Question 6
There are $n\ge3$ pupils standing on a circle, always facing their teacher at its center. Each time the teacher blows a whistle, some two adjacent pupils exchange positions and all others stay still. Find the smallest number $M$ of whistles that allows suitable exchanges with this final property: every two pupils who were initially adjacent are again adjacent, but their left/right roles are reversed. Thus, if pupil $A$ was initially on pupil $B$'s left, $A$ is finally on $B$'s right.