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?

## Saturday, 29 May 2010

## Monday, 24 May 2010

### Greenwich Maths Challenge 3

The winner of the third Greenwich Maths Challenge was Nic Mortimer, who was the first (and only) person to break the Vigenere cipher. The text was Hardy's famous reminiscence of Ramanujan,

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number **** and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Here the missing number is of course 1729. The keyword to the cipher was "Hardy".

Greenwich Maths Challenge 4 will be posted here on or around Friday May 28, to mark the end of the exams at Greenwich!

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