We have looked at change ringing with four bells in several homework questions. With four bells, there are four possible moves between lines: in permutation cycle notation, they are (1 2), (2 3), (3 4), (1 2)(3 4). For n bells, you can have any product of disjoint transpositions each of the form (k k + 1) for 1 ≤ k ≤ n − 1. The goal is to determine the number of possible moves between lines for n bells, for any positive integer n ≥ 2. But it’s OK not to reach that goal. Compute the number of possible moves for small values of n. Look for patterns and see which ones you can prove. If you use any online or printed material, cite it.