Generalizing exercise 23, let's say that a Josephus subset of f1, 2, . . . , ng is a set of k numbers such that, for some q, the people with the other n−k numbers will be eliminated first. (These...

Generalizing exercise 23, let's say that a Josephus subset of f1, 2, . . . , ng is a set of k numbers such that, for some q, the people with the other n−k numbers will be eliminated first. (These are the k positions of the “good guys" Josephus wants to save.) It turns out that when n = 9, three of the 2⁹
possible subsets are non-Josephus, namely {1, 2, 5, 8, 9}, {2, 3, 4, 5, 8}, and {2, 5, 6, 7, 8}. There are 13 non-Josephus sets when n = 12, none for any other values of n
12. Are non-Josephus subsets rare for large n?