The Unexpected Pleasures of Counting
This course is pure – for those interested primarily in mathematical thinking for its own sake. Starting from an array of numbers constructed according to apparently arbitrary rules, we’ll expose some amazing patterns, show that these are real, not just coincidence, then ‘explain’ the construction rules and the patterns by showing that the numbers involved are actually counting significant things. The techniques developed in this activity will then be used to pose and solve other counting problems, and to expose more unexpected connections: how can rooks on a chess board help with a job allocation problem? If 49 boxes contain a total of 50 balls, at least one box must contain more than one ball. How can that be profound?
algebraic experience useful but only up to GCSE standard