Ringing the Changes - Martin Bright
26th February 2005
English church bells do not ring tunes – in fact they cannot, because of they way they are rung. Instead they ring changes. When we ring changes, we start with all of the bells ringing in descending order. We then move the bells into different orders, or rows, each bell moving at most one place at a time. What mathematics is involved? There is plenty of combinatorics in counting the number of possible rows, the number of ways of changing between them, and how we can move between the different rows without ringing the same one twice. There is also some group theory which can show, for example, that two sets of rows are all different without having to compare them all with each other.