Here, to give people something to do now that the exams have finished, is the final Greenwich Maths Challenge for the 2009/2010 academic year. A prize will be awarded for the first correct solution emailed to A.Mann@gre.ac.uk by a Greenwich maths undergraduate.
You have to paint the marked regions in the diagram using four colours so that each region is a single colour and no regions with a common boundary are the same colour. Each region is 8 square metres in area except for the top area which is 16 square metres. You have only the following paint available: enough red for 24 square metres, enough yellow for 24 square metres, enough green for 16 square metres and enough blue for 8 square metres. Can you find a way to do this?