4pm, Friday 13th November: Jonny Griffiths, ‘The Dot Problem’.

This lecture is aimed at Key Stage 4 and 5 pupils.

You are given a row of dots that are either black or white. You form a row underneath with one less dot using these rules;

Two blacks go to a white, two whites go to a white, and a black and a white, or a white and a black, go to a black.

Keep going until you get down to one dot. Can you predict the colour of the final dot without drawing out the whole triangle? This deceptively simple problem has hidden depths, that mean students of any age can come away with a satisfying mathematical experience. Areas covered include odd and even numbers, the use of algebra, Pascal’s Triangle and the nature of proof. The link will be posted on Friday’s daily page.