so that any two regions with a common boundary are different colours. This is impossible if the colours are red, yellow, green and blue. So you have to mix the blue with an equal quantity of red, so that you now have enough yellow for 24 square metres and enough purple, green and red for 16 square metres each: the problem can now be solved!