Suppose there are 2n people in a circle; the first n are “good guys” and the last n are
“bad guys”. Show that there is always an integer m (depending on n) such that, if we
go around the circle executing every mth person, all the bad guys are first to go. (For
example, when n = 3 wecan take m = 5; when n = 4 we can take m = 30.)