Suppose we are presented with a long string of beads. The beads come in two colours, red and blue, but there is not necessarily any 'pattern' to the way they are threaded on the string. Can we guarantee to find three equally spaced beads of the same colour? For example, if the 5th, 7th and 9th beads were all blue then this would count. This question leads to some beautiful mathematics, and some surprising numbers. (Suggested age range 16+ and General Public.)
